In Vivo Protein Dynamics on the Nanometer Length Scale and Nanosecond Time Scale

DOE Office of Scientific and Technical Information (OSTI.GOV)

Anunciado, Divina B.; Nyugen, Vyncent P.; Hurst, Gregory B.

Selectively labeled GroEL protein was produced in living deuterated bacterial cells to enhance its neutron scattering signal above that of the intracellular milieu. Quasi-elastic neutron scattering shows that the in-cell diffusion coefficient of GroEL was (4.7 ± 0.3) × 10 –12 m 2/s, a factor of 4 slower than its diffusion coefficient in buffer solution. Furthermore, for internal protein dynamics we see a relaxation time of (65 ± 6) ps, a factor of 2 slower compared to the protein in solution. Comparison to the literature suggests that the effective diffusivity of proteins depends on the length and time scale beingmore » probed. Retardation of in-cell diffusion compared to the buffer becomes more significant with the increasing probe length scale, suggesting that intracellular diffusion of biomolecules is nonuniform over the cellular volume. This approach outlined here enables investigation of protein dynamics within living cells to open up new lines of research using “in-cell neutron scattering” to study the dynamics of complex biomolecular systems.« less

Underdamped scaled Brownian motion: (non-)existence of the overdamped limit in anomalous diffusion.

PubMed

Bodrova, Anna S; Chechkin, Aleksei V; Cherstvy, Andrey G; Safdari, Hadiseh; Sokolov, Igor M; Metzler, Ralf

2016-07-27

It is quite generally assumed that the overdamped Langevin equation provides a quantitative description of the dynamics of a classical Brownian particle in the long time limit. We establish and investigate a paradigm anomalous diffusion process governed by an underdamped Langevin equation with an explicit time dependence of the system temperature and thus the diffusion and damping coefficients. We show that for this underdamped scaled Brownian motion (UDSBM) the overdamped limit fails to describe the long time behaviour of the system and may practically even not exist at all for a certain range of the parameter values. Thus persistent inertial effects play a non-negligible role even at significantly long times. From this study a general questions on the applicability of the overdamped limit to describe the long time motion of an anomalously diffusing particle arises, with profound consequences for the relevance of overdamped anomalous diffusion models. We elucidate our results in view of analytical and simulations results for the anomalous diffusion of particles in free cooling granular gases.

The narrow pulse approximation and long length scale determination in xenon gas diffusion NMR studies of model porous media

NASA Technical Reports Server (NTRS)

Mair, R. W.; Sen, P. N.; Hurlimann, M. D.; Patz, S.; Cory, D. G.; Walsworth, R. L.

2002-01-01

We report a systematic study of xenon gas diffusion NMR in simple model porous media, random packs of mono-sized glass beads, and focus on three specific areas peculiar to gas-phase diffusion. These topics are: (i) diffusion of spins on the order of the pore dimensions during the application of the diffusion encoding gradient pulses in a PGSE experiment (breakdown of the narrow pulse approximation and imperfect background gradient cancellation), (ii) the ability to derive long length scale structural information, and (iii) effects of finite sample size. We find that the time-dependent diffusion coefficient, D(t), of the imbibed xenon gas at short diffusion times in small beads is significantly affected by the gas pressure. In particular, as expected, we find smaller deviations between measured D(t) and theoretical predictions as the gas pressure is increased, resulting from reduced diffusion during the application of the gradient pulse. The deviations are then completely removed when water D(t) is observed in the same samples. The use of gas also allows us to probe D(t) over a wide range of length scales and observe the long time asymptotic limit which is proportional to the inverse tortuosity of the sample, as well as the diffusion distance where this limit takes effect (approximately 1-1.5 bead diameters). The Pade approximation can be used as a reference for expected xenon D(t) data between the short and the long time limits, allowing us to explore deviations from the expected behavior at intermediate times as a result of finite sample size effects. Finally, the application of the Pade interpolation between the long and the short time asymptotic limits yields a fitted length scale (the Pade length), which is found to be approximately 0.13b for all bead packs, where b is the bead diameter. c. 2002 Elsevier Sciences (USA).

The narrow pulse approximation and long length scale determination in xenon gas diffusion NMR studies of model porous media.

PubMed

Mair, R W; Sen, P N; Hürlimann, M D; Patz, S; Cory, D G; Walsworth, R L

2002-06-01

We report a systematic study of xenon gas diffusion NMR in simple model porous media, random packs of mono-sized glass beads, and focus on three specific areas peculiar to gas-phase diffusion. These topics are: (i) diffusion of spins on the order of the pore dimensions during the application of the diffusion encoding gradient pulses in a PGSE experiment (breakdown of the narrow pulse approximation and imperfect background gradient cancellation), (ii) the ability to derive long length scale structural information, and (iii) effects of finite sample size. We find that the time-dependent diffusion coefficient, D(t), of the imbibed xenon gas at short diffusion times in small beads is significantly affected by the gas pressure. In particular, as expected, we find smaller deviations between measured D(t) and theoretical predictions as the gas pressure is increased, resulting from reduced diffusion during the application of the gradient pulse. The deviations are then completely removed when water D(t) is observed in the same samples. The use of gas also allows us to probe D(t) over a wide range of length scales and observe the long time asymptotic limit which is proportional to the inverse tortuosity of the sample, as well as the diffusion distance where this limit takes effect (approximately 1-1.5 bead diameters). The Padé approximation can be used as a reference for expected xenon D(t) data between the short and the long time limits, allowing us to explore deviations from the expected behavior at intermediate times as a result of finite sample size effects. Finally, the application of the Padé interpolation between the long and the short time asymptotic limits yields a fitted length scale (the Padé length), which is found to be approximately 0.13b for all bead packs, where b is the bead diameter. c. 2002 Elsevier Sciences (USA).

Simulations of eddy kinetic energy transport in barotropic turbulence

NASA Astrophysics Data System (ADS)

Grooms, Ian

2017-11-01

Eddy energy transport in rotating two-dimensional turbulence is investigated using numerical simulation. Stochastic forcing is used to generate an inhomogeneous field of turbulence and the time-mean energy profile is diagnosed. An advective-diffusive model for the transport is fit to the simulation data by requiring the model to accurately predict the observed time-mean energy distribution. Isotropic harmonic diffusion of energy is found to be an accurate model in the case of uniform, solid-body background rotation (the f plane), with a diffusivity that scales reasonably well with a mixing-length law κ ∝V ℓ , where V and ℓ are characteristic eddy velocity and length scales. Passive tracer dynamics are added and it is found that the energy diffusivity is 75 % of the tracer diffusivity. The addition of a differential background rotation with constant vorticity gradient β leads to significant changes to the energy transport. The eddies generate and interact with a mean flow that advects the eddy energy. Mean advection plus anisotropic diffusion (with reduced diffusivity in the direction of the background vorticity gradient) is moderately accurate for flows with scale separation between the eddies and mean flow, but anisotropic diffusion becomes a much less accurate model of the transport when scale separation breaks down. Finally, it is observed that the time-mean eddy energy does not look like the actual eddy energy distribution at any instant of time. In the future, stochastic models of the eddy energy transport may prove more useful than models of the mean transport for predicting realistic eddy energy distributions.

Anomalous diffusion of brain metabolites evidenced by diffusion-weighted magnetic resonance spectroscopy in vivo

PubMed Central

Marchadour, Charlotte; Brouillet, Emmanuel; Hantraye, Philippe; Lebon, Vincent; Valette, Julien

2012-01-01

Translational displacement of molecules within cells is a key process in cellular biology. Molecular motion potentially depends on many factors, including active transport, cytosol viscosity and molecular crowding, tortuosity resulting from cytoskeleton and organelles, and restriction barriers. However, the relative contribution of these factors to molecular motion in the cytoplasm remains poorly understood. In this work, we designed an original diffusion-weighted magnetic resonance spectroscopy strategy to probe molecular motion at subcellular scales in vivo. This led to the first observation of anomalous diffusion, that is, dependence of the apparent diffusion coefficient (ADC) on the diffusion time, for endogenous intracellular metabolites in the brain. The observed increase of the ADC at short diffusion time yields evidence that metabolite motion is characteristic of hindered random diffusion rather than active transport, for time scales up to the dozen milliseconds. Armed with this knowledge, data modeling based on geometrically constrained diffusion was performed. Results suggest that metabolite diffusion occurs in a low-viscosity cytosol hindered by ∼2-μm structures, which is consistent with known intracellular organization. PMID:22929443

Scaling behavior in corrosion and growth of a passive film.

PubMed

Aarão Reis, F D A; Stafiej, Janusz

2007-07-01

We study a simple model for metal corrosion controlled by the reaction rate of the metal with an anionic species and the diffusion of that species in the growing passive film between the solution and the metal. A crossover from the reaction-controlled to the diffusion-controlled growth regime with different roughening properties is observed. Scaling arguments provide estimates of the crossover time and film thickness as functions of the reaction and diffusion rates and the concentration of anionic species in the film-solution interface, including a nontrivial square-root dependence on that concentration. At short times, the metal-film interface exhibits Kardar-Parisi-Zhang (KPZ) scaling, which crosses over to a diffusion-limited erosion (Laplacian growth) regime at long times. The roughness of the metal-film interface at long times is obtained as a function of the rates of reaction and diffusion and of the KPZ growth exponent. The predictions have been confirmed by simulations of a lattice version of the model in two dimensions. Relations with other erosion and corrosion models and possible applications are discussed.

Microscopic diffusion processes measured in living planarians

DOE PAGES

Mamontov, Eugene

2018-03-08

Living planarian flatworms were probed using quasielastic neutron scattering to measure, on the pico-to-nanosecond time scale and nanometer length scale, microscopic diffusion of water and cell constituents in the planarians. Measurable microscopic diffusivities were surprisingly well defined in such a complex system as living animals. The overall variation in the microscopic diffusivity of cell constituents was found to be far lower than the variation in the microscopic diffusivity of water in planarians in a temperature range of 284.5 to 304.1K.

Microscopic diffusion processes measured in living planarians

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mamontov, Eugene

Living planarian flatworms were probed using quasielastic neutron scattering to measure, on the pico-to-nanosecond time scale and nanometer length scale, microscopic diffusion of water and cell constituents in the planarians. Measurable microscopic diffusivities were surprisingly well defined in such a complex system as living animals. The overall variation in the microscopic diffusivity of cell constituents was found to be far lower than the variation in the microscopic diffusivity of water in planarians in a temperature range of 284.5 to 304.1K.

Oscillating and pulsed gradient diffusion magnetic resonance microscopy over an extended b-value range: implications for the characterization of tissue microstructure.

PubMed

Portnoy, S; Flint, J J; Blackband, S J; Stanisz, G J

2013-04-01

Oscillating gradient spin-echo (OGSE) pulse sequences have been proposed for acquiring diffusion data with very short diffusion times, which probe tissue structure at the subcellular scale. OGSE sequences are an alternative to pulsed gradient spin echo measurements, which typically probe longer diffusion times due to gradient limitations. In this investigation, a high-strength (6600 G/cm) gradient designed for small-sample microscopy was used to acquire OGSE and pulsed gradient spin echo data in a rat hippocampal specimen at microscopic resolution. Measurements covered a broad range of diffusion times (TDeff = 1.2-15.0 ms), frequencies (ω = 67-1000 Hz), and b-values (b = 0-3.2 ms/μm2). Variations in apparent diffusion coefficient with frequency and diffusion time provided microstructural information at a scale much smaller than the imaging resolution. For a more direct comparison of the techniques, OGSE and pulsed gradient spin echo data were acquired with similar effective diffusion times. Measurements with similar TDeff were consistent at low b-value (b < 1 ms/μm(2) ), but diverged at higher b-values. Experimental observations suggest that the effective diffusion time can be helpful in the interpretation of low b-value OGSE data. However, caution is required at higher b, where enhanced sensitivity to restriction and exchange render the effective diffusion time an unsuitable representation. Oscillating and pulsed gradient diffusion techniques offer unique, complementary information. In combination, the two methods provide a powerful tool for characterizing complex diffusion within biological tissues. Copyright © 2012 Wiley Periodicals, Inc.

Diffusive dynamics of nanoparticles in ultra-confined media

DOE PAGES

Jacob, Jack Deodato; Conrad, Jacinta; Krishnamoorti, Ramanan; ...

2015-08-10

Differential dynamic microscopy (DDM) was used to investigate the diffusive dynamics of nanoparticles of diameter 200 400 nm that were strongly confined in a periodic square array of cylindrical nanoposts. The minimum distance between posts was 1.3 5 times the diameter of the nanoparticles. The image structure functions obtained from the DDM analysis were isotropic and could be fit by a stretched exponential function. The relaxation time scaled diffusively across the range of wave vectors studied, and the corresponding scalar diffusivities decreased monotonically with increased confinement. The decrease in diffusivity could be described by models for hindered diffusion that accountedmore » for steric restrictions and hydrodynamic interactions. The stretching exponent decreased linearly as the nanoparticles were increasingly confined by the posts. Altogether, these results are consistent with a picture in which strongly confined nanoparticles experience a heterogeneous spatial environment arising from hydrodynamics and volume exclusion on time scales comparable to cage escape, leading to multiple relaxation processes and Fickian but non-Gaussian diffusive dynamics.« less

Pathways for diffusion in the potential energy landscape of the network glass former SiO2

NASA Astrophysics Data System (ADS)

Niblett, S. P.; Biedermann, M.; Wales, D. J.; de Souza, V. K.

2017-10-01

We study the dynamical behaviour of a computer model for viscous silica, the archetypal strong glass former, and compare its diffusion mechanism with earlier studies of a fragile binary Lennard-Jones liquid. Three different methods of analysis are employed. First, the temperature and time scale dependence of the diffusion constant is analysed. Negative correlation of particle displacements influences transport properties in silica as well as in fragile liquids. We suggest that the difference between Arrhenius and super-Arrhenius diffusive behaviour results from competition between the correlation time scale and the caging time scale. Second, we analyse the dynamics using a geometrical definition of cage-breaking transitions that was proposed previously for fragile glass formers. We find that this definition accurately captures the bond rearrangement mechanisms that control transport in open network liquids, and reproduces the diffusion constants accurately at low temperatures. As the same method is applicable to both strong and fragile glass formers, we can compare correlation time scales in these two types of systems. We compare the time spent in chains of correlated cage breaks with the characteristic caging time and find that correlations in the fragile binary Lennard-Jones system persist for an order of magnitude longer than those in the strong silica system. We investigate the origin of the correlation behaviour by sampling the potential energy landscape for silica and comparing it with the binary Lennard-Jones model. We find no qualitative difference between the landscapes, but several metrics suggest that the landscape of the fragile liquid is rougher and more frustrated. Metabasins in silica are smaller than those in binary Lennard-Jones and contain fewer high-barrier processes. This difference probably leads to the observed separation of correlation and caging time scales.

Underdamped scaled Brownian motion: (non-)existence of the overdamped limit in anomalous diffusion

PubMed Central

Bodrova, Anna S.; Chechkin, Aleksei V.; Cherstvy, Andrey G.; Safdari, Hadiseh; Sokolov, Igor M.; Metzler, Ralf

2016-01-01

It is quite generally assumed that the overdamped Langevin equation provides a quantitative description of the dynamics of a classical Brownian particle in the long time limit. We establish and investigate a paradigm anomalous diffusion process governed by an underdamped Langevin equation with an explicit time dependence of the system temperature and thus the diffusion and damping coefficients. We show that for this underdamped scaled Brownian motion (UDSBM) the overdamped limit fails to describe the long time behaviour of the system and may practically even not exist at all for a certain range of the parameter values. Thus persistent inertial effects play a non-negligible role even at significantly long times. From this study a general questions on the applicability of the overdamped limit to describe the long time motion of an anomalously diffusing particle arises, with profound consequences for the relevance of overdamped anomalous diffusion models. We elucidate our results in view of analytical and simulations results for the anomalous diffusion of particles in free cooling granular gases. PMID:27462008

Diffusion in random networks

DOE PAGES

Zhang, Duan Z.; Padrino, Juan C.

2017-06-01

The ensemble averaging technique is applied to model mass transport by diffusion in random networks. The system consists of an ensemble of random networks, where each network is made of pockets connected by tortuous channels. Inside a channel, fluid transport is assumed to be governed by the one-dimensional diffusion equation. Mass balance leads to an integro-differential equation for the pocket mass density. The so-called dual-porosity model is found to be equivalent to the leading order approximation of the integration kernel when the diffusion time scale inside the channels is small compared to the macroscopic time scale. As a test problem,more » we consider the one-dimensional mass diffusion in a semi-infinite domain. Because of the required time to establish the linear concentration profile inside a channel, for early times the similarity variable is xt $-$1/4 rather than xt $-$1/2 as in the traditional theory. We found this early time similarity can be explained by random walk theory through the network.« less

Lagrangian Statistics of Slightly Buoyant Droplets in Isotropic Turbulence

NASA Astrophysics Data System (ADS)

Gopalan, Balaji; Malkiel, Edwin; Katz, Joseph

2006-11-01

This project examines the dynamics of slightly buoyant diesel droplets in isotropic turbulence using high speed in-line digital Holographic PIV. A cloud of droplets with specific gravity of 0.85 is injected into the central portion of an isotropic turbulence facility. The droplet trajectories are measured in a 50x50x50 mm̂3 sample volume using high speed in-line digital holography. An automated program has been developed to obtain accurate time history of droplet velocities. Data analysis determines the PDF of velocity and acceleration in three dimensions. The time histories enable us to calculate the three dimensional Lagrangian velocity autocorrelation function, and from them the diffusion coefficients. Due to buoyancy the vertical diffusion time scale exceeds the horizontal one by about 65% .The diffusion coefficients vary between 2.8 cm̂2/sec in the horizontal direction to 5.5 cm̂2/sec in the vertical direction. For droplets with size varying from 2 to 11 Kolmogorov scales there are no clear trends with size. The variations of diffusion rates for different turbulent intensities and the effect of finite window size are presently examined. For shorter time scales, when the diffusion need not be Fickian the three dimensional trajectories can be used to calculate the generalized dispersion tensor and measure the time elapsed for diffusion to become Fickian.

Generalized fractional diffusion equations for accelerating subdiffusion and truncated Lévy flights

NASA Astrophysics Data System (ADS)

Chechkin, A. V.; Gonchar, V. Yu.; Gorenflo, R.; Korabel, N.; Sokolov, I. M.

2008-08-01

Fractional diffusion equations are widely used to describe anomalous diffusion processes where the characteristic displacement scales as a power of time. For processes lacking such scaling the corresponding description may be given by diffusion equations with fractional derivatives of distributed order. Such equations were introduced in A. V. Chechkin, R. Gorenflo, and I. Sokolov [Phys. Rev. E 66, 046129 (2002)] for the description of the processes getting more anomalous in the course of time (decelerating subdiffusion and accelerating superdiffusion). Here we discuss the properties of diffusion equations with fractional derivatives of the distributed order for the description of anomalous relaxation and diffusion phenomena getting less anomalous in the course of time, which we call, respectively, accelerating subdiffusion and decelerating superdiffusion. For the former process, by taking a relatively simple particular example with two fixed anomalous diffusion exponents we show that the proposed equation effectively describes the subdiffusion phenomenon with diffusion exponent varying in time. For the latter process we demonstrate by a particular example how the power-law truncated Lévy stable distribution evolves in time to the distribution with power-law asymptotics and Gaussian shape in the central part. The special case of two different orders is characteristic for the general situation in which the extreme orders dominate the asymptotics.

Membrane properties change in fine-pore aeration diffusers: full-scale variations of transfer efficiency and headloss.

PubMed

Rosso, Diego; Libra, Judy A; Wiehe, Wolfgang; Stenstrom, Michael K

2008-05-01

Fine-pore diffusers are the most common aeration system in municipal wastewater treatment. Punched polymeric membranes are often used in fine-pore aeration due to their advantageous initial performance. These membranes are subject to fouling and scaling, resulting in increased headloss and reduced oxygen transfer efficiency, both contributing to increased plant energy costs. This paper describes and discusses the change in material properties for polymeric fine-pore diffusers, comparing new and used membranes. Three different diffuser technologies were tested and sample diffusers from two wastewater treatment facilities were analysed. The polymeric membranes analysed in this paper were composed of ethylene-propylene-diene monomer (EPDM), polyurethane, and silicon. Transfer efficiency is usually lower with longer times in operation, as older, dilated orifices produce larger bubbles, which are unfavourable to mass transfer. At the same time, headloss increases with time in operation, since membranes increase in rigidity and hardness, and fouling and scaling phenomena occur at the orifice opening. Change in polymer properties and laboratory test results correlate with the decrease in oxygen transfer efficiency.

Mean-cluster approach indicates cell sorting time scales are determined by collective dynamics

NASA Astrophysics Data System (ADS)

Beatrici, Carine P.; de Almeida, Rita M. C.; Brunnet, Leonardo G.

2017-03-01

Cell migration is essential to cell segregation, playing a central role in tissue formation, wound healing, and tumor evolution. Considering random mixtures of two cell types, it is still not clear which cell characteristics define clustering time scales. The mass of diffusing clusters merging with one another is expected to grow as td /d +2 when the diffusion constant scales with the inverse of the cluster mass. Cell segregation experiments deviate from that behavior. Explanations for that could arise from specific microscopic mechanisms or from collective effects, typical of active matter. Here we consider a power law connecting diffusion constant and cluster mass to propose an analytic approach to model cell segregation where we explicitly take into account finite-size corrections. The results are compared with active matter model simulations and experiments available in the literature. To investigate the role played by different mechanisms we considered different hypotheses describing cell-cell interaction: differential adhesion hypothesis and different velocities hypothesis. We find that the simulations yield normal diffusion for long time intervals. Analytic and simulation results show that (i) cluster evolution clearly tends to a scaling regime, disrupted only at finite-size limits; (ii) cluster diffusion is greatly enhanced by cell collective behavior, such that for high enough tendency to follow the neighbors, cluster diffusion may become independent of cluster size; (iii) the scaling exponent for cluster growth depends only on the mass-diffusion relation, not on the detailed local segregation mechanism. These results apply for active matter systems in general and, in particular, the mechanisms found underlying the increase in cell sorting speed certainly have deep implications in biological evolution as a selection mechanism.

Diffusion and spectroscopy of water and lipids in fully hydrated dimyristoylphosphatidylcholine bilayer membranes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yang, J.; Martí, J., E-mail: jordi.marti@upc.edu; Calero, C.

2014-03-14

Microscopic structure and dynamics of water and lipids in a fully hydrated dimyristoylphosphatidylcholine phospholipid lipid bilayer membrane in the liquid-crystalline phase have been analyzed with all-atom molecular dynamics simulations based on the recently parameterized CHARMM36 force field. The diffusive dynamics of the membrane lipids and of its hydration water, their reorientational motions as well as their corresponding spectral densities, related to the absorption of radiation, have been considered for the first time using the present force field. In addition, structural properties such as density and pressure profiles, a deuterium-order parameter, surface tension, and the extent of water penetration in themore » membrane have been analyzed. Molecular self-diffusion, reorientational motions, and spectral densities of atomic species reveal a variety of time scales playing a role in membrane dynamics. The mechanisms of lipid motion strongly depend on the time scale considered, from fast ballistic translation at the scale of picoseconds (effective diffusion coefficients of the order of 10{sup −5} cm{sup 2}/s) to diffusive flow of a few lipids forming nanodomains at the scale of hundreds of nanoseconds (diffusion coefficients of the order of 10{sup −8} cm{sup 2}/s). In the intermediate regime of sub-diffusion, collisions with nearest neighbors prevent the lipids to achieve full diffusion. Lipid reorientations along selected directions agree well with reported nuclear magnetic resonance data and indicate two different time scales, one about 1 ns and a second one in the range of 2–8 ns. We associated the two time scales of reorientational motions with angular distributions of selected vectors. Calculated spectral densities corresponding to lipid and water reveal an overall good qualitative agreement with Fourier transform infrared spectroscopy experiments. Our simulations indicate a blue-shift of the low frequency spectral bands of hydration water as a result of its interaction with lipids. We have thoroughly analyzed the physical meaning of all spectral features from lipid atomic sites and correlated them with experimental data. Our findings include a “wagging of the tails” frequency around 30 cm{sup −1}, which essentially corresponds to motions of the tail-group along the instantaneous plane formed by the two lipid tails, i.e., in-plane oscillations are clearly of bigger importance than those along the normal-to-the plane direction.« less

Turbulent mixing and removal of ozone within an Amazon rainforest canopy

NASA Astrophysics Data System (ADS)

Freire, L. S.; Gerken, T.; Ruiz-Plancarte, J.; Wei, D.; Fuentes, J. D.; Katul, G. G.; Dias, N. L.; Acevedo, O. C.; Chamecki, M.

2017-03-01

Simultaneous profiles of turbulence statistics and mean ozone mixing ratio are used to establish a relation between eddy diffusivity and ozone mixing within the Amazon forest. A one-dimensional diffusion model is proposed and used to infer mixing time scales from the eddy diffusivity profiles. Data and model results indicate that during daytime conditions, the upper (lower) half of the canopy is well (partially) mixed most of the time and that most of the vertical extent of the forest can be mixed in less than an hour. During nighttime, most of the canopy is predominantly poorly mixed, except for periods with bursts of intermittent turbulence. Even though turbulence is faster than chemistry during daytime, both processes have comparable time scales in the lower canopy layers during nighttime conditions. Nonchemical loss time scales (associated with stomatal uptake and dry deposition) for the entire forest are comparable to turbulent mixing time scale in the lower canopy during the day and in the entire canopy during the night, indicating a tight coupling between turbulent transport and dry deposition and stomatal uptake processes. Because of the significant time of day and height variability of the turbulent mixing time scale inside the canopy, it is important to take it into account when studying chemical and biophysical processes happening in the forest environment. The method proposed here to estimate turbulent mixing time scales is a reliable alternative to currently used models, especially for situations in which the vertical distribution of the time scale is relevant.

String-like collective motion in the α- and β-relaxation of a coarse-grained polymer melt

NASA Astrophysics Data System (ADS)

Pazmiño Betancourt, Beatriz A.; Starr, Francis W.; Douglas, Jack F.

2018-03-01

Relaxation in glass-forming liquids occurs as a multi-stage hierarchical process involving cooperative molecular motion. First, there is a "fast" relaxation process dominated by the inertial motion of the molecules whose amplitude grows upon heating, followed by a longer time α-relaxation process involving both large-scale diffusive molecular motion and momentum diffusion. Our molecular dynamics simulations of a coarse-grained glass-forming polymer melt indicate that the fast, collective motion becomes progressively suppressed upon cooling, necessitating large-scale collective motion by molecular diffusion for the material to relax approaching the glass-transition. In each relaxation regime, the decay of the collective intermediate scattering function occurs through collective particle exchange motions having a similar geometrical form, and quantitative relationships are derived relating the fast "stringlet" collective motion to the larger scale string-like collective motion at longer times, which governs the temperature-dependent activation energies associated with both thermally activated molecular diffusion and momentum diffusion.

A Transition in the Cumulative Reaction Rate of Two Species Diffusion with Bimolecular Reaction

NASA Astrophysics Data System (ADS)

Rajaram, Harihar; Arshadi, Masoud

2015-04-01

Diffusion and bimolecular reaction between two initially separated reacting species is a prototypical small-scale description of reaction induced by transverse mixing. It is also relevant to diffusion controlled transport regimes as encountered in low-permeability matrix blocks in fractured media. In previous work, the reaction-diffusion problem has been analyzed as a Stefan problem involving a distinct moving boundary (reaction front), which predicts that front motion scales as √t, and the cumulative reaction rate scales as 1/√t-. We present a general non-dimensionalization of the problem and a perturbation analysis to show that there is an early time regime where the cumulative reaction rate scales as √t- rather than 1/√t. The duration of this early time regime (where the cumulative rate is kinetically rather than diffusion controlled) depends on the rate parameter, in a manner that is consistently predicted by our non-dimensionalization. We also present results on the scaling of the reaction front width. We present numerical simulations in homogeneous and heterogeneous porous media to demonstrate the limited influence of heterogeneity on the behavior of the reaction-diffusion system. We illustrate applications to the practical problem of in-situ chemical oxidation of TCE and PCE by permanganate, which is employed to remediate contaminated sites where the DNAPLs are largely dissolved in the rock matrix.

Spin-diffusions and diffusive molecular dynamics

NASA Astrophysics Data System (ADS)

Farmer, Brittan; Luskin, Mitchell; Plecháč, Petr; Simpson, Gideon

2017-12-01

Metastable configurations in condensed matter typically fluctuate about local energy minima at the femtosecond time scale before transitioning between local minima after nanoseconds or microseconds. This vast scale separation limits the applicability of classical molecular dynamics (MD) methods and has spurned the development of a host of approximate algorithms. One recently proposed method is diffusive MD which aims at integrating a system of ordinary differential equations describing the likelihood of occupancy by one of two species, in the case of a binary alloy, while quasistatically evolving the locations of the atoms. While diffusive MD has shown itself to be efficient and provide agreement with observations, it is fundamentally a model, with unclear connections to classical MD. In this work, we formulate a spin-diffusion stochastic process and show how it can be connected to diffusive MD. The spin-diffusion model couples a classical overdamped Langevin equation to a kinetic Monte Carlo model for exchange amongst the species of a binary alloy. Under suitable assumptions and approximations, spin-diffusion can be shown to lead to diffusive MD type models. The key assumptions and approximations include a well-defined time scale separation, a choice of spin-exchange rates, a low temperature approximation, and a mean field type approximation. We derive several models from different assumptions and show their relationship to diffusive MD. Differences and similarities amongst the models are explored in a simple test problem.

Tracer diffusion in active suspensions

NASA Astrophysics Data System (ADS)

Burkholder, Eric W.; Brady, John F.

2017-05-01

We study the diffusion of a Brownian probe particle of size R in a dilute dispersion of active Brownian particles of size a , characteristic swim speed U0, reorientation time τR, and mechanical energy ksTs=ζaU02τR/6 , where ζa is the Stokes drag coefficient of a swimmer. The probe has a thermal diffusivity DP=kBT /ζP , where kBT is the thermal energy of the solvent and ζP is the Stokes drag coefficient for the probe. When the swimmers are inactive, collisions between the probe and the swimmers sterically hinder the probe's diffusive motion. In competition with this steric hindrance is an enhancement driven by the activity of the swimmers. The strength of swimming relative to thermal diffusion is set by Pes=U0a /DP . The active contribution to the diffusivity scales as Pes2 for weak swimming and Pes for strong swimming, but the transition between these two regimes is nonmonotonic. When fluctuations in the probe motion decay on the time scale τR, the active diffusivity scales as ksTs/ζP : the probe moves as if it were immersed in a solvent with energy ksTs rather than kBT .

Diffuse pollution of soil and water: Long term trends at large scales?

NASA Astrophysics Data System (ADS)

Grathwohl, P.

2012-04-01

Industrialization and urbanization, which consequently increased pressure on the environment to cause degradation of soil and water quality over more than a century, is still ongoing. The number of potential environmental contaminants detected in surface and groundwater is continuously increasing; from classical industrial and agricultural chemicals, to flame retardants, pharmaceuticals, and personal care products. While point sources of pollution can be managed in principle, diffuse pollution is only reversible at very long time scales if at all. Compounds which were phased out many decades ago such as PCBs or DDT are still abundant in soils, sediments and biota. How diffuse pollution is processed at large scales in space (e.g. catchments) and time (centuries) is unknown. The relevance to the field of processes well investigated at the laboratory scale (e.g. sorption/desorption and (bio)degradation kinetics) is not clear. Transport of compounds is often coupled to the water cycle and in order to assess trends in diffuse pollution, detailed knowledge about the hydrology and the solute fluxes at the catchment scale is required (e.g. input/output fluxes, transformation rates at the field scale). This is also a prerequisite in assessing management options for reversal of adverse trends.

Spin diffusion from an inhomogeneous quench in an integrable system.

PubMed

Ljubotina, Marko; Žnidarič, Marko; Prosen, Tomaž

2017-07-13

Generalized hydrodynamics predicts universal ballistic transport in integrable lattice systems when prepared in generic inhomogeneous initial states. However, the ballistic contribution to transport can vanish in systems with additional discrete symmetries. Here we perform large scale numerical simulations of spin dynamics in the anisotropic Heisenberg XXZ spin 1/2 chain starting from an inhomogeneous mixed initial state which is symmetric with respect to a combination of spin reversal and spatial reflection. In the isotropic and easy-axis regimes we find non-ballistic spin transport which we analyse in detail in terms of scaling exponents of the transported magnetization and scaling profiles of the spin density. While in the easy-axis regime we find accurate evidence of normal diffusion, the spin transport in the isotropic case is clearly super-diffusive, with the scaling exponent very close to 2/3, but with universal scaling dynamics which obeys the diffusion equation in nonlinearly scaled time.

Spectral Definition of the Characteristic Times for Anomalous Diffusion in a Potential

NASA Astrophysics Data System (ADS)

Kalmykov, Yuri P.; Coffey, William T.; Titov, Serguey V.

Characteristic times of the noninertial fractional diffusion of a particle in a potential are defined in terms of three time constants, viz., the integral, effective, and longest relaxation times. These times are described using the eigenvalues of the corresponding Fokker-Planck operator for the normal diffusion. Knowledge of them is sufficient to accurately predict the anomalous relaxation behavior for all time scales of interest. As a particular example, we consider the subdiffusion of a planar rotor in a double-well potential.

Hypothesis on the nature of time

NASA Astrophysics Data System (ADS)

Coumbe, D. N.

2015-06-01

We present numerical evidence that fictitious diffusing particles in the causal dynamical triangulation (CDT) approach to quantum gravity exceed the speed of light on small distance scales. We argue this superluminal behavior is responsible for the appearance of dimensional reduction in the spectral dimension. By axiomatically enforcing a scale invariant speed of light we show that time must dilate as a function of relative scale, just as it does as a function of relative velocity. By calculating the Hausdorff dimension of CDT diffusion paths we present a seemingly equivalent dual description in terms of a scale dependent Wick rotation of the metric. Such a modification to the nature of time may also have relevance for other approaches to quantum gravity.

Nonequilibrium diffusive gas dynamics: Poiseuille microflow

NASA Astrophysics Data System (ADS)

Abramov, Rafail V.; Otto, Jasmine T.

2018-05-01

We test the recently developed hierarchy of diffusive moment closures for gas dynamics together with the near-wall viscosity scaling on the Poiseuille flow of argon and nitrogen in a one micrometer wide channel, and compare it against the corresponding Direct Simulation Monte Carlo computations. We find that the diffusive regularized Grad equations with viscosity scaling provide the most accurate approximation to the benchmark DSMC results. At the same time, the conventional Navier-Stokes equations without the near-wall viscosity scaling are found to be the least accurate among the tested closures.

Anomalous diffusion and dynamics of fluorescence recovery after photobleaching in the random-comb model

NASA Astrophysics Data System (ADS)

Yuste, S. B.; Abad, E.; Baumgaertner, A.

2016-07-01

We address the problem of diffusion on a comb whose teeth display varying lengths. Specifically, the length ℓ of each tooth is drawn from a probability distribution displaying power law behavior at large ℓ ,P (ℓ ) ˜ℓ-(1 +α ) (α >0 ). To start with, we focus on the computation of the anomalous diffusion coefficient for the subdiffusive motion along the backbone. This quantity is subsequently used as an input to compute concentration recovery curves mimicking fluorescence recovery after photobleaching experiments in comblike geometries such as spiny dendrites. Our method is based on the mean-field description provided by the well-tested continuous time random-walk approach for the random-comb model, and the obtained analytical result for the diffusion coefficient is confirmed by numerical simulations of a random walk with finite steps in time and space along the backbone and the teeth. We subsequently incorporate retardation effects arising from binding-unbinding kinetics into our model and obtain a scaling law characterizing the corresponding change in the diffusion coefficient. Finally, we show that recovery curves obtained with the help of the analytical expression for the anomalous diffusion coefficient cannot be fitted perfectly by a model based on scaled Brownian motion, i.e., a standard diffusion equation with a time-dependent diffusion coefficient. However, differences between the exact curves and such fits are small, thereby providing justification for the practical use of models relying on scaled Brownian motion as a fitting procedure for recovery curves arising from particle diffusion in comblike systems.

Two-particle diffusion and locality assumption

NASA Astrophysics Data System (ADS)

Nicolleau, F.; Yu, G.

2004-07-01

A three-dimensional kinematic simulation (KS) model is used to study one- and two-particle diffusion in turbulent flows. The energy spectrum E(k) takes a power law form E(k)˜k-p. The value of this power p is varied from 1.2 to 3, so that its effects on the diffusion of one and two particles can be studied. The two-particle diffusion behaves differently depending on whether the two-particle separation is larger or smaller than the smallest scale of turbulence (Kolmogorov length scale η). When the two-particle mean square separation <Δ2(t)> is smaller than η2 it experiences a time exponential growth <Δ2(t)>=Δ02eγ(t/tη) but for a very short time. For longer times, when η2<<Δ2(t)>. In this inertial range we observe that d/dt<Δ2(t)>={a ln(<Δ(t)2>1/2/η)+b}u'L(η/L)(p+1)/2(<Δ(t)2>1/2/η)(p+1)/2 for p⩽3. For Δ0/η≫1 a=0, but a≠0 for Δ0/η⩽1 and as a consequence the pair diffusion cannot have lost its dependence on the initial separation during the exponential growth, i.e., γ is a function of Δ0/η. Our modified Richardson law is compared with two other proposed modifications to Richardson's power law, namely the virtual time [G. K. Batchelor, Proc. Cambridge Philos. Soc. 48, 345 (1952)] and the correction factor [F. Nicolleau and J. C. Vassilicos, Phys. Rev. Lett. 90, 245003 (2003)]. Further investigations on two-particle diffusion when p=3 give an excellent agreement with the experimental results in P. Morel and M. Larchevêque, J. Atmos. Sci. 31 (1974) for atmospheric turbulent flows. Finally, using two different combined power law energy spectra in KS, the isotropic small scales are found to have no significant role when their largest scale lT is less than 10 times the Kolmogorov length scale η.

Diffusion in random networks: Asymptotic properties, and numerical and engineering approximations

NASA Astrophysics Data System (ADS)

Padrino, Juan C.; Zhang, Duan Z.

2016-11-01

The ensemble phase averaging technique is applied to model mass transport by diffusion in random networks. The system consists of an ensemble of random networks, where each network is made of a set of pockets connected by tortuous channels. Inside a channel, we assume that fluid transport is governed by the one-dimensional diffusion equation. Mass balance leads to an integro-differential equation for the pores mass density. The so-called dual porosity model is found to be equivalent to the leading order approximation of the integration kernel when the diffusion time scale inside the channels is small compared to the macroscopic time scale. As a test problem, we consider the one-dimensional mass diffusion in a semi-infinite domain, whose solution is sought numerically. Because of the required time to establish the linear concentration profile inside a channel, for early times the similarity variable is xt- 1 / 4 rather than xt- 1 / 2 as in the traditional theory. This early time sub-diffusive similarity can be explained by random walk theory through the network. In addition, by applying concepts of fractional calculus, we show that, for small time, the governing equation reduces to a fractional diffusion equation with known solution. We recast this solution in terms of special functions easier to compute. Comparison of the numerical and exact solutions shows excellent agreement.

Experimental investigation of turbulent diffusion of slightly buoyant droplets in locally isotropic turbulence

NASA Astrophysics Data System (ADS)

Gopalan, Balaji; Malkiel, Edwin; Katz, Joseph

2008-09-01

High-speed inline digital holographic cinematography is used for studying turbulent diffusion of slightly buoyant 0.5-1.2 mm diameter diesel droplets and 50 μm diameter neutral density particles. Experiments are performed in a 50×50×70 mm3 sample volume in a controlled, nearly isotropic turbulence facility, which is characterized by two dimensional particle image velocimetry. An automated tracking program has been used for measuring velocity time history of more than 17 000 droplets and 15 000 particles. For most of the present conditions, rms values of horizontal droplet velocity exceed those of the fluid. The rms values of droplet vertical velocity are higher than those of the fluid only for the highest turbulence level. The turbulent diffusion coefficient is calculated by integration of the ensemble-averaged Lagrangian velocity autocovariance. Trends of the asymptotic droplet diffusion coefficient are examined by noting that it can be viewed as a product of a mean square velocity and a diffusion time scale. To compare the effects of turbulence and buoyancy, the turbulence intensity (ui') is scaled by the droplet quiescent rise velocity (Uq). The droplet diffusion coefficients in horizontal and vertical directions are lower than those of the fluid at low normalized turbulence intensity, but exceed it with increasing normalized turbulence intensity. For most of the present conditions the droplet horizontal diffusion coefficient is higher than the vertical diffusion coefficient, consistent with trends of the droplet velocity fluctuations and in contrast to the trends of the diffusion timescales. The droplet diffusion coefficients scaled by the product of turbulence intensity and an integral length scale are a monotonically increasing function of ui'/Uq.

Diffusion in Jammed Particle Packs.

PubMed

Bolintineanu, Dan S; Grest, Gary S; Lechman, Jeremy B; Silbert, Leonardo E

2015-08-21

Using random walk simulations we explore diffusive transport through monodisperse sphere packings over a range of packing fractions ϕ in the vicinity of the jamming transition at ϕ(c). Various diffusion properties are computed over several orders of magnitude in both time and packing pressure. Two well-separated regimes of normal "Fickian" diffusion, where the mean squared displacement is linear in time, are observed. The first corresponds to diffusion inside individual spheres, while the latter is the long-time bulk diffusion. The intermediate anomalous diffusion regime and the long-time value of the diffusion coefficient are both shown to be controlled by particle contacts, which in turn depend on proximity to ϕ(c). The time required to recover normal diffusion t* scales as (ϕ-ϕ(c))(-0.5) and the long-time diffusivity D(∞)∼(ϕ-ϕ(c))0.5, or D(∞)∼1/t*. It is shown that the distribution of mean first passage times associated with the escape of random walkers between neighboring particles controls both t* and D(∞) in the limit ϕ→ϕ(c).

The effects of heterogeneities on memory-dependent diffusion

NASA Astrophysics Data System (ADS)

Adib, Farhad; Neogi, P.

1993-07-01

Case II diffusion is often seen in glassy polymers, where the mass uptake in sorption is proportional to time t instead of sqrt{t}. A memory dependent diffusion is needed to explain such effects, where the relaxation function used to describe the memory effect has a characteristic time. The ratio of this time to the overall diffusion times is the diffusional Deborah number. Simple models show that case II results when the Deborah number is around one, that is, when the two time scales are comparable. Under investigation are the possible effects of the fact that the glassy polymers are heterogeneous over molecular scales. The averaging form given by DiMarzio and Sanchez has been used to obtain the averaged response. The calculated dynamics of sorption show that whereas case II is still observed, the long term tails change dramatically from the oscillatory to torpid, to chaotic, which are all observed in the experiments. The Deborah number defined here in a self-consistent manner collapses in those cases, but causes no other ill-effects.

Impact of morphology on diffusive dynamics on curved surfaces

NASA Astrophysics Data System (ADS)

Kusters, Remy; Storm, Cornelis

2014-03-01

Diffusive processes on nonplanar substrates are deeply relevant for cellular function and transport and increasingly used to probe and characterize the behavior of proteins in membranes. We present analytical and numerical analyses of in-plane diffusion of discrete particles on curved geometries reflecting various generic motifs in biology and explore, in particular, the effect that the shape of the substrate has on the characteristic time scales of diffusive processes. To this end, we consider both collective measures (the relaxation of concentration profiles towards equilibrium) and single-particle measures (escape rates and first passage times of individual diffusing molecules): the first relevant for the correct interpretation of FRAP experiments in curved environments; the second, for single-particle tracking probes. Each of these measures is sensitively affected by the morphology of the substrate, and we find that the exit rate out of a domain is not uniquely set by the size of its boundary, illustrating the general principle we reveal: By varying the shape of a substrate, Nature can control the diffusive time scales in a microenvironment without changing the bare substrate properties.

An investigation of turbulent transport in the extreme lower atmosphere

NASA Technical Reports Server (NTRS)

Koper, C. A., Jr.; Sadeh, W. Z.

1975-01-01

A model in which the Lagrangian autocorrelation is expressed by a domain integral over a set of usual Eulerian autocorrelations acquired concurrently at all points within a turbulence box is proposed along with a method for ascertaining the statistical stationarity of turbulent velocity by creating an equivalent ensemble to investigate the flow in the extreme lower atmosphere. Simultaneous measurements of turbulent velocity on a turbulence line along the wake axis were carried out utilizing a longitudinal array of five hot-wire anemometers remotely operated. The stationarity test revealed that the turbulent velocity is approximated as a realization of a weakly self-stationary random process. Based on the Lagrangian autocorrelation it is found that: (1) large diffusion time predominated; (2) ratios of Lagrangian to Eulerian time and spatial scales were smaller than unity; and, (3) short and long diffusion time scales and diffusion spatial scales were constrained within their Eulerian counterparts.

Multi-scale continuum modeling of biological processes: from molecular electro-diffusion to sub-cellular signaling transduction

NASA Astrophysics Data System (ADS)

Cheng, Y.; Kekenes-Huskey, P.; Hake, J. E.; Holst, M. J.; McCammon, J. A.; Michailova, A. P.

2012-01-01

This paper presents a brief review of multi-scale modeling at the molecular to cellular scale, with new results for heart muscle cells. A finite element-based simulation package (SMOL) was used to investigate the signaling transduction at molecular and sub-cellular scales (http://mccammon.ucsd.edu/smol/, http://FETK.org) by numerical solution of the time-dependent Smoluchowski equations and a reaction-diffusion system. At the molecular scale, SMOL has yielded experimentally validated estimates of the diffusion-limited association rates for the binding of acetylcholine to mouse acetylcholinesterase using crystallographic structural data. The predicted rate constants exhibit increasingly delayed steady-state times, with increasing ionic strength, and demonstrate the role of an enzyme's electrostatic potential in influencing ligand binding. At the sub-cellular scale, an extension of SMOL solves a nonlinear, reaction-diffusion system describing Ca2+ ligand buffering and diffusion in experimentally derived rodent ventricular myocyte geometries. Results reveal the important role of mobile and stationary Ca2+ buffers, including Ca2+ indicator dye. We found that alterations in Ca2+-binding and dissociation rates of troponin C (TnC) and total TnC concentration modulate sub-cellular Ca2+ signals. The model predicts that reduced off-rate in the whole troponin complex (TnC, TnI, TnT) versus reconstructed thin filaments (Tn, Tm, actin) alters cytosolic Ca2+ dynamics under control conditions or in disease-linked TnC mutations. The ultimate goal of these studies is to develop scalable methods and theories for the integration of molecular-scale information into simulations of cellular-scale systems.

Scaled Brownian motion: a paradoxical process with a time dependent diffusivity for the description of anomalous diffusion.

PubMed

Jeon, Jae-Hyung; Chechkin, Aleksei V; Metzler, Ralf

2014-08-14

Anomalous diffusion is frequently described by scaled Brownian motion (SBM), a Gaussian process with a power-law time dependent diffusion coefficient. Its mean squared displacement is 〈x(2)(t)〉 ≃ 2K(t)t with K(t) ≃ t(α-1) for 0 < α < 2. SBM may provide a seemingly adequate description in the case of unbounded diffusion, for which its probability density function coincides with that of fractional Brownian motion. Here we show that free SBM is weakly non-ergodic but does not exhibit a significant amplitude scatter of the time averaged mean squared displacement. More severely, we demonstrate that under confinement, the dynamics encoded by SBM is fundamentally different from both fractional Brownian motion and continuous time random walks. SBM is highly non-stationary and cannot provide a physical description for particles in a thermalised stationary system. Our findings have direct impact on the modelling of single particle tracking experiments, in particular, under confinement inside cellular compartments or when optical tweezers tracking methods are used.

Solute-defect interactions in Al-Mg alloys from diffusive variational Gaussian calculations

NASA Astrophysics Data System (ADS)

Dontsova, E.; Rottler, J.; Sinclair, C. W.

2014-11-01

Resolving atomic-scale defect topologies and energetics with accurate atomistic interaction models provides access to the nonlinear phenomena inherent at atomic length and time scales. Coarse graining the dynamics of such simulations to look at the migration of, e.g., solute atoms, while retaining the rich atomic-scale detail required to properly describe defects, is a particular challenge. In this paper, we present an adaptation of the recently developed "diffusive molecular dynamics" model to describe the energetics and kinetics of binary alloys on diffusive time scales. The potential of the technique is illustrated by applying it to the classic problems of solute segregation to a planar boundary (stacking fault) and edge dislocation in the Al-Mg system. Our approach provides fully dynamical solutions in situations with an evolving energy landscape in a computationally efficient way, where atomistic kinetic Monte Carlo simulations are difficult or impractical to perform.

Tracer diffusion in active suspensions.

PubMed

Burkholder, Eric W; Brady, John F

2017-05-01

We study the diffusion of a Brownian probe particle of size R in a dilute dispersion of active Brownian particles of size a, characteristic swim speed U_{0}, reorientation time τ_{R}, and mechanical energy k_{s}T_{s}=ζ_{a}U_{0}^{2}τ_{R}/6, where ζ_{a} is the Stokes drag coefficient of a swimmer. The probe has a thermal diffusivity D_{P}=k_{B}T/ζ_{P}, where k_{B}T is the thermal energy of the solvent and ζ_{P} is the Stokes drag coefficient for the probe. When the swimmers are inactive, collisions between the probe and the swimmers sterically hinder the probe's diffusive motion. In competition with this steric hindrance is an enhancement driven by the activity of the swimmers. The strength of swimming relative to thermal diffusion is set by Pe_{s}=U_{0}a/D_{P}. The active contribution to the diffusivity scales as Pe_{s}^{2} for weak swimming and Pe_{s} for strong swimming, but the transition between these two regimes is nonmonotonic. When fluctuations in the probe motion decay on the time scale τ_{R}, the active diffusivity scales as k_{s}T_{s}/ζ_{P}: the probe moves as if it were immersed in a solvent with energy k_{s}T_{s} rather than k_{B}T.

Scaling of seismicity induced by nonlinear fluid-rock interaction after an injection stop

NASA Astrophysics Data System (ADS)

Johann, L.; Dinske, C.; Shapiro, S. A.

2016-11-01

Fluid injections into unconventional reservoirs, performed for fluid-mobility enhancement, are accompanied by microseismic activity also after the injection. Previous studies revealed that the triggering of seismic events can be effectively described by nonlinear diffusion of pore fluid pressure perturbations where the hydraulic diffusivity becomes pressure dependent. The spatiotemporal distribution of postinjection-induced microseismicity has two important features: the triggering front, corresponding to early and distant events, and the back front, representing the time-dependent spatial envelope of the growing seismic quiescence zone. Here for the first time, we describe analytically the temporal behavior of these two fronts after the injection stop in the case of nonlinear pore fluid pressure diffusion. We propose a scaling law for the fronts and show that they are sensitive to the degree of nonlinearity and to the Euclidean dimension of the dominant growth of seismicity clouds. To validate the theoretical finding, we numerically model nonlinear pore fluid pressure diffusion and generate synthetic catalogs of seismicity. Additionally, we apply the new scaling relation to several case studies of injection-induced seismicity. The derived scaling laws describe well synthetic and real data.

Anomalous diffusion and scaling in coupled stochastic processes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bel, Golan; Nemenman, Ilya

2009-01-01

Inspired by problems in biochemical kinetics, we study statistical properties of an overdamped Langevin processes with the friction coefficient depending on the state of a similar, unobserved, process. Integrating out the latter, we derive the Pocker-Planck the friction coefficient of the first depends on the state of the second. Integrating out the latter, we derive the Focker-Planck equation for the probability distribution of the former. This has the fonn of diffusion equation with time-dependent diffusion coefficient, resulting in an anomalous diffusion. The diffusion exponent can not be predicted using a simple scaling argument, and anomalous scaling appears as well. Themore » diffusion exponent of the Weiss-Havlin comb model is derived as a special case, and the same exponent holds even for weakly coupled processes. We compare our theoretical predictions with numerical simulations and find an excellent agreement. The findings caution against treating biochemical systems with unobserved dynamical degrees of freedom by means of standandard, diffusive Langevin descritpion.« less

Apparent diffusive motion of centrin foci in living cells: implications for diffusion-based motion in centriole duplication

NASA Astrophysics Data System (ADS)

Rafelski, Susanne M.; Keller, Lani C.; Alberts, Jonathan B.; Marshall, Wallace F.

2011-04-01

The degree to which diffusion contributes to positioning cellular structures is an open question. Here we investigate the question of whether diffusive motion of centrin granules would allow them to interact with the mother centriole. The role of centrin granules in centriole duplication remains unclear, but some proposed functions of these granules, for example, in providing pre-assembled centriole subunits, or by acting as unstable 'pre-centrioles' that need to be captured by the mother centriole (La Terra et al 2005 J. Cell Biol. 168 713-22), require the centrin foci to reach the mother. To test whether diffusive motion could permit such interactions in the necessary time scale, we measured the motion of centrin-containing foci in living human U2OS cells. We found that these centrin foci display apparently diffusive undirected motion. Using the apparent diffusion constant obtained from these measurements, we calculated the time scale required for diffusion to capture by the mother centrioles and found that it would greatly exceed the time available in the cell cycle. We conclude that mechanisms invoking centrin foci capture by the mother, whether as a pre-centriole or as a source of components to support later assembly, would require a form of directed motility of centrin foci that has not yet been observed.

Fine-pore aeration diffusers: accelerated membrane ageing studies.

PubMed

Kaliman, An; Rosso, Diego; Leu, Shao-Yuan; Stenstrom, Michael K

2008-01-01

Polymeric membranes are widely used in aeration systems for biological treatment. These membranes may degrade over time and are sensitive to fouling and scaling. Membrane degradation is reflected in a decline in operating performance and higher headloss, resulting in increased energy costs. Mechanical property parameters, such as membrane hardness, Young's modulus, and orifice creep, were used to characterize the performance of membranes over time in operation and to predict their failure. Used diffusers from municipal wastewater treatment plants were collected and tested for efficiency and headloss, and then dissected to facilitate measurements of Young's modulus, hardness, and orifice creep. Higher degree of membrane fouling corresponded consistently with larger orifice creep. A lab-scale membrane ageing simulation was performed with polyurethane and four different ethylene-propylene-diene (EPDM) membrane diffusers by subjecting them to chemical ageing cycles and periodic testing. The results confirmed full-scale plant results and showed the superiority of orifice creep over Young's modulus and hardness in predicting diffuser deterioration.

Global diffusion of cosmic rays in random magnetic fields

NASA Astrophysics Data System (ADS)

Snodin, A. P.; Shukurov, A.; Sarson, G. R.; Bushby, P. J.; Rodrigues, L. F. S.

2016-04-01

The propagation of charged particles, including cosmic rays, in a partially ordered magnetic field is characterized by a diffusion tensor whose components depend on the particle's Larmor radius RL and the degree of order in the magnetic field. Most studies of the particle diffusion presuppose a scale separation between the mean and random magnetic fields (e.g. there being a pronounced minimum in the magnetic power spectrum at intermediate scales). Scale separation is often a good approximation in laboratory plasmas, but not in most astrophysical environments such as the interstellar medium (ISM). Modern simulations of the ISM have numerical resolution of the order of 1 pc, so the Larmor radius of the cosmic rays that dominate in energy density is at least 106 times smaller than the resolved scales. Large-scale simulations of cosmic ray propagation in the ISM thus rely on oversimplified forms of the diffusion tensor. We take the first steps towards a more realistic description of cosmic ray diffusion for such simulations, obtaining direct estimates of the diffusion tensor from test particle simulations in random magnetic fields (with the Larmor radius scale being fully resolved), for a range of particle energies corresponding to 10-2 ≲ RL/lc ≲ 103, where lc is the magnetic correlation length. We obtain explicit expressions for the cosmic ray diffusion tensor for RL/lc ≪ 1, that might be used in a sub-grid model of cosmic ray diffusion. The diffusion coefficients obtained are closely connected with existing transport theories that include the random walk of magnetic lines.

Multimodel analysis of anisotropic diffusive tracer-gas transport in a deep arid unsaturated zone

USGS Publications Warehouse

Green, Christopher T.; Walvoord, Michelle Ann; Andraski, Brian J.; Striegl, Robert G.; Stonestrom, David A.

2015-01-01

Gas transport in the unsaturated zone affects contaminant flux and remediation, interpretation of groundwater travel times from atmospheric tracers, and mass budgets of environmentally important gases. Although unsaturated zone transport of gases is commonly treated as dominated by diffusion, the characteristics of transport in deep layered sediments remain uncertain. In this study, we use a multimodel approach to analyze results of a gas-tracer (SF6) test to clarify characteristics of gas transport in deep unsaturated alluvium. Thirty-five separate models with distinct diffusivity structures were calibrated to the tracer-test data and were compared on the basis of Akaike Information Criteria estimates of posterior model probability. Models included analytical and numerical solutions. Analytical models provided estimates of bulk-scale apparent diffusivities at the scale of tens of meters. Numerical models provided information on local-scale diffusivities and feasible lithological features producing the observed tracer breakthrough curves. The combined approaches indicate significant anisotropy of bulk-scale diffusivity, likely associated with high-diffusivity layers. Both approaches indicated that diffusivities in some intervals were greater than expected from standard models relating porosity to diffusivity. High apparent diffusivities and anisotropic diffusivity structures were consistent with previous observations at the study site of rapid lateral transport and limited vertical spreading of gas-phase contaminants. Additional processes such as advective oscillations may be involved. These results indicate that gases in deep, layered unsaturated zone sediments can spread laterally more quickly, and produce higher peak concentrations, than predicted by homogeneous, isotropic diffusion models.

The Relationship of Dynamical Heterogeneity to the Adam-Gibbs and Random First-Order Transition Theories of Glass Formation

NASA Astrophysics Data System (ADS)

Starr, Francis; Douglas, Jack; Sastry, Srikanth

2013-03-01

We examine measures of dynamical heterogeneity for a bead-spring polymer melt and test how these scales compare with the scales hypothesized by the Adam and Gibbs (AG) and random first-order transition (RFOT) theories. We show that the time scale of the high-mobility clusters and strings is associated with a diffusive time scale, while the low-mobility particles' time scale relates to a structural relaxation time. The difference of the characteristic times naturally explains the decoupling of diffusion and structural relaxation time scales. We examine the appropriateness of identifying the size scales of mobile particle clusters or strings with the size of cooperatively rearranging regions (CRR) in the AG and RFOT theories. We find that the string size appears to be the most consistent measure of CRR for both the AG and RFOT models. Identifying strings or clusters with the``mosaic'' length of the RFOT model relaxes the conventional assumption that the``entropic droplet'' are compact. We also confirm the validity of the entropy formulation of the AG theory, constraining the exponent values of the RFOT theory. This constraint, together with the analysis of size scales, enables us to estimate the characteristic exponents of RFOT.

Evaluation of scale invariance in physiological signals by means of balanced estimation of diffusion entropy.

PubMed

Zhang, Wenqing; Qiu, Lu; Xiao, Qin; Yang, Huijie; Zhang, Qingjun; Wang, Jianyong

2012-11-01

By means of the concept of the balanced estimation of diffusion entropy, we evaluate the reliable scale invariance embedded in different sleep stages and stride records. Segments corresponding to waking, light sleep, rapid eye movement (REM) sleep, and deep sleep stages are extracted from long-term electroencephalogram signals. For each stage the scaling exponent value is distributed over a considerably wide range, which tell us that the scaling behavior is subject and sleep cycle dependent. The average of the scaling exponent values for waking segments is almost the same as that for REM segments (∼0.8). The waking and REM stages have a significantly higher value of the average scaling exponent than that for light sleep stages (∼0.7). For the stride series, the original diffusion entropy (DE) and the balanced estimation of diffusion entropy (BEDE) give almost the same results for detrended series. The evolutions of local scaling invariance show that the physiological states change abruptly, although in the experiments great efforts have been made to keep conditions unchanged. The global behavior of a single physiological signal may lose rich information on physiological states. Methodologically, the BEDE can evaluate with considerable precision the scale invariance in very short time series (∼10^{2}), while the original DE method sometimes may underestimate scale-invariance exponents or even fail in detecting scale-invariant behavior. The BEDE method is sensitive to trends in time series. The existence of trends may lead to an unreasonably high value of the scaling exponent and consequent mistaken conclusions.

Evaluation of scale invariance in physiological signals by means of balanced estimation of diffusion entropy

NASA Astrophysics Data System (ADS)

Zhang, Wenqing; Qiu, Lu; Xiao, Qin; Yang, Huijie; Zhang, Qingjun; Wang, Jianyong

2012-11-01

By means of the concept of the balanced estimation of diffusion entropy, we evaluate the reliable scale invariance embedded in different sleep stages and stride records. Segments corresponding to waking, light sleep, rapid eye movement (REM) sleep, and deep sleep stages are extracted from long-term electroencephalogram signals. For each stage the scaling exponent value is distributed over a considerably wide range, which tell us that the scaling behavior is subject and sleep cycle dependent. The average of the scaling exponent values for waking segments is almost the same as that for REM segments (˜0.8). The waking and REM stages have a significantly higher value of the average scaling exponent than that for light sleep stages (˜0.7). For the stride series, the original diffusion entropy (DE) and the balanced estimation of diffusion entropy (BEDE) give almost the same results for detrended series. The evolutions of local scaling invariance show that the physiological states change abruptly, although in the experiments great efforts have been made to keep conditions unchanged. The global behavior of a single physiological signal may lose rich information on physiological states. Methodologically, the BEDE can evaluate with considerable precision the scale invariance in very short time series (˜102), while the original DE method sometimes may underestimate scale-invariance exponents or even fail in detecting scale-invariant behavior. The BEDE method is sensitive to trends in time series. The existence of trends may lead to an unreasonably high value of the scaling exponent and consequent mistaken conclusions.

A model of return intervals between earthquake events

NASA Astrophysics Data System (ADS)

Zhou, Yu; Chechkin, Aleksei; Sokolov, Igor M.; Kantz, Holger

2016-06-01

Application of the diffusion entropy analysis and the standard deviation analysis to the time sequence of the southern California earthquake events from 1976 to 2002 uncovered scaling behavior typical for anomalous diffusion. However, the origin of such behavior is still under debate. Some studies attribute the scaling behavior to the correlations in the return intervals, or waiting times, between aftershocks or mainshocks. To elucidate a nature of the scaling, we applied specific reshulffling techniques to eliminate correlations between different types of events and then examined how it affects the scaling behavior. We demonstrate that the origin of the scaling behavior observed is the interplay between mainshock waiting time distribution and the structure of clusters of aftershocks, but not correlations in waiting times between the mainshocks and aftershocks themselves. Our findings are corroborated by numerical simulations of a simple model showing a very similar behavior. The mainshocks are modeled by a renewal process with a power-law waiting time distribution between events, and aftershocks follow a nonhomogeneous Poisson process with the rate governed by Omori's law.

Propagation of Galactic cosmic rays: the influence of anisotropic diffusion

NASA Astrophysics Data System (ADS)

AL-Zetoun, A.; Achterberg, A.

2018-06-01

We consider the anisotropic diffusion of cosmic rays in the large-scale Galactic magnetic field, where diffusion along the field and diffusion across the field proceeds at different rates. To calculate this diffusion, we use stochastic differential equations to describe the cosmic ray propagation, solving these numerically. The Galactic magnetic field is described using the Jansson-Farrar model for the Galactic magnetic field. In this paper, we study the influence of perpendicular diffusion on the residence time of cosmic rays in the Galaxy. This provides an estimate for the influence of anisotropic diffusion on the residence time and the amount of matter (grammage) that a typical cosmic ray traverses during its residence in the Galaxy.

Real time visualization of quantum walk

DOE Office of Scientific and Technical Information (OSTI.GOV)

Miyazaki, Akihide; Hamada, Shinji; Sekino, Hideo

2014-02-20

Time evolution of quantum particles like electrons is described by time-dependent Schrödinger equation (TDSE). The TDSE is regarded as the diffusion equation of electrons with imaginary diffusion coefficients. And the TDSE is solved by quantum walk (QW) which is regarded as a quantum version of a classical random walk. The diffusion equation is solved in discretized space/time as in the case of classical random walk with additional unitary transformation of internal degree of freedom typical for quantum particles. We call the QW for solution of the TDSE a Schrödinger walk (SW). For observation of one quantum particle evolution under amore » given potential in atto-second scale, we attempt a successive computation and visualization of the SW. Using Pure Data programming, we observe the correct behavior of a probability distribution under the given potential in real time for observers of atto-second scale.« less

Molecular dynamics on diffusive time scales from the phase-field-crystal equation.

PubMed

Chan, Pak Yuen; Goldenfeld, Nigel; Dantzig, Jon

2009-03-01

We extend the phase-field-crystal model to accommodate exact atomic configurations and vacancies by requiring the order parameter to be non-negative. The resulting theory dictates the number of atoms and describes the motion of each of them. By solving the dynamical equation of the model, which is a partial differential equation, we are essentially performing molecular dynamics simulations on diffusive time scales. To illustrate this approach, we calculate the two-point correlation function of a fluid.

Super-Arrhenius diffusion in an undercooled binary Lennard-Jones liquid results from a quantifiable correlation effect.

PubMed

de Souza, Vanessa K; Wales, David J

2006-02-10

On short time scales an underlying Arrhenius temperature dependence of the diffusion constant can be extracted from the fragile, super-Arrhenius diffusion of a binary Lennard-Jones mixture. This Arrhenius diffusion is related to the true super-Arrhenius behavior by a factor that depends on the average angle between steps in successive time windows. The correction factor accounts for the fact that on average, successive displacements are negatively correlated, and this effect can therefore be linked directly with the higher apparent activation energy for diffusion at low temperature.

Localized diffusive motion on two different time scales in solid alkane nanoparticles

NASA Astrophysics Data System (ADS)

Wang, S.-K.; Mamontov, E.; Bai, M.; Hansen, F. Y.; Taub, H.; Copley, J. R. D.; García Sakai, V.; Gasparovic, G.; Jenkins, T.; Tyagi, M.; Herwig, K. W.; Neumann, D. A.; Montfrooij, W.; Volkmann, U. G.

2010-09-01

High-energy-resolution quasielastic neutron scattering on three complementary spectrometers has been used to investigate molecular diffusive motion in solid nano- to bulk-sized particles of the alkane n-C32H66. The crystalline-to-plastic and plastic-to-fluid phase transition temperatures are observed to decrease as the particle size decreases. In all samples, localized molecular diffusive motion in the plastic phase occurs on two different time scales: a "fast" motion corresponding to uniaxial rotation about the long molecular axis; and a "slow" motion attributed to conformational changes of the molecule. Contrary to the conventional interpretation in bulk alkanes, the fast uniaxial rotation begins in the low-temperature crystalline phase.

Non-Brownian diffusion in lipid membranes: Experiments and simulations.

PubMed

Metzler, R; Jeon, J-H; Cherstvy, A G

2016-10-01

The dynamics of constituents and the surface response of cellular membranes-also in connection to the binding of various particles and macromolecules to the membrane-are still a matter of controversy in the membrane biophysics community, particularly with respect to crowded membranes of living biological cells. We here put into perspective recent single particle tracking experiments in the plasma membranes of living cells and supercomputing studies of lipid bilayer model membranes with and without protein crowding. Special emphasis is put on the observation of anomalous, non-Brownian diffusion of both lipid molecules and proteins embedded in the lipid bilayer. While single component, pure lipid bilayers in simulations exhibit only transient anomalous diffusion of lipid molecules on nanosecond time scales, the persistence of anomalous diffusion becomes significantly longer ranged on the addition of disorder-through the addition of cholesterol or proteins-and on passing of the membrane lipids to the gel phase. Concurrently, experiments demonstrate the anomalous diffusion of membrane embedded proteins up to macroscopic time scales in the minute time range. Particular emphasis will be put on the physical character of the anomalous diffusion, in particular, the occurrence of ageing observed in the experiments-the effective diffusivity of the measured particles is a decreasing function of time. Moreover, we present results for the time dependent local scaling exponent of the mean squared displacement of the monitored particles. Recent results finding deviations from the commonly assumed Gaussian diffusion patterns in protein crowded membranes are reported. The properties of the displacement autocorrelation function of the lipid molecules are discussed in the light of their appropriate physical anomalous diffusion models, both for non-crowded and crowded membranes. In the last part of this review we address the upcoming field of membrane distortion by elongated membrane-binding particles. We discuss how membrane compartmentalisation and the particle-membrane binding energy may impact the dynamics and response of lipid membranes. This article is part of a Special Issue entitled: Biosimulations edited by Ilpo Vattulainen and Tomasz Róg. Copyright © 2016 The Authors. Published by Elsevier B.V. All rights reserved.

Predicting the influence of long-range molecular interactions on macroscopic-scale diffusion by homogenization of the Smoluchowski equation

NASA Astrophysics Data System (ADS)

Kekenes-Huskey, P. M.; Gillette, A. K.; McCammon, J. A.

2014-05-01

The macroscopic diffusion constant for a charged diffuser is in part dependent on (1) the volume excluded by solute "obstacles" and (2) long-range interactions between those obstacles and the diffuser. Increasing excluded volume reduces transport of the diffuser, while long-range interactions can either increase or decrease diffusivity, depending on the nature of the potential. We previously demonstrated [P. M. Kekenes-Huskey et al., Biophys. J. 105, 2130 (2013)] using homogenization theory that the configuration of molecular-scale obstacles can both hinder diffusion and induce diffusional anisotropy for small ions. As the density of molecular obstacles increases, van der Waals (vdW) and electrostatic interactions between obstacle and a diffuser become significant and can strongly influence the latter's diffusivity, which was neglected in our original model. Here, we extend this methodology to include a fixed (time-independent) potential of mean force, through homogenization of the Smoluchowski equation. We consider the diffusion of ions in crowded, hydrophilic environments at physiological ionic strengths and find that electrostatic and vdW interactions can enhance or depress effective diffusion rates for attractive or repulsive forces, respectively. Additionally, we show that the observed diffusion rate may be reduced independent of non-specific electrostatic and vdW interactions by treating obstacles that exhibit specific binding interactions as "buffers" that absorb free diffusers. Finally, we demonstrate that effective diffusion rates are sensitive to distribution of surface charge on a globular protein, Troponin C, suggesting that the use of molecular structures with atomistic-scale resolution can account for electrostatic influences on substrate transport. This approach offers new insight into the influence of molecular-scale, long-range interactions on transport of charged species, particularly for diffusion-influenced signaling events occurring in crowded cellular environments.

Confinement, Desolvation, And Electrosorption Effects on the Diffusion of Ions in Nanoporous Carbon Electrodes

PubMed Central

2015-01-01

Supercapacitors are electrochemical devices which store energy by ion adsorption on the surface of a porous carbon. They are characterized by high power delivery. The use of nanoporous carbon to increase their energy density should not hinder their fast charging. However, the mechanisms for ion transport inside electrified nanopores remain largely unknown. Here we show that the diffusion is characterized by a hierarchy of time scales arising from ion confinement, solvation, and electrosorption effects. By combining electrochemistry experiments with molecular dynamics simulations, we determine the in-pore conductivities and diffusion coefficients and their variations with the applied potential. We show that the diffusion of the ions is slower by 1 order of magnitude compared to the bulk electrolyte. The desolvation of the ions occurs on much faster time scales than electrosorption. PMID:26369420

Hopping Diffusion of Nanoparticles Subjected to Topological Constraints

NASA Astrophysics Data System (ADS)

Cai, Li-Heng; Panyukov, Sergey; Rubinstein, Michael

2013-03-01

We describe a novel hopping mechanism for diffusion of large non-sticky nanoparticles subjected to topological constraints in polymer solids (networks and gels) and entangled polymer liquids (melts and solutions). Probe particles with size larger than the mesh size of unentangled polymer networks (tube diameter of entangled polymer liquids) are trapped by the network (entanglement) cages at time scales longer than the relaxation time of the network (entanglement) strand. At long time scales, however, these particles can move further by hopping between neighboring confinement cages. This hopping is controlled by fluctuations of surrounding confinement cages, which could be large enough to allow particles to slip through. The terminal particle diffusion coefficient dominated by this hopping diffusion is appreciable for particles with size slightly larger than the network mesh size (tube diameter). Very large particles in polymer solids will be permanently trapped by local network cages, whereas they can still move in polymer liquids by waiting for entanglement cages to rearrange on the relaxation time scale of the liquids. We would like to acknowledge the financial support of NSF CHE-0911588, DMR-0907515, DMR-1121107, DMR-1122483, and CBET-0609087, NIH R01HL077546 and P50HL107168, and Cystic Fibrosis Foundation under grant RUBIN09XX0.

The dynamics of oceanic fronts. I - The Gulf Stream

NASA Technical Reports Server (NTRS)

Kao, T. W.

1980-01-01

The establishment and maintenance of the mean hydrographic properties of large-scale density fronts in the upper ocean is considered. The dynamics is studied by posing an initial value problem starting with a near-surface discharge of buoyant water with a prescribed density deficit into an ambient stationary fluid of uniform density; full time dependent diffusion and Navier-Stokes equations are then used with constant eddy diffusion and viscosity coefficients, together with a constant Coriolis parameter. Scaling analysis reveals three independent scales of the problem including the radius of deformation of the inertial length, buoyancy length, and diffusive length scales. The governing equations are then suitably scaled and the resulting normalized equations are shown to depend on the Ekman number alone for problems of oceanic interest. It is concluded that the mean Gulf Stream dynamics can be interpreted in terms of a solution of the Navier-Stokes and diffusion equations, with the cross-stream circulation responsible for the maintenance of the front; this mechanism is suggested for the maintenance of the Gulf Stream dynamics.

Electronic shot noise in fractal conductors.

PubMed

Groth, C W; Tworzydło, J; Beenakker, C W J

2008-05-02

By solving a master equation in the Sierpiński lattice and in a planar random-resistor network, we determine the scaling with size L of the shot noise power P due to elastic scattering in a fractal conductor. We find a power-law scaling P proportional, variantL;{d_{f}-2-alpha}, with an exponent depending on the fractal dimension d_{f} and the anomalous diffusion exponent alpha. This is the same scaling as the time-averaged current I[over ], which implies that the Fano factor F=P/2eI[over ] is scale-independent. We obtain a value of F=1/3 for anomalous diffusion that is the same as for normal diffusion, even if there is no smallest length scale below which the normal diffusion equation holds. The fact that F remains fixed at 1/3 as one crosses the percolation threshold in a random-resistor network may explain recent measurements of a doping-independent Fano factor in a graphene flake.

Scaling laws of passive-scalar diffusion in the interstellar medium

NASA Astrophysics Data System (ADS)

Colbrook, Matthew J.; Ma, Xiangcheng; Hopkins, Philip F.; Squire, Jonathan

2017-05-01

Passive-scalar mixing (metals, molecules, etc.) in the turbulent interstellar medium (ISM) is critical for abundance patterns of stars and clusters, galaxy and star formation, and cooling from the circumgalactic medium. However, the fundamental scaling laws remain poorly understood in the highly supersonic, magnetized, shearing regime relevant for the ISM. We therefore study the full scaling laws governing passive-scalar transport in idealized simulations of supersonic turbulence. Using simple phenomenological arguments for the variation of diffusivity with scale based on Richardson diffusion, we propose a simple fractional diffusion equation to describe the turbulent advection of an initial passive scalar distribution. These predictions agree well with the measurements from simulations, and vary with turbulent Mach number in the expected manner, remaining valid even in the presence of a large-scale shear flow (e.g. rotation in a galactic disc). The evolution of the scalar distribution is not the same as obtained using simple, constant 'effective diffusivity' as in Smagorinsky models, because the scale dependence of turbulent transport means an initially Gaussian distribution quickly develops highly non-Gaussian tails. We also emphasize that these are mean scalings that apply only to ensemble behaviours (assuming many different, random scalar injection sites): individual Lagrangian 'patches' remain coherent (poorly mixed) and simply advect for a large number of turbulent flow-crossing times.

Applicability of a diffusion model to lateral transport in the terrestrial and lunar exospheres.

NASA Technical Reports Server (NTRS)

Hodges, R. R., Jr.

1972-01-01

Kinetic theory is used to determine a series expansion of the vertical flux of particles in an exosphere in terms of time and space derivatives of particle concentration, exobase velocity, and temperature. For sufficiently large scale variations of these parameters in time and space, the series can be truncated to a form that is similar to a diffusion equation. Owing to this analogy, it is possible to unite the mathematical description of molecular diffusion, which governs thermospheric flow, and the corresponding exospheric equation by using effective transport coefficients which change smoothly with altitude through the transition from thermosphere to exosphere. A new definition of the exobase for lateral flow emerges from the analogy of exospheric and thermospheric diffusion, as the altitude where the horizontal mean free path length equals the mean horizontal extent of ballistic trajectories of the transported gas, as opposed to the scale height of the dominant gas which determines the exobase for escape. It is shown that the approximation of exospheric lateral flow as a diffusion process is applicable to global scale problems concerning terrestrial helium and heavier gases, and lunar gases heavier than helium.

Decontamination of chemical tracers in droplets by a submerging thin film flow

NASA Astrophysics Data System (ADS)

Landel, Julien R.; McEvoy, Harry; Dalziel, Stuart B.

2016-11-01

We investigate the decontamination of chemical tracers contained in small viscous drops by a submerging falling film. This problem has applications in the decontamination of hazardous chemicals, following accidental releases or terrorist attacks. Toxic droplets lying on surfaces are cleaned by spraying a liquid decontaminant over the surface. The decontaminant film submerges the droplets, without detaching them, in order to neutralize toxic chemicals in the droplets. The decontamination process is controlled by advection, diffusion and reaction processes near the drop-film interface. Chemical tracers dissolve into the film flow forming a thin diffusive boundary layer at the interface. The chemical tracers are then neutralized through a reaction with a chemical decontaminant transported in the film. We assume in this work that the decontamination process occurs mainly in the film phase owing to low solubility of the decontaminant in the drop phase. We analyze the impact of the reaction time scale, assuming first-order reaction, in relation with the characteristic advection and diffusion time scales in the case of a single droplet. Using theoretical, numerical and experimental means, we find that the reaction time scale need to be significantly smaller than the characteristic time scale in the diffusive boundary layer in order to enhance noticeably the decontamination of a single toxic droplet. We discuss these results in the more general case of the decontamination of a large number of droplets. This material is based upon work supported by the Defense Threat Reduction Agency under Contract No. HDTRA1-12-D-0003-0001.

Electrochemical Ionization and Analyte Charging in the Array of Micromachined UltraSonic Electrospray (AMUSE) Ion Source

PubMed Central

Forbes, Thomas P.; Degertekin, F. Levent; Fedorov, Andrei G.

2010-01-01

Electrochemistry and ion transport in a planar array of mechanically-driven, droplet-based ion sources are investigated using an approximate time scale analysis and in-depth computational simulations. The ion source is modeled as a controlled-current electrolytic cell, in which the piezoelectric transducer electrode, which mechanically drives the charged droplet generation using ultrasonic atomization, also acts as the oxidizing/corroding anode (positive mode). The interplay between advective and diffusive ion transport of electrochemically generated ions is analyzed as a function of the transducer duty cycle and electrode location. A time scale analysis of the relative importance of advective vs. diffusive ion transport provides valuable insight into optimality, from the ionization prospective, of alternative design and operation modes of the ion source operation. A computational model based on the solution of time-averaged, quasi-steady advection-diffusion equations for electroactive species transport is used to substantiate the conclusions of the time scale analysis. The results show that electrochemical ion generation at the piezoelectric transducer electrodes located at the back-side of the ion source reservoir results in poor ionization efficiency due to insufficient time for the charged analyte to diffuse away from the electrode surface to the ejection location, especially at near 100% duty cycle operation. Reducing the duty cycle of droplet/analyte ejection increases the analyte residence time and, in turn, improves ionization efficiency, but at an expense of the reduced device throughput. For applications where this is undesirable, i.e., multiplexed and disposable device configurations, an alternative electrode location is incorporated. By moving the charging electrode to the nozzle surface, the diffusion length scale is greatly reduced, drastically improving ionization efficiency. The ionization efficiency of all operating conditions considered is expressed as a function of the dimensionless Peclet number, which defines the relative effect of advection as compared to diffusion. This analysis is general enough to elucidate an important role of electrochemistry in ionization efficiency of any arrayed ion sources, be they mechanically-driven or electrosprays, and is vital for determining optimal design and operation conditions. PMID:20607111

First passage times for a tracer particle in single file diffusion and fractional Brownian motion.

PubMed

Sanders, Lloyd P; Ambjörnsson, Tobias

2012-05-07

We investigate the full functional form of the first passage time density (FPTD) of a tracer particle in a single-file diffusion (SFD) system whose population is: (i) homogeneous, i.e., all particles having the same diffusion constant and (ii) heterogeneous, with diffusion constants drawn from a heavy-tailed power-law distribution. In parallel, the full FPTD for fractional Brownian motion [fBm-defined by the Hurst parameter, H ∈ (0, 1)] is studied, of interest here as fBm and SFD systems belong to the same universality class. Extensive stochastic (non-Markovian) SFD and fBm simulations are performed and compared to two analytical Markovian techniques: the method of images approximation (MIA) and the Willemski-Fixman approximation (WFA). We find that the MIA cannot approximate well any temporal scale of the SFD FPTD. Our exact inversion of the Willemski-Fixman integral equation captures the long-time power-law exponent, when H ≥ 1/3, as predicted by Molchan [Commun. Math. Phys. 205, 97 (1999)] for fBm. When H < 1/3, which includes homogeneous SFD (H = 1/4), and heterogeneous SFD (H < 1/4), the WFA fails to agree with any temporal scale of the simulations and Molchan's long-time result. SFD systems are compared to their fBm counter parts; and in the homogeneous system both scaled FPTDs agree on all temporal scales including also, the result by Molchan, thus affirming that SFD and fBm dynamics belong to the same universality class. In the heterogeneous case SFD and fBm results for heterogeneity-averaged FPTDs agree in the asymptotic time limit. The non-averaged heterogeneous SFD systems display a lack of self-averaging. An exponential with a power-law argument, multiplied by a power-law pre-factor is shown to describe well the FPTD for all times for homogeneous SFD and sub-diffusive fBm systems.

Short- and long-time diffusion and dynamic scaling in suspensions of charged colloidal particles

NASA Astrophysics Data System (ADS)

Banchio, Adolfo J.; Heinen, Marco; Holmqvist, Peter; Nägele, Gerhard

2018-04-01

We report on a comprehensive theory-simulation-experimental study of collective and self-diffusion in concentrated suspensions of charge-stabilized colloidal spheres. In theory and simulation, the spheres are assumed to interact directly by a hard-core plus screened Coulomb effective pair potential. The intermediate scattering function, fc(q, t), is calculated by elaborate accelerated Stokesian dynamics (ASD) simulations for Brownian systems where many-particle hydrodynamic interactions (HIs) are fully accounted for, using a novel extrapolation scheme to a macroscopically large system size valid for all correlation times. The study spans the correlation time range from the colloidal short-time to the long-time regime. Additionally, Brownian Dynamics (BD) simulation and mode-coupling theory (MCT) results of fc(q, t) are generated where HIs are neglected. Using these results, the influence of HIs on collective and self-diffusion and the accuracy of the MCT method are quantified. It is shown that HIs enhance collective and self-diffusion at intermediate and long times. At short times self-diffusion, and for wavenumbers outside the structure factor peak region also collective diffusion, are slowed down by HIs. MCT significantly overestimates the slowing influence of dynamic particle caging. The dynamic scattering functions obtained in the ASD simulations are in overall good agreement with our dynamic light scattering (DLS) results for a concentration series of charged silica spheres in an organic solvent mixture, in the experimental time window and wavenumber range. From the simulation data for the time derivative of the width function associated with fc(q, t), there is indication of long-time exponential decay of fc(q, t), for wavenumbers around the location of the static structure factor principal peak. The experimental scattering functions in the probed time range are consistent with a time-wavenumber factorization scaling behavior of fc(q, t) that was first reported by Segrè and Pusey [Phys. Rev. Lett. 77, 771 (1996)] for suspensions of hard spheres. Our BD simulation and MCT results predict a significant violation of exact factorization scaling which, however, is approximately restored according to the ASD results when HIs are accounted for, consistent with the experimental findings for fc(q, t). Our study of collective diffusion is amended by simulation and theoretical results for the self-intermediate scattering function, fs(q, t), and its non-Gaussian parameter α2(t) and for the particle mean squared displacement W(t) and its time derivative. Since self-diffusion properties are not assessed in standard DLS measurements, a method to deduce W(t) approximately from fc(q, t) is theoretically validated.

A Computational Approach to Increase Time Scales in Brownian Dynamics–Based Reaction-Diffusion Modeling

PubMed Central

Frazier, Zachary

2012-01-01

Abstract Particle-based Brownian dynamics simulations offer the opportunity to not only simulate diffusion of particles but also the reactions between them. They therefore provide an opportunity to integrate varied biological data into spatially explicit models of biological processes, such as signal transduction or mitosis. However, particle based reaction-diffusion methods often are hampered by the relatively small time step needed for accurate description of the reaction-diffusion framework. Such small time steps often prevent simulation times that are relevant for biological processes. It is therefore of great importance to develop reaction-diffusion methods that tolerate larger time steps while maintaining relatively high accuracy. Here, we provide an algorithm, which detects potential particle collisions prior to a BD-based particle displacement and at the same time rigorously obeys the detailed balance rule of equilibrium reactions. We can show that for reaction-diffusion processes of particles mimicking proteins, the method can increase the typical BD time step by an order of magnitude while maintaining similar accuracy in the reaction diffusion modelling. PMID:22697237

Variable order fractional Fokker-Planck equations derived from Continuous Time Random Walks

NASA Astrophysics Data System (ADS)

Straka, Peter

2018-08-01

Continuous Time Random Walk models (CTRW) of anomalous diffusion are studied, where the anomalous exponent β(x) ∈(0 , 1) varies in space. This type of situation occurs e.g. in biophysics, where the density of the intracellular matrix varies throughout a cell. Scaling limits of CTRWs are known to have probability distributions which solve fractional Fokker-Planck type equations (FFPE). This correspondence between stochastic processes and FFPE solutions has many useful extensions e.g. to nonlinear particle interactions and reactions, but has not yet been sufficiently developed for FFPEs of the "variable order" type with non-constant β(x) . In this article, variable order FFPEs (VOFFPE) are derived from scaling limits of CTRWs. The key mathematical tool is the 1-1 correspondence of a CTRW scaling limit to a bivariate Langevin process, which tracks the cumulative sum of jumps in one component and the cumulative sum of waiting times in the other. The spatially varying anomalous exponent is modelled by spatially varying β(x) -stable Lévy noise in the waiting time component. The VOFFPE displays a spatially heterogeneous temporal scaling behaviour, with generalized diffusivity and drift coefficients whose units are length2/timeβ(x) resp. length/timeβ(x). A global change of the time scale results in a spatially varying change in diffusivity and drift. A consequence of the mathematical derivation of a VOFFPE from CTRW limits in this article is that a solution of a VOFFPE can be approximated via Monte Carlo simulations. Based on such simulations, we are able to confirm that the VOFFPE is consistent under a change of the global time scale.

Fractional Diffusion Processes: Probability Distributions and Continuous Time Random Walk

NASA Astrophysics Data System (ADS)

Gorenflo, R.; Mainardi, F.

A physical-mathematical approach to anomalous diffusion may be based on generalized diffusion equations (containing derivatives of fractional order in space or/and time) and related random walk models. By the space-time fractional diffusion equation we mean an evolution equation obtained from the standard linear diffusion equation by replacing the second-order space derivative with a Riesz-Feller derivative of order alpha in (0,2] and skewness theta (\\verttheta\\vertlemin \\{alpha ,2-alpha \\}), and the first-order time derivative with a Caputo derivative of order beta in (0,1] . The fundamental solution (for the Cauchy problem) of the fractional diffusion equation can be interpreted as a probability density evolving in time of a peculiar self-similar stochastic process. We view it as a generalized diffusion process that we call fractional diffusion process, and present an integral representation of the fundamental solution. A more general approach to anomalous diffusion is however known to be provided by the master equation for a continuous time random walk (CTRW). We show how this equation reduces to our fractional diffusion equation by a properly scaled passage to the limit of compressed waiting times and jump widths. Finally, we describe a method of simulation and display (via graphics) results of a few numerical case studies.

Diffuse charge dynamics in ionic thermoelectrochemical systems.

PubMed

Stout, Robert F; Khair, Aditya S

2017-08-01

Thermoelectrics are increasingly being studied as promising electrical generators in the ongoing search for alternative energy sources. In particular, recent experimental work has examined thermoelectric materials containing ionic charge carriers; however, the majority of mathematical modeling has been focused on their steady-state behavior. Here, we determine the time scales over which the diffuse charge dynamics in ionic thermoelectrochemical systems occur by analyzing the simplest model thermoelectric cell: a binary electrolyte between two parallel, blocking electrodes. We consider the application of a temperature gradient across the device while the electrodes remain electrically isolated from each other. This results in a net voltage, called the thermovoltage, via the Seebeck effect. At the same time, the Soret effect results in migration of the ions toward the cold electrode. The charge dynamics are described mathematically by the Poisson-Nernst-Planck equations for dilute solutions, in which the ion flux is driven by electromigration, Brownian diffusion, and thermal diffusion under a temperature gradient. The temperature evolves according to the heat equation. This nonlinear set of equations is linearized in the (experimentally relevant) limit of a "weak" temperature gradient. From this, we show that the time scale on which the thermovoltage develops is the Debye time, 1/Dκ^{2}, where D is the Brownian diffusion coefficient of both ion species, and κ^{-1} is the Debye length. However, the concentration gradient due to the Soret effect develops on the bulk diffusion time, L^{2}/D, where L is the distance between the electrodes. For thin diffuse layers, which is the condition under which most real devices operate, the Debye time is orders of magnitude less than the diffusion time. Therefore, rather surprisingly, the majority of ion motion occurs after the steady thermovoltage has developed. Moreover, the dynamics are independent of the thermal diffusion coefficients, which simply set the magnitude of the steady-state thermovoltage.

Diffuse charge dynamics in ionic thermoelectrochemical systems

NASA Astrophysics Data System (ADS)

Stout, Robert F.; Khair, Aditya S.

2017-08-01

Thermoelectrics are increasingly being studied as promising electrical generators in the ongoing search for alternative energy sources. In particular, recent experimental work has examined thermoelectric materials containing ionic charge carriers; however, the majority of mathematical modeling has been focused on their steady-state behavior. Here, we determine the time scales over which the diffuse charge dynamics in ionic thermoelectrochemical systems occur by analyzing the simplest model thermoelectric cell: a binary electrolyte between two parallel, blocking electrodes. We consider the application of a temperature gradient across the device while the electrodes remain electrically isolated from each other. This results in a net voltage, called the thermovoltage, via the Seebeck effect. At the same time, the Soret effect results in migration of the ions toward the cold electrode. The charge dynamics are described mathematically by the Poisson-Nernst-Planck equations for dilute solutions, in which the ion flux is driven by electromigration, Brownian diffusion, and thermal diffusion under a temperature gradient. The temperature evolves according to the heat equation. This nonlinear set of equations is linearized in the (experimentally relevant) limit of a "weak" temperature gradient. From this, we show that the time scale on which the thermovoltage develops is the Debye time, 1 /D κ2 , where D is the Brownian diffusion coefficient of both ion species, and κ-1 is the Debye length. However, the concentration gradient due to the Soret effect develops on the bulk diffusion time, L2/D , where L is the distance between the electrodes. For thin diffuse layers, which is the condition under which most real devices operate, the Debye time is orders of magnitude less than the diffusion time. Therefore, rather surprisingly, the majority of ion motion occurs after the steady thermovoltage has developed. Moreover, the dynamics are independent of the thermal diffusion coefficients, which simply set the magnitude of the steady-state thermovoltage.

Time-dependent, optically thick accretion onto a black hole

NASA Technical Reports Server (NTRS)

Gilden, D. L.; Wheeler, J. C.

1980-01-01

A fully relativistic hydrodynamics code which incorporates diffusive radiation transport is used to study time-dependent, spherically symmetric, optically thick accretion onto a black hole. It is found that matter free-falls into the hole regardless of whether the diffusion time scale is longer or shorter than the dynamical time. Nonadiabatic heating due to magnetic field reconnection is included. The internal energy thus generated affects the flow in a purely relativistic way, again ensuring free-fall collapse of the inflowing matter. Any matter enveloping a black hole will thus be swallowed on a dynamical time scale with relatively small net release of energy. The inclusion of angular momentum will not necessarily affect this conclusion.

Characterization of single-file diffusion in one-dimensional dusty plasma

NASA Astrophysics Data System (ADS)

Theisen, W. L.; Sheridan, T. E.

2010-11-01

Single-file diffusion occurs in one-dimensional systems when particles cannot pass each other and the mean-squared displacement (msd) of these particles increases with time t. Diffusive processes that follow Ficks law predict that the msd increases as t, however, single-file diffusion is sub-Fickean meaning that the msd is predicted to increase as t^1/2. One-dimensional dusty plasma rings have been created under strongly coupled, over-damped conditions. Particle position data from these rings will be analyzed to determine the scaling of the msd with time. Results will be compared with predictions of single-file diffusion theory.

Microscopic diffusion and hydrodynamic interactions of hemoglobin in red blood cells.

PubMed

Doster, Wolfgang; Longeville, Stéphane

2007-08-15

The cytoplasm of red blood cells is congested with the oxygen storage protein hemoglobin occupying a quarter of the cell volume. The high protein concentration leads to a reduced mobility; the self-diffusion coefficient of hemoglobin in blood cells is six times lower than in dilute solution. This effect is generally assigned to excluded volume effects in crowded media. However, the collective or gradient diffusion coefficient of hemoglobin is only weakly dependent on concentration, suggesting the compensation of osmotic and friction forces. This would exclude hydrodynamic interactions, which are of dynamic origin and do not contribute to the osmotic pressure. Hydrodynamic coupling between protein molecules is dominant at short time- and length scales before direct interactions are fully established. Employing neutron spin-echo-spectroscopy, we study hemoglobin diffusion on a nanosecond timescale and protein displacements on the scale of a few nanometers. A time- and wave-vector dependent diffusion coefficient is found, suggesting the crossover of self- and collective diffusion. Moreover, a wave-vector dependent friction function is derived, which is a characteristic feature of hydrodynamic interactions. The wave-vector and concentration dependence of the long-time self-diffusion coefficient of hemoglobin agree qualitatively with theoretical results on hydrodynamics in hard spheres suspensions. Quantitative agreement requires us to adjust the volume fraction by including part of the hydration shell: Proteins exhibit a larger surface/volume ratio compared to standard colloids of much larger size. It is concluded that hydrodynamic and not direct interactions dominate long-range molecular transport at high concentration.

Fokker-Planck electron diffusion caused by an obliquely propagating electromagnetic wave packet of narrow bandwidth

NASA Technical Reports Server (NTRS)

Hizanidis, Kyriakos

1989-01-01

The relativistic motion of electrons in an intense electromagnetic wave packet propagating obliquely to a uniform magnetic field is analytically studied on the basis of the Fokker-Planck-Kolmogorov (FPK) approach. The wavepacket consists of circularly polarized electron-cyclotron waves. The dynamical system in question is shown to be reducible to one with three degrees of freedom. Within the framework of the Hamiltonian analysis the nonlinear diffusion tensor is derived, and it is shown that this tensor can be separated into zeroth-, first-, and second-order parts with respect to the relative bandwidth. The zeroth-order part describes diffusive acceleration along lines of constant unperturbed Hamiltonian. The second-order part, which corresponds to the longest time scale, describes diffusion across those lines. A possible transport theory is outlined on the basis of this separation of the time scales.

Non-translational Molecular Diffusive Motion on Two Different Time Scales in Alkane Nanoparticles

NASA Astrophysics Data System (ADS)

Wang, S.-K.; Bai, M.; Taub, H.; Mamontov, E.; Herwig, K. W.; Hansen, F. Y.; Copley, J. R. D.; Jenkins, T.; Tyagi, M.; Volkmann, U. G.

2009-03-01

Using quasielastic neutron scattering, we have investigated molecular diffusive motion in n-C32H66 nanoparticles whose structure and phase transitions have been studied previously.^2 The spectra reveal non-translational (dispersionless) diffusive motion occurring simultaneously on time scales of ˜1 ns and ˜40 ps. The onset of the faster motion occurs in the crystalline phase at least 15 K below the melting point and is tentatively identified with rotation about the long molecular axis. Similarly, we suggest that the slower motion involves molecular conformational changes whose onset appears to coincide with the abrupt transition to the bulk rotator phase about 3 K below melting. These two types of diffusive motion bear a strong resemblance to those observed previously in C24 monolayers adsorbed on a graphite surface.^3 ^2M. Bai et al., Europhys. Lett. 79, 26003 (2007). ^3F. Y. Hansen et al., Phys. Rev. Lett. 92, 046103 (2004)].

Molecular dynamics simulations of propane in slit shaped silica nano-pores: direct comparison with quasielastic neutron scattering experiments.

PubMed

Gautam, Siddharth; Le, Thu; Striolo, Alberto; Cole, David

2017-12-13

Molecular motion under confinement has important implications for a variety of applications including gas recovery and catalysis. Propane confined in mesoporous silica aerogel as studied using quasielastic neutron scattering (QENS) showed anomalous pressure dependence in its diffusion coefficient (J. Phys. Chem. C, 2015, 119, 18188). Molecular dynamics (MD) simulations are often employed to complement the information obtained from QENS experiments. Here, we report an MD simulation study to probe the anomalous pressure dependence of propane diffusion in silica aerogel. Comparison is attempted based on the self-diffusion coefficients and on the time scales of the decay of the simulated intermediate scattering functions. While the self-diffusion coefficients obtained from the simulated mean squared displacement profiles do not exhibit the anomalous pressure dependence observed in the experiments, the time scales of the decay of the intermediate scattering functions calculated from the simulation data match the corresponding quantities obtained in the QENS experiment and thus confirm the anomalous pressure dependence of the diffusion coefficient. The origin of the anomaly in pressure dependence lies in the presence of an adsorbed layer of propane molecules that seems to dominate the confined propane dynamics at low pressure, thereby lowering the diffusion coefficient. Further, time scales for rotational motion obtained from the simulations explain the absence of rotational contribution to the QENS spectra in the experiments. In particular, the rotational motion of the simulated propane molecules is found to exhibit large angular jumps at lower pressure. The present MD simulation work thus reveals important new insights into the origin of anomalous pressure dependence of propane diffusivity in silica mesopores and supplements the information obtained experimentally by QENS data.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Michaud, G.; Bergeron, P.; Wesemael, F.

The abundance anomalies generated by diffusion in the envelopes of hot, hydrogen-rich subdwarfs are studied. It is shown that unimpeded diffusion cannot lead to the large silicon underabundance observed in those stars at effective temperatures above 30,000 K. Calculations of diffusion of heavy elements in the presence of mass loss are also performed. For a mass-loss rate of 2.5 x 10 to the -15th solar masses/year, the observed abundance patterns of C, N, and Si are reproduced on a time scale of about 100,000 yr. Lower mass-loss rates would necessitate longer time scales. The pattern of abundance anomalies may eventuallymore » be used to constrain both the mass-loss rate and the stellar lifetime in the sdB evolutionary phase. 12 references.« less

Analytical solutions of the space-time fractional Telegraph and advection-diffusion equations

NASA Astrophysics Data System (ADS)

Tawfik, Ashraf M.; Fichtner, Horst; Schlickeiser, Reinhard; Elhanbaly, A.

2018-02-01

The aim of this paper is to develop a fractional derivative model of energetic particle transport for both uniform and non-uniform large-scale magnetic field by studying the fractional Telegraph equation and the fractional advection-diffusion equation. Analytical solutions of the space-time fractional Telegraph equation and space-time fractional advection-diffusion equation are obtained by use of the Caputo fractional derivative and the Laplace-Fourier technique. The solutions are given in terms of Fox's H function. As an illustration they are applied to the case of solar energetic particles.

Theory of linear sweep voltammetry with diffuse charge: Unsupported electrolytes, thin films, and leaky membranes

NASA Astrophysics Data System (ADS)

Yan, David; Bazant, Martin Z.; Biesheuvel, P. M.; Pugh, Mary C.; Dawson, Francis P.

2017-03-01

Linear sweep and cyclic voltammetry techniques are important tools for electrochemists and have a variety of applications in engineering. Voltammetry has classically been treated with the Randles-Sevcik equation, which assumes an electroneutral supported electrolyte. In this paper, we provide a comprehensive mathematical theory of voltammetry in electrochemical cells with unsupported electrolytes and for other situations where diffuse charge effects play a role, and present analytical and simulated solutions of the time-dependent Poisson-Nernst-Planck equations with generalized Frumkin-Butler-Volmer boundary conditions for a 1:1 electrolyte and a simple reaction. Using these solutions, we construct theoretical and simulated current-voltage curves for liquid and solid thin films, membranes with fixed background charge, and cells with blocking electrodes. The full range of dimensionless parameters is considered, including the dimensionless Debye screening length (scaled to the electrode separation), Damkohler number (ratio of characteristic diffusion and reaction times), and dimensionless sweep rate (scaled to the thermal voltage per diffusion time). The analysis focuses on the coupling of Faradaic reactions and diffuse charge dynamics, although capacitive charging of the electrical double layers is also studied, for early time transients at reactive electrodes and for nonreactive blocking electrodes. Our work highlights cases where diffuse charge effects are important in the context of voltammetry, and illustrates which regimes can be approximated using simple analytical expressions and which require more careful consideration.

An Extended Eddy-Diffusivity Mass-Flux Scheme for Unified Representation of Subgrid-Scale Turbulence and Convection

NASA Astrophysics Data System (ADS)

Tan, Zhihong; Kaul, Colleen M.; Pressel, Kyle G.; Cohen, Yair; Schneider, Tapio; Teixeira, João.

2018-03-01

Large-scale weather forecasting and climate models are beginning to reach horizontal resolutions of kilometers, at which common assumptions made in existing parameterization schemes of subgrid-scale turbulence and convection—such as that they adjust instantaneously to changes in resolved-scale dynamics—cease to be justifiable. Additionally, the common practice of representing boundary-layer turbulence, shallow convection, and deep convection by discontinuously different parameterizations schemes, each with its own set of parameters, has contributed to the proliferation of adjustable parameters in large-scale models. Here we lay the theoretical foundations for an extended eddy-diffusivity mass-flux (EDMF) scheme that has explicit time-dependence and memory of subgrid-scale variables and is designed to represent all subgrid-scale turbulence and convection, from boundary layer dynamics to deep convection, in a unified manner. Coherent up and downdrafts in the scheme are represented as prognostic plumes that interact with their environment and potentially with each other through entrainment and detrainment. The more isotropic turbulence in their environment is represented through diffusive fluxes, with diffusivities obtained from a turbulence kinetic energy budget that consistently partitions turbulence kinetic energy between plumes and environment. The cross-sectional area of up and downdrafts satisfies a prognostic continuity equation, which allows the plumes to cover variable and arbitrarily large fractions of a large-scale grid box and to have life cycles governed by their own internal dynamics. Relatively simple preliminary proposals for closure parameters are presented and are shown to lead to a successful simulation of shallow convection, including a time-dependent life cycle.

Response to a small external force and fluctuations of a passive particle in a one-dimensional diffusive environment

NASA Astrophysics Data System (ADS)

Huveneers, François

2018-04-01

We investigate the long-time behavior of a passive particle evolving in a one-dimensional diffusive random environment, with diffusion constant D . We consider two cases: (a) The particle is pulled forward by a small external constant force and (b) there is no systematic bias. Theoretical arguments and numerical simulations provide evidence that the particle is eventually trapped by the environment. This is diagnosed in two ways: The asymptotic speed of the particle scales quadratically with the external force as it goes to zero, and the fluctuations scale diffusively in the unbiased environment, up to possible logarithmic corrections in both cases. Moreover, in the large D limit (homogenized regime), we find an important transient region giving rise to other, finite-size scalings, and we describe the crossover to the true asymptotic behavior.

Molecular dynamics at low time resolution.

PubMed

Faccioli, P

2010-10-28

The internal dynamics of macromolecular systems is characterized by widely separated time scales, ranging from fraction of picoseconds to nanoseconds. In ordinary molecular dynamics simulations, the elementary time step Δt used to integrate the equation of motion needs to be chosen much smaller of the shortest time scale in order not to cut-off physical effects. We show that in systems obeying the overdamped Langevin equation, it is possible to systematically correct for such discretization errors. This is done by analytically averaging out the fast molecular dynamics which occurs at time scales smaller than Δt, using a renormalization group based technique. Such a procedure gives raise to a time-dependent calculable correction to the diffusion coefficient. The resulting effective Langevin equation describes by construction the same long-time dynamics, but has a lower time resolution power, hence it can be integrated using larger time steps Δt. We illustrate and validate this method by studying the diffusion of a point-particle in a one-dimensional toy model and the denaturation of a protein.

Transport of Internetwork Magnetic Flux Elements in the Solar Photosphere

NASA Astrophysics Data System (ADS)

Agrawal, Piyush; Rast, Mark P.; Gošić, Milan; Bellot Rubio, Luis R.; Rempel, Matthias

2018-02-01

The motions of small-scale magnetic flux elements in the solar photosphere can provide some measure of the Lagrangian properties of the convective flow. Measurements of these motions have been critical in estimating the turbulent diffusion coefficient in flux-transport dynamo models and in determining the Alfvén wave excitation spectrum for coronal heating models. We examine the motions of internetwork flux elements in Hinode/Narrowband Filter Imager magnetograms and study the scaling of their mean squared displacement and the shape of their displacement probability distribution as a function of time. We find that the mean squared displacement scales super-diffusively with a slope of about 1.48. Super-diffusive scaling has been observed in other studies for temporal increments as small as 5 s, increments over which ballistic scaling would be expected. Using high-cadence MURaM simulations, we show that the observed super-diffusive scaling at short increments is a consequence of random changes in barycenter positions due to flux evolution. We also find that for long temporal increments, beyond granular lifetimes, the observed displacement distribution deviates from that expected for a diffusive process, evolving from Rayleigh to Gaussian. This change in distribution can be modeled analytically by accounting for supergranular advection along with granular motions. These results complicate the interpretation of magnetic element motions as strictly advective or diffusive on short and long timescales and suggest that measurements of magnetic element motions must be used with caution in turbulent diffusion or wave excitation models. We propose that passive tracer motions in measured photospheric flows may yield more robust transport statistics.

Data assimilation experiments using the diffusive back and forth nudging for the NEMO ocean model

NASA Astrophysics Data System (ADS)

Ruggiero, G. A.; Ourmières, Y.; Cosme, E.; Blum, J.; Auroux, D.; Verron, J.

2014-07-01

The Diffusive Back and Forth Nudging (DBFN) is an easy-to-implement iterative data assimilation method based on the well-known Nudging method. It consists in a sequence of forward and backward model integrations, within a given time window, both of them using a feedback term to the observations. Therefore in the DBFN, the Nudging asymptotic behavior is translated into an infinite number of iterations within a bounded time domain. In this method, the backward integration is carried out thanks to what is called backward model, which is basically the forward model with reversed time step sign. To maintain numeral stability the diffusion terms also have their sign reversed, giving a diffusive character to the algorithm. In this article the DBFN performance to control a primitive equation ocean model is investigated. In this kind of model non-resolved scales are modeled by diffusion operators which dissipate energy that cascade from large to small scales. Thus, in this article the DBFN approximations and their consequences on the data assimilation system set-up are analyzed. Our main result is that the DBFN may provide results which are comparable to those produced by a 4Dvar implementation with a much simpler implementation and a shorter CPU time for convergence.

Prediction of the blowout of jet diffusion flames in a coflowing stream of air

DOE Office of Scientific and Technical Information (OSTI.GOV)

Karbasi, M.; Wierzba, I.

1995-12-31

The blowout limits of a lifted diffusion flame in a coflowing stream of air are estimated using a simple model for extinction, for a range of fuels, jet diameters and co-flowing stream velocities. The proposed model uses a parameter which relates to the ratio of a time associated with the mixing processes in a turbulent jet to a characteristic chemical time. The Kolmogorov microscale of time is used as time scale in this model. It is shown that turbulent diffusion flames are quenched by excessive turbulence for a critical value of this parameter. The predicted blowout velocity of diffusion flamesmore » obtained using this model is in good agreement with the available experimental data.« less

Non-local damage rheology and size effect

NASA Astrophysics Data System (ADS)

Lyakhovsky, V.

2011-12-01

We study scaling relations controlling the onset of transiently-accelerating fracturing and transition to dynamic rupture propagation in a non-local damage rheology model. The size effect is caused principally by growth of a fracture process zone, involving stress redistribution and energy release associated with a large fracture. This implies that rupture nucleation and transition to dynamic propagation are inherently scale-dependent processes. Linear elastic fracture mechanics (LEFM) and local damage mechanics are formulated in terms of dimensionless strain components and thus do not allow introducing any space scaling, except linear relations between fracture length and displacements. Generalization of Weibull theory provides scaling relations between stress and crack length at the onset of failure. A powerful extension of the LEFM formulation is the displacement-weakening model which postulates that yielding is complete when the crack wall displacement exceeds some critical value or slip-weakening distance Dc at which a transition to kinetic friction is complete. Scaling relations controlling the transition to dynamic rupture propagation in slip-weakening formulation are widely accepted in earthquake physics. Strong micro-crack interaction in a process zone may be accounted for by adopting either integral or gradient type non-local damage models. We formulate a gradient-type model with free energy depending on the scalar damage parameter and its spatial derivative. The damage-gradient term leads to structural stresses in the constitutive stress-strain relations and a damage diffusion term in the kinetic equation for damage evolution. The damage diffusion eliminates the singular localization predicted by local models. The finite width of the localization zone provides a fundamental length scale that allows numerical simulations with the model to achieve the continuum limit. A diffusive term in the damage evolution gives rise to additional damage diffusive time scale associated with the structural length scale. The ratio between two time scales associated with damage accumulation and diffusion, the damage diffusivity ratio, reflects the role of the diffusion-controlled delocalization. We demonstrate that localized fracturing occurs at the damage diffusivity ratio below certain critical value leading to a linear scaling between stress and crack length compatible with size effect for failures at crack initiation. A subseuqent quasi-static fracture growth is self-similar with increasing size of the process zone proportional to the fracture length. At a certain stage, controlled by dynamic weakening, the self-similarity breaks down and crack velocity significantly deviates from that predicted by the quasi-static regime, the size of the process zone decreases, and the rate of crack growth ceases to be controlled by the rate of damage increase. Furthermore, the crack speed approaches that predicted by the elasto-dynamic equation. The non-local damage rheology model predicts that the nucleation size of the dynamic fracture scales with fault zone thickness distance of the stress interraction.

Preliminary investigation of single-file diffusion in complex plasma rings

NASA Astrophysics Data System (ADS)

Theisen, W. L.; Sheridan, T. E.

2010-04-01

Particles in one-dimensional (1D) systems cannot pass each other. However, it is still possible to define a diffusion process where the mean-squared displacement (msd) of an ensemble of particles in a 1D chain increases with time t. This process is called single-file diffusion. In contrast to diffusive processes that follow Fick's law, msdt, single-file diffusion is sub-Fickean and the msd is predicted to increase as t^1/2. We have recently created 1D dusty (complex) plasma rings in the DONUT (Dusty ONU experimenT) apparatus. Particle position data from these rings will be analyzed to determine the scaling of the msd with time and results will be compared with predictions of single-file diffusion theory.

Excess entropy scaling for the segmental and global dynamics of polyethylene melts.

PubMed

Voyiatzis, Evangelos; Müller-Plathe, Florian; Böhm, Michael C

2014-11-28

The range of validity of the Rosenfeld and Dzugutov excess entropy scaling laws is analyzed for unentangled linear polyethylene chains. We consider two segmental dynamical quantities, i.e. the bond and the torsional relaxation times, and two global ones, i.e. the chain diffusion coefficient and the viscosity. The excess entropy is approximated by either a series expansion of the entropy in terms of the pair correlation function or by an equation of state for polymers developed in the context of the self associating fluid theory. For the whole range of temperatures and chain lengths considered, the two estimates of the excess entropy are linearly correlated. The scaled bond and torsional relaxation times fall into a master curve irrespective of the chain length and the employed scaling scheme. Both quantities depend non-linearly on the excess entropy. For a fixed chain length, the reduced diffusion coefficient and viscosity scale linearly with the excess entropy. An empirical reduction to a chain length-independent master curve is accessible for both dynamic quantities. The Dzugutov scheme predicts an increased value of the scaled diffusion coefficient with increasing chain length which contrasts physical expectations. The origin of this trend can be traced back to the density dependence of the scaling factors. This finding has not been observed previously for Lennard-Jones chain systems (Macromolecules, 2013, 46, 8710-8723). Thus, it limits the applicability of the Dzugutov approach to polymers. In connection with diffusion coefficients and viscosities, the Rosenfeld scaling law appears to be of higher quality than the Dzugutov approach. An empirical excess entropy scaling is also proposed which leads to a chain length-independent correlation. It is expected to be valid for polymers in the Rouse regime.

Persistent-random-walk approach to anomalous transport of self-propelled particles

NASA Astrophysics Data System (ADS)

Sadjadi, Zeinab; Shaebani, M. Reza; Rieger, Heiko; Santen, Ludger

2015-06-01

The motion of self-propelled particles is modeled as a persistent random walk. An analytical framework is developed that allows the derivation of exact expressions for the time evolution of arbitrary moments of the persistent walk's displacement. It is shown that the interplay of step length and turning angle distributions and self-propulsion produces various signs of anomalous diffusion at short time scales and asymptotically a normal diffusion behavior with a broad range of diffusion coefficients. The crossover from the anomalous short-time behavior to the asymptotic diffusion regime is studied and the parameter dependencies of the crossover time are discussed. Higher moments of the displacement distribution are calculated and analytical expressions for the time evolution of the skewness and the kurtosis of the distribution are presented.

Ultrafast charge separation dynamics in opaque, operational dye-sensitized solar cells revealed by femtosecond diffuse reflectance spectroscopy

PubMed Central

Ghadiri, Elham; Zakeeruddin, Shaik M.; Hagfeldt, Anders; Grätzel, Michael; Moser, Jacques-E.

2016-01-01

Efficient dye-sensitized solar cells are based on highly diffusive mesoscopic layers that render these devices opaque and unsuitable for ultrafast transient absorption spectroscopy measurements in transmission mode. We developed a novel sub-200 femtosecond time-resolved diffuse reflectance spectroscopy scheme combined with potentiostatic control to study various solar cells in fully operational condition. We studied performance optimized devices based on liquid redox electrolytes and opaque TiO2 films, as well as other morphologies, such as TiO2 fibers and nanotubes. Charge injection from the Z907 dye in all TiO2 morphologies was observed to take place in the sub-200 fs time scale. The kinetics of electron-hole back recombination has features in the picosecond to nanosecond time scale. This observation is significantly different from what was reported in the literature where the electron-hole back recombination for transparent films of small particles is generally accepted to occur on a longer time scale of microseconds. The kinetics of the ultrafast electron injection remained unchanged for voltages between +500 mV and –690 mV, where the injection yield eventually drops steeply. The primary charge separation in Y123 organic dye based devices was clearly slower occurring in two picoseconds and no kinetic component on the shorter femtosecond time scale was recorded. PMID:27095505

The Time Dependent Propensity Function for Acceleration of Spatial Stochastic Simulation of Reaction-Diffusion Systems

PubMed Central

Wu, Sheng; Li, Hong; Petzold, Linda R.

2015-01-01

The inhomogeneous stochastic simulation algorithm (ISSA) is a fundamental method for spatial stochastic simulation. However, when diffusion events occur more frequently than reaction events, simulating the diffusion events by ISSA is quite costly. To reduce this cost, we propose to use the time dependent propensity function in each step. In this way we can avoid simulating individual diffusion events, and use the time interval between two adjacent reaction events as the simulation stepsize. We demonstrate that the new algorithm can achieve orders of magnitude efficiency gains over widely-used exact algorithms, scales well with increasing grid resolution, and maintains a high level of accuracy. PMID:26609185

Diffusion of liquid polystyrene into glassy poly(phenylene oxide) characterized by DSC

NASA Astrophysics Data System (ADS)

Li, Linling; Wang, Xiaoliang; Zhou, Dongshan; Xue, Gi

2013-03-01

We report a diffusion study on the polystyrene/poly(phenylene oxide) (PS/PPO) mixture consisted by the PS and PPO nanoparticles. Diffusion of liquid PS into glassy PPO (l-PS/g-PPO) is promoted by annealing the PS/PPO mixture at several temperatures below Tg of the PPO. By tracing the Tgs of the PS-rich domain behind the diffusion front using DSC, we get the relationships of PS weight fractions and diffusion front advances with the elapsed diffusion times at different diffusion temperatures using the Gordon-Taylor equation and core-shell model. We find that the plots of weight fraction of PS vs. elapsed diffusion times at different temperatures can be converted to a master curve by Time-Temperature superposition, and the shift factors obey the Arrhenius equation. Besides, the diffusion front advances of l-PS into g-PPO show an excellent agreement with the t1/2 scaling law at the beginning of the diffusion process, and the diffusion coefficients of different diffusion temperatures also obey the Arrhenius equation. We believe the diffusion mechanism for l-PS/g-PPO should be the Fickean law rather than the Case II, though there are departures of original linearity at longer diffusion times due to the limited liquid supply system. Diffusion of liquid polystyrene into glassy poly(phenylene oxide) characterized by DSC

Diffusion behavior of the fluorescent proteins eGFP and Dreiklang in solvents of different viscosity monitored by fluorescence correlation spectroscopy

NASA Astrophysics Data System (ADS)

Junghans, Cornelia; Schmitt, Franz-Josef; Vukojević, Vladana; Friedrich, Thomas

2016-12-01

Fluorescence correlation spectroscopy relies on temporal autocorrelation analysis of fluorescence intensity fluctuations that spontaneously arise in systems at equilibrium due to molecular motion and changes of state that cause changes in fluorescence, such as triplet state transition, photoisomerization and other photophysical transformations, to determine the rates of these processes. The stability of a fluorescent molecule against dark state conversion is of particular concern for chromophores intended to be used as reference tags for comparing diffusion processes on multiple time scales. In this work, we analyzed properties of two fluorescent proteins, the photoswitchable Dreiklang and its parental eGFP, in solvents of different viscosity to vary the diffusion time through the observation volume element by several orders of magnitude. In contrast to eGFP, Dreiklang undergoes a dark-state conversion on the time scale of tens to hundreds of microseconds under conditions of intense fluorescence excitation, which results in artificially shortened diffusion times if the diffusional motion through the observation volume is sufficiently slowed down. Such photophysical quenching processes have also been observed in FCS studies on other photoswitchable fluorescent proteins including Citrine, from which Dreiklang was derived by genetic engineering. This property readily explains the discrepancies observed previously between the diffusion times of eGFP- and Dreiklang-labeled plasma membrane protein complexes.

Observations of the birth of a small coronal hole

NASA Technical Reports Server (NTRS)

Solodyna, C. V.; Krieger, A. S.; Nolte, J. T.

1977-01-01

Using soft X-ray data from the S-054 X-ray spectrographic telescope aboard Skylab, we observed temporal changes in the emission structure of the X-ray corona associated with the birth of a small coronal hole. Designated as CH6, this coronal hole was born near the equator in a time interval less than 9-1/2 hr. By constructing a light curve for a point near the center of CH6, we observed a sudden 40% decrease in X-ray emission associated with the birth of this coronal hole. On a time scale of hours, the growth of CH6 in area proceeded faster than the average rate predicted by the diffusion of solar fields. The short term decay of CH6 followed the diffusive rate to within experimental uncertainty. On a time scale of one rotation, the subsequent development of CH6 was not consistent with steady growth at the average rate predicted by diffusion.

Solute segregation kinetics and dislocation depinning in a binary alloy

NASA Astrophysics Data System (ADS)

Dontsova, E.; Rottler, J.; Sinclair, C. W.

2015-06-01

Static strain aging, a phenomenon caused by diffusion of solute atoms to dislocations, is an important contributor to the strength of substitutional alloys. Accurate modeling of this complex process requires both atomic spatial resolution and diffusional time scales, which is very challenging to achieve with commonly used atomistic computational methods. In this paper, we use the recently developed "diffusive molecular dynamics" (DMD) method that is capable of describing the kinetics of the solute segregation process at the atomic level while operating on diffusive time scales in a computationally efficient way. We study static strain aging in the Al-Mg system and calculate the depinning shear stress between edge and screw dislocations and their solute atmospheres formed for various waiting times with different solute content and for a range of temperatures. A simple phenomenological model is also proposed that describes the observed behavior of the critical shear stress as a function of segregation level.

Time-resolved production and detection of reactive atoms

DOE Office of Scientific and Technical Information (OSTI.GOV)

Grossman, L. W.; Hurst, G. S.

1977-09-01

Cesium iodide in the presence of a buffer gas was dissociated with a pulsed ultraviolet laser, which will be referred to as the source laser. This created a population of atoms at a well defined time and in a compact, well defined volume. A second pulsed laser, with a beam that completely surrounded that of the first, photoionized the cesium after a known time delay. This laser will be referred to as the detector laser. It was determined that for short time delays, all of the cesium atoms were easily ionized. When focused, the source laser generated an extremely intensemore » fluence. By accounting for the beam intensity profile it was shown that all of the molecules in the central portion of the beam can be dissociated and detected. Besides proving the feasibility of single-molecule detection, this enabled a determination of the absolute photodissociation cross section as a function of wavelength. Initial studies of the time decay of the cesium signal at low argon pressures indicated a non-exponential decay. This was consistent with a diffusion mechanism transporting cesium atoms out of the laser beam. Therefore, it was desired to conduct further experiments using a tightly focused source beam, passing along the axis of the detector beam. The theoretical behavior of this simple geometry accounting for diffusion and reaction is easily calculated. A diffusion coefficient can then be extracted by data fitting. If reactive decay is due to impurities constituting a fixed percentage of the buffer gas, then two-body reaction rates will scale linearly with pressure and three-body reaction rates will scale quadratically. Also, the diffusion coefficient will scale inversely with pressure. At low pressures it is conceivable that decay due to diffusion would be sufficiently rapid that all other processes can be neglected. Extraction of a diffusion coefficient would then be quite direct. Finally, study of the reaction of cesium and oxygen was undertaken.« less

Causes and implications of suppressed vesiculation and crystallization in phenocryst embayments

NASA Astrophysics Data System (ADS)

Cashman, K. V.; Rust, A.

2016-12-01

Recent studies of crystal-hosted melt embayments have modeled water diffusion to estimate rates of magma ascent. Uncertainties in these calculations have been linked primarily to the assumed initial pressure. None of these studies, however, have addressed the conditions under which crystal-hosted clear glass channels form in samples dominated by crystal- and bubble-rich groundmass. Embayments are common in phenocrysts from the 1974 basaltic eruption of Fuego volcano. They are hosted by both plagioclase and olivine phenocrysts where rapid and spatially heterogeneous growth creates a local melt channel. Embayment shapes differ in the two phases, however, depending on the characteristic rapid growth morphologies. Embayment channels are typically 20-50 µm wide and may reach 100-200 µm in length. Interestingly, these length scales are similar to those of melt embayments in plagioclase within the dacitic Mount St. Helens. We suggest that these characteristic length scales are key to embayment preservation as clear glass. We explore two hypotheses: (1) that the space constraints of the embayment inhibit bubble nucleation and growth, or (2) that rapid decompression-driven crystal growth on all sides of the melt channel temporarily increases the melt temperature and water content (and therefore element diffusivity) above ambient. Support for the second hypothesis - that diffusion out of the melt channels is energetically more favorable than nucleation of new bubble and crystal phases - is suggested by observed diffusion profiles of melt components within the embayments. Understanding the origin of melt channels has important implications for diffusion-based studies of magma decompression. First, if the embayments are formed by rapid, syn-eruptive crystal growth, then the effective diffusion length scale must increase with time. Second, if local and temporary heating increase elemental diffusion rates, then characteristic diffusion time scales will be overestimated. By extension, we also note that similar conditions may characterize rapid growth of skeletal and hopper crystals.

Short- and long-time diffusion and dynamic scaling in suspensions of charged colloidal particles.

PubMed

Banchio, Adolfo J; Heinen, Marco; Holmqvist, Peter; Nägele, Gerhard

2018-04-07

We report on a comprehensive theory-simulation-experimental study of collective and self-diffusion in concentrated suspensions of charge-stabilized colloidal spheres. In theory and simulation, the spheres are assumed to interact directly by a hard-core plus screened Coulomb effective pair potential. The intermediate scattering function, f c (q, t), is calculated by elaborate accelerated Stokesian dynamics (ASD) simulations for Brownian systems where many-particle hydrodynamic interactions (HIs) are fully accounted for, using a novel extrapolation scheme to a macroscopically large system size valid for all correlation times. The study spans the correlation time range from the colloidal short-time to the long-time regime. Additionally, Brownian Dynamics (BD) simulation and mode-coupling theory (MCT) results of f c (q, t) are generated where HIs are neglected. Using these results, the influence of HIs on collective and self-diffusion and the accuracy of the MCT method are quantified. It is shown that HIs enhance collective and self-diffusion at intermediate and long times. At short times self-diffusion, and for wavenumbers outside the structure factor peak region also collective diffusion, are slowed down by HIs. MCT significantly overestimates the slowing influence of dynamic particle caging. The dynamic scattering functions obtained in the ASD simulations are in overall good agreement with our dynamic light scattering (DLS) results for a concentration series of charged silica spheres in an organic solvent mixture, in the experimental time window and wavenumber range. From the simulation data for the time derivative of the width function associated with f c (q, t), there is indication of long-time exponential decay of f c (q, t), for wavenumbers around the location of the static structure factor principal peak. The experimental scattering functions in the probed time range are consistent with a time-wavenumber factorization scaling behavior of f c (q, t) that was first reported by Segrè and Pusey [Phys. Rev. Lett. 77, 771 (1996)] for suspensions of hard spheres. Our BD simulation and MCT results predict a significant violation of exact factorization scaling which, however, is approximately restored according to the ASD results when HIs are accounted for, consistent with the experimental findings for f c (q, t). Our study of collective diffusion is amended by simulation and theoretical results for the self-intermediate scattering function, f s (q, t), and its non-Gaussian parameter α 2 (t) and for the particle mean squared displacement W(t) and its time derivative. Since self-diffusion properties are not assessed in standard DLS measurements, a method to deduce W(t) approximately from f c (q, t) is theoretically validated.

Time scales of porphyry Cu deposit formation: insights from titanium diffusion in quartz

USGS Publications Warehouse

Mercer, Celestine N.; Reed, Mark H.; Mercer, Cameron M.

2015-01-01

Porphyry dikes and hydrothermal veins from the porphyry Cu-Mo deposit at Butte, Montana, contain multiple generations of quartz that are distinct in scanning electron microscope-cathodoluminescence (SEM-CL) images and in Ti concentrations. A comparison of microprobe trace element profiles and maps to SEM-CL images shows that the concentration of Ti in quartz correlates positively with CL brightness but Al, K, and Fe do not. After calibrating CL brightness in relation to Ti concentration, we use the brightness gradient between different quartz generations as a proxy for Ti gradients that we model to determine time scales of quartz formation and cooling. Model results indicate that time scales of porphyry magma residence are ~1,000s of years and time scales from porphyry quartz phenocryst rim formation to porphyry dike injection and cooling are ~10s of years. Time scales for the formation and cooling of various generations of hydrothermal vein quartz range from 10s to 10,000s of years. These time scales are considerably shorter than the ~0.6 m.y. overall time frame for each porphyry-style mineralization pulse determined from isotopic studies at Butte, Montana. Simple heat conduction models provide a temporal reference point to compare chemical diffusion time scales, and we find that they support short dike and vein formation time scales. We interpret these relatively short time scales to indicate that the Butte porphyry deposit formed by short-lived episodes of hydrofracturing, dike injection, and vein formation, each with discrete thermal pulses, which repeated over the ~3 m.y. generation of the deposit.

Diffusion-limited mixing by incompressible flows

NASA Astrophysics Data System (ADS)

Miles, Christopher J.; Doering, Charles R.

2018-05-01

Incompressible flows can be effective mixers by appropriately advecting a passive tracer to produce small filamentation length scales. In addition, diffusion is generally perceived as beneficial to mixing due to its ability to homogenize a passive tracer. However we provide numerical evidence that, in cases where advection and diffusion are both actively present, diffusion may produce negative effects by limiting the mixing effectiveness of incompressible optimal flows. This limitation appears to be due to the presence of a limiting length scale given by a generalised Batchelor length (Batchelor 1959 J. Fluid Mech. 5 113–33). This length scale limitation may in turn affect long-term mixing rates. More specifically, we consider local-in-time flow optimisation under energy and enstrophy flow constraints with the objective of maximising the mixing rate. We observe that, for enstrophy-bounded optimal flows, the strength of diffusion may not impact the long-term mixing rate. For energy-constrained optimal flows, however, an increase in the strength of diffusion can decrease the mixing rate. We provide analytical lower bounds on mixing rates and length scales achievable under related constraints (point-wise bounded speed and rate-of-strain) by extending the work of Lin et al (2011 J. Fluid Mech. 675 465–76) and Poon (1996 Commun. PDE 21 521–39).

A study of a diffusive model of asset returns and an empirical analysis of financial markets

NASA Astrophysics Data System (ADS)

Alejandro Quinones, Angel Luis

A diffusive model for market dynamics is studied and the predictions of the model are compared to real financial markets. The model has a non-constant diffusion coefficient which depends both on the asset value and the time. A general solution for the distribution of returns is obtained and shown to match the results of computer simulations for two simple cases, piecewise linear and quadratic diffusion. The effects of discreteness in the market dynamics on the model are also studied. For the quadratic diffusion case, a type of phase transition leading to fat tails is observed as the discrete distribution approaches the continuum limit. It is also found that the model captures some of the empirical stylized facts observed in real markets, including fat-tails and scaling behavior in the distribution of returns. An analysis of empirical data for the EUR/USD currency exchange rate and the S&P 500 index is performed. Both markets show time scaling behavior consistent with a value of 1/2 for the Hurst exponent. Finally, the results show that the distribution of returns for the two markets is well fitted by the model, and the corresponding empirical diffusion coefficients are determined.

Hopping Diffusion of Nanoparticles in Polymer Matrices

PubMed Central

2016-01-01

We propose a hopping mechanism for diffusion of large nonsticky nanoparticles subjected to topological constraints in both unentangled and entangled polymer solids (networks and gels) and entangled polymer liquids (melts and solutions). Probe particles with size larger than the mesh size ax of unentangled polymer networks or tube diameter ae of entangled polymer liquids are trapped by the network or entanglement cells. At long time scales, however, these particles can diffuse by overcoming free energy barrier between neighboring confinement cells. The terminal particle diffusion coefficient dominated by this hopping diffusion is appreciable for particles with size moderately larger than the network mesh size ax or tube diameter ae. Much larger particles in polymer solids will be permanently trapped by local network cells, whereas they can still move in polymer liquids by waiting for entanglement cells to rearrange on the relaxation time scales of these liquids. Hopping diffusion in entangled polymer liquids and networks has a weaker dependence on particle size than that in unentangled networks as entanglements can slide along chains under polymer deformation. The proposed novel hopping model enables understanding the motion of large nanoparticles in polymeric nanocomposites and the transport of nano drug carriers in complex biological gels such as mucus. PMID:25691803

Thin film growth studies using time-resolved x-ray scattering

NASA Astrophysics Data System (ADS)

Kowarik, Stefan

2017-02-01

Thin-film growth is important for novel functional materials and new generations of devices. The non-equilibrium growth physics involved is very challenging, because the energy landscape for atomic scale processes is determined by many parameters, such as the diffusion and Ehrlich-Schwoebel barriers. We review the in situ real-time techniques of x-ray diffraction (XRD), x-ray growth oscillations and diffuse x-ray scattering (GISAXS) for the determination of structure and morphology on length scales from Å to µm. We give examples of time resolved growth experiments mainly from molecular thin film growth, but also highlight growth of inorganic materials using molecular beam epitaxy (MBE) and electrochemical deposition from liquids. We discuss how scaling parameters of rate equation models and fundamental energy barriers in kinetic Monte Carlo methods can be determined from fits of the real-time x-ray data.

Thin film growth studies using time-resolved x-ray scattering.

PubMed

Kowarik, Stefan

2017-02-01

Thin-film growth is important for novel functional materials and new generations of devices. The non-equilibrium growth physics involved is very challenging, because the energy landscape for atomic scale processes is determined by many parameters, such as the diffusion and Ehrlich-Schwoebel barriers. We review the in situ real-time techniques of x-ray diffraction (XRD), x-ray growth oscillations and diffuse x-ray scattering (GISAXS) for the determination of structure and morphology on length scales from Å to µm. We give examples of time resolved growth experiments mainly from molecular thin film growth, but also highlight growth of inorganic materials using molecular beam epitaxy (MBE) and electrochemical deposition from liquids. We discuss how scaling parameters of rate equation models and fundamental energy barriers in kinetic Monte Carlo methods can be determined from fits of the real-time x-ray data.

Thermal diffusivity study of aged Li-ion batteries using flash method

NASA Astrophysics Data System (ADS)

Nagpure, Shrikant C.; Dinwiddie, Ralph; Babu, S. S.; Rizzoni, Giorgio; Bhushan, Bharat; Frech, Tim

Advanced Li-ion batteries with high energy and power density are fast approaching compatibility with automotive demands. While the mechanism of operation of these batteries is well understood, the aging mechanisms are still under investigation. Investigation of aging mechanisms in Li-ion batteries becomes very challenging, as aging does not occur due to a single process, but because of multiple physical processes occurring at the same time in a cascading manner. As the current characterization techniques such as Raman spectroscopy, X-ray diffraction, and atomic force microscopy are used independent of each other they do not provide a comprehensive understanding of material degradation at different length (nm 2 to m 2) scales. Thus to relate the damage mechanisms of the cathode at mm length scale to micro/nanoscale, data at an intermediate length scale is needed. As such, we demonstrate here the use of thermal diffusivity analysis by flash method to bridge the gap between different length scales. In this paper we present the thermal diffusivity analysis of an unaged and aged cell. Thermal diffusivity analysis maps the damage to the cathode samples at millimeter scale lengths. Based on these maps we also propose a mechanism leading to the increase of the thermal diffusivity as the cells are aged.

Nonlinear Landau damping in the ionosphere

NASA Technical Reports Server (NTRS)

Kiwamoto, Y.; Benson, R. F.

1978-01-01

A model is presented to explain the non-resonant waves which give rise to the diffuse resonance observed near 3/2 f sub H by the Alouette and ISIS topside sounders, where f sub H is the ambient electron cyclotron frequency. In a strictly linear analysis, these instability driven waves will decay due to Landau damping on a time scale much shorter than the observed time duration of the diffuse resonance. Calculations of the nonlinear wave particle coupling coefficients, however, indicate that the diffuse resonance wave can be maintained by the nonlinear Landau damping of the sounder stimulated 2f sub H wave. The time duration of the diffuse resonance is determined by the transit time of the instability generated and nonlinearly maintained diffuse resonance wave from the remote short lived hot region back to the antenna. The model is consistent with the Alouette/ISIS observations, and clearly demonstrates the existence of nonlinear wave-particle interactions in the ionosphere.

Cumulant expansions for measuring water exchange using diffusion MRI

NASA Astrophysics Data System (ADS)

Ning, Lipeng; Nilsson, Markus; Lasič, Samo; Westin, Carl-Fredrik; Rathi, Yogesh

2018-02-01

The rate of water exchange across cell membranes is a parameter of biological interest and can be measured by diffusion magnetic resonance imaging (dMRI). In this work, we investigate a stochastic model for the diffusion-and-exchange of water molecules. This model provides a general solution for the temporal evolution of dMRI signal using any type of gradient waveform, thereby generalizing the signal expressions for the Kärger model. Moreover, we also derive a general nth order cumulant expansion of the dMRI signal accounting for water exchange, which has not been explored in earlier studies. Based on this analytical expression, we compute the cumulant expansion for dMRI signals for the special case of single diffusion encoding (SDE) and double diffusion encoding (DDE) sequences. Our results provide a theoretical guideline on optimizing experimental parameters for SDE and DDE sequences, respectively. Moreover, we show that DDE signals are more sensitive to water exchange at short-time scale but provide less attenuation at long-time scale than SDE signals. Our theoretical analysis is also validated using Monte Carlo simulations on synthetic structures.

Physics of ultra-high bioproductivity in algal photobioreactors

NASA Astrophysics Data System (ADS)

Greenwald, Efrat; Gordon, Jeffrey M.; Zarmi, Yair

2012-04-01

Cultivating algae at high densities in thin photobioreactors engenders time scales for random cell motion that approach photosynthetic rate-limiting time scales. This synchronization allows bioproductivity above that achieved with conventional strategies. We show that a diffusion model for cell motion (1) accounts for high bioproductivity at irradiance values previously deemed restricted by photoinhibition, (2) predicts the existence of optimal culture densities and their dependence on irradiance, consistent with available data, (3) accounts for the observed degree to which mixing improves bioproductivity, and (4) provides an estimate of effective cell diffusion coefficients, in accord with independent hydrodynamic estimates.

Aging underdamped scaled Brownian motion: Ensemble- and time-averaged particle displacements, nonergodicity, and the failure of the overdamping approximation.

PubMed

Safdari, Hadiseh; Cherstvy, Andrey G; Chechkin, Aleksei V; Bodrova, Anna; Metzler, Ralf

2017-01-01

We investigate both analytically and by computer simulations the ensemble- and time-averaged, nonergodic, and aging properties of massive particles diffusing in a medium with a time dependent diffusivity. We call this stochastic diffusion process the (aging) underdamped scaled Brownian motion (UDSBM). We demonstrate how the mean squared displacement (MSD) and the time-averaged MSD of UDSBM are affected by the inertial term in the Langevin equation, both at short, intermediate, and even long diffusion times. In particular, we quantify the ballistic regime for the MSD and the time-averaged MSD as well as the spread of individual time-averaged MSD trajectories. One of the main effects we observe is that, both for the MSD and the time-averaged MSD, for superdiffusive UDSBM the ballistic regime is much shorter than for ordinary Brownian motion. In contrast, for subdiffusive UDSBM, the ballistic region extends to much longer diffusion times. Therefore, particular care needs to be taken under what conditions the overdamped limit indeed provides a correct description, even in the long time limit. We also analyze to what extent ergodicity in the Boltzmann-Khinchin sense in this nonstationary system is broken, both for subdiffusive and superdiffusive UDSBM. Finally, the limiting case of ultraslow UDSBM is considered, with a mixed logarithmic and power-law dependence of the ensemble- and time-averaged MSDs of the particles. In the limit of strong aging, remarkably, the ordinary UDSBM and the ultraslow UDSBM behave similarly in the short time ballistic limit. The approaches developed here open ways for considering other stochastic processes under physically important conditions when a finite particle mass and aging in the system cannot be neglected.

First passage times and asymmetry of DNA translocation

NASA Astrophysics Data System (ADS)

Lua, Rhonald C.; Grosberg, Alexander Y.

2005-12-01

Motivated by experiments in which single-stranded DNA with a short hairpin loop at one end undergoes unforced diffusion through a narrow pore, we study the first passage times for a particle, executing one-dimensional Brownian motion in an asymmetric sawtooth potential, to exit one of the boundaries. We consider the first passage times for the case of classical diffusion, characterized by a mean-square displacement of the form ⟨(Δx)2⟩˜t , and for the case of anomalous diffusion or subdiffusion, characterized by a mean-square displacement of the form ⟨(Δx)2⟩˜tγ with 0<γ<1 . In the context of classical diffusion, we obtain an expression for the mean first passage time and show that this quantity changes when the direction of the sawtooth is reversed or, equivalently, when the reflecting and absorbing boundaries are exchanged. We discuss at which numbers of “teeth” N (or number of DNA nucleotides) and at which heights of the sawtooth potential this difference becomes significant. For large N , it is well known that the mean first passage time scales as N2 . In the context of subdiffusion, the mean first passage time does not exist. Therefore, we obtain instead the distribution of first passage times in the limit of long times. We show that the prefactor in the power relation for this distribution is simply the expression for the mean first passage time in classical diffusion. We also describe a hypothetical experiment to calculate the average of the first passage times for a fraction of passage events that each end within some time t* . We show that this average first passage time scales as N2/γ in subdiffusion.

Aging underdamped scaled Brownian motion: Ensemble- and time-averaged particle displacements, nonergodicity, and the failure of the overdamping approximation

NASA Astrophysics Data System (ADS)

Safdari, Hadiseh; Cherstvy, Andrey G.; Chechkin, Aleksei V.; Bodrova, Anna; Metzler, Ralf

2017-01-01

We investigate both analytically and by computer simulations the ensemble- and time-averaged, nonergodic, and aging properties of massive particles diffusing in a medium with a time dependent diffusivity. We call this stochastic diffusion process the (aging) underdamped scaled Brownian motion (UDSBM). We demonstrate how the mean squared displacement (MSD) and the time-averaged MSD of UDSBM are affected by the inertial term in the Langevin equation, both at short, intermediate, and even long diffusion times. In particular, we quantify the ballistic regime for the MSD and the time-averaged MSD as well as the spread of individual time-averaged MSD trajectories. One of the main effects we observe is that, both for the MSD and the time-averaged MSD, for superdiffusive UDSBM the ballistic regime is much shorter than for ordinary Brownian motion. In contrast, for subdiffusive UDSBM, the ballistic region extends to much longer diffusion times. Therefore, particular care needs to be taken under what conditions the overdamped limit indeed provides a correct description, even in the long time limit. We also analyze to what extent ergodicity in the Boltzmann-Khinchin sense in this nonstationary system is broken, both for subdiffusive and superdiffusive UDSBM. Finally, the limiting case of ultraslow UDSBM is considered, with a mixed logarithmic and power-law dependence of the ensemble- and time-averaged MSDs of the particles. In the limit of strong aging, remarkably, the ordinary UDSBM and the ultraslow UDSBM behave similarly in the short time ballistic limit. The approaches developed here open ways for considering other stochastic processes under physically important conditions when a finite particle mass and aging in the system cannot be neglected.

Turbulent mixing within the Kuroshio in the Tokara Strait

NASA Astrophysics Data System (ADS)

Tsutsumi, Eisuke; Matsuno, Takeshi; Lien, Ren-Chieh; Nakamura, Hirohiko; Senjyu, Tomoharu; Guo, Xinyu

2017-09-01

Turbulent mixing and background current were observed using a microstructure profiler and acoustic Doppler current profilers in the Tokara Strait, where many seamounts and small islands exist within the route of the Kuroshio in the East China Sea. Vertical structure and water properties of the Kuroshio were greatly modified downstream from shallow seamounts. In the lee of a seamount crest at 200 m depth, the modification made the flow tend to shear instability, and the vertical eddy diffusivity is enhanced by nearly 100 times that of the upstream site, to Kρ ˜ O(10-3)-O(10-2) m2 s-1. A one-dimensional diffusion model using the observed eddy diffusivity reproduced the observed downstream evolution of the temperature-salinity profile. However, the estimated diffusion time-scale is at least 10 times longer than the observed advection time-scale. This suggests that the eddy diffusivity reaches to O(10-1) m2 s-1 in the vicinity of the seamount. At a site away from the abrupt topography, eddy diffusivity was also elevated to O(10-3) m2 s-1, and was associated with shear instability presumably induced by the Kuroshio shear and near-inertial internal-wave shear. Our study suggests that a better prediction of current, water-mass properties, and nutrients within the Kuroshio requires accurate understanding and parameterization of flow-topography interaction such as internal hydraulics, the associated internal-wave processes, and turbulent mixing processes.

Multiscale diffusion of a molecular probe in a crowded environment: a concept

NASA Astrophysics Data System (ADS)

Currie, Megan; Thao, Chang; Timerman, Randi; Welty, Robb; Berry, Brenden; Sheets, Erin D.; Heikal, Ahmed A.

2015-08-01

Living cells are crowded with macromolecules and organelles. Yet, it is not fully understood how macromolecular crowding affects the myriad of biochemical reactions, transport and the structural stability of biomolecules that are essential to cellular function and survival. These molecular processes, with or without electrostatic interactions, in living cells are therefore expected to be distinct from those carried out in test tube in dilute solutions where excluded volumes are absent. Thus there is an urgent need to understand the macromolecular crowding effects on cellular and molecular biophysics towards quantitative cell biology. In this report, we investigated how biomimetic crowding affects both the rotational and translation diffusion of a small probe (rhodamine green, RhG). For biomimetic crowding agents, we used Ficoll-70 (synthetic polymer), bovine serum albumin and ovalbumin (proteins) at various concentrations in a buffer at room temperature. As a control, we carried out similar measurements on glycerolenriched buffer as an environment with homogeneous viscosity as a function of glycerol concentration. The corresponding bulk viscosity was measured independently to test the validity of the Stokes-Einstein model of a diffusing species undergoing a random walk. For rotational diffusion (ps-ns time scale), we used time-resolved anisotropy measurements to examine potential binding of RhG as a function of the crowding agents (surface structure and size). For translational diffusion (μs-s time scale), we used fluorescence correlation spectroscopy for single-molecule fluctuation analysis. Our results allow us to examine the diffusion model of a molecular probe in crowded environments as a function of concentration, length scale, homogeneous versus heterogeneous viscosity, size and surface structures. These biomimetic crowding studies, using non-invasive fluorescence spectroscopy methods, represent an important step towards understanding cellular biophysics and quantitative cell biology.

Diffusion in jammed particle packs

NASA Astrophysics Data System (ADS)

Bolintineanu, Dan S.; Silbert, Leonardo E.; Grest, Gary S.; Lechman, Jeremy B.

2015-03-01

Diffusive transport in jammed particle packs is of interest for a number of applications, as well as being a potential indicator of structural properties near the jamming point. To this end, we report stochastic simulations of equilibrium diffusion through monodisperse sphere packs near the jamming point in the limit of a perfectly insulating surrounding medium. The time dependence of various diffusion properties is resolved over several orders of magnitude. Two time regimes of expected Fickian diffusion are observed, separated by an intermediate regime of anomalous diffusion. This intermediate regime grows as the particle volume fraction approaches the critical jamming transition. The diffusion behavior is fully controlled by the extent of the contacts between neighboring particles, which in turn depend on proximity to the jamming point. In particular, the mean first passage time associated with the escape of random walkers between neighboring particles is shown to control both the time to recover Fickian diffusion and the long time diffusivity. Scaling laws are established that relate these quantities to the difference between the actual and critical jamming volume fractions. Sandia National Laboratories is a multiprogram laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's NNSA under Contract DE- AC04-94AL85000.

On the vanishing of the t-term in the short-time expansion of the diffusion coefficient for oscillating gradients in diffusion NMR

NASA Astrophysics Data System (ADS)

Laun, Frederik B.; Demberg, Kerstin; Nagel, Armin M.; Uder, Micheal; Kuder, Tristan A.

2017-11-01

Nuclear magnetic resonance (NMR) diffusion measurements can be used to probe porous structures or biological tissues by means of the random motion of water molecules. The short-time expansion of the diffusion coefficient in powers of sqrt(t), where t is the diffusion time related to the duration of the diffusion-weighting magnetic field gradient profile, is universally connected to structural parameters of the boundaries restricting the diffusive motion. The sqrt(t)-term is proportional to the surface to volume ratio. The t-term is related to permeability and curvature. The short time expansion can be measured with two approaches in NMR-based diffusion experiments: First, by the use of diffusion encodings of short total duration and, second, by application of oscillating gradients of long total duration. For oscillating gradients, the inverse of the oscillation frequency becomes the relevant time scale. The purpose of this manuscript is to show that the oscillating gradient approach is blind to the t-term. On the one hand, this prevents fitting of permeability and curvature measures from this term. On the other hand, the t-term does not bias the determination of the sqrt(t)-term in experiments.

A double medium model for diffusion in fluid-bearing rock

NASA Astrophysics Data System (ADS)

Wang, H. F.

1993-09-01

The concept of a double porosity medium to model fluid flow in fractured rock has been applied to model diffusion in rock containing a small amount of a continuous fluid phase that surrounds small volume elements of the solid matrix. The model quantifies the relative role of diffusion in the fluid and solid phases of the rock. The fluid is the fast diffusion path, but the solid contains the volumetrically significant amount of the diffusing species. The double medium model consists of two coupled differential equations. One equation is the diffusion equation for the fluid concentration; it contains a source term for change in the average concentration of the diffusing species in the solid matrix. The second equation represents the assumption that the change in average concentration in a solid element is proportional to the difference between the average concentration in the solid and the concentration in the fluid times the solid-fluid partition coefficient. The double medium model is shown to apply to laboratory data on iron diffusion in fluid-bearing dunite and to measured oxygen isotope ratios at marble-metagranite contacts. In both examples, concentration profiles are calculated for diffusion taking place at constant temperature, where a boundary value changes suddenly and is subsequently held constant. Knowledge of solid diffusivities can set a lower bound to the length of time over which diffusion occurs, but only the product of effective fluid diffusivity and time is constrained for times longer than the characteristic solid diffusion time. The double medium results approach a local, grain-scale equilibrium model for times that are large relative to the time constant for solid diffusion.

New Insights into the Fractional Order Diffusion Equation Using Entropy and Kurtosis.

PubMed

Ingo, Carson; Magin, Richard L; Parrish, Todd B

2014-11-01

Fractional order derivative operators offer a concise description to model multi-scale, heterogeneous and non-local systems. Specifically, in magnetic resonance imaging, there has been recent work to apply fractional order derivatives to model the non-Gaussian diffusion signal, which is ubiquitous in the movement of water protons within biological tissue. To provide a new perspective for establishing the utility of fractional order models, we apply entropy for the case of anomalous diffusion governed by a fractional order diffusion equation generalized in space and in time. This fractional order representation, in the form of the Mittag-Leffler function, gives an entropy minimum for the integer case of Gaussian diffusion and greater values of spectral entropy for non-integer values of the space and time derivatives. Furthermore, we consider kurtosis, defined as the normalized fourth moment, as another probabilistic description of the fractional time derivative. Finally, we demonstrate the implementation of anomalous diffusion, entropy and kurtosis measurements in diffusion weighted magnetic resonance imaging in the brain of a chronic ischemic stroke patient.

18,000 displacement vectors and 44 positions surveys of RFID tracers show a normal diffusion of the bedload in a proglacial stream (Bossons glacier, France)

NASA Astrophysics Data System (ADS)

Guillon, Hervé; Mugnier, Jean-Louis; Buoncristiani, Jean-François

2016-04-01

Bedload transport is a stochastic process during which each particle hops for a random length then rests for a random duration. In recent years, this probabilistic approach was investigated by theoretical models, numerical simulations and laboratory experiments. These experiments are generally carried out on short time scales with sand, but underline the diffusive behaviour of the bedload. Conversely, marked pebbles in natural streams have mainly be used to infer about transport processes and transport time of the bedload. In this study, the stochastic characteristics of bedload transport are inferred from the radio-frequency identification (RFID) of pebbles. In particular, we provide insights for answering the following question : is the bedload transport sub-diffusive, normally diffusive or super-diffusive at the long time scale (i.e. global range)? Experiments designed to investigate the phenomenology of bedload transport have been carried out in the proglacial area of Bossons glacier. This 350 m long alluvial plain exhibits daily flood from the glacial system and is still redistributing material from catastrophic events pre-dating our investigations. From 2011 to 2014, the position of the ˜ 1000 RFID tracers have been measured by a mobile antenna and a differential GPS during 44 surveys providing ˜ 2500 tracer positions. Additionnaly, in 2014, 650 new tracers were seeded upstream from a static RFID antenna located at the outlet of the study area. For the 1 to 32 cm fraction surveyed, both mobile and static antenna results show no evidence for a significant export outside of the surveyed zone. Initial data have been maximized by using each possible campaign pairs leading to ˜700 campaign pairs and more than 18,000 displacement vectors. To our knowledge, this is one of the most extensive dataset of tracers positions measured in a natural stream using the RFID methodology. Using 152 campaigns pairs with at least 20 retrieved tracers,r standard probability distributions were tested against the observed travel distances. Regardless of the time scale, heavy- and light-tailed distributions provide a convincing statistical description of measured data. No single distribution is significantly better than the others. Conversely, the distribution of tracers positions in the system and its time evolution is best described by the normal distribution. Its standard deviation scales with time as σ ∝ t0.45±0.12 which suggests a nearly normal diffusive behaviour. The measured virtual velocities and a simple probabilistic model using the time evolution of the mean (i.e. drift) and standard deviation (i.e diffusion) show that the mean bedload transfer time is greater than 5 years. RFID tracers appear as a promising tool to investigate stochastic characteristics of bedload transport.

Interpreting high time resolution galactic cosmic ray observations in a diffusive context

NASA Astrophysics Data System (ADS)

Jordan, A.; Spence, H. E.; Blake, J. B.; Shaul, D. A.

2009-12-01

We interpret galactic cosmic ray (GCR) variations near Earth within a diffusive context. The variations occur on time-/size-scales ranging from Forbush decreases (Fds), to substructure embedded within Fds, to smaller amplitude and shorter duration variations during relatively benign interplanetary conditions. We use high time resolution GCR observations from the High Sensitivity Telescope (HIST) on Polar and from the Spectrometer for INTEGRAL (SPI) and also use solar wind plasma and magnetic field observations from ACE and/or Wind. To calculate the coefficient of diffusion, we combine these datasets with a simple convection-diffusion model for relativistic charged particles in a magnetic field. We find reasonable agreement between our and previous estimates of the coefficient. We also show whether changes in the coefficient of diffusion are sufficient to explain the above GCR variations.

Unstable vicinal crystal growth from cellular automata

NASA Astrophysics Data System (ADS)

Krasteva, A.; Popova, H.; KrzyŻewski, F.; Załuska-Kotur, M.; Tonchev, V.

2016-03-01

In order to study the unstable step motion on vicinal crystal surfaces we devise vicinal Cellular Automata. Each cell from the colony has value equal to its height in the vicinal, initially the steps are regularly distributed. Another array keeps the adatoms, initially distributed randomly over the surface. The growth rule defines that each adatom at right nearest neighbor position to a (multi-) step attaches to it. The update of whole colony is performed at once and then time increases. This execution of the growth rule is followed by compensation of the consumed particles and by diffusional update(s) of the adatom population. Two principal sources of instability are employed - biased diffusion and infinite inverse Ehrlich-Schwoebel barrier (iiSE). Since these factors are not opposed by step-step repulsion the formation of multi-steps is observed but in general the step bunches preserve a finite width. We monitor the developing surface patterns and quantify the observations by scaling laws with focus on the eventual transition from diffusion-limited to kinetics-limited phenomenon. The time-scaling exponent of the bunch size N is 1/2 for the case of biased diffusion and 1/3 for the case of iiSE. Additional distinction is possible based on the time-scaling exponents of the sizes of multi-step Nmulti, these are 0.36÷0.4 (for biased diffusion) and 1/4 (iiSE).

Effect of Hydrodynamic Interactions on Self-Diffusion of Quasi-Two-Dimensional Colloidal Hard Spheres.

PubMed

Thorneywork, Alice L; Rozas, Roberto E; Dullens, Roel P A; Horbach, Jürgen

2015-12-31

We compare experimental results from a quasi-two-dimensional colloidal hard sphere fluid to a Monte Carlo simulation of hard disks with small particle displacements. The experimental short-time self-diffusion coefficient D(S) scaled by the diffusion coefficient at infinite dilution, D(0), strongly depends on the area fraction, pointing to significant hydrodynamic interactions at short times in the experiment, which are absent in the simulation. In contrast, the area fraction dependence of the experimental long-time self-diffusion coefficient D(L)/D(0) is in quantitative agreement with D(L)/D(0) obtained from the simulation. This indicates that the reduction in the particle mobility at short times due to hydrodynamic interactions does not lead to a proportional reduction in the long-time self-diffusion coefficient. Furthermore, the quantitative agreement between experiment and simulation at long times indicates that hydrodynamic interactions effectively do not affect the dependence of D(L)/D(0) on the area fraction. In light of this, we discuss the link between structure and long-time self-diffusion in terms of a configurational excess entropy and do not find a simple exponential relation between these quantities for all fluid area fractions.

Computation of shear-induced collective-diffusivity in emulsions

NASA Astrophysics Data System (ADS)

Malipeddi, Abhilash Reddy; Sarkar, Kausik

2017-11-01

The shear-induced collective-diffusivity of drops in an emulsion is calculated through simulation. A front-tracking finite difference method is used to integrate the Navier-Stokes equations. When a cloud of drops is subjected to shear flow, after a certain time, the width of the cloud increases with the 1/3 power of time. This scaling of drop-cloud-width with time is characteristic of (sub-)diffusion that arises from irreversible two-drop interactions. The collective diffusivity is calculated from this relationship. A feature of the procedure adopted here is the modest computational requirement, wherein, a few drops ( 70) in shear for short time ( 70 strain) is found to be sufficient to get a good estimate. As far as we know, collective-diffusivity has not been calculated for drops through simulation till now. The computed values match with experimental measurements reported in the literature. The diffusivity in emulsions is calculated for a range of Capillary (Ca) and Reynolds (Re) numbers. It is found to be a unimodal function of Ca , similar to self-diffusivity. A sub-linear increase of the diffusivity with Re is seen for Re < 5 . This work has been limited to a viscosity matched case.

In Vivo Anomalous Diffusion and Weak Ergodicity Breaking of Lipid Granules

NASA Astrophysics Data System (ADS)

Jeon, Jae-Hyung; Tejedor, Vincent; Burov, Stas; Barkai, Eli; Selhuber-Unkel, Christine; Berg-Sørensen, Kirstine; Oddershede, Lene; Metzler, Ralf

2011-01-01

Combining extensive single particle tracking microscopy data of endogenous lipid granules in living fission yeast cells with analytical results we show evidence for anomalous diffusion and weak ergodicity breaking. Namely we demonstrate that at short times the granules perform subdiffusion according to the laws of continuous time random walk theory. The associated violation of ergodicity leads to a characteristic turnover between two scaling regimes of the time averaged mean squared displacement. At longer times the granule motion is consistent with fractional Brownian motion.

Picosecond to nanosecond dynamics provide a source of conformational entropy for protein folding.

PubMed

Stadler, Andreas M; Demmel, Franz; Ollivier, Jacques; Seydel, Tilo

2016-08-03

Myoglobin can be trapped in fully folded structures, partially folded molten globules, and unfolded states under stable equilibrium conditions. Here, we report an experimental study on the conformational dynamics of different folded conformational states of apo- and holomyoglobin in solution. Global protein diffusion and internal molecular motions were probed by neutron time-of-flight and neutron backscattering spectroscopy on the picosecond and nanosecond time scales. Global protein diffusion was found to depend on the α-helical content of the protein suggesting that charges on the macromolecule increase the short-time diffusion of protein. With regard to the molten globules, a gel-like phase due to protein entanglement and interactions with neighbouring macromolecules was visible due to a reduction of the global diffusion coefficients on the nanosecond time scale. Diffusion coefficients, residence and relaxation times of internal protein dynamics and root mean square displacements of localised internal motions were determined for the investigated structural states. The difference in conformational entropy ΔSconf of the protein between the unfolded and the partially or fully folded conformations was extracted from the measured root mean square displacements. Using thermodynamic parameters from the literature and the experimentally determined ΔSconf values we could identify the entropic contribution of the hydration shell ΔShydr of the different folded states. Our results point out the relevance of conformational entropy of the protein and the hydration shell for stability and folding of myoglobin.

Eddy diffusivity of quasi-neutrally-buoyant inertial particles

NASA Astrophysics Data System (ADS)

Martins Afonso, Marco; Muratore-Ginanneschi, Paolo; Gama, Sílvio M. A.; Mazzino, Andrea

2018-04-01

We investigate the large-scale transport properties of quasi-neutrally-buoyant inertial particles carried by incompressible zero-mean periodic or steady ergodic flows. We show how to compute large-scale indicators such as the inertial-particle terminal velocity and eddy diffusivity from first principles in a perturbative expansion around the limit of added-mass factor close to unity. Physically, this limit corresponds to the case where the mass density of the particles is constant and close in value to the mass density of the fluid, which is also constant. Our approach differs from the usual over-damped expansion inasmuch as we do not assume a separation of time scales between thermalization and small-scale convection effects. For a general flow in the class of incompressible zero-mean periodic velocity fields, we derive closed-form cell equations for the auxiliary quantities determining the terminal velocity and effective diffusivity. In the special case of parallel flows these equations admit explicit analytic solution. We use parallel flows to show that our approach sheds light onto the behavior of terminal velocity and effective diffusivity for Stokes numbers of the order of unity.

Forward and back diffusion through argillaceous formations

NASA Astrophysics Data System (ADS)

Yang, Minjune; Annable, Michael D.; Jawitz, James W.

2017-05-01

The exchange of solutes between aquifers and lower-permeability argillaceous formations is of considerable interest for solute and contaminant fate and transport. We present a synthesis of analytical solutions for solute diffusion between aquifers and single aquitard systems, validated in well-controlled experiments, and applied to several data sets from laboratory and field-scale problems with diffusion time and length scales ranging from 10-2 to 108 years and 10-2 to 102 m. One-dimensional diffusion models were applied using the method of images to consider the general cases of a finite aquitard bounded by two aquifers at the top and bottom, or a semiinfinite aquitard bounded by an aquifer. The simpler semiinfinite equations are appropriate for all domains with dimensionless relative diffusion length, ZD < 0.7. At dimensionless length scales above this threshold, application of semiinfinite equations to aquitards of finite thickness leads to increasing errors and solutions based on the method of images are required. Measured resident solute concentration profiles in aquitards and flux-averaged solute concentrations in surrounding aquifers were accurately modeled by appropriately accounting for generalized dynamic aquifer-aquitard boundary conditions, including concentration gradient reversals. Dimensionless diffusion length scales were used to illustrate the transferability of these relatively simple models to physical systems with dimensions that spanned 10 orders of magnitude. The results of this study offer guidance on the application of a simplified analytical approach to environmentally important layered problems with one or two diffusion interfaces.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Naughton, M.J.; Bourke, W.; Browning, G.L.

The convergence of spectral model numerical solutions of the global shallow-water equations is examined as a function of the time step and the spectral truncation. The contributions to the errors due to the spatial and temporal discretizations are separately identified and compared. Numerical convergence experiments are performed with the inviscid equations from smooth (Rossby-Haurwitz wave) and observed (R45 atmospheric analysis) initial conditions, and also with the diffusive shallow-water equations. Results are compared with the forced inviscid shallow-water equations case studied by Browning et al. Reduction of the time discretization error by the removal of fast waves from the solution usingmore » initialization is shown. The effects of forcing and diffusion on the convergence are discussed. Time truncation errors are found to dominate when a feature is large scale and well resolved; spatial truncation errors dominate for small-scale features and also for large scale after the small scales have affected them. Possible implications of these results for global atmospheric modeling are discussed. 31 refs., 14 figs., 4 tabs.« less

Characterization of Tissue Structure at Varying Length Scales Using Temporal Diffusion Spectroscopy

PubMed Central

Gore, John C.; Xu, Junzhong; Colvin, Daniel C.; Yankeelov, Thomas E.; Parsons, Edward C.; Does, Mark D.

2011-01-01

The concepts, theoretical behavior and experimental applications of temporal diffusion spectroscopy are reviewed and illustrated. Temporal diffusion spectra are obtained by using oscillating gradient waveforms in diffusion-weighted measurements, and represent the manner in which various spectral components of molecular velocity correlations vary in different geometrical structures that restrict or hinder free movements. Measurements made at different gradient frequencies reveal information on the scale of restrictions or hindrances to free diffusion, and the shape of a spectrum reveals the relative contributions of spatial restrictions at different distance scales. Such spectra differ from other so-called diffusion spectra which depict spatial frequencies and are defined at a fixed diffusion time. Experimentally, oscillating gradients at moderate frequency are more feasible for exploring restrictions at very short distances, which in tissues correspond to structures smaller than cells. We describe the underlying concepts of temporal diffusion spectra and provide analytical expressions for the behavior of the diffusion coefficient as a function of gradient frequency in simple geometries with different dimensions. Diffusion in more complex model media that mimic tissues has been simulated using numerical methods. Experimental measurements of diffusion spectra have been obtained in suspensions of particles and cells, as well as in vivo in intact animals. An observation of particular interest is the increased contrast and heterogeneity observed in tumors using oscillating gradients at moderate frequency compared to conventional pulse gradient methods, and the potential for detecting changes in tumors early in their response to treatment. Computer simulations suggest that diffusion spectral measurements may be sensitive to intracellular structures such as nuclear size, and that changes in tissue diffusion properties may be measured before there are changes in cell density. PMID:20677208

Diffusive leakage of brine from aquifers during CO2 geological storage

NASA Astrophysics Data System (ADS)

Dejam, Morteza; Hassanzadeh, Hassan

2018-01-01

The area of investigation in this study is designed around an improved understanding of fundamentals of the diffusive leakage of brine from a storage aquifer into overlying and underlying low permeability layers during geosequestration of carbon dioxide (CO2) through development of a theoretical model. Here, we consider a two-dimensional domain in cylindrical coordinates, comprised of an aquifer and an overburden, where the interaction between the two media is handled by imposing the continuities of pressures and fluid fluxes at the aquifer-overburden interface. This coupled problem is solved by successive implementation of the Laplace and finite Hankel transforms. The developed solutions can be used to analyze diffusive leakage of brine from the aquifer into overburden and generate type curves for average pressures in the aquifer and overburden during injection and post injection periods. The results show that the leakage rate at early times is scaled with t1/2 while it remains constant at late times. It is also shown that the average pressure in the aquifer is scaled with t for short and long times. Moreover, the average pressure in the overburden is scaled with t at late times while it is scaled with t3/2 at early times. In addition, the results reveal that factors affecting diffusive leakage rate through intact overburden during CO2 storage are, in decreasing order of significance, thickness of overburden, thickness of aquifer, aquifer to overburden permeability ratio, and aquifer to overburden porosity ratio. However, thickness of aquifer has minimal effect on diffusive leakage of brine within post injection period. To evaluate the theoretical model, case studies for two potential sites in United Kingdom, one in Lincolnshire and the other one in the Firth of Forth, are conducted. The field studies show that the diffusive leakage from the aquifer into the overburden diminishes ∼40 years after the injection has ceased for Lincolnshire while it stops after ∼12 years for Firth of Forth. The average amount of the brine leaked from the aquifers per standard cubic meter (Sm3) of the injected CO2 through diffusive leakage was found to be 6.28 × 10-4 m3 of brine (or 0.330 kg of brine/kg of CO2) over ∼70 years for Lincolnshire and 4.59 × 10-4 m3 of brine (or 0.242 kg of brine/kg of CO2) over ∼42 years for Firth of Forth.

The influence of cosmic rays on the stability and large-scale dynamics of the interstellar medium

NASA Astrophysics Data System (ADS)

Kuznetsov, V. D.

1986-06-01

The diffusion-convection formulation is used to study the influence of galactic cosmic rays on the stability and dynamics of the interstellar medium which is supposedly kept in equilibrium by the gravitational field of stars. It is shown that the influence of cosmic rays on the growth rate of MHD instability depends largely on a dimensionless parameter expressing the ratio of the characteristic acoustic time scale to the cosmic-ray diffusion time. If this parameter is small, the cosmic rays will decelerate the build-up of instabilities, thereby stabilizing the system; in contrast, if the parameter is large, the system will be destabilized.

Electron acceleration by an obliquely propagating electromagnetic wave in the regime of validity of the Fokker-Planck-Kolmogorov approach

NASA Technical Reports Server (NTRS)

Hizanidis, Kyriakos; Vlahos, L.; Polymilis, C.

1989-01-01

The relativistic motion of an ensemble of electrons in an intense monochromatic electromagnetic wave propagating obliquely in a uniform external magnetic field is studied. The problem is formulated from the viewpoint of Hamiltonian theory and the Fokker-Planck-Kolmogorov approach analyzed by Hizanidis (1989), leading to a one-dimensional diffusive acceleration along paths of constant zeroth-order generalized Hamiltonian. For values of the wave amplitude and the propagating angle inside the analytically predicted stochastic region, the numerical results suggest that the diffusion probes proceeds in stages. In the first stage, the electrons are accelerated to relatively high energies by sampling the first few overlapping resonances one by one. During that stage, the ensemble-average square deviation of the variable involved scales quadratically with time. During the second stage, they scale linearly with time. For much longer times, deviation from linear scaling slowly sets in.

Regimes of stability and scaling relations for the removal time in the asteroid belt: a simple kinetic model and numerical tests

NASA Astrophysics Data System (ADS)

Cubrovic, Mihailo

2005-02-01

We report on our theoretical and numerical results concerning the transport mechanisms in the asteroid belt. We first derive a simple kinetic model of chaotic diffusion and show how it gives rise to some simple correlations (but not laws) between the removal time (the time for an asteroid to experience a qualitative change of dynamical behavior and enter a wide chaotic zone) and the Lyapunov time. The correlations are shown to arise in two different regimes, characterized by exponential and power-law scalings. We also show how is the so-called “stable chaos” (exponential regime) related to anomalous diffusion. Finally, we check our results numerically and discuss their possible applications in analyzing the motion of particular asteroids.

Data assimilation experiments using diffusive back-and-forth nudging for the NEMO ocean model

NASA Astrophysics Data System (ADS)

Ruggiero, G. A.; Ourmières, Y.; Cosme, E.; Blum, J.; Auroux, D.; Verron, J.

2015-04-01

The diffusive back-and-forth nudging (DBFN) is an easy-to-implement iterative data assimilation method based on the well-known nudging method. It consists of a sequence of forward and backward model integrations, within a given time window, both of them using a feedback term to the observations. Therefore, in the DBFN, the nudging asymptotic behaviour is translated into an infinite number of iterations within a bounded time domain. In this method, the backward integration is carried out thanks to what is called backward model, which is basically the forward model with reversed time step sign. To maintain numeral stability, the diffusion terms also have their sign reversed, giving a diffusive character to the algorithm. In this article the DBFN performance to control a primitive equation ocean model is investigated. In this kind of model non-resolved scales are modelled by diffusion operators which dissipate energy that cascade from large to small scales. Thus, in this article, the DBFN approximations and their consequences for the data assimilation system set-up are analysed. Our main result is that the DBFN may provide results which are comparable to those produced by a 4Dvar implementation with a much simpler implementation and a shorter CPU time for convergence. The conducted sensitivity tests show that the 4Dvar profits of long assimilation windows to propagate surface information downwards, and that for the DBFN, it is worth using short assimilation windows to reduce the impact of diffusion-induced errors. Moreover, the DBFN is less sensitive to the first guess than the 4Dvar.

Mean Field Limits for Interacting Diffusions in a Two-Scale Potential

NASA Astrophysics Data System (ADS)

Gomes, S. N.; Pavliotis, G. A.

2018-06-01

In this paper, we study the combined mean field and homogenization limits for a system of weakly interacting diffusions moving in a two-scale, locally periodic confining potential, of the form considered in Duncan et al. (Brownian motion in an N-scale periodic potential, arXiv:1605.05854, 2016b). We show that, although the mean field and homogenization limits commute for finite times, they do not, in general, commute in the long time limit. In particular, the bifurcation diagrams for the stationary states can be different depending on the order with which we take the two limits. Furthermore, we construct the bifurcation diagram for the stationary McKean-Vlasov equation in a two-scale potential, before passing to the homogenization limit, and we analyze the effect of the multiple local minima in the confining potential on the number and the stability of stationary solutions.

Self-similar space-time evolution of an initial density discontinuity

NASA Astrophysics Data System (ADS)

Rekaa, V. L.; Pécseli, H. L.; Trulsen, J. K.

2013-07-01

The space-time evolution of an initial step-like plasma density variation is studied. We give particular attention to formulate the problem in a way that opens for the possibility of realizing the conditions experimentally. After a short transient time interval of the order of the electron plasma period, the solution is self-similar as illustrated by a video where the space-time evolution is reduced to be a function of the ratio x/t. Solutions of this form are usually found for problems without characteristic length and time scales, in our case the quasi-neutral limit. By introducing ion collisions with neutrals into the numerical analysis, we introduce a length scale, the collisional mean free path. We study the breakdown of the self-similarity of the solution as the mean free path is made shorter than the system length. Analytical results are presented for charge exchange collisions, demonstrating a short time collisionless evolution with an ensuing long time diffusive relaxation of the initial perturbation. For large times, we find a diffusion equation as the limiting analytical form for a charge-exchange collisional plasma, with a diffusion coefficient defined as the square of the ion sound speed divided by the (constant) ion collision frequency. The ion-neutral collision frequency acts as a parameter that allows a collisionless result to be obtained in one limit, while the solution of a diffusion equation is recovered in the opposite limit of large collision frequencies.

A coupled theory for chemically active and deformable solids with mass diffusion and heat conduction

NASA Astrophysics Data System (ADS)

Zhang, Xiaolong; Zhong, Zheng

2017-10-01

To analyse the frequently encountered thermo-chemo-mechanical problems in chemically active material applications, we develop a thermodynamically-consistent continuum theory of coupled deformation, mass diffusion, heat conduction and chemical reaction. Basic balance equations of force, mass and energy are presented at first, and then fully coupled constitutive laws interpreting multi-field interactions and evolving equations governing irreversible fluxes are constructed according to the energy dissipation inequality and the chemical kinetics. To consider the essential distinction between mass diffusion and chemical reactions in affecting free energy and dissipations of a highly coupled system, we regard both the concentrations of diffusive species and the extent of reaction as independent state variables. This new formulation then distinguishes between the energy contribution from the diffusive species entering the solid and that from the subsequent chemical reactions occurring among these species and the host solid, which not only interact with stresses or strains in different manners and on different time scales, but also induce different variations of solid microstructures and material properties. Taking advantage of this new description, we further establish a specialized isothermal model to predict precisely the transient chemo-mechanical response of a swelling solid with a proposed volumetric constraint that accounts for material incompressibility. Coupled kinetics is incorporated to capture the volumetric swelling of the solid caused by imbibition of external species and the simultaneous dilation arised from chemical reactions between the diffusing species and the solid. The model is then exemplified with two numerical examples of transient swelling accompanied by chemical reaction. Various ratios of characteristic times of diffusion and chemical reaction are taken into account to shed light on the dependency on kinetic time scales of evolution patterns for a diffusion-reaction controlled deformable solid.

The two-parametric scaling and new temporal asymptotic of survival probability of diffusing particle in the medium with traps.

PubMed

Arkhincheev, V E

2017-03-01

The new asymptotic behavior of the survival probability of particles in a medium with absorbing traps in an electric field has been established in two ways-by using the scaling approach and by the direct solution of the diffusion equation in the field. It has shown that at long times, this drift mechanism leads to a new temporal behavior of the survival probability of particles in a medium with absorbing traps.

The two-parametric scaling and new temporal asymptotic of survival probability of diffusing particle in the medium with traps

NASA Astrophysics Data System (ADS)

Arkhincheev, V. E.

2017-03-01

The new asymptotic behavior of the survival probability of particles in a medium with absorbing traps in an electric field has been established in two ways—by using the scaling approach and by the direct solution of the diffusion equation in the field. It has shown that at long times, this drift mechanism leads to a new temporal behavior of the survival probability of particles in a medium with absorbing traps.

Fast-dynamo action in unsteady flows and maps in three dimensions

NASA Technical Reports Server (NTRS)

Bayly, B. J.; Childress, S.

1987-01-01

Unsteady fast-dynamo action is obtained in a family of stretch-fold-shear maps applied to a spatially periodic magnetic field in three dimensions. Exponential growth of a mean field in the limit of vanishing diffusivity is demonstrated by a numerical method which alternates instantaneous deformations with molecular diffusion over a finite time interval. Analysis indicates that the dynamo is a coherent feature of the large scales, essentially independent of the cascade of structure to small scales.

Nonequilibrium scheme for computing the flux of the convection-diffusion equation in the framework of the lattice Boltzmann method.

PubMed

Chai, Zhenhua; Zhao, T S

2014-07-01

In this paper, we propose a local nonequilibrium scheme for computing the flux of the convection-diffusion equation with a source term in the framework of the multiple-relaxation-time (MRT) lattice Boltzmann method (LBM). Both the Chapman-Enskog analysis and the numerical results show that, at the diffusive scaling, the present nonequilibrium scheme has a second-order convergence rate in space. A comparison between the nonequilibrium scheme and the conventional second-order central-difference scheme indicates that, although both schemes have a second-order convergence rate in space, the present nonequilibrium scheme is more accurate than the central-difference scheme. In addition, the flux computation rendered by the present scheme also preserves the parallel computation feature of the LBM, making the scheme more efficient than conventional finite-difference schemes in the study of large-scale problems. Finally, a comparison between the single-relaxation-time model and the MRT model is also conducted, and the results show that the MRT model is more accurate than the single-relaxation-time model, both in solving the convection-diffusion equation and in computing the flux.

Effect of rotational diffusion in an orientational potential well on the point spread function of electric dipole emitters.

PubMed

Stallinga, Sjoerd

2015-02-01

A study is presented of the point spread function (PSF) of electric dipole emitters that go through a series of absorption-emission cycles while the dipole orientation is changing due to rotational diffusion within the constraint of an orientational potential well. An analytical expression for the PSF is derived valid for arbitrary orientational potential wells in the limit of image acquisition times much larger than the rotational relaxation time. This framework is used to study the effects of the direction of incidence, polarization, and degree of coherence of the illumination. In the limit of fast rotational diffusion on the scale of the fluorescence lifetime the illumination influences only the PSF height, not its shape. In the limit of slow rotational diffusion on the scale of the fluorescence lifetime there is a significant effect on the PSF shape as well, provided the illumination is (partially) coherent. For oblique incidence, illumination asymmetries can arise in the PSF that give rise to position offsets in localization based on Gaussian spot fitting. These asymmetries persist in the limit of free diffusion in a zero orientational potential well.

Subdiffusion in Membrane Permeation of Small Molecules.

PubMed

Chipot, Christophe; Comer, Jeffrey

2016-11-02

Within the solubility-diffusion model of passive membrane permeation of small molecules, translocation of the permeant across the biological membrane is traditionally assumed to obey the Smoluchowski diffusion equation, which is germane for classical diffusion on an inhomogeneous free-energy and diffusivity landscape. This equation, however, cannot accommodate subdiffusive regimes, which have long been recognized in lipid bilayer dynamics, notably in the lateral diffusion of individual lipids. Through extensive biased and unbiased molecular dynamics simulations, we show that one-dimensional translocation of methanol across a pure lipid membrane remains subdiffusive on timescales approaching typical permeation times. Analysis of permeant motion within the lipid bilayer reveals that, in the absence of a net force, the mean squared displacement depends on time as t 0.7 , in stark contrast with the conventional model, which assumes a strictly linear dependence. We further show that an alternate model using a fractional-derivative generalization of the Smoluchowski equation provides a rigorous framework for describing the motion of the permeant molecule on the pico- to nanosecond timescale. The observed subdiffusive behavior appears to emerge from a crossover between small-scale rattling of the permeant around its present position in the membrane and larger-scale displacements precipitated by the formation of transient voids.

Sub-Fickean Diffusion in a One-Dimensional Plasma Ring

NASA Astrophysics Data System (ADS)

Theisen, W. L.

2013-12-01

A one-dimensional dusty plasma ring is formed in a strongly-coupled complex plasma. The dust particles in the ring can be characterized as a one-dimensional system where the particles cannot pass each other. The particles perform random walks due to thermal motions. This single-file self diffusion is characterized by the mean-squared displacement (msd) of the individual particles which increases with time t. Diffusive processes that follow Ficks law predict that the msd increases as t, however, single-file diffusion is sub-Fickean meaning that the msd is predicted to increase as t^(1/2). Particle position data from the dusty plasma ring is analyzed to determine the scaling of the msd with time. Results are compared with predictions of single-file diffusion theory.

A method for modeling oxygen diffusion in an agent-based model with application to host-pathogen infection

DOE PAGES

Plimpton, Steven J.; Sershen, Cheryl L.; May, Elebeoba E.

2015-01-01

This paper describes a method for incorporating a diffusion field modeling oxygen usage and dispersion in a multi-scale model of Mycobacterium tuberculosis (Mtb) infection mediated granuloma formation. We implemented this method over a floating-point field to model oxygen dynamics in host tissue during chronic phase response and Mtb persistence. The method avoids the requirement of satisfying the Courant-Friedrichs-Lewy (CFL) condition, which is necessary in implementing the explicit version of the finite-difference method, but imposes an impractical bound on the time step. Instead, diffusion is modeled by a matrix-based, steady state approximate solution to the diffusion equation. Moreover, presented in figuremore » 1 is the evolution of the diffusion profiles of a containment granuloma over time.« less

Centimetre-scale electron diffusion in photoactive organic heterostructures

NASA Astrophysics Data System (ADS)

Burlingame, Quinn; Coburn, Caleb; Che, Xiaozhou; Panda, Anurag; Qu, Yue; Forrest, Stephen R.

2018-02-01

The unique properties of organic semiconductors, such as flexibility and lightness, are increasingly important for information displays, lighting and energy generation. But organics suffer from both static and dynamic disorder, and this can lead to variable-range carrier hopping, which results in notoriously poor electrical properties, with low electron and hole mobilities and correspondingly short charge-diffusion lengths of less than a micrometre. Here we demonstrate a photoactive (light-responsive) organic heterostructure comprising a thin fullerene channel sandwiched between an electron-blocking layer and a blended donor:C70 fullerene heterojunction that generates charges by dissociating excitons. Centimetre-scale diffusion of electrons is observed in the fullerene channel, and this can be fitted with a simple electron diffusion model. Our experiments enable the direct measurement of charge diffusivity in organic semiconductors, which is as high as 0.83 ± 0.07 square centimetres per second in a C60 channel at room temperature. The high diffusivity of the fullerene combined with the extraordinarily long charge-recombination time yields diffusion lengths of more than 3.5 centimetres, orders of magnitude larger than expected for an organic system.

The hydrogen diffusion in liquid aluminum alloys from ab initio molecular dynamics

NASA Astrophysics Data System (ADS)

Jakse, N.; Pasturel, A.

2014-09-01

We study the hydrogen diffusion in liquid aluminum alloys through extensive ab initio molecular dynamics simulations. At the microscopic scale, we show that the hydrogen motion is characterized by a broad distribution of spatial jumps that does not correspond to a Brownian motion. To determine the self-diffusion coefficient of hydrogen in liquid aluminum alloys, we use a generalized continuous time random walk model recently developed to describe the hydrogen diffusion in pure aluminum. In particular, we show that the model successfully accounts the effects of alloying elements on the hydrogen diffusion in agreement with experimental features.

Melt inclusion shapes: Timekeepers of short-lived giant magma bodies

DOE PAGES

Pamukcu, Ayla S.; Gualda, Guilherme A. R.; Bégué, Florence; ...

2015-09-24

The longevity of giant magma bodies in the Earth’s crust prior to eruption is poorly constrained, but recognition of short time scales by multiple methods suggests that the accumulation and eruption of these giant bodies may occur rapidly. We describe a new method that uses textures of quartz-hosted melt inclusions, determined using quantitative three-dimensional propagation phase-contrast X-ray tomography, to estimate quartz crystallization times and growth rates, and we compare the results to those from Ti diffusion profiles. We investigate three large-volume, high-silica rhyolite eruptions: the 240 ka Ohakuri-Mamaku and 26.5 ka Oruanui (Taupo Volcanic Zone, New Zealand), and the 760more » ka Bishop Tuff (California, USA). Our results show that (1) longevity estimates from melt inclusion textures and Ti diffusion profiles are comparable, (2) quartz growth rates average ∼10−12 m/s, and (3) quartz melt inclusions give decadal to centennial time scales, revealing that giant magma bodies can develop over notably short historical time scales.« less

Two-time scale subordination in physical processes with long-term memory

NASA Astrophysics Data System (ADS)

Stanislavsky, Aleksander; Weron, Karina

2008-03-01

We describe dynamical processes in continuous media with a long-term memory. Our consideration is based on a stochastic subordination idea and concerns two physical examples in detail. First we study a temporal evolution of the species concentration in a trapping reaction in which a diffusing reactant is surrounded by a sea of randomly moving traps. The analysis uses the random-variable formalism of anomalous diffusive processes. We find that the empirical trapping-reaction law, according to which the reactant concentration decreases in time as a product of an exponential and a stretched exponential function, can be explained by a two-time scale subordination of random processes. Another example is connected with a state equation for continuous media with memory. If the pressure and the density of a medium are subordinated in two different random processes, then the ordinary state equation becomes fractional with two-time scales. This allows one to arrive at the Bagley-Torvik type of state equation.

Diffuse-charge dynamics of ionic liquids in electrochemical systems.

PubMed

Zhao, Hui

2011-11-01

We employ a continuum theory of solvent-free ionic liquids accounting for both short-range electrostatic correlations and steric effects (finite ion size) [Bazant et al., Phys. Rev. Lett. 106, 046102 (2011)] to study the response of a model microelectrochemical cell to a step voltage. The model problem consists of a 1-1 symmetric ionic liquid between two parallel blocking electrodes, neglecting any transverse transport phenomena. Matched asymptotic expansions in the limit of thin double layers are applied to analyze the resulting one-dimensional equations and study the overall charge-time relation in the weakly nonlinear regime. One important conclusion is that our simple scaling analysis suggests that the length scale √(λ*(D)l*(c)) accurately characterizes the double-layer structure of ionic liquids with strong electrostatic correlations where l*(c) is the electrostatic correlation length (in contrast, the Debye screening length λ*(D) is the primary double-layer length for electrolytes) and the response time of λ(D)(*3/2)L*/(D*l(c)(1/2)) (not λ*(D)L*/D* that is the primary charging time of electrolytes) is the correct charging time scale of ionic liquids with strong electrostatic correlations where D* is the diffusivity and L* is the separation length of the cell. With these two new scales, data of both electric potential versus distance from the electrode and the total diffuse charge versus time collapse onto each individual master curve in the presence of strong electrostatic correlations. In addition, the dependance of the total diffuse charge on steric effects, short-range correlations, and driving voltages is thoroughly examined. The results from the asymptotic analysis are compared favorably with those from full numerical simulations. Finally, the absorption of excess salt by the double layer creates a depletion region outside the double layer. Such salt depletion may bring a correction to the leading order terms and break down the weakly nonlinear analysis. A criterion which justifies the weakly nonlinear analysis is verified with numerical simulations.

2ND EF Conference in Turbulent Heat Transfer, Manchester, UK 1998. Volume 1

DTIC Science & Technology

1998-06-01

study the effect of Pr on statistical properties characterizing the scalar field. Turbulent diffusivities are presented for Pr=0.1-2400. A time scale, r...can be defined from the kinetic energy, fc, and the dissipation of turbulence, e, where r = -. The observed influence of Pr (0.05-10) on a time ...dimensional, time -dependent Navier-Stokes equa- tion in a skew-symmetric form and the advection- diffusion equation. du = (u x w) - VIE - Pxex

Tuning Adsorption Duration To Control the Diffusion of a Nanoparticle in Adsorbing Polymers.

PubMed

Cao, Xue-Zheng; Merlitz, Holger; Wu, Chen-Xu

2017-06-15

Controlling the nanoparticle (NP) diffusion in polymers is a prerequisite to obtain polymer nanocomposites (PNCs) with desired dynamical and rheological properties and to achieve targeted delivery of nanomedicine in biological systems. Here we determine the suppression mechanism of direct NP-polymer attraction to hamper the NP mobility in adsorbing polymers and then quantify the dependence of the effective viscosity η eff felt by the NP on the adsorption duration τ ads of polymers on the NP using scaling theory analysis and molecular dynamics simulations. We propose and confirm that participation of adsorbed chains in the NP motion break up at time intervals beyond τ ads due to the rearrangement of polymer segments at the NP surface, which accounts for the onset of Fickian NP diffusion on a time scale of t ≈ τ ads . We develop a power law, η eff ∼ (τ ads ) ν , where ν is the scaling exponent of the dependence of polymer coil size on the chain length, which leads to a theoretical basis for the design of PNCs and nanomedicine with desired applications through tuning the polymer adsorption duration.

Time of flight imaging through scattering environments (Conference Presentation)

NASA Astrophysics Data System (ADS)

Le, Toan H.; Breitbach, Eric C.; Jackson, Jonathan A.; Velten, Andreas

2017-02-01

Light scattering is a primary obstacle to imaging in many environments. On small scales in biomedical microscopy and diffuse tomography scenarios scattering is caused by tissue. On larger scales scattering from dust and fog provide challenges to vision systems for self driving cars and naval remote imaging systems. We are developing scale models for scattering environments and investigation methods for improved imaging particularly using time of flight transient information. With the emergence of Single Photon Avalanche Diode detectors and fast semiconductor lasers, illumination and capture on picosecond timescales are becoming possible in inexpensive, compact, and robust devices. This opens up opportunities for new computational imaging techniques that make use of photon time of flight. Time of flight or range information is used in remote imaging scenarios in gated viewing and in biomedical imaging in time resolved diffuse tomography. In addition spatial filtering is popular in biomedical scenarios with structured illumination and confocal microscopy. We are presenting a combination analytical, computational, and experimental models that allow us develop and test imaging methods across scattering scenarios and scales. This framework will be used for proof of concept experiments to evaluate new computational imaging methods.

Tortuosity measurement and the effects of finite pulse widths on xenon gas diffusion NMR studies of porous media

NASA Technical Reports Server (NTRS)

Mair, R. W.; Hurlimann, M. D.; Sen, P. N.; Schwartz, L. M.; Patz, S.; Walsworth, R. L.

2001-01-01

We have extended the utility of NMR as a technique to probe porous media structure over length scales of approximately 100-2000 microm by using the spin 1/2 noble gas 129Xe imbibed into the system's pore space. Such length scales are much greater than can be probed with NMR diffusion studies of water-saturated porous media. We utilized Pulsed Gradient Spin Echo NMR measurements of the time-dependent diffusion coefficient, D(t), of the xenon gas filling the pore space to study further the measurements of both the pore surface-area-to-volume ratio, S/V(p), and the tortuosity (pore connectivity) of the medium. In uniform-size glass bead packs, we observed D(t) decreasing with increasing t, reaching an observed asymptote of approximately 0.62-0.65D(0), that could be measured over diffusion distances extending over multiple bead diameters. Measurements of D(t)/D(0) at differing gas pressures showed this tortuosity limit was not affected by changing the characteristic diffusion length of the spins during the diffusion encoding gradient pulse. This was not the case at the short time limit, where D(t)/D(0) was noticeably affected by the gas pressure in the sample. Increasing the gas pressure, and hence reducing D(0) and the diffusion during the gradient pulse served to reduce the previously observed deviation of D(t)/D(0) from the S/V(p) relation. The Pade approximation is used to interpolate between the long and short time limits in D(t). While the short time D(t) points lay above the interpolation line in the case of small beads, due to diffusion during the gradient pulse on the order of the pore size, it was also noted that the experimental D(t) data fell below the Pade line in the case of large beads, most likely due to finite size effects.

Diffusive flux in a model of stochastically gated oxygen transport in insect respiration

DOE Office of Scientific and Technical Information (OSTI.GOV)

Berezhkovskii, Alexander M.; Shvartsman, Stanislav Y.

Oxygen delivery to insect tissues is controlled by transport through a branched tubular network that is connected to the atmosphere by valve-like gates, known as spiracles. In certain physiological regimes, the spiracles appear to be randomly switching between open and closed states. Quantitative analysis of this regime leads a reaction-diffusion problem with stochastically switching boundary condition. We derive an expression for the diffusive flux at long times in this problem. Our approach starts with the derivation of the passage probability for a single particle that diffuses between a stochastically gated boundary, which models the opening and closing spiracle, and themore » perfectly absorbing boundary, which models oxygen absorption by the tissue. This passage probability is then used to derive an expression giving the diffusive flux as a function of the geometric parameters of the tube and characteristic time scales of diffusion and gate dynamics.« less

Diffusive flux in a model of stochastically gated oxygen transport in insect respiration.

PubMed

Berezhkovskii, Alexander M; Shvartsman, Stanislav Y

2016-05-28

Oxygen delivery to insect tissues is controlled by transport through a branched tubular network that is connected to the atmosphere by valve-like gates, known as spiracles. In certain physiological regimes, the spiracles appear to be randomly switching between open and closed states. Quantitative analysis of this regime leads a reaction-diffusion problem with stochastically switching boundary condition. We derive an expression for the diffusive flux at long times in this problem. Our approach starts with the derivation of the passage probability for a single particle that diffuses between a stochastically gated boundary, which models the opening and closing spiracle, and the perfectly absorbing boundary, which models oxygen absorption by the tissue. This passage probability is then used to derive an expression giving the diffusive flux as a function of the geometric parameters of the tube and characteristic time scales of diffusion and gate dynamics.

Expanding the calculation of activation volumes: Self-diffusion in liquid water

NASA Astrophysics Data System (ADS)

Piskulich, Zeke A.; Mesele, Oluwaseun O.; Thompson, Ward H.

2018-04-01

A general method for calculating the dependence of dynamical time scales on macroscopic thermodynamic variables from a single set of simulations is presented. The approach is applied to the pressure dependence of the self-diffusion coefficient of liquid water as a particularly useful illustration. It is shown how the activation volume associated with diffusion can be obtained directly from simulations at a single pressure, avoiding approximations that are typically invoked.

Revisiting the time until fixation of a neutral mutant in a finite population - A coalescent theory approach.

PubMed

Greenbaum, Gili

2015-09-07

Evaluation of the time scale of the fixation of neutral mutations is crucial to the theoretical understanding of the role of neutral mutations in evolution. Diffusion approximations of the Wright-Fisher model are most often used to derive analytic formulations of genetic drift, as well as for the time scales of the fixation of neutral mutations. These approximations require a set of assumptions, most notably that genetic drift is a stochastic process in a continuous allele-frequency space, an assumption appropriate for large populations. Here equivalent approximations are derived using a coalescent theory approach which relies on a different set of assumptions than the diffusion approach, and adopts a discrete allele-frequency space. Solutions for the mean and variance of the time to fixation of a neutral mutation derived from the two approaches converge for large populations but slightly differ for small populations. A Markov chain analysis of the Wright-Fisher model for small populations is used to evaluate the solutions obtained, showing that both the mean and the variance are better approximated by the coalescent approach. The coalescence approximation represents a tighter upper-bound for the mean time to fixation than the diffusion approximation, while the diffusion approximation and coalescence approximation form an upper and lower bound, respectively, for the variance. The converging solutions and the small deviations of the two approaches strongly validate the use of diffusion approximations, but suggest that coalescent theory can provide more accurate approximations for small populations. Copyright © 2015 Elsevier Ltd. All rights reserved.

Fractional Brownian motion run with a multi-scaling clock mimics diffusion of spherical colloids in microstructural fluids.

PubMed

Park, Moongyu; Cushman, John Howard; O'Malley, Dan

2014-09-30

The collective molecular reorientations within a nematic liquid crystal fluid bathing a spherical colloid cause the colloid to diffuse anomalously on a short time scale (i.e., as a non-Brownian particle). The deformations and fluctuations of long-range orientational order in the liquid crystal profoundly influence the transient diffusive regimes. Here we show that an anisotropic fractional Brownian process run with a nonlinear multiscaling clock effectively mimics this collective and transient phenomenon. This novel process has memory, Gaussian increments, and a multiscale mean square displacement that can be chosen independently from the fractal dimension of a particle trajectory. The process is capable of modeling multiscale sub-, super-, or classical diffusion. The finite-size Lyapunov exponents for this multiscaling process are defined for future analysis of related mixing processes.

Nanorod Mobility within Entangled Wormlike Micelle Solutions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lee, Jonghun; Grein-Iankovski, Aline; Narayanan, Suresh

In the semi-dilute regime, wormlike micelles form an isotropic entangled microstructure that is similar to that of an entangled polymer solution with a characteristic, nanometer-scale entanglement mesh size. We report a combined x-ray photon correlation spectroscopy (XPCS) and rheology study to investigate the translational dynamics of gold nanorods in semi-dilute solutions of entangled wormlike micelles formed by the surfactant cetylpyridinium chloride (CPyCl) and the counter-ion sodium salicylate (NaSal). The CPyCl concentration is varied to tune the entanglement mesh size over a range that spans from approximately equal to the nanorod diameter to larger than the nanorod length. The NaSal concentrationmore » is varied along with the CPyCl concentration so that the solutions have the maximum viscosity for given CPyCl concentration. On short time scales the nanorods are localized on a length scale matching that expected from the high-frequency elastic modulus of the solutions as long as the mesh size is smaller than the rod length. On longer time scales, the nanorods undergo free diffusion. At the highest CPyCl concentrations, the nanorod diffusivity approaches the value expected based on the macroscopic viscosity of the solutions, but it increases with decreasing CPyCl concentration more rapidly than expected from the macroscopic viscosity. A recent model by Cai et al. [Cai, L.-H.; Panyukov, S.; Rubinstein, M. Macromolecules 2015, 48, 847-862.] for nanoparticle “hopping” diffusion in entangled polymer solutions accounts quantitatively for this enhanced diffusivity.« less

Nanorod Mobility within Entangled Wormlike Micelle Solutions

DOE PAGES

Lee, Jonghun; Grein-Iankovski, Aline; Narayanan, Suresh; ...

2016-12-20

In the semi-dilute regime, wormlike micelles form an isotropic entangled microstructure that is similar to that of an entangled polymer solution with a characteristic, nanometer-scale entanglement mesh size. We report a combined x-ray photon correlation spectroscopy (XPCS) and rheology study to investigate the translational dynamics of gold nanorods in semi-dilute solutions of entangled wormlike micelles formed by the surfactant cetylpyridinium chloride (CPyCl) and the counter-ion sodium salicylate (NaSal). The CPyCl concentration is varied to tune the entanglement mesh size over a range that spans from approximately equal to the nanorod diameter to larger than the nanorod length. The NaSal concentrationmore » is varied along with the CPyCl concentration so that the solutions have the maximum viscosity for given CPyCl concentration. On short time scales the nanorods are localized on a length scale matching that expected from the high-frequency elastic modulus of the solutions as long as the mesh size is smaller than the rod length. On longer time scales, the nanorods undergo free diffusion. At the highest CPyCl concentrations, the nanorod diffusivity approaches the value expected based on the macroscopic viscosity of the solutions, but it increases with decreasing CPyCl concentration more rapidly than expected from the macroscopic viscosity. A recent model by Cai et al. [Cai, L.-H.; Panyukov, S.; Rubinstein, M. Macromolecules 2015, 48, 847-862.] for nanoparticle “hopping” diffusion in entangled polymer solutions accounts quantitatively for this enhanced diffusivity.« less

Analytical approach to impurity transport studies: Charge state dynamics in tokamak plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shurygin, V. A.

2006-08-15

Ionization and recombination of plasma impurities govern their charge state kinetics, which is imposed upon the dynamics of ions that implies a superposition of the appropriate probabilities and causes an impurity charge state dynamics. The latter is considered in terms of a vector field of conditional probabilities and presented by a vector charge state distribution function with coupled equations of the Kolmogorov type. Analytical solutions of a diffusion problem are derived with the basic spatial and temporal dimensionless parameters. Analysis shows that the empirical scaling D{sub A}{proportional_to}n{sub e}{sup -1} [K. Krieger, G. Fussmann, and the ASDEX Upgrade Team, Nucl. Fusionmore » 30, 2392 (1990)] can be explained by the ratio of the diffusive and kinetic terms, D{sub A}/(n{sub e}a{sup 2}), being used instead of diffusivity, D{sub A}. The derived time scales of charge state dynamics are given by a sum of the diffusive and kinetic times. Detailed simulations of charge state dynamics are performed for argon impurity and compared with the reference modeling.« less

Under What Conditions Can Equilibrium Gas-Particle Partitioning Be Expected to Hold in the Atmosphere?

PubMed

Mai, Huajun; Shiraiwa, Manabu; Flagan, Richard C; Seinfeld, John H

2015-10-06

The prevailing treatment of secondary organic aerosol formation in atmospheric models is based on the assumption of instantaneous gas-particle equilibrium for the condensing species, yet compelling experimental evidence indicates that organic aerosols can exhibit the properties of highly viscous, semisolid particles, for which gas-particle equilibrium may be achieved slowly. The approach to gas-particle equilibrium partitioning is controlled by gas-phase diffusion, interfacial transport, and particle-phase diffusion. Here we evaluate the controlling processes and the time scale to achieve gas-particle equilibrium as a function of the volatility of the condensing species, its surface accommodation coefficient, and its particle-phase diffusivity. For particles in the size range of typical atmospheric organic aerosols (∼50-500 nm), the time scale to establish gas-particle equilibrium is generally governed either by interfacial accommodation or particle-phase diffusion. The rate of approach to equilibrium varies, depending on whether the bulk vapor concentration is constant, typical of an open system, or decreasing as a result of condensation into the particles, typical of a closed system.

Stochastic modeling of experimental chaotic time series.

PubMed

Stemler, Thomas; Werner, Johannes P; Benner, Hartmut; Just, Wolfram

2007-01-26

Methods developed recently to obtain stochastic models of low-dimensional chaotic systems are tested in electronic circuit experiments. We demonstrate that reliable drift and diffusion coefficients can be obtained even when no excessive time scale separation occurs. Crisis induced intermittent motion can be described in terms of a stochastic model showing tunneling which is dominated by state space dependent diffusion. Analytical solutions of the corresponding Fokker-Planck equation are in excellent agreement with experimental data.

Scaling Law for Cross-stream Diffusion in Microchannels under Combined Electroosmotic and Pressure Driven Flow.

PubMed

Song, Hongjun; Wang, Yi; Pant, Kapil

2013-01-01

This paper presents an analytical study of the cross-stream diffusion of an analyte in a rectangular microchannel under combined electroosmotic flow (EOF) and pressure driven flow to investigate the heterogeneous transport behavior and spatially-dependent diffusion scaling law. An analytical model capable of accurately describing 3D steady-state convection-diffusion in microchannels with arbitrary aspect ratios is developed based on the assumption of the thin Electric Double Layer (EDL). The model is verified against high-fidelity numerical simulation in terms of flow velocity and analyte concentration profiles with excellent agreement (<0.5% relative error). An extensive parametric analysis is then undertaken to interrogate the effect of the combined flow velocity field on the transport behavior in both the positive pressure gradient (PPG) and negative pressure gradient (NPG) cases. For the first time, the evolution from the spindle-shaped concentration profile in the PPG case, via the stripe-shaped profile (pure EOF), and finally to the butterfly-shaped profile in the PPG case is obtained using the analytical model along with a quantitative depiction of the spatially-dependent diffusion layer thickness and scaling law across a wide range of the parameter space.

Scaling Law for Cross-stream Diffusion in Microchannels under Combined Electroosmotic and Pressure Driven Flow

PubMed Central

Song, Hongjun; Wang, Yi; Pant, Kapil

2012-01-01

This paper presents an analytical study of the cross-stream diffusion of an analyte in a rectangular microchannel under combined electroosmotic flow (EOF) and pressure driven flow to investigate the heterogeneous transport behavior and spatially-dependent diffusion scaling law. An analytical model capable of accurately describing 3D steady-state convection-diffusion in microchannels with arbitrary aspect ratios is developed based on the assumption of the thin Electric Double Layer (EDL). The model is verified against high-fidelity numerical simulation in terms of flow velocity and analyte concentration profiles with excellent agreement (<0.5% relative error). An extensive parametric analysis is then undertaken to interrogate the effect of the combined flow velocity field on the transport behavior in both the positive pressure gradient (PPG) and negative pressure gradient (NPG) cases. For the first time, the evolution from the spindle-shaped concentration profile in the PPG case, via the stripe-shaped profile (pure EOF), and finally to the butterfly-shaped profile in the PPG case is obtained using the analytical model along with a quantitative depiction of the spatially-dependent diffusion layer thickness and scaling law across a wide range of the parameter space. PMID:23554584

Violation of Field Line Conservation and Associated Spatial Scales in Particle-in-Cell Simulations and MMS Data

NASA Astrophysics Data System (ADS)

Wendel, D. E.; Liu, Y. H.; Giles, B. L.; Torbert, R. B.

2017-12-01

For the first time, space flight technology exists to detect, in situ, violation of magnetic field line conservation. The violation of magnetic line conservation on scales smaller than the system size is a necessary and sufficient condition for magnetic reconnection. We demonstrate that violation of line conservation produces a detectable, structured signature in both particle-in-cell simulations of reconnection and in data from the Magnetospheric Multi-Scale mission. In particle-in-cell simulations of asymmetric reconnection, the quantity-which we call M-that identifies this violation achieves a significant value in electron skin depth-scale layers that extend from the electron diffusion region along the separatrices, with higher values emerging on the low density, high magnetic field side of the current sheet. In two MMS burst data intervals associated with detection of the electron diffusion region—one interval with antiparallel reconnecting fields and the other with a guide field-we determine the location and scale of M and of the diffusion region relative to electron outflows and the magnetic separatrices. We find that M exceeds measurement uncertainties both at the diffusion region and near the separatrices, where it attains its highest values in layered structures. The observed magnitude scales as the simulated magnitude after adjusting for the artificial parameters of the simulation. Bipolar forms of the quantity also appear further from the diffusion region, possibly associated with electron holes. The measure serves not only as a powerful diagnostic for magnetic reconnection, but reveals that electrons transport this signature of reconnection away from the x-line.

Two reference time scales for studying the dynamic cavitation of liquid films

NASA Technical Reports Server (NTRS)

Sun, D. C.; Brewe, D. E.

1992-01-01

Two formulas, one for the characteristic time of filling a void with the vapor of the surrounding liquid, and one of filling the void by diffusion of the dissolved gas in the liquid, are derived. By comparing these time scales with that of the dynamic operation of oil film bearings, it is concluded that the evaporation process is usually fast enough to fill the cavitation bubble with oil vapor; whereas the diffusion process is much too slow for the dissolved air to liberate itself and enter the cavitation bubble. These results imply that the formation of a two phase fluid in dynamically loaded bearings, as often reported in the literature, is caused by air entrainment. They further indicate a way to simplify the treatment of the dynamic problem of bubble evolution.

Asymptotic Analysis of Time-Dependent Neutron Transport Coupled with Isotopic Depletion and Radioactive Decay

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brantley, P S

2006-09-27

We describe an asymptotic analysis of the coupled nonlinear system of equations describing time-dependent three-dimensional monoenergetic neutron transport and isotopic depletion and radioactive decay. The classic asymptotic diffusion scaling of Larsen and Keller [1], along with a consistent small scaling of the terms describing the radioactive decay of isotopes, is applied to this coupled nonlinear system of equations in a medium of specified initial isotopic composition. The analysis demonstrates that to leading order the neutron transport equation limits to the standard time-dependent neutron diffusion equation with macroscopic cross sections whose number densities are determined by the standard system of ordinarymore » differential equations, the so-called Bateman equations, describing the temporal evolution of the nuclide number densities.« less

Diagnosing isopycnal diffusivity in an eddying, idealized midlatitude ocean basin via Lagrangian, in Situ, Global, High-Performance Particle Tracking (LIGHT)

DOE PAGES

Wolfram, Phillip J.; Ringler, Todd D.; Maltrud, Mathew E.; ...

2015-08-01

Isopycnal diffusivity due to stirring by mesoscale eddies in an idealized, wind-forced, eddying, midlatitude ocean basin is computed using Lagrangian, in Situ, Global, High-Performance Particle Tracking (LIGHT). Simulation is performed via LIGHT within the Model for Prediction across Scales Ocean (MPAS-O). Simulations are performed at 4-, 8-, 16-, and 32-km resolution, where the first Rossby radius of deformation (RRD) is approximately 30 km. Scalar and tensor diffusivities are estimated at each resolution based on 30 ensemble members using particle cluster statistics. Each ensemble member is composed of 303 665 particles distributed across five potential density surfaces. Diffusivity dependence upon modelmore » resolution, velocity spatial scale, and buoyancy surface is quantified and compared with mixing length theory. The spatial structure of diffusivity ranges over approximately two orders of magnitude with values of O(10 5) m 2 s –1 in the region of western boundary current separation to O(10 3) m 2 s –1 in the eastern region of the basin. Dominant mixing occurs at scales twice the size of the first RRD. Model resolution at scales finer than the RRD is necessary to obtain sufficient model fidelity at scales between one and four RRD to accurately represent mixing. Mixing length scaling with eddy kinetic energy and the Lagrangian time scale yield mixing efficiencies that typically range between 0.4 and 0.8. In conclusion, a reduced mixing length in the eastern region of the domain relative to the west suggests there are different mixing regimes outside the baroclinic jet region.« less

Slow-Down in Diffusion in Crowded Protein Solutions Correlates with Transient Cluster Formation.

PubMed

Nawrocki, Grzegorz; Wang, Po-Hung; Yu, Isseki; Sugita, Yuji; Feig, Michael

2017-12-14

For a long time, the effect of a crowded cellular environment on protein dynamics has been largely ignored. Recent experiments indicate that proteins diffuse more slowly in a living cell than in a diluted solution, and further studies suggest that the diffusion depends on the local surroundings. Here, detailed insight into how diffusion depends on protein-protein contacts is presented based on extensive all-atom molecular dynamics simulations of concentrated villin headpiece solutions. After force field adjustments in the form of increased protein-water interactions to reproduce experimental data, translational and rotational diffusion was analyzed in detail. Although internal protein dynamics remained largely unaltered, rotational diffusion was found to slow down more significantly than translational diffusion as the protein concentration increased. The decrease in diffusion is interpreted in terms of a transient formation of protein clusters. These clusters persist on sub-microsecond time scales and follow distributions that increasingly shift toward larger cluster size with increasing protein concentrations. Weighting diffusion coefficients estimated for different clusters extracted from the simulations with the distribution of clusters largely reproduces the overall observed diffusion rates, suggesting that transient cluster formation is a primary cause for a slow-down in diffusion upon crowding with other proteins.

Performance of the fixed-bed of granular activated carbon for the removal of pesticides from water supply.

PubMed

Alves, Alcione Aparecida de Almeida; Ruiz, Giselle Louise de Oliveira; Nonato, Thyara Campos Martins; Müller, Laura Cecilia; Sens, Maurício Luiz

2018-02-26

The application of a fixed bed adsorption column of granular activated carbon (FBAC-GAC), in the removal of carbaryl, methomyl and carbofuran at a concentration of 25 μg L -1 for each carbamate, from the public water supply was investigated. For the determination of the presence of pesticides in the water supply, the analytical technique of high-performance liquid chromatography with post-column derivatization was used. Under conditions of constant diffusivity, the FBAC-GAC was saturated after 196 h of operation on a pilot scale. The exhaust rate of the granular activated carbon (GAC) in the FBAC-GAC until the point of saturation was 0.02 kg GAC m -3 of treated water. By comparing a rapid small-scale column test and FBAC-GAC, it was confirmed that the predominant intraparticle diffusivity in the adsorption column was constant diffusivity. Based on the results obtained on a pilot scale, it was possible to estimate the values to be applied in the FBAC-GAC (full scale) to remove the pesticides, which are particle size with an average diameter of 1.5 mm GAC; relationship between the internal diameter of the column and the average diameter of GAC ≥50 in order to avoid preferential flow near the adsorption column wall; surface application rate 240 m 3  m -2  d -1 and an empty bed contact time of 3 min. BV: bed volume; CD: constant diffusivity; EBCT: empty bed contact time; FBAC-GAC: fixed bed adsorption column of granular activated carbon; GAC: granular activated carbon; MPV: maximum permitted values; NOM: natural organic matter; PD: proportional diffusivity; pH PCZ : pH of the zero charge point; SAR: surface application rate; RSSCT: rapid small-scale column test; WTCS: water treated conventional system.

Investigating the Eddy Diffusivity Concept in the Coastal Ocean

NASA Astrophysics Data System (ADS)

Rypina, I.; Kirincich, A.; Lentz, S. J.; Sundermeyer, M. A.

2016-12-01

We test the validity, utility, and limitations of the lateral eddy diffusivity concept in a coastal environment through analyzing data from coupled drifter and dye releases within the footprint of a high-resolution (800 m) high-frequency radar south of Martha's Vineyard, Massachusetts. Specifically, we investigate how well a combination of radar-based velocities and drifter-derived diffusivities can reproduce observed dye spreading over an 8-h time interval. A drifter-based estimate of an anisotropic diffusivity tensor is used to parameterize small-scale motions that are unresolved and under-resolved by the radar system. This leads to a significant improvement in the ability of the radar to reproduce the observed dye spreading. Our drifter-derived diffusivity estimates are O(10 m2/s), are consistent with the diffusivity inferred from aerial images of the dye taken using the quadcopter-mounted digital camera during the dye release, and are roughly an order of magnitude larger than diffusivity estimates of Okubo (O(1 m2/s)) for similar spatial scales ( 1 km). Despite the fact that the drifter-based diffusivity approach was successful in improving the ability of the radar to reproduce the observed dye spreading, the dispersion of drifters was, for the most part, not consistent with the diffusive spreading regime.

Multi-scale modeling of diffusion-controlled reactions in polymers: renormalisation of reactivity parameters.

PubMed

Everaers, Ralf; Rosa, Angelo

2012-01-07

The quantitative description of polymeric systems requires hierarchical modeling schemes, which bridge the gap between the atomic scale, relevant to chemical or biomolecular reactions, and the macromolecular scale, where the longest relaxation modes occur. Here, we use the formalism for diffusion-controlled reactions in polymers developed by Wilemski, Fixman, and Doi to discuss the renormalisation of the reactivity parameters in polymer models with varying spatial resolution. In particular, we show that the adjustments are independent of chain length. As a consequence, it is possible to match reactions times between descriptions with different resolution for relatively short reference chains and to use the coarse-grained model to make quantitative predictions for longer chains. We illustrate our results by a detailed discussion of the classical problem of chain cyclization in the Rouse model, which offers the simplest example of a multi-scale descriptions, if we consider differently discretized Rouse models for the same physical system. Moreover, we are able to explore different combinations of compact and non-compact diffusion in the local and large-scale dynamics by varying the embedding dimension.

Oxidation mechanism of T91 steel in liquid lead-bismuth eutectic: with consideration of internal oxidation

PubMed Central

Ye, Zhongfei; Wang, Pei; Dong, Hong; Li, Dianzhong; Zhang, Yutuo; Li, Yiyi

2016-01-01

Clarification of the microscopic events that occur during oxidation is of great importance for understanding and consequently controlling the oxidation process. In this study the oxidation product formed on T91 ferritic/martensitic steel in oxygen saturated liquid lead-bismuth eutectic (LBE) at 823 K was characterized at the nanoscale using focused-ion beam and transmission electron microscope. An internal oxidation zone (IOZ) under the duplex oxide scale has been confirmed and characterized systematically. Through the microscopic characterization of the IOZ and the inner oxide layer, the micron-scale and nano-scale diffusion of Cr during the oxidation in LBE has been determined for the first time. The micron-scale diffusion of Cr ensures the continuous advancement of IOZ and inner oxide layer, and nano-scale diffusion of Cr gives rise to the typical appearance of the IOZ. Finally, a refined oxidation mechanism including the internal oxidation and the transformation of IOZ to inner oxide layer is proposed based on the discussion. The proposed oxidation mechanism succeeds in bridging the gap between the existing models and experimental observations. PMID:27734928

Revealing mesoscopic structural universality with diffusion.

PubMed

Novikov, Dmitry S; Jensen, Jens H; Helpern, Joseph A; Fieremans, Els

2014-04-08

Measuring molecular diffusion is widely used for characterizing materials and living organisms noninvasively. This characterization relies on relations between macroscopic diffusion metrics and structure at the mesoscopic scale commensurate with the diffusion length. Establishing such relations remains a fundamental challenge, hindering progress in materials science, porous media, and biomedical imaging. Here we show that the dynamical exponent in the time dependence of the diffusion coefficient distinguishes between the universality classes of the mesoscopic structural complexity. Our approach enables the interpretation of diffusion measurements by objectively selecting and modeling the most relevant structural features. As an example, the specific values of the dynamical exponent allow us to identify the relevant mesoscopic structure affecting MRI-measured water diffusion in muscles and in brain, and to elucidate the structural changes behind the decrease of diffusion coefficient in ischemic stroke.

Field-scale effective matrix diffusion coefficient for fractured rock: results from literature survey.

PubMed

Zhou, Quanlin; Liu, Hui-Hai; Molz, Fred J; Zhang, Yingqi; Bodvarsson, Gudmundur S

2007-08-15

Matrix diffusion is an important mechanism for solute transport in fractured rock. We recently conducted a literature survey on the effective matrix diffusion coefficient, D(m)(e), a key parameter for describing matrix diffusion processes at the field scale. Forty field tracer tests at 15 fractured geologic sites were surveyed and selected for the study, based on data availability and quality. Field-scale D(m)(e) values were calculated, either directly using data reported in the literature, or by reanalyzing the corresponding field tracer tests. The reanalysis was conducted for the selected tracer tests using analytic or semi-analytic solutions for tracer transport in linear, radial, or interwell flow fields. Surveyed data show that the scale factor of the effective matrix diffusion coefficient (defined as the ratio of D(m)(e) to the lab-scale matrix diffusion coefficient, D(m), of the same tracer) is generally larger than one, indicating that the effective matrix diffusion coefficient in the field is comparatively larger than the matrix diffusion coefficient at the rock-core scale. This larger value can be attributed to the many mass-transfer processes at different scales in naturally heterogeneous, fractured rock systems. Furthermore, we observed a moderate, on average trend toward systematic increase in the scale factor with observation scale. This trend suggests that the effective matrix diffusion coefficient is likely to be statistically scale-dependent. The scale-factor value ranges from 0.5 to 884 for observation scales from 5 to 2000 m. At a given scale, the scale factor varies by two orders of magnitude, reflecting the influence of differing degrees of fractured rock heterogeneity at different geologic sites. In addition, the surveyed data indicate that field-scale longitudinal dispersivity generally increases with observation scale, which is consistent with previous studies. The scale-dependent field-scale matrix diffusion coefficient (and dispersivity) may have significant implications for assessing long-term, large-scale radionuclide and contaminant transport events in fractured rock, both for nuclear waste disposal and contaminant remediation.

Spectral Analysis and Computation of Effective Diffusivities for Steady Random Flows

DTIC Science & Technology

2016-04-28

even in the motion of sea ice floes influenced by winds and ocean currents. The long time, large scale behavior of such systems is equivalent to an...flow plays a key role in many important processes in the global climate system [55] and Earth’s ecosys- tems [14]. Advection of geophysical fluids...HOMOGENIZATION OF THE ADVECTION-DIFFUSION EQUATION The dispersion of a cloud of passive scalars with density φ diffusing with molecular dif- fusivity ε and

Transport and Lagrangian Statistics in Rotating Stratified Turbulence

NASA Astrophysics Data System (ADS)

Rosenberg, D. L.

2015-12-01

Transport plays a crucial role in geophysical flows, both in theatmosphere and in the ocean. Transport in such flows is ultimatelycontrolled by small-scale turbulence, although the large scales arein geostrophic balance between pressure gradient, gravity and Coriolisforces. As a result of the seemingly random nature of the flow, singleparticles are dispersed by the flow and on time scales significantlylonger than the eddy turn-over time, they undergo a diffusive motionwhose diffusion coefficient is the integral of the velocity correlationfunction. On intermediate time scales, in homogeneous, isotropic turbuilence(HIT) the separation between particle pairs has been argued to grow withtime according to the Richardson law: <(Δ x)2(t)> ~ t3, with aproportionality constant that depends on the initial particleseparation. The description of the phenomena associated withthe dispersion of single particles, or of particle pairs, ultimatelyrests on relatively simple statistical properties of the flowvelocity transporting the particles, in particular on its temporalcorrelation function. In this work, we investigate particle dispersionin the anisotropic case of rotating stratified turbulence examining whetherthe dependence on initial particle separation differs from HIT,particularly in the presence of an inverse cascade.

Hydrogen diffusion in liquid aluminum from ab initio molecular dynamics

NASA Astrophysics Data System (ADS)

Jakse, N.; Pasturel, A.

2014-05-01

Ab initio molecular dynamics simulations are used to describe the diffusion of hydrogen in liquid aluminum at different temperatures. Quasi-instantaneous jumps separating periods of localized vibrations around a mean position are found to characterize the hydrogen motion at the microscopic scale. The hydrogen motion is furthermore analyzed using the van Hove function. We highlight a non-Fickian behavior for the hydrogen diffusion due to a large spatial distribution of hydrogen jumps. We show that a generalized continuous time random walk (CTRW) model describes the experimental diffusion coefficients in a satisfactory manner. Finally, the impact of impurities and alloying elements on hydrogen diffusion in aluminum is discussed.

Interstitial and Interlayer Ion Diffusion Geometry Extraction in Graphitic Nanosphere Battery Materials.

PubMed

Gyulassy, Attila; Knoll, Aaron; Lau, Kah Chun; Wang, Bei; Bremer, Peer-Timo; Papka, Michael E; Curtiss, Larry A; Pascucci, Valerio

2016-01-01

Large-scale molecular dynamics (MD) simulations are commonly used for simulating the synthesis and ion diffusion of battery materials. A good battery anode material is determined by its capacity to store ion or other diffusers. However, modeling of ion diffusion dynamics and transport properties at large length and long time scales would be impossible with current MD codes. To analyze the fundamental properties of these materials, therefore, we turn to geometric and topological analysis of their structure. In this paper, we apply a novel technique inspired by discrete Morse theory to the Delaunay triangulation of the simulated geometry of a thermally annealed carbon nanosphere. We utilize our computed structures to drive further geometric analysis to extract the interstitial diffusion structure as a single mesh. Our results provide a new approach to analyze the geometry of the simulated carbon nanosphere, and new insights into the role of carbon defect size and distribution in determining the charge capacity and charge dynamics of these carbon based battery materials.

Interstitial and Interlayer Ion Diffusion Geometry Extraction in Graphitic Nanosphere Battery Materials

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gyulassy, Attila; Knoll, Aaron; Lau, Kah Chun

2016-01-01

Large-scale molecular dynamics (MD) simulations are commonly used for simulating the synthesis and ion diffusion of battery materials. A good battery anode material is determined by its capacity to store ion or other diffusers. However, modeling of ion diffusion dynamics and transport properties at large length and long time scales would be impossible with current MD codes. To analyze the fundamental properties of these materials, therefore, we turn to geometric and topological analysis of their structure. In this paper, we apply a novel technique inspired by discrete Morse theory to the Delaunay triangulation of the simulated geometry of a thermallymore » annealed carbon nanosphere. We utilize our computed structures to drive further geometric analysis to extract the interstitial diffusion structure as a single mesh. Our results provide a new approach to analyze the geometry of the simulated carbon nanosphere, and new insights into the role of carbon defect size and distribution in determining the charge capacity and charge dynamics of these carbon based battery materials.« less

Interstitial and interlayer ion diffusion geometry extraction in graphitic nanosphere battery materials

DOE PAGES

Gyulassy, Attila; Knoll, Aaron; Lau, Kah Chun; ...

2016-01-31

Large-scale molecular dynamics (MD) simulations are commonly used for simulating the synthesis and ion diffusion of battery materials. A good battery anode material is determined by its capacity to store ion or other diffusers. However, modeling of ion diffusion dynamics and transport properties at large length and long time scales would be impossible with current MD codes. To analyze the fundamental properties of these materials, therefore, we turn to geometric and topological analysis of their structure. In this paper, we apply a novel technique inspired by discrete Morse theory to the Delaunay triangulation of the simulated geometry of a thermallymore » annealed carbon nanosphere. We utilize our computed structures to drive further geometric analysis to extract the interstitial diffusion structure as a single mesh. Lastly, our results provide a new approach to analyze the geometry of the simulated carbon nanosphere, and new insights into the role of carbon defect size and distribution in determining the charge capacity and charge dynamics of these carbon based battery materials.« less

Real scale experimental study for performance evaluation of unidirectional air diffuser perforated panels

NASA Astrophysics Data System (ADS)

Tăcutu, Laurenţiu; Nastase, Ilinca; Iordache, Vlad; Catalina, Tiberiu; Croitoru, Cristiana Verona

2018-02-01

Nowadays, there is an increasing emphasis on indoor air quality due to technological evolution and the fact that people spend most of the time in enclosed spaces. Also, energy efficiency is another related factor that gains more and more attention. Improving air distribution in an enclosure can lead to achieve these goals. This improvement can be done by adjustingthe air terminals position, theredimensions or the air diffuser perforations. The paper presents the study of 8 types of panels with different perforations shapes. The systems were characterized by flow, pressure loss and noise. Usualand special geometries were chosen, all having the same flowsurface. The perforated panels were mounted in a unidirectional air flow (UAF)diffuser, also called a laminar air flow (LAF)diffuser, that is placed in a real scale operating room (OR) in our laboratory.The purpose of this study is to determine whether changing the shape in the perforated panels can improve the technical parameters of the diffuser.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wolfram, Phillip J.; Ringler, Todd D.; Maltrud, Mathew E.

Isopycnal diffusivity due to stirring by mesoscale eddies in an idealized, wind-forced, eddying, midlatitude ocean basin is computed using Lagrangian, in Situ, Global, High-Performance Particle Tracking (LIGHT). Simulation is performed via LIGHT within the Model for Prediction across Scales Ocean (MPAS-O). Simulations are performed at 4-, 8-, 16-, and 32-km resolution, where the first Rossby radius of deformation (RRD) is approximately 30 km. Scalar and tensor diffusivities are estimated at each resolution based on 30 ensemble members using particle cluster statistics. Each ensemble member is composed of 303 665 particles distributed across five potential density surfaces. Diffusivity dependence upon modelmore » resolution, velocity spatial scale, and buoyancy surface is quantified and compared with mixing length theory. The spatial structure of diffusivity ranges over approximately two orders of magnitude with values of O(10 5) m 2 s –1 in the region of western boundary current separation to O(10 3) m 2 s –1 in the eastern region of the basin. Dominant mixing occurs at scales twice the size of the first RRD. Model resolution at scales finer than the RRD is necessary to obtain sufficient model fidelity at scales between one and four RRD to accurately represent mixing. Mixing length scaling with eddy kinetic energy and the Lagrangian time scale yield mixing efficiencies that typically range between 0.4 and 0.8. In conclusion, a reduced mixing length in the eastern region of the domain relative to the west suggests there are different mixing regimes outside the baroclinic jet region.« less

Realizing the electric-vehicle revolution

NASA Astrophysics Data System (ADS)

Tran, Martino; Banister, David; Bishop, Justin D. K.; McCulloch, Malcolm D.

2012-05-01

Full battery electric vehicles (BEVs) have become an important policy option to mitigate climate change, but there are major uncertainties in the scale and timing of market diffusion. Although there has been substantial work showing the potential energy and climate benefits of BEVs, demand-side factors, such as consumer behaviour, are less recognized in the debate. We show the importance of assessing BEV diffusion from an integrated perspective, focusing on key interactions between technology and behaviour across different scales, including power-system demand, charging infrastructure, vehicle performance, driving patterns and individual adoption behaviour.

Transition from large-scale to small-scale dynamo.

PubMed

Ponty, Y; Plunian, F

2011-04-15

The dynamo equations are solved numerically with a helical forcing corresponding to the Roberts flow. In the fully turbulent regime the flow behaves as a Roberts flow on long time scales, plus turbulent fluctuations at short time scales. The dynamo onset is controlled by the long time scales of the flow, in agreement with the former Karlsruhe experimental results. The dynamo mechanism is governed by a generalized α effect, which includes both the usual α effect and turbulent diffusion, plus all higher order effects. Beyond the onset we find that this generalized α effect scales as O(Rm(-1)), suggesting the takeover of small-scale dynamo action. This is confirmed by simulations in which dynamo occurs even if the large-scale field is artificially suppressed.

Evidence for Enhanced Matrix Diffusion in Geological Environment

NASA Astrophysics Data System (ADS)

Sato, Kiminori; Fujimoto, Koichiro; Nakata, Masataka; Shikazono, Naotatsu

2013-01-01

Molecular diffusion in rock matrix, called as matrix diffusion, has been appreciated as a static process for elemental migration in geological environment that has been acknowledged in the context of geological disposal of radioactive waste. However, incomprehensible enhancement of matrix diffusion has been reported at a number of field test sites. Here, the matrix diffusion of saline water at Horonobe, Hokkaido, Japan is highlighted directly probing angstrom-scale pores on a field scale up to 1 km by positron--positronium annihilation spectroscopy. The first application of positron--positronium annihilation spectroscopy to field-scale geophysical research reveals the slight variation of angstrom-scale pores influenced by saline water diffusion with complete accuracy. We found widely interconnected 3 Å pores, which offer the pathway of saline water diffusion with the highly enhanced effective matrix diffusion coefficient of 4× 10-6 cm2 s-1. The present findings provide unambiguous evidence that the angstrom-scale pores enhance effective matrix diffusion on a field scale in geological environment.

Effective matrix diffusion in kilometer‐scale transport in fractured crystalline rock

USGS Publications Warehouse

Shapiro, Allen M.

2001-01-01

Concentrations of tritium (3H) and dichlorodifluoromethane (CFC‐12) in water samples taken from glacial drift and fractured crystalline rock over 4 km2 in central New Hampshire are interpreted to identify a conceptual model of matrix diffusion and the magnitude of the diffusion coefficient. Dispersion and mass transfer to and from fractures has affected the 3H concentration to the extent that the peak 3H concentration of the 1960s is no longer distinguishable. Because of heterogeneity in the bedrock the sparsely distributed chemical data do not warrant a three‐dimensional transport model. Instead, a one‐dimensional model of CFC‐12 and 3H migration along flow lines in the glacial drift and bedrock is used to place bounds on the processes affecting kilometer‐scale transport, arid model parameters are varied to reproduce the measured relation between 3H and CFC‐12, rather than their spatial distributions. A model of mass exchange to and from fractures that is dependent on the time‐varying concentration gradient at fracture surfaces qualitatively reproduces the measured relation between 3H and CFC‐12 with an upper bound for the fracture dispersivity approximately equal to 250 m and a lower bound for the effective matrix diffusion coefficient equal to 1 m2 yr−1. The diffusion coefficient at the kilometer scale is at least 3 orders of magnitude greater than laboratory estimates of diffusion in crystalline rock. The large diffusion coefficient indicates that diffusion into an immobile fluid phase (rock matrix) is masked at the kilometer scale by advective mass exchange between fractures with large contrasts in trarismissivity. The measured transmissivity of fractures in the study area varies over more than 6 orders of magnitude. Advective mass exchange from high‐permeability fractures to low‐permeability fractures results in short migration distances of a chemical constituent in low‐permeability fractures over an extended period of time before reentering high‐permeability fractures; viewed at the kilometer scale, this process is analogous to the chemical constituent diffusing into and out of an immobile fluid phase.

An asymptotic-preserving stochastic Galerkin method for the radiative heat transfer equations with random inputs and diffusive scalings

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jin, Shi, E-mail: sjin@wisc.edu; Institute of Natural Sciences, Department of Mathematics, MOE-LSEC and SHL-MAC, Shanghai Jiao Tong University, Shanghai 200240; Lu, Hanqing, E-mail: hanqing@math.wisc.edu

2017-04-01

In this paper, we develop an Asymptotic-Preserving (AP) stochastic Galerkin scheme for the radiative heat transfer equations with random inputs and diffusive scalings. In this problem the random inputs arise due to uncertainties in cross section, initial data or boundary data. We use the generalized polynomial chaos based stochastic Galerkin (gPC-SG) method, which is combined with the micro–macro decomposition based deterministic AP framework in order to handle efficiently the diffusive regime. For linearized problem we prove the regularity of the solution in the random space and consequently the spectral accuracy of the gPC-SG method. We also prove the uniform (inmore » the mean free path) linear stability for the space-time discretizations. Several numerical tests are presented to show the efficiency and accuracy of proposed scheme, especially in the diffusive regime.« less

Future trends in transport and fate of diffuse contaminants in catchments, with special emphasis on stable isotope applications

USGS Publications Warehouse

Turner, J.; Albrechtsen, H.-J.; Bonell, M.; Duguet, J.-P.; Harris, B.; Meckenstock, R.; McGuire, K.; Moussa, R.; Peters, N.; Richnow, H.H.; Sherwood-Lollar, B.; Uhlenbrook, S.; van, Lanen H.

2006-01-01

A summary is provided of the first of a series of proposed Integrated Science Initiative workshops supported by the UNESCO International Hydrological Programme. The workshop brought together hydrologists, environmental chemists, microbiologists, stable isotope specialists and natural resource managers with the purpose of communicating new ideas on ways to assess microbial degradation processes and reactive transport at catchment scales. The focus was on diffuse contamination at catchment scales and the application of compound-specific isotope analysis (CSIA) in the assessment of biological degradation processes of agrochemicals. Major outcomes were identifying the linkage between water residence time distribution and rates of contaminant degradation, identifying the need for better information on compound specific microbial degradation isotope fractionation factors and the potential of CSIA in identifying key degradative processes. In the natural resource management context, a framework was developed where CSIA techniques were identified as practically unique in their capacity to serve as distributed integrating indicators of process across a range of scales (micro to diffuse) of relevance to the problem of diffuse pollution assessment. Copyright ?? 2006 John Wiley & Sons, Ltd.

Technical report series on global modeling and data assimilation. Volume 2: Direct solution of the implicit formulation of fourth order horizontal diffusion for gridpoint models on the sphere

NASA Technical Reports Server (NTRS)

Li, Yong; Moorthi, S.; Bates, J. Ray; Suarez, Max J.

1994-01-01

High order horizontal diffusion of the form K Delta(exp 2m) is widely used in spectral models as a means of preventing energy accumulation at the shortest resolved scales. In the spectral context, an implicit formation of such diffusion is trivial to implement. The present note describes an efficient method of implementing implicit high order diffusion in global finite difference models. The method expresses the high order diffusion equation as a sequence of equations involving Delta(exp 2). The solution is obtained by combining fast Fourier transforms in longitude with a finite difference solver for the second order ordinary differential equation in latitude. The implicit diffusion routine is suitable for use in any finite difference global model that uses a regular latitude/longitude grid. The absence of a restriction on the timestep makes it particularly suitable for use in semi-Lagrangian models. The scale selectivity of the high order diffusion gives it an advantage over the uncentering method that has been used to control computational noise in two-time-level semi-Lagrangian models.

Characteristic Time Scales of Characteristic Magmatic Processes and Systems

NASA Astrophysics Data System (ADS)

Marsh, B. D.

2004-05-01

Every specific magmatic process, regardless of spatial scale, has an associated characteristic time scale. Time scales associated with crystals alone are rates of growth, dissolution, settling, aggregation, annealing, and nucleation, among others. At the other extreme are the time scales associated with the dynamics of the entire magmatic system. These can be separated into two groups: those associated with system genetics (e.g., the production and transport of magma, establishment of the magmatic system) and those due to physical characteristics of the established system (e.g., wall rock failure, solidification front propagation and instability, porous flow). The detailed geometry of a specific magmatic system is particularly important to appreciate; although generic systems are useful, care must be taken to make model systems as absolutely realistic as possible. Fuzzy models produce fuzzy science. Knowledge of specific time scales is not necessarily useful or meaningful unless the hierarchical context of the time scales for a realistic magmatic system is appreciated. The age of a specific phenocryst or ensemble of phenocrysts, as determined from isotopic or CSD studies, is not meaningful unless something can be ascertained of the provenance of the crystals. For example, crystal size multiplied by growth rate gives a meaningful crystal age only if it is from a part of the system that has experienced semi-monotonic cooling prior to chilling; crystals entrained from a long-standing cumulate bed that were mechanically sorted in ascending magma may not reveal this history. Ragged old crystals rolling about in the system for untold numbers of flushing times record specious process times, telling more about the noise in the system than the life of typical, first generation crystallization processes. The most helpful process-related time scales are those that are known well and that bound or define the temporal style of the system. Perhaps the most valuable of these times comes from the observed durations and rates of volcanism. There can be little doubt that the temporal styles of volcanism are the same as those of magmatism in general. Volcano repose times, periodicity, eruptive fluxes, acoustic emission structures, lava volumes, longevity, etc. must also be characteristic of pluton-dominated systems. We must therefore give up some classical concepts (e.g., instantaneous injection of crystal-free magma as an initial condition) for any plutonic/chambered system and move towards an integrated concept of magmatism. Among the host of process-related time scales, probably the three most fundamental of any magmatic system are (1) the time scale associated with crystal nucleation (J) and growth (G) (tx}=C{1(G3 J)-{1}/4; Zieg & Marsh, J. Pet. 02') along with the associated scales for mean crystal size (L) and population (N), (2) the time scale associated with conductive cooling controlled by a local length scale (d) (tc}=C{2 d2/K; K is thermal diffusivity), and (3) the time scale associated with intra-crystal diffusion (td}=C{3 L2/D; D is chemical diffusivity). It is the subtle, clever, and insightful application of time scales, dovetailed with realistic system geometry and attention paid to the analogous time scales of volcanism, that promises to reveal the true dynamic integration of magmatic systems.

Differential water sorption studies on Kevlar 49 and As-polymerized poly(p-phenylene terephthalamide): determination of water transport properties.

PubMed

Mooney, Damian A; MacElroy, J M Don

2007-11-06

Water vapor sorption experiments have been conducted on Kevlar 49 at 30 degrees C over a range of water vapor pressures in 0-90% of saturation and on the as-polymerized form of the material at 30, 45, and 60 degrees C over a series of water vapor pressures of 0-60%, 0-25%, and 0-15%, respectively. For each of the differential steps in water vapor pressure, dynamic uptake curves were generated and analyzed according to a number of different mathematical models, including Fickian, Coaxial cylindrical, and intercalation models. The intercalation model was demonstrated to be the most successful model and considered two time-scales involved in the diffusion process, i.e., a penetrant-diffusive time-scale and a polymer-local-matrix-relaxation time-scale. The success of this model reinforces previously reported adsorption and desorption isotherms which suggested that water may penetrate into the surface layers of the polymer crystallite through a process known as intercalation.

Particle dynamics in a viscously decaying cat's eye: The effect of finite Schmidt numbers

NASA Astrophysics Data System (ADS)

Newton, P. K.; Meiburg, Eckart

1991-05-01

The dynamics and mixing of passive marker particles for the model problem of a decaying cat's eye flow is studied. The flow field corresponds to Stuart's one-parameter family of solutions [J. Fluid Mech. 29, 417 (1967)]. It is time dependent as a result of viscosity, which is modeled by allowing the free parameter to depend on time according to the self-similar solution of the Navier-Stokes equations for an isolated point vortex. Particle diffusion is numerically simulated by a random walk model. While earlier work had shown that, for small values of time over Reynolds number t/Re≪1, the interval length characterizing the formation of lobes of fluid escaping from the cat's eye scales as Re-1/2, the present study shows that, for the case of diffusive effects and t/Pe≪1, the scaling follows Pe-1/4. A simple argument, taking into account streamline convergence and divergence in different parts of the flow field, explains the Pe-1/4 scaling.

Dynamics of a magnetic active Brownian particle under a uniform magnetic field.

PubMed

Vidal-Urquiza, Glenn C; Córdova-Figueroa, Ubaldo M

2017-11-01

The dynamics of a magnetic active Brownian particle undergoing three-dimensional Brownian motion, both translation and rotation, under the influence of a uniform magnetic field is investigated. The particle self-propels at a constant speed along its magnetic dipole moment, which reorients due to the interplay between Brownian and magnetic torques, quantified by the Langevin parameter α. In this work, the time-dependent active diffusivity and the crossover time (τ^{cross})-from ballistic to diffusive regimes-are calculated through the time-dependent correlation function of the fluctuations of the propulsion direction. The results reveal that, for any value of α, the particle undergoes a directional (or ballistic) propulsive motion at very short times (t≪τ^{cross}). In this regime, the correlation function decreases linearly with time, and the active diffusivity increases with it. It the opposite time limit (t≫τ^{cross}), the particle moves in a purely diffusive regime with a correlation function that decays asymptotically to zero and an active diffusivity that reaches a constant value equal to the long-time active diffusivity of the particle. As expected in the absence of a magnetic field (α=0), the crossover time is equal to the characteristic time scale for rotational diffusion, τ_{rot}. In the presence of a magnetic field (α>0), the correlation function, the active diffusivity, and the crossover time decrease with increasing α. The magnetic field regulates the regimes of propulsion of the particle. Here, the field reduces the period of time at which the active particle undergoes a directional motion. Consequently, the active particle rapidly reaches a diffusive regime at τ^{cross}≪τ_{rot}. In the limit of weak fields (α≪1), the crossover time decreases quadratically with α, while in the limit of strong fields (α≫1) it decays asymptotically as α^{-1}. The results are in excellent agreement with those obtained by Brownian dynamics simulations.

Dynamics of a magnetic active Brownian particle under a uniform magnetic field

NASA Astrophysics Data System (ADS)

Vidal-Urquiza, Glenn C.; Córdova-Figueroa, Ubaldo M.

2017-11-01

The dynamics of a magnetic active Brownian particle undergoing three-dimensional Brownian motion, both translation and rotation, under the influence of a uniform magnetic field is investigated. The particle self-propels at a constant speed along its magnetic dipole moment, which reorients due to the interplay between Brownian and magnetic torques, quantified by the Langevin parameter α . In this work, the time-dependent active diffusivity and the crossover time (τcross)—from ballistic to diffusive regimes—are calculated through the time-dependent correlation function of the fluctuations of the propulsion direction. The results reveal that, for any value of α , the particle undergoes a directional (or ballistic) propulsive motion at very short times (t ≪τcross ). In this regime, the correlation function decreases linearly with time, and the active diffusivity increases with it. It the opposite time limit (t ≫τcross ), the particle moves in a purely diffusive regime with a correlation function that decays asymptotically to zero and an active diffusivity that reaches a constant value equal to the long-time active diffusivity of the particle. As expected in the absence of a magnetic field (α =0 ), the crossover time is equal to the characteristic time scale for rotational diffusion, τrot. In the presence of a magnetic field (α >0 ), the correlation function, the active diffusivity, and the crossover time decrease with increasing α . The magnetic field regulates the regimes of propulsion of the particle. Here, the field reduces the period of time at which the active particle undergoes a directional motion. Consequently, the active particle rapidly reaches a diffusive regime at τcross≪τrot . In the limit of weak fields (α ≪1 ), the crossover time decreases quadratically with α , while in the limit of strong fields (α ≫1 ) it decays asymptotically as α-1. The results are in excellent agreement with those obtained by Brownian dynamics simulations.

Dynamic cross-correlations between entangled biofilaments as they diffuse

PubMed Central

Tsang, Boyce; Dell, Zachary E.; Jiang, Lingxiang; Schweizer, Kenneth S.; Granick, Steve

2017-01-01

Entanglement in polymer and biological physics involves a state in which linear interthreaded macromolecules in isotropic liquids diffuse in a spatially anisotropic manner beyond a characteristic mesoscopic time and length scale (tube diameter). The physical reason is that linear macromolecules become transiently localized in directions transverse to their backbone but diffuse with relative ease parallel to it. Within the resulting broad spectrum of relaxation times there is an extended period before the longest relaxation time when filaments occupy a time-averaged cylindrical space of near-constant density. Here we show its implication with experiments based on fluorescence tracking of dilutely labeled macromolecules. The entangled pairs of aqueous F-actin biofilaments diffuse with separation-dependent dynamic cross-correlations that exceed those expected from continuum hydrodynamics up to strikingly large spatial distances of ≈15 µm, which is more than 104 times the size of the solvent water molecules in which they are dissolved, and is more than 50 times the dynamic tube diameter, but is almost equal to the filament length. Modeling this entangled system as a collection of rigid rods, we present a statistical mechanical theory that predicts these long-range dynamic correlations as an emergent consequence of an effective long-range interpolymer repulsion due to the de Gennes correlation hole, which is a combined consequence of chain connectivity and uncrossability. The key physical assumption needed to make theory and experiment agree is that solutions of entangled biofilaments localized in tubes that are effectively dynamically incompressible over the relevant intermediate time and length scales. PMID:28283664

Seasonal to multi-decadal trends in apparent optical properties in the Sargasso Sea

NASA Astrophysics Data System (ADS)

Allen, James G.; Nelson, Norman B.; Siegel, David A.

2017-01-01

Multi-decadal, monthly observations of optical and biogeochemical properties, made as part of the Bermuda Bio-Optics Project (BBOP) at the Bermuda Atlantic Time-series Study (BATS) site in the Sargasso Sea, allow for the examination of temporal trends in vertical light attenuation and their potential controls. Trends in the magnitude of the diffuse attenuation coefficient, Kd(λ), and a proxy for its spectral shape reflect changes in phytoplankton and chromophoric dissolved organic matter (CDOM) characteristics. The length and methodological consistency of this time series provide an excellent opportunity to extend analyses of seasonal cycles of apparent optical properties to interannual and decadal time scales. Here, we characterize changes in the magnitude and spectral shape proxy of diffuse attenuation coefficient spectra and compare them to available biological and optical data from the BATS time series program. The time series analyses reveal a 1.01%±0.18% annual increase of the magnitude of the diffuse attenuation coefficient at 443 nm over the upper 75 m of the water column while showing no significant change in selected spectral characteristics over the study period. These and other observations indicate that changes in phytoplankton rather than changes in CDOM abundance are the primary driver for the diffuse attenuation trends on multi-year timescales for this region. Our findings are inconsistent with previous decadal-scale global ocean water clarity and global satellite ocean color analyses yet are consistent with recent analyses of the BATS time series and highlight the value of long-term consistent observation at ocean time series sites.

An exact and efficient first passage time algorithm for reaction-diffusion processes on a 2D-lattice

NASA Astrophysics Data System (ADS)

Bezzola, Andri; Bales, Benjamin B.; Alkire, Richard C.; Petzold, Linda R.

2014-01-01

We present an exact and efficient algorithm for reaction-diffusion-nucleation processes on a 2D-lattice. The algorithm makes use of first passage time (FPT) to replace the computationally intensive simulation of diffusion hops in KMC by larger jumps when particles are far away from step-edges or other particles. Our approach computes exact probability distributions of jump times and target locations in a closed-form formula, based on the eigenvectors and eigenvalues of the corresponding 1D transition matrix, maintaining atomic-scale resolution of resulting shapes of deposit islands. We have applied our method to three different test cases of electrodeposition: pure diffusional aggregation for large ranges of diffusivity rates and for simulation domain sizes of up to 4096×4096 sites, the effect of diffusivity on island shapes and sizes in combination with a KMC edge diffusion, and the calculation of an exclusion zone in front of a step-edge, confirming statistical equivalence to standard KMC simulations. The algorithm achieves significant speedup compared to standard KMC for cases where particles diffuse over long distances before nucleating with other particles or being captured by larger islands.

Two-photon time-lapse microscopy of BODIPY-cholesterol reveals anomalous sterol diffusion in chinese hamster ovary cells

PubMed Central

2012-01-01

Background Cholesterol is an important membrane component, but our knowledge about its transport in cells is sparse. Previous imaging studies using dehydroergosterol (DHE), an intrinsically fluorescent sterol from yeast, have established that vesicular and non-vesicular transport modes contribute to sterol trafficking from the plasma membrane. Significant photobleaching, however, limits the possibilities for in-depth analysis of sterol dynamics using DHE. Co-trafficking studies with DHE and the recently introduced fluorescent cholesterol analog BODIPY-cholesterol (BChol) suggested that the latter probe has utility for prolonged live-cell imaging of sterol transport. Results We found that BChol is very photostable under two-photon (2P)-excitation allowing the acquisition of several hundred frames without significant photobleaching. Therefore, long-term tracking and diffusion measurements are possible. Two-photon temporal image correlation spectroscopy (2P-TICS) provided evidence for spatially heterogeneous diffusion constants of BChol varying over two orders of magnitude from the cell interior towards the plasma membrane, where D ~ 1.3 μm2/s. Number and brightness (N&B) analysis together with stochastic simulations suggest that transient partitioning of BChol into convoluted membranes slows local sterol diffusion. We observed sterol endocytosis as well as fusion and fission of sterol-containing endocytic vesicles. The mobility of endocytic vesicles, as studied by particle tracking, is well described by a model for anomalous subdiffusion on short time scales with an anomalous exponent α ~ 0.63 and an anomalous diffusion constant of Dα = 1.95 x 10-3 μm2/sα. On a longer time scale (t > ~5 s), a transition to superdiffusion consistent with slow directed transport with an average velocity of v ~ 6 x 10-3 μm/s was observed. We present an analytical model that bridges the two regimes and fit this model to vesicle trajectories from control cells and cells with disrupted microtubule or actin filaments. Both treatments reduced the anomalous diffusion constant and the velocity by ~40-50%. Conclusions The mobility of sterol-containing vesicles on the short time scale could reflect dynamic rearrangements of the cytoskeleton, while directed transport of sterol vesicles occurs likely along both, microtubules and actin filaments. Spatially varying anomalous diffusion could contribute to fine-tuning and local regulation of intracellular sterol transport. PMID:23078907

Ameba-like diffusion in two-dimensional polymer melts: how critical exponents determine the structural relaxation

NASA Astrophysics Data System (ADS)

Kreer, Torsten; Meyer, Hendrik; Baschnagel, Joerg

2008-03-01

By means of numerical investigations we demonstrate that the structural relaxation of linear polymers in two dimensional (space-filling) melts is characterized by ameba-like diffusion, where the chains relax via frictional dissipation at their interfacial contact lines. The perimeter length of the contact line determines a new length scale, which does not exist in three dimensions. We show how this length scale follows from the critical exponents, which hence characterize not only the static but also the dynamic properties of the melt. Our data is in agreement with recent theoretical predictions, concerning the time-dependence of single-monomer mean-square displacements and the scaling of concomitant relaxation times with the degree of polymerization. For the latter we demonstrate a density crossover-scaling as an additional test for ameba-like relaxation. We compare our results to the conceptually different Rouse model, which predicts numerically close exponents. Our data can clearly rule out the classical picture as the relevant relaxation mechanism in two-dimensional polymer melts.

Density scaling on n  =  1 error field penetration in ohmically heated discharges in EAST

NASA Astrophysics Data System (ADS)

Wang, Hui-Hui; Sun, You-Wen; Shi, Tong-Hui; Zang, Qing; Liu, Yue-Qiang; Yang, Xu; Gu, Shuai; He, Kai-Yang; Gu, Xiang; Qian, Jin-Ping; Shen, Biao; Luo, Zheng-Ping; Chu, Nan; Jia, Man-Ni; Sheng, Zhi-Cai; Liu, Hai-Qing; Gong, Xian-Zu; Wan, Bao-Nian; Contributors, EAST

2018-05-01

Density scaling of error field penetration in EAST is investigated with different n  =  1 magnetic perturbation coil configurations in ohmically heated discharges. The density scalings of error field penetration thresholds under two magnetic perturbation spectra are br\\propto n_e0.5 and br\\propto n_e0.6 , where b r is the error field and n e is the line averaged electron density. One difficulty in understanding the density scaling is that key parameters other than density in determining the field penetration process may also be changed when the plasma density changes. Therefore, they should be determined from experiments. The estimated theoretical analysis (br\\propto n_e0.54 in lower density region and br\\propto n_e0.40 in higher density region), using the density dependence of viscosity diffusion time, electron temperature and mode frequency measured from the experiments, is consistent with the observed scaling. One of the key points to reproduce the observed scaling in EAST is that the viscosity diffusion time estimated from energy confinement time is almost constant. It means that the plasma confinement lies in saturation ohmic confinement regime rather than the linear Neo-Alcator regime causing weak density dependence in the previous theoretical studies.

Modelling accelerated degradation data using Wiener diffusion with a time scale transformation.

PubMed

Whitmore, G A; Schenkelberg, F

1997-01-01

Engineering degradation tests allow industry to assess the potential life span of long-life products that do not fail readily under accelerated conditions in life tests. A general statistical model is presented here for performance degradation of an item of equipment. The degradation process in the model is taken to be a Wiener diffusion process with a time scale transformation. The model incorporates Arrhenius extrapolation for high stress testing. The lifetime of an item is defined as the time until performance deteriorates to a specified failure threshold. The model can be used to predict the lifetime of an item or the extent of degradation of an item at a specified future time. Inference methods for the model parameters, based on accelerated degradation test data, are presented. The model and inference methods are illustrated with a case application involving self-regulating heating cables. The paper also discusses a number of practical issues encountered in applications.

Strange kinetics of bulk-mediated diffusion on lipid bilayers

PubMed Central

Campagnola, Grace; Nepal, Kanti; Peersen, Olve B.

2016-01-01

Diffusion at solid-liquid interfaces is crucial in many technological and biophysical processes. Although its behavior seems deceivingly simple, recent studies showing passive superdiffusive transport suggest diffusion on surfaces may hide rich complexities. In particular, bulk-mediated diffusion occurs when molecules are transiently released from the surface to perform three-dimensional excursions into the liquid bulk. This phenomenon bears the dichotomy where a molecule always return to the surface but the mean jump length is infinite. Such behavior is associated with a breakdown of the central limit theorem and weak ergodicity breaking. Here, we use single-particle tracking to study the statistics of bulk-mediated diffusion on a supported lipid bilayer. We find that the time-averaged mean square displacement (MSD) of individual trajectories, the archetypal measure in diffusion processes, does not converge to the ensemble MSD but it remains a random variable, even in the long observation-time limit. The distribution of time averages is shown to agree with a Lévy flight model. Our results also unravel intriguing anomalies in the statistics of displacements. The time averaged MSD is shown to depend on experimental time and investigations of fractional moments show a scaling 〈|r(t)|q〉 ∼ tqv(q) with non-linear exponents, i.e. v(q) ≠ const. This type of behavior is termed strong anomalous diffusion and is rare among experimental observations. PMID:27095275

Identifying time scales for violation/preservation of Stokes-Einstein relation in supercooled water

PubMed Central

Kawasaki, Takeshi; Kim, Kang

2017-01-01

The violation of the Stokes-Einstein (SE) relation D ~ (η/T)−1 between the shear viscosity η and the translational diffusion constant D at temperature T is of great importance for characterizing anomalous dynamics of supercooled water. Determining which time scales play key roles in the SE violation remains elusive without the measurement of η. We provide comprehensive simulation results of the dynamic properties involving η and D in the TIP4P/2005 supercooled water. This enabled the thorough identification of the appropriate time scales for the SE relation Dη/T. In particular, it is demonstrated that the temperature dependence of various time scales associated with structural relaxation, hydrogen bond breakage, stress relaxation, and dynamic heterogeneities can be definitely classified into only two classes. That is, we propose the generalized SE relations that exhibit “violation” or “preservation.” The classification depends on the examined time scales that are coupled or decoupled with the diffusion. On the basis of the classification, we explain the physical origins of the violation in terms of the increase in the plateau modulus and the nonexponentiality of stress relaxation. This implies that the mechanism of SE violation is attributed to the attained solidity upon supercooling, which is in accord with the growth of non-Gaussianity and spatially heterogeneous dynamics. PMID:28835918

Stellar differential rotation and coronal time-scales

NASA Astrophysics Data System (ADS)

Gibb, G. P. S.; Jardine, M. M.; Mackay, D. H.

2014-10-01

We investigate the time-scales of evolution of stellar coronae in response to surface differential rotation and diffusion. To quantify this, we study both the formation time and lifetime of a magnetic flux rope in a decaying bipolar active region. We apply a magnetic flux transport model to prescribe the evolution of the stellar photospheric field, and use this to drive the evolution of the coronal magnetic field via a magnetofrictional technique. Increasing the differential rotation (i.e. decreasing the equator-pole lap time) decreases the flux rope formation time. We find that the formation time is dependent upon the lap time and the surface diffusion time-scale through the relation τ_Form ∝ √{τ_Lapτ_Diff}. In contrast, the lifetimes of flux ropes are proportional to the lap time (τLife∝τLap). With this, flux ropes on stars with a differential rotation of more than eight times the solar value have a lifetime of less than 2 d. As a consequence, we propose that features such as solar-like quiescent prominences may not be easily observable on such stars, as the lifetimes of the flux ropes which host the cool plasma are very short. We conclude that such high differential rotation stars may have very dynamical coronae.

Enhancement of diffusive transport in oscillatory flows

NASA Technical Reports Server (NTRS)

Knobloch, E.; Merryfield, W. J.

1992-01-01

The theory of transport of passive scalars in oscillatory flows is reexamined. The differences between transport in standing and traveling waves are emphasized. Both Lagrangian and Eulerian diffusivities are calculated, and the conditions for their applicability are discussed. Numerical simulations are conducted to understand the expulsion of gradients from time-dependent eddies and the resulting transport. The results indicate that it is the Eulerian diffusivity that is of primary relevance for describing enhanced transport on spatial scales larger than that of the eddies.

Connecting the molecular scale to the continuum scale for diffusion processes in smectite-rich porous media.

PubMed

Bourg, Ian C; Sposito, Garrison

2010-03-15

In this paper, we address the manner in which the continuum-scale diffusive properties of smectite-rich porous media arise from their molecular- and pore-scale features. Our starting point is a successful model of the continuum-scale apparent diffusion coefficient for water tracers and cations, which decomposes it as a sum of pore-scale terms describing diffusion in macropore and interlayer "compartments." We then apply molecular dynamics (MD) simulations to determine molecular-scale diffusion coefficients D(interlayer) of water tracers and representative cations (Na(+), Cs(+), Sr(2+)) in Na-smectite interlayers. We find that a remarkably simple expression relates D(interlayer) to the pore-scale parameter δ(nanopore) ≤ 1, a constrictivity factor that accounts for the lower mobility in interlayers as compared to macropores: δ(nanopore) = D(interlayer)/D(0), where D(0) is the diffusion coefficient in bulk liquid water. Using this scaling expression, we can accurately predict the apparent diffusion coefficients of tracers H(2)0, Na(+), Sr(2+), and Cs(+) in compacted Na-smectite-rich materials.

Diffusion of flexible, charged, nanoscopic molecules in solution: Size and pH dependence for PAMAM dendrimer

NASA Astrophysics Data System (ADS)

Maiti, Prabal K.; Bagchi, Biman

2009-12-01

In order to understand self-diffusion (D) of a charged, flexible, and porous nanoscopic molecule in water, we carry out very long, fully atomistic molecular dynamics simulation of PAMAM dendrimer up to eight generations in explicit salt water under varying pH. We find that while the radius of gyration (Rg) varies as N1/3, the self-diffusion constant (D ) scales, surprisingly, as N-α, with α =0.39 at high pH and 0.5 at neutral pH, indicating a dramatic breakdown of Stokes-Einstein relation for diffusion of charged nanoscopic molecules. The variation in D as a function of radius of gyration demonstrates the importance of treating water and ions explicitly in the diffusion process of a flexible nanoscopic molecule. In agreement with recent experiments, the self-diffusion constant increases with pH, revealing the importance of dielectric friction in the diffusion process. The shape of a dendrimer is found to fluctuate on a nanosecond time scale. We argue that this flexibility (and also the porosity) of the dendrimer may play an important role in determining the mean square displacement of the dendrimer and the breakdown of the Stokes-Einstein relation between diffusion constant and the radius.

Self diffusion of interacting membrane proteins.

PubMed Central

Abney, J R; Scalettar, B A; Owicki, J C

1989-01-01

A two-dimensional version of the generalized Smoluchowski equation is used to analyze the time (or distance) dependent self diffusion of interacting membrane proteins in concentrated membrane systems. This equation provides a well established starting point for descriptions of the diffusion of particles that interact through both direct and hydrodynamic forces; in this initial work only the effects of direct interactions are explicitly considered. Data describing diffusion in the presence of hard-core repulsions, soft repulsions, and soft repulsions with weak attractions are presented. The effect that interactions have on the self-diffusion coefficient of a real protein molecule from mouse liver gap junctions is also calculated. The results indicate that self diffusion is always inhibited by direct interactions; this observation is interpreted in terms of the caging that will exist at finite protein concentration. It is also noted that, over small distance scales, the diffusion coefficient is determined entirely by the very strong Brownian forces; therefore, as a function of displacement the self-diffusion coefficient decays (rapidly) from its value at infinite dilution to its steady-state interaction-averaged value. The steady-state self-diffusion coefficient describes motion over distance scales that range from approximately 10 nm to cellular dimensions and is the quantity measured in fluorescence recovery after photobleaching experiments. The short-ranged behavior of the diffusion coefficient is important on the interparticle-distance scale and may therefore influence the rate at which nearest-neighbor collisional processes take place. The hard-disk theoretical results presented here are in excellent agreement with lattice Monte-Carlo results obtained by other workers. The concentration dependence of experimentally measured diffusion coefficients of antibody-hapten complexes bound to the membrane surface is consistent with that predicted by the theory. The variation in experimental diffusion coefficients of integral membrane proteins is greater than that predicted by the theory, and may also reflect protein-induced perturbations in membrane viscosity. PMID:2720077

ANALYTIC FORMS OF THE PERPENDICULAR DIFFUSION COEFFICIENT IN NRMHD TURBULENCE

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shalchi, A., E-mail: andreasm4@yahoo.com

2015-02-01

In the past different analytic limits for the perpendicular diffusion coefficient of energetic particles interacting with magnetic turbulence were discussed. These different limits or cases correspond to different transport modes describing how the particles are diffusing across the large-scale magnetic field. In the current paper we describe a new transport regime by considering the model of noisy reduced magnetohydrodynamic turbulence. We derive different analytic forms of the perpendicular diffusion coefficient, and while we do this, we focus on the aforementioned new transport mode. We show that for this turbulence model a small perpendicular diffusion coefficient can be obtained so thatmore » the latter diffusion coefficient is more than hundred times smaller than the parallel diffusion coefficient. This result is relevant to explain observations in the solar system where such small perpendicular diffusion coefficients have been reported.« less

Revealing mesoscopic structural universality with diffusion

PubMed Central

Novikov, Dmitry S.; Jensen, Jens H.; Helpern, Joseph A.; Fieremans, Els

2014-01-01

Measuring molecular diffusion is widely used for characterizing materials and living organisms noninvasively. This characterization relies on relations between macroscopic diffusion metrics and structure at the mesoscopic scale commensurate with the diffusion length. Establishing such relations remains a fundamental challenge, hindering progress in materials science, porous media, and biomedical imaging. Here we show that the dynamical exponent in the time dependence of the diffusion coefficient distinguishes between the universality classes of the mesoscopic structural complexity. Our approach enables the interpretation of diffusion measurements by objectively selecting and modeling the most relevant structural features. As an example, the specific values of the dynamical exponent allow us to identify the relevant mesoscopic structure affecting MRI-measured water diffusion in muscles and in brain, and to elucidate the structural changes behind the decrease of diffusion coefficient in ischemic stroke. PMID:24706873

MSM/RD: Coupling Markov state models of molecular kinetics with reaction-diffusion simulations

NASA Astrophysics Data System (ADS)

Dibak, Manuel; del Razo, Mauricio J.; De Sancho, David; Schütte, Christof; Noé, Frank

2018-06-01

Molecular dynamics (MD) simulations can model the interactions between macromolecules with high spatiotemporal resolution but at a high computational cost. By combining high-throughput MD with Markov state models (MSMs), it is now possible to obtain long time-scale behavior of small to intermediate biomolecules and complexes. To model the interactions of many molecules at large length scales, particle-based reaction-diffusion (RD) simulations are more suitable but lack molecular detail. Thus, coupling MSMs and RD simulations (MSM/RD) would be highly desirable, as they could efficiently produce simulations at large time and length scales, while still conserving the characteristic features of the interactions observed at atomic detail. While such a coupling seems straightforward, fundamental questions are still open: Which definition of MSM states is suitable? Which protocol to merge and split RD particles in an association/dissociation reaction will conserve the correct bimolecular kinetics and thermodynamics? In this paper, we make the first step toward MSM/RD by laying out a general theory of coupling and proposing a first implementation for association/dissociation of a protein with a small ligand (A + B ⇌ C). Applications on a toy model and CO diffusion into the heme cavity of myoglobin are reported.

Using Global Invariant Manifolds to Understand Metastability in the Burgers Equation With Small Viscosity

NASA Astrophysics Data System (ADS)

Beck, Margaret; Wayne, C. Eugene

2009-01-01

The large-time behavior of solutions to the Burgers equation with small viscosity is described using invariant manifolds. In particular, a geometric explanation is provided for a phenomenon known as metastability, which in the present context means that solutions spend a very long time near the family of solutions known as diffusive N-waves before finally converging to a stable self-similar diffusion wave. More precisely, it is shown that in terms of similarity, or scaling, variables in an algebraically weighted L^2 space, the self-similar diffusion waves correspond to a one-dimensional global center manifold of stationary solutions. Through each of these fixed points there exists a one-dimensional, global, attractive, invariant manifold corresponding to the diffusive N-waves. Thus, metastability corresponds to a fast transient in which solutions approach this metastable manifold of diffusive N-waves, followed by a slow decay along this manifold, and, finally, convergence to the self-similar diffusion wave.

Rotational and translational diffusions of fluorescent probes during gelation process

NASA Astrophysics Data System (ADS)

Hattori, Yusuke; Panizza, Pascal; Letamendia, Louis; Ushiki, Hideharu

2006-04-01

Gelation process has been investigated by using light scattering techniques in recent years. We measured both of rotational and translational motions of fluorescent probes during gelation process. The measurements were performed after the temperature quenched at 30 °C. As the results, rotational diffusion coefficient of fluorescein was decreased after 6.0 × 10 4 s and energy transfer rate was reduced after 2.0 × 10 4 s. We sorted the gelation process into the following three parts, (I) pre-gelation, (II) reduction of translational diffusion (aging), and (III) reduction of rotational diffusion with saturating translational diffusion (post-gelation). The time scale of the process was completely different from the results of other methods.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zaveri, Rahul A.; Shilling, John E.; Zelenyuk, Alla

Low bulk diffusivity inside viscous semisolid atmospheric secondary organic aerosol (SOA) can prolong equilibration time scale, but its broader impacts on aerosol growth and size distribution dynamics are poorly understood. In this article, we present quantitative insights into the effects of bulk diffusivity on the growth and evaporation kinetics of SOA formed under dry conditions from photooxidation of isoprene in the presence of a bimodal aerosol consisting of Aitken (ammonium sulfate) and accumulation (isoprene or α-pinene SOA) mode particles. Aerosol composition measurements and evaporation kinetics indicate that isoprene SOA is composed of several semivolatile organic compounds (SVOCs), with some reversiblymore » reacting to form oligomers. Model analysis shows that liquid-like bulk diffusivities can be used to fit the observed evaporation kinetics of accumulation mode particles but fail to explain the growth kinetics of bimodal aerosol by significantly under-predicting the evolution of the Aitken mode. In contrast, the semisolid scenario successfully reproduces both evaporation and growth kinetics, with the interpretation that hindered partitioning of SVOCs into large viscous particles effectively promotes the growth of smaller particles that have shorter diffusion time scales. This effect has important implications for the growth of atmospheric ultrafine particles to climatically active sizes.« less

Growth Kinetics and Size Distribution Dynamics of Viscous Secondary Organic Aerosol

DOE PAGES

Zaveri, Rahul A.; Shilling, John E.; Zelenyuk, Alla; ...

2017-12-15

Low bulk diffusivity inside viscous semisolid atmospheric secondary organic aerosol (SOA) can prolong equilibration time scale, but its broader impacts on aerosol growth and size distribution dynamics are poorly understood. In this article, we present quantitative insights into the effects of bulk diffusivity on the growth and evaporation kinetics of SOA formed under dry conditions from photooxidation of isoprene in the presence of a bimodal aerosol consisting of Aitken (ammonium sulfate) and accumulation (isoprene or α-pinene SOA) mode particles. Aerosol composition measurements and evaporation kinetics indicate that isoprene SOA is composed of several semivolatile organic compounds (SVOCs), with some reversiblymore » reacting to form oligomers. Model analysis shows that liquid-like bulk diffusivities can be used to fit the observed evaporation kinetics of accumulation mode particles but fail to explain the growth kinetics of bimodal aerosol by significantly under-predicting the evolution of the Aitken mode. In contrast, the semisolid scenario successfully reproduces both evaporation and growth kinetics, with the interpretation that hindered partitioning of SVOCs into large viscous particles effectively promotes the growth of smaller particles that have shorter diffusion time scales. This effect has important implications for the growth of atmospheric ultrafine particles to climatically active sizes.« less

Growth Kinetics and Size Distribution Dynamics of Viscous Secondary Organic Aerosol

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zaveri, Rahul A.; Shilling, John E.; Zelenyuk, Alla

Low bulk diffusivity inside viscous semisolid atmospheric secondary organic aerosol (SOA) can prolong equilibration time scale, but its broader impacts on aerosol growth and size distribution dynamics are poorly understood. In this article, we present quantitative insights into the effects of bulk diffusivity on the growth and evaporation kinetics of SOA formed under dry conditions from photooxidation of isoprene in the presence of a bimodal aerosol consisting of Aitken (ammonium sulfate) and accumulation (isoprene or α-pinene SOA) mode particles. Aerosol composition measurements and evaporation kinetics indicate that isoprene SOA is composed of several semivolatile organic compounds (SVOCs), with some reversiblymore » reacting to form oligomers. Model analysis shows that liquid-like bulk diffusivities can be used to fit the observed evaporation kinetics of accumulation mode particles but fail to explain the growth kinetics of bimodal aerosol by significantly under-predicting the evolution of the Aitken mode. In contrast, the semisolid scenario successfully reproduces both evaporation and growth kinetics, with the interpretation that hindered partitioning of SVOCs into large viscous particles effectively promotes the growth of smaller particles that have shorter diffusion time scales. This effect has important implications for the growth of atmospheric ultrafine particles to climatically active sizes.« less

Prediction and validation of blowout limits of co-flowing jet diffusion flames -- effect of dilution

DOE Office of Scientific and Technical Information (OSTI.GOV)

Karbasi, M.; Wierzba, I.

1996-10-01

The blowout limits of a co-flowing turbulent methane jet diffusion flame with addition of diluent in either jet fuel or surrounding air stream is studied both analytically and experimentally. Helium, nitrogen and carbon dioxide were employed as the diluents. Experiments indicated that an addition of diluents to the jet fuel or surrounding air stream decreased the stability limit of the jet diffusion flames. The strongest effect was observed with carbon dioxide as the diluent followed by nitrogen and then by helium. A model of extinction based on recognized criterion of the mixing time scale to characteristic combustion time scale ratiomore » using experimentally derived correlations is proposed. It is capable of predicting the large reduction of the jet blowout velocity due to a relatively small increase in the co-flow stream velocity along with an increase in the concentration of diluent in either the jet fuel or surrounding air stream. Experiments were carried out to validate the model. The predicted blowout velocities of turbulent jet diffusion flames obtained using this model are in good agreement with the corresponding experimental data.« less

Monitoring Local Changes in Granite Rock Under Biaxial Test: A Spatiotemporal Imaging Application With Diffuse Waves

NASA Astrophysics Data System (ADS)

Xie, Fan; Ren, Yaqiong; Zhou, Yongsheng; Larose, Eric; Baillet, Laurent

2018-03-01

Diffuse acoustic or seismic waves are highly sensitive to detect changes of mechanical properties in heterogeneous geological materials. In particular, thanks to acoustoelasticity, we can quantify stress changes by tracking acoustic or seismic relative velocity changes in the material at test. In this paper, we report on a small-scale laboratory application of an innovative time-lapse tomography technique named Locadiff to image spatiotemporal mechanical changes on a granite sample under biaxial loading, using diffuse waves at ultrasonic frequencies (300 kHz to 900 kHz). We demonstrate the ability of the method to image reversible stress evolution and deformation process, together with the development of reversible and irreversible localized microdamage in the specimen at an early stage. Using full-field infrared thermography, we visualize stress-induced temperature changes and validate stress images obtained from diffuse ultrasound. We demonstrate that the inversion with a good resolution can be achieved with only a limited number of receivers distributed around a single source, all located at the free surface of the specimen. This small-scale experiment is a proof of concept for frictional earthquake-like failure (e.g., stick-slip) research at laboratory scale as well as large-scale seismic applications, potentially including active fault monitoring.

An idealised study of the effects of small scales on chemistry in a two-dimensional turbulent flow.

NASA Astrophysics Data System (ADS)

Chaalal, F. Ait; Bartello, P.; Bourqui, M.

2009-04-01

The non-linear nature of stratospheric chemical reactions makes them sensitive to mixing and diffusion. Most stratospheric Climate-Chemistry Models neglect the effects of sub-grid flow structures on chemistry. Several previous studies have pointed out that such unresolved small scales could significantly affect the chemistry. However this problem has not been thoroughly studied from a theoretical point of view. To fulfill this gap, we investigate the interactions between advection, diffusion and chemistry for a simple bimolecular reaction between two initially unmixed reactants, within the framework of two-dimensional isotropic and homogenous turbulence. This is a highly simplified representation of quasi-isentropic mixing in the stratosphere. Our goal here is to describe and understand how the production rate of the product species is affected by the size of the smallest scales of the tracer field, as determined by the tracer diffusion coefficient ΰ. The spatial average of the prognostic equation for the product's concentration involves the covariance of the reactants. The time evolution of this covariance depends in turn on a dissipative term, and on second and third order chemical terms. The set of equations is not closed and any finite resolution model would need a parameterization of the dissipation and a closure hypothesis on the chemical terms. To study these terms, we perform ensembles of direct numerical simulations using a pseudo-spectral two-dimensional periodic model. The ensembles span different initial conditions of the flow and different tracer diffusion coefficients ΰ. Our results show a strong dependence of the total production on the diffusion coefficient. This production scales like ΰp(t) , where p(t) is a positive decreasing function of time. This scaling is very similar to the one found by Tan et al. (1998) for atmospheric flows on the deactivation of chlorine by nitrogen oxide at the southern edge of the winter time polar vortex. Furthermore, the time derivative of the reactants' covariance is found to be only very weakly dependent on the chemical reaction rate, for both slow and fast chemistries compared to the advection. The variations of the dissipation and of the chemical terms with the reaction speed compensate each other. As a consequence, the calculation of the product's concentration using the covariance of the dissipation without chemistry is a good approximation of the effect of diffusion with chemistry. Reference Tan, DGH; Haynes, PH; MacKenzie, AR; et al., Effects of fluid-dynamical stirring and mixing on the deactivation of stratospheric chlorine, Journal of Geophysical Research-Atmospheres, Volume: 103 Issue: D1 Pages: 1585-1605 (1998).

Estimating Pore Properties from NMR Relaxation Time Measurements in Heterogeneous Media

NASA Astrophysics Data System (ADS)

Grunewald, E.; Knight, R.

2008-12-01

The link between pore geometry and the nuclear magnetic resonance (NMR) relaxation time T2 is well- established for simple systems but is poorly understood for complex media with heterogeneous pores. Conventional interpretation of NMR relaxation data employs a model of isolated pores in which each hydrogen proton samples only one pore type, and the T2-distribution is directly scaled to estimate a pore-size distribution. During an actual NMR measurement, however, each proton diffuses through a finite volume of the pore network, and so may sample multiple pore types encountered within this diffusion cell. For cases in which heterogeneous pores are strongly coupled by diffusion, the meaning of the T2- distribution is not well understood and further research is required to determine how such measurements should be interpreted. In this study we directly investigate the implications of pore coupling in two groups of laboratory NMR experiments. We conduct two suites of experiments, in which samples are synthesized to exhibit a range of pore coupling strengths using two independent approaches: (a) varying the scale of the diffusion cell and (b) varying the scale over which heterogeneous pores are encountered. In the first set of experiments, we vary the scale of the diffusion cell in silica gels which have a bimodal pore-size distribution comprised of intragrannular micropores and much larger intergrannular pores. The untreated gel exhibits strong pore coupling with a single broad peak observed in the T2-distribution. By treating the gel with varied amounts of paramagnetic iron surface coatings, we decrease the surface relaxation time, T2S, and effectively decrease both the size of the diffusion cell and the degree of pore coupling. As more iron is coated to the grain surfaces, we observe a separation of the broad T2-distribution into two peaks that more accurately represent the true bimodal pore-size distribution. In the second set of experiments, we vary the scale over which heterogeneous pores are encountered in bimodal grain packs of pure quartz (long T2S) and hematite (short T2S). The scale of heterogeneity is varied by changing the mean grain size and relative mineral concentrations. When the mean grain size is small and the mineral concentrations are comparable, the T2-distribution is roughly monomodal indicating strong pore coupling. As the grain size is increased or the mineral concentrations are made increasingly uneven, the T2- distribution develops a bimodal character, more representative of the actual distribution of pore types. Numerical simulations of measurements in both experiment groups allow us to more closely investigate how the relaxing magnetization evolves in both time and space. Collectively, these experiments provide important insights into the effects of pore coupling on NMR measurements in heterogeneous systems and contribute to our ultimate goal of improving the interpretation of these data in complex near-surface sediments.

Chaotic dynamics of large-scale double-diffusive convection in a porous medium

NASA Astrophysics Data System (ADS)

Kondo, Shutaro; Gotoda, Hiroshi; Miyano, Takaya; Tokuda, Isao T.

2018-02-01

We have studied chaotic dynamics of large-scale double-diffusive convection of a viscoelastic fluid in a porous medium from the viewpoint of dynamical systems theory. A fifth-order nonlinear dynamical system modeling the double-diffusive convection is theoretically obtained by incorporating the Darcy-Brinkman equation into transport equations through a physical dimensionless parameter representing porosity. We clearly show that the chaotic convective motion becomes much more complicated with increasing porosity. The degree of dynamic instability during chaotic convective motion is quantified by two important measures: the network entropy of the degree distribution in the horizontal visibility graph and the Kaplan-Yorke dimension in terms of Lyapunov exponents. We also present an interesting on-off intermittent phenomenon in the probability distribution of time intervals exhibiting nearly complete synchronization.

Diffusion of two-dimensional epitaxial clusters on metal (100) surfaces: Facile versus nucleation-mediated behavior and their merging for larger sizes

NASA Astrophysics Data System (ADS)

Lai, King C.; Liu, Da-Jiang; Evans, James W.

2017-12-01

For diffusion of two-dimensional homoepitaxial clusters of N atoms on metal (100) surfaces mediated by edge atom hopping, macroscale continuum theory suggests that the diffusion coefficient scales like DN˜ N-β with β =3 /2 . However, we find quite different and diverse behavior in multiple size regimes. These include: (i) facile diffusion for small sizes N <9 ; (ii) slow nucleation-mediated diffusion with small β <1 for "perfect" sizes N = Np= L2 or L (L +1 ) , for L =3 ,4 , ... having unique ground-state shapes, for moderate sizes 9 ≤N ≤O (102) ; the same also applies for N =Np+3 , Np+ 4 , ... (iii) facile diffusion but with large β >2 for N =Np+1 and Np+2 also for moderate sizes 9 ≤N ≤O (102) ; (iv) merging of the above distinct branches and subsequent anomalous scaling with 1 ≲β <3 /2 , reflecting the quasifacetted structure of clusters, for larger N =O (102) to N =O (103) ; (v) classic scaling with β =3 /2 for very large N =O (103) and above. The specified size ranges apply for typical model parameters. We focus on the moderate size regime where we show that diffusivity cycles quasiperiodically from the slowest branch for Np+3 (not Np) to the fastest branch for Np+1 . Behavior is quantified by kinetic Monte Carlo simulation of an appropriate stochastic lattice-gas model. However, precise analysis must account for a strong enhancement of diffusivity for short time increments due to back correlation in the cluster motion. Further understanding of this enhancement, of anomalous size scaling behavior, and of the merging of various branches, is facilitated by combinatorial analysis of the number of the ground-state and low-lying excited state cluster configurations, and also of kink populations.

Diffusion of two-dimensional epitaxial clusters on metal (100) surfaces: Facile versus nucleation-mediated behavior and their merging for larger sizes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lai, King C.; Liu, Da -Jiang; Evans, James W.

For diffusion of two-dimensional homoepitaxial clusters of N atoms on metal(100) surfaces mediated by edge atom hopping, macroscale continuum theory suggests that the diffusion coefficient scales like DN ~ N -β with β = 3/2. However, we find quite different and diverse behavior in multiple size regimes. These include: (i) facile diffusion for small sizes N < 9; (ii) slow nucleation-mediated diffusion with small β < 1 for “perfect” sizes N = N p = L 2 or L(L+1), for L = 3, 4,… having unique ground state shapes, for moderate sizes 9 ≤ N ≤ O(10 2); the samemore » also applies for N = N p +3, N p + 4,… (iii) facile diffusion but with large β > 2 for N = Np + 1 and N p + 2 also for moderate sizes 9 ≤ N ≤ O(10 2); (iv) merging of the above distinct branches and subsequent anomalous scaling with 1 ≲ β < 3/2, reflecting the quasi-facetted structure of clusters, for larger N = O(10 2) to N = O(10 3); and (v) classic scaling with β = 3/2 for very large N = O(103) and above. The specified size ranges apply for typical model parameters. We focus on the moderate size regime where show that diffusivity cycles quasi-periodically from the slowest branch for N p + 3 (not Np) to the fastest branch for Np + 1. Behavior is quantified by Kinetic Monte Carlo simulation of an appropriate stochastic lattice-gas model. However, precise analysis must account for a strong enhancement of diffusivity for short time increments due to back-correlation in the cluster motion. Further understanding of this enhancement, of anomalous size scaling behavior, and of the merging of various branches, is facilitated by combinatorial analysis of the number of the ground state and low-lying excited state cluster configurations, and also of kink populations.« less

Diffusion of two-dimensional epitaxial clusters on metal (100) surfaces: Facile versus nucleation-mediated behavior and their merging for larger sizes

DOE PAGES

Lai, King C.; Liu, Da -Jiang; Evans, James W.

2017-12-05

For diffusion of two-dimensional homoepitaxial clusters of N atoms on metal(100) surfaces mediated by edge atom hopping, macroscale continuum theory suggests that the diffusion coefficient scales like DN ~ N -β with β = 3/2. However, we find quite different and diverse behavior in multiple size regimes. These include: (i) facile diffusion for small sizes N < 9; (ii) slow nucleation-mediated diffusion with small β < 1 for “perfect” sizes N = N p = L 2 or L(L+1), for L = 3, 4,… having unique ground state shapes, for moderate sizes 9 ≤ N ≤ O(10 2); the samemore » also applies for N = N p +3, N p + 4,… (iii) facile diffusion but with large β > 2 for N = Np + 1 and N p + 2 also for moderate sizes 9 ≤ N ≤ O(10 2); (iv) merging of the above distinct branches and subsequent anomalous scaling with 1 ≲ β < 3/2, reflecting the quasi-facetted structure of clusters, for larger N = O(10 2) to N = O(10 3); and (v) classic scaling with β = 3/2 for very large N = O(103) and above. The specified size ranges apply for typical model parameters. We focus on the moderate size regime where show that diffusivity cycles quasi-periodically from the slowest branch for N p + 3 (not Np) to the fastest branch for Np + 1. Behavior is quantified by Kinetic Monte Carlo simulation of an appropriate stochastic lattice-gas model. However, precise analysis must account for a strong enhancement of diffusivity for short time increments due to back-correlation in the cluster motion. Further understanding of this enhancement, of anomalous size scaling behavior, and of the merging of various branches, is facilitated by combinatorial analysis of the number of the ground state and low-lying excited state cluster configurations, and also of kink populations.« less

Superdiffusion revisited in view of collisionless reconnection

NASA Astrophysics Data System (ADS)

Treumann, R. A.; Baumjohann, W.

2014-06-01

The concept of diffusion in collisionless space plasmas like those near the magnetopause and in the geomagnetic tail during reconnection is reexamined making use of the division of particle orbits into waiting orbits and break-outs into ballistic motion lying at the bottom, for instance, of Lévy flights. The rms average displacement in this case increases with time, describing superdiffusion, though faster than classical, is still a weak process, being however strong enough to support fast reconnection. Referring to two kinds of numerical particle-in-cell simulations we determine the anomalous diffusion coefficient, the anomalous collision frequency on which the diffusion process is based, and construct a relation between the diffusion coefficients and the resistive scale. The anomalous collision frequency from electron pseudo-viscosity in reconnection turns out to be of the order of the lower-hybrid frequency with the latter providing a lower limit, thus making similar assumptions physically meaningful. Tentative though not completely justified use of the κ distribution yields κ ≈ 6 in the reconnection diffusion region and, for the anomalous diffusion coefficient, the order of several times Bohm diffusivity.

Diffusion NMR methods applied to xenon gas for materials study

NASA Technical Reports Server (NTRS)

Mair, R. W.; Rosen, M. S.; Wang, R.; Cory, D. G.; Walsworth, R. L.

2002-01-01

We report initial NMR studies of (i) xenon gas diffusion in model heterogeneous porous media and (ii) continuous flow laser-polarized xenon gas. Both areas utilize the pulsed gradient spin-echo (PGSE) techniques in the gas phase, with the aim of obtaining more sophisticated information than just translational self-diffusion coefficients--a brief overview of this area is provided in the Introduction. The heterogeneous or multiple-length scale model porous media consisted of random packs of mixed glass beads of two different sizes. We focus on observing the approach of the time-dependent gas diffusion coefficient, D(t) (an indicator of mean squared displacement), to the long-time asymptote, with the aim of understanding the long-length scale structural information that may be derived from a heterogeneous porous system. We find that D(t) of imbibed xenon gas at short diffusion times is similar for the mixed bead pack and a pack of the smaller sized beads alone, hence reflecting the pore surface area to volume ratio of the smaller bead sample. The approach of D(t) to the long-time limit follows that of a pack of the larger sized beads alone, although the limiting D(t) for the mixed bead pack is lower, reflecting the lower porosity of the sample compared to that of a pack of mono-sized glass beads. The Pade approximation is used to interpolate D(t) data between the short- and long-time limits. Initial studies of continuous flow laser-polarized xenon gas demonstrate velocity-sensitive imaging of much higher flows than can generally be obtained with liquids (20-200 mm s-1). Gas velocity imaging is, however, found to be limited to a resolution of about 1 mm s-1 owing to the high diffusivity of gases compared with liquids. We also present the first gas-phase NMR scattering, or diffusive-diffraction, data, namely flow-enhanced structural features in the echo attenuation data from laser-polarized xenon flowing through a 2 mm glass bead pack. c2002 John Wiley & Sons, Ltd.

Microscopic theory for dynamics in entangled polymer nanocomposites

NASA Astrophysics Data System (ADS)

Yamamoto, Umi

New microscopic theories for describing dynamics in polymer nanocomposites are developed and applied. The problem is addressed from two distinct perspectives and using two different theoretical approaches. The first half of this dissertation studies the long-time and intermediate-time dynamics of nanoparticles in entangled and unentangled polymer melts for dilute particle concentrations. Using a combination of mode-coupling, Brownian motion, and polymer physics ideas, the nanoparticle long-time diffusion coefficients is formulated in terms of multiple length-scales, packing microstructures, and spatially-resolved polymer density fluctuation dynamics. The key motional mechanism is described via the parallel relaxation of the force exerted on the particle controlled by collective polymer constraint-release and the particle self-motion. A sharp but smooth crossover from the hydrodynamic to the non-hydrodynamic regime is predicted based on the Stokes-Einstein violation ratio as a function of all the system variables. Quantitative predictions are made for the recovery of the Stokes-Einstein law, and the diffusivity in the crossover regime agrees surprisingly well with large-scale molecular dynamics simulations for all particle sizes and chain lengths studied. The approach is also extended to address intermediate-time anomalous transport of a single nanoparticle and two-particle relative diffusion. The second half of this dissertation focuses on developing a novel dynamical theory for a liquid of infinitely-thin rods in the presence of hard spherical obstacles, aiming at a technical and conceptual extension of the existing paradigm for entangled polymer dynamics. As a fundamental theoretical development, the two-component generalization of a first-principles dynamic meanfield approach is presented. The theory enforces inter-needle topological uncrossability and needlesphere impenetrability in a unified manner, leading to a generalized theory of entanglements that includes the sphere excluded volume effect. Coupled self-consistent equations for the generalized diffusion tensors are constructed, and the expressions for the transverse localization lengths and the long-time diffusion coefficients are derived. In the static sphere limit, we find the effective tube diameter is generally reduced as a function of a single confinement parameter that quantifies the number of particles penetrating into the pure-polymer tube. A preliminary extension to treat flexible chain melts has also been achieved, and shown to agree reasonably well with simulations. The anisotropic needle diffusion constants are rich functions of the length-scale ratios, needle concentration and particle volume fraction. We show that the steric blocking of the longitudinal motion causes a literal and simultaneous localization of the two diffusion channels, and entangled needles can diffuse via a modified reptation dynamics over a window of polymer concentration but the compression of the tube and the blocking of the reptation motion must be accounted for. Generalization to treat mobile spheres is also possible and fully formulated.

Hybrid MD-Nernst Planck Model of Alpha-hemolysin Conductance Properties

NASA Technical Reports Server (NTRS)

Cozmuta, Ioana; O'Keefer, James T.; Bose, Deepak; Stolc, Viktor

2006-01-01

Motivated by experiments in which an applied electric field translocates polynucleotides through an alpha-hemolysin protein channel causing ionic current transient blockade, a hybrid simulation model is proposed to predict the conductance properties of the open channel. Time scales corresponding to ion permeation processes are reached using the Poisson-Nemst-Planck (PNP) electro-diffusion model in which both solvent and local ion concentrations are represented as a continuum. The diffusion coefficients of the ions (K(+) and Cl(-)) input in the PNP model are, however, calculated from all-atom molecular dynamics (MD). In the MD simulations, a reduced representation of the channel is used. The channel is solvated in a 1 M KCI solution, and an external electric field is applied. The pore specific diffusion coefficients for both ionic species are reduced 5-7 times in comparison to bulk values. Significant statistical variations (17-45%) of the pore-ions diffusivities are observed. Within the statistics, the ionic diffusivities remain invariable for a range of external applied voltages between 30 and 240mV. In the 2D-PNP calculations, the pore stem is approximated by a smooth cylinder of radius approx. 9A with two constriction blocks where the radius is reduced to approx. 6A. The electrostatic potential includes the contribution from the atomistic charges. The MD-PNP model shows that the atomic charges are responsible for the rectifying behaviour and for the slight anion selectivity of the a-hemolysin pore. Independent of the hierarchy between the anion and cation diffusivities, the anionic contribution to the total ionic current will dominate. The predictions of the MD-PNP model are in good agreement with experimental data and give confidence in the present approach of bridging time scales by combining a microscopic and macroscopic model.

The closure problem for turbulence in meteorology and oceanography

NASA Technical Reports Server (NTRS)

Pierson, W. J., Jr.

1985-01-01

The dependent variables used for computer based meteorological predictions and in plans for oceanographic predictions are wave number and frequency filtered values that retain only scales resolvable by the model. Scales unresolvable by the grid in use become 'turbulence'. Whether or not properly processed data are used for initial values is important, especially for sparce data. Fickian diffusion with a constant eddy diffusion is used as a closure for many of the present models. A physically realistic closure based on more modern turbulence concepts, especially one with a reverse cascade at the right times and places, could help improve predictions.

Chaos and noise in a truncated Toda potential

DOE Office of Scientific and Technical Information (OSTI.GOV)

Habib, S.; Kandrup, H.E.; Mahon, M.E.

Results are reported from a numerical investigation of orbits in a truncated Toda potential that is perturbed by weak friction and noise. Aside from the perturbations displaying a simple scaling in the amplitude of the friction and noise, it is found that even very weak friction and noise can induce an extrinsic diffusion through cantori on a time scale that is much shorter than that associated with intrinsic diffusion in the unperturbed system. The results have applications in galactic dynamics and in the formation of a beam halo in charged particle beams. {copyright} {ital 1996 The American Physical Society.}

Parameterization of large-scale turbulent diffusion in the presence of both well-mixed and weakly mixed patchy layers

NASA Astrophysics Data System (ADS)

Osman, M. K.; Hocking, W. K.; Tarasick, D. W.

2016-06-01

Vertical diffusion and mixing of tracers in the upper troposphere and lower stratosphere (UTLS) are not uniform, but primarily occur due to patches of turbulence that are intermittent in time and space. The effective diffusivity of regions of patchy turbulence is related to statistical parameters describing the morphology of turbulent events, such as lifetime, number, width, depth and local diffusivity (i.e., diffusivity within the turbulent patch) of the patches. While this has been recognized in the literature, the primary focus has been on well-mixed layers, with few exceptions. In such cases the local diffusivity is irrelevant, but this is not true for weakly and partially mixed layers. Here, we use both theory and numerical simulations to consider the impact of intermediate and weakly mixed layers, in addition to well-mixed layers. Previous approaches have considered only one dimension (vertical), and only a small number of layers (often one at each time step), and have examined mixing of constituents. We consider a two-dimensional case, with multiple layers (10 and more, up to hundreds and even thousands), having well-defined, non-infinite, lengths and depths. We then provide new formulas to describe cases involving well-mixed layers which supersede earlier expressions. In addition, we look in detail at layers that are not well mixed, and, as an interesting variation on previous models, our procedure is based on tracking the dispersion of individual particles, which is quite different to the earlier approaches which looked at mixing of constituents. We develop an expression which allows determination of the degree of mixing, and show that layers used in some previous models were in fact not well mixed and so produced erroneous results. We then develop a generalized model based on two dimensional random-walk theory employing Rayleigh distributions which allows us to develop a universal formula for diffusion rates for multiple two-dimensional layers with general degrees of mixing. We show that it is the largest, most vigorous and less common turbulent layers that make the major contribution to global diffusion. Finally, we make estimates of global-scale diffusion coefficients in the lower stratosphere and upper troposphere. For the lower stratosphere, κeff ≈ 2x10-2 m2 s-1, assuming no other processes contribute to large-scale diffusion.

Thermodynamic scaling in ionically conducting glasses and melts

NASA Astrophysics Data System (ADS)

Habasaki, Junko

2013-02-01

Molecular dynamics simulations have been performed to learn temperature, composition, pressure dependencies of the diffusivity and structures in the system having ion channels and network formers. Validity of the thermodynamic scaling in the lithium silicate glasses and melts is shown, where the scaling concept is extended with an aid of a percolation aspect of the ion channels. All diffusion coefficients of ions of different compositions, temperatures, pressures are successfully represented by a single master curve as a function of system volumes, temperatures and volume fraction of M2O part. It enables us to predict the diffusivity in different conditions. Furthermore, it suggests an applicability of scaling concept for the sub-structures in more complex systems. Nearby points on the master curve have the comparable MSD as well as self-part of the van Hove functions. Similarity is observed from an early term region. This observation is consistent to our previous claims [K. L. Ngai, J. Habasaki, D. Prevosto, S. Capaccioli, Marian Paluch, J. Chem. Phys. 137, 034511 (2012)] that the thermodynamic scaling of α-Relaxation time stems from the Johari-Goldstein β-relaxation or the primitive relaxation of the coupling model.

Mild hypothermia for treatment of diffuse axonal injury: a quantitative analysis of diffusion tensor imaging

PubMed Central

Jing, Guojie; Yao, Xiaoteng; Li, Yiyi; Xie, Yituan; Li, Wang#x2019;an; Liu, Kejun; Jing, Yingchao; Li, Baisheng; Lv, Yifan; Ma, Baoxin

2014-01-01

Fractional anisotropy values in diffusion tensor imaging can quantitatively reflect the consistency of nerve fibers after brain damage, where higher values generally indicate less damage to nerve fibers. Therefore, we hypothesized that diffusion tensor imaging could be used to evaluate the effect of mild hypothermia on diffuse axonal injury. A total of 102 patients with diffuse axonal injury were randomly divided into two groups: normothermic and mild hypothermic treatment groups. Patient's modified Rankin scale scores 2 months after mild hypothermia were significantly lower than those for the normothermia group. The difference in average fractional anisotropy value for each region of interest before and after mild hypothermia was 1.32-1.36 times higher than the value in the normothermia group. Quantitative assessment of diffusion tensor imaging indicates that mild hypothermia therapy may be beneficial for patients with diffuse axonal injury. PMID:25206800

Critical time scales for advection-diffusion-reaction processes.

PubMed

Ellery, Adam J; Simpson, Matthew J; McCue, Scott W; Baker, Ruth E

2012-04-01

The concept of local accumulation time (LAT) was introduced by Berezhkovskii and co-workers to give a finite measure of the time required for the transient solution of a reaction-diffusion equation to approach the steady-state solution [A. M. Berezhkovskii, C. Sample, and S. Y. Shvartsman, Biophys. J. 99, L59 (2010); A. M. Berezhkovskii, C. Sample, and S. Y. Shvartsman, Phys. Rev. E 83, 051906 (2011)]. Such a measure is referred to as a critical time. Here, we show that LAT is, in fact, identical to the concept of mean action time (MAT) that was first introduced by McNabb [A. McNabb and G. C. Wake, IMA J. Appl. Math. 47, 193 (1991)]. Although McNabb's initial argument was motivated by considering the mean particle lifetime (MPLT) for a linear death process, he applied the ideas to study diffusion. We extend the work of these authors by deriving expressions for the MAT for a general one-dimensional linear advection-diffusion-reaction problem. Using a combination of continuum and discrete approaches, we show that MAT and MPLT are equivalent for certain uniform-to-uniform transitions; these results provide a practical interpretation for MAT by directly linking the stochastic microscopic processes to a meaningful macroscopic time scale. We find that for more general transitions, the equivalence between MAT and MPLT does not hold. Unlike other critical time definitions, we show that it is possible to evaluate the MAT without solving the underlying partial differential equation (pde). This makes MAT a simple and attractive quantity for practical situations. Finally, our work explores the accuracy of certain approximations derived using MAT, showing that useful approximations for nonlinear kinetic processes can be obtained, again without treating the governing pde directly.

Parallel multispot smFRET analysis using an 8-pixel SPAD array

NASA Astrophysics Data System (ADS)

Ingargiola, A.; Colyer, R. A.; Kim, D.; Panzeri, F.; Lin, R.; Gulinatti, A.; Rech, I.; Ghioni, M.; Weiss, S.; Michalet, X.

2012-02-01

Single-molecule Förster resonance energy transfer (smFRET) is a powerful tool for extracting distance information between two fluorophores (a donor and acceptor dye) on a nanometer scale. This method is commonly used to monitor binding interactions or intra- and intermolecular conformations in biomolecules freely diffusing through a focal volume or immobilized on a surface. The diffusing geometry has the advantage to not interfere with the molecules and to give access to fast time scales. However, separating photon bursts from individual molecules requires low sample concentrations. This results in long acquisition time (several minutes to an hour) to obtain sufficient statistics. It also prevents studying dynamic phenomena happening on time scales larger than the burst duration and smaller than the acquisition time. Parallelization of acquisition overcomes this limit by increasing the acquisition rate using the same low concentrations required for individual molecule burst identification. In this work we present a new two-color smFRET approach using multispot excitation and detection. The donor excitation pattern is composed of 4 spots arranged in a linear pattern. The fluorescent emission of donor and acceptor dyes is then collected and refocused on two separate areas of a custom 8-pixel SPAD array. We report smFRET measurements performed on various DNA samples synthesized with various distances between the donor and acceptor fluorophores. We demonstrate that our approach provides identical FRET efficiency values to a conventional single-spot acquisition approach, but with a reduced acquisition time. Our work thus opens the way to high-throughput smFRET analysis on freely diffusing molecules.

An exact and efficient first passage time algorithm for reaction–diffusion processes on a 2D-lattice

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bezzola, Andri, E-mail: andri.bezzola@gmail.com; Bales, Benjamin B., E-mail: bbbales2@gmail.com; Alkire, Richard C., E-mail: r-alkire@uiuc.edu

2014-01-01

We present an exact and efficient algorithm for reaction–diffusion–nucleation processes on a 2D-lattice. The algorithm makes use of first passage time (FPT) to replace the computationally intensive simulation of diffusion hops in KMC by larger jumps when particles are far away from step-edges or other particles. Our approach computes exact probability distributions of jump times and target locations in a closed-form formula, based on the eigenvectors and eigenvalues of the corresponding 1D transition matrix, maintaining atomic-scale resolution of resulting shapes of deposit islands. We have applied our method to three different test cases of electrodeposition: pure diffusional aggregation for largemore » ranges of diffusivity rates and for simulation domain sizes of up to 4096×4096 sites, the effect of diffusivity on island shapes and sizes in combination with a KMC edge diffusion, and the calculation of an exclusion zone in front of a step-edge, confirming statistical equivalence to standard KMC simulations. The algorithm achieves significant speedup compared to standard KMC for cases where particles diffuse over long distances before nucleating with other particles or being captured by larger islands.« less

Solution Phase Exciton Diffusion Dynamics of a Charge-Transfer Copolymer PTB7 and a Homopolymer P3HT

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cho, Sung; Rolczynski, Brian S.; Xu, Tao

2015-06-18

Using ultrafast polarization-controlled transient absorption (TA) measurements, dynamics of the initial exciton states were investigated on the time scale of tens of femtoseconds to about 80 ps in two different types of conjugated polymers extensively used in active layers of organic photovoltaic devices. These polymers are poly(3-fluorothienothiophenebenzodithiophene) (PTB7) and poly-3-hexylthiophene (P3HT), which are charge-transfer polymers and homopolymers, respectively. In PTB7, the initial excitons with excess vibrational energy display two observable ultrafast time constants, corresponding to coherent exciton diffusion before the vibrational relaxation, and followed by incoherent exciton diffusion processes to a neighboring local state after the vibrational relaxation. In contrast,more » P3HT shows only one exciton diffusion or conformational motion time constant of 34 ps, even though its exciton decay kinetics are multiexponential. Based on the experimental results, an exciton dynamics mechanism is conceived taking into account the excitation energy and structural dependence in coherent and incoherent exciton diffusion processes, as well as other possible deactivation processes including the formation of the pseudo-charge-transfer and charge separate states, as well as interchain exciton hopping or coherent diffusion.« less

Solution Phase Exciton Diffusion Dynamics of a Charge-Transfer Copolymer PTB7 and a Homopolymer P3HT.

PubMed

Cho, Sung; Rolczynski, Brian S; Xu, Tao; Yu, Luping; Chen, Lin X

2015-06-18

Using ultrafast polarization-controlled transient absorption (TA) measurements, dynamics of the initial exciton states were investigated on the time scale of tens of femtoseconds to about 80 ps in two different types of conjugated polymers extensively used in active layers of organic photovoltaic devices. These polymers are poly(3-fluorothienothiophenebenzodithiophene) (PTB7) and poly-3-hexylthiophene (P3HT), which are charge-transfer polymers and homopolymers, respectively. In PTB7, the initial excitons with excess vibrational energy display two observable ultrafast time constants, corresponding to coherent exciton diffusion before the vibrational relaxation, and followed by incoherent exciton diffusion processes to a neighboring local state after the vibrational relaxation. In contrast, P3HT shows only one exciton diffusion or conformational motion time constant of 34 ps, even though its exciton decay kinetics are multiexponential. Based on the experimental results, an exciton dynamics mechanism is conceived taking into account the excitation energy and structural dependence in coherent and incoherent exciton diffusion processes, as well as other possible deactivation processes including the formation of the pseudo-charge-transfer and charge separate states, as well as interchain exciton hopping or coherent diffusion.

Absence of a charge diffusion pole at finite energies in an exactly solvable interacting flat-band model in d dimensions

NASA Astrophysics Data System (ADS)

Phillips, Philip W.; Setty, Chandan; Zhang, Shuyi

2018-05-01

Motivated by recent bounds for charge diffusion in critical matter, we investigate the following question: What sets the scale for the velocity for diffusing degrees of freedom in a scale-invariant system? To make our statements precise, we analyze the diffusion pole in an exactly solvable model for a Mott transition in the presence of a long-range interaction term. To achieve scale invariance, we limit our discussion to the flat-band regime. We find in this limit that the diffusion pole, which would normally obtain at finite energy, is pushed to zero energy, resulting in a vanishing of the diffusion constant. This occurs even in the presence of interactions in certain limits, indicating the robustness of this result to the inclusion of a scale in the problem. Consequently, scale invariance precludes any reasonable definition of the diffusion constant. Nonetheless, we do find that a scale can be defined, albeit irrelevant to diffusion, which is the product of the squared band velocity and the density of states.

Modeling elasticity in crystal growth.

PubMed

Elder, K R; Katakowski, Mark; Haataja, Mikko; Grant, Martin

2002-06-17

A new model of crystal growth is presented that describes the phenomena on atomic length and diffusive time scales. The former incorporates elastic and plastic deformation in a natural manner, and the latter enables access to time scales much larger than conventional atomic methods. The model is shown to be consistent with the predictions of Read and Shockley for grain boundary energy, and Matthews and Blakeslee for misfit dislocations in epitaxial growth.

Correlation between information diffusion and opinion evolution on social media

NASA Astrophysics Data System (ADS)

Xiong, Fei; Liu, Yun; Zhang, Zhenjiang

2014-12-01

Information diffusion and opinion evolution are often treated as two independent processes. Opinion models assume the topic reaches each agent and agents initially have their own ideas. In fact, the processes of information diffusion and opinion evolution often intertwine with each other. Whether the influence between these two processes plays a role in the system state is unclear. In this paper, we collected more than one million real data from a well-known social platform, and analysed large-scale user diffusion behaviour and opinion formation. We found that user inter-event time follows a two-scaling power-law distribution with two different power exponents. Public opinion stabilizes quickly and evolves toward the direction of convergence, but the consensus state is prevented by a few opponents. We propose a three-state opinion model accompanied by information diffusion. Agents form and exchange their opinions during information diffusion. Conversely, agents' opinions also influence their diffusion actions. Simulations show that the model with a correlation of the two processes produces similar statistical characteristics as empirical results. A fast epidemic process drives individual opinions to converge more obviously. Unlike previous epidemic models, the number of infected agents does not always increase with the update rate, but has a peak with an intermediate value of the rate.

Modeling Transport of Cesium in Grimsel Granodiorite With Micrometer Scale Heterogeneities and Dynamic Update of Kd

NASA Astrophysics Data System (ADS)

Voutilainen, Mikko; Kekäläinen, Pekka; Siitari-Kauppi, Marja; Sardini, Paul; Muuri, Eveliina; Timonen, Jussi; Martin, Andrew

2017-11-01

Transport and retardation of cesium in Grimsel granodiorite taking into account heterogeneity of mineral and pore structure was studied using rock samples overcored from an in situ diffusion test at the Grimsel Test Site. The field test was part of the Long-Term Diffusion (LTD) project designed to characterize retardation properties (diffusion and distribution coefficients) under in situ conditions. Results of the LTD experiment for cesium showed that in-diffusion profiles and spatial concentration distributions were strongly influenced by the heterogeneous pore structure and mineral distribution. In order to study the effect of heterogeneity on the in-diffusion profile and spatial concentration distribution, a Time Domain Random Walk (TDRW) method was applied along with a feature for modeling chemical sorption in geological materials. A heterogeneous mineral structure of Grimsel granodiorite was constructed using X-ray microcomputed tomography (X-μCT) and the map was linked to previous results for mineral specific porosities and distribution coefficients (Kd) that were determined using C-14-PMMA autoradiography and batch sorption experiments, respectively. After this the heterogeneous structure contains information on local porosity and Kd in 3-D. It was found that the heterogeneity of the mineral structure on the micrometer scale affects significantly the diffusion and sorption of cesium in Grimsel granodiorite at the centimeter scale. Furthermore, the modeled in-diffusion profiles and spatial concentration distributions show similar shape and pattern to those from the LTD experiment. It was concluded that the use of detailed structure characterization and quantitative data on heterogeneity can significantly improve the interpretation and evaluation of transport experiments.

Atomistic simulations of materials: Methods for accurate potentials and realistic time scales

NASA Astrophysics Data System (ADS)

Tiwary, Pratyush

This thesis deals with achieving more realistic atomistic simulations of materials, by developing accurate and robust force-fields, and algorithms for practical time scales. I develop a formalism for generating interatomic potentials for simulating atomistic phenomena occurring at energy scales ranging from lattice vibrations to crystal defects to high-energy collisions. This is done by fitting against an extensive database of ab initio results, as well as to experimental measurements for mixed oxide nuclear fuels. The applicability of these interactions to a variety of mixed environments beyond the fitting domain is also assessed. The employed formalism makes these potentials applicable across all interatomic distances without the need for any ambiguous splining to the well-established short-range Ziegler-Biersack-Littmark universal pair potential. We expect these to be reliable potentials for carrying out damage simulations (and molecular dynamics simulations in general) in nuclear fuels of varying compositions for all relevant atomic collision energies. A hybrid stochastic and deterministic algorithm is proposed that while maintaining fully atomistic resolution, allows one to achieve milliseconds and longer time scales for several thousands of atoms. The method exploits the rare event nature of the dynamics like other such methods, but goes beyond them by (i) not having to pick a scheme for biasing the energy landscape, (ii) providing control on the accuracy of the boosted time scale, (iii) not assuming any harmonic transition state theory (HTST), and (iv) not having to identify collective coordinates or interesting degrees of freedom. The method is validated by calculating diffusion constants for vacancy-mediated diffusion in iron metal at low temperatures, and comparing against brute-force high temperature molecular dynamics. We also calculate diffusion constants for vacancy diffusion in tantalum metal, where we compare against low-temperature HTST as well. The robustness of the algorithm with respect to the only free parameter it involves is ascertained. The method is then applied to perform tensile tests on gold nanopillars on strain rates as low as 100/s, bringing out the perils of high strain-rate molecular dynamics calculations. We also calculate temperature and stress dependence of activation free energy for surface nucleation of dislocations in pristine gold nanopillars under realistic loads. While maintaining fully atomistic resolution, we reach the fraction-of-a-second time scale regime. It is found that the activation free energy depends significantly and nonlinearly on the driving force (stress or strain) and temperature, leading to very high activation entropies for surface dislocation nucleation.

Ion-Scale Structure in Mercury's Magnetopause Reconnection Diffusion Region

NASA Technical Reports Server (NTRS)

Gershman, Daniel J.; Dorelli, John C.; DiBraccio, Gina A.; Raines, Jim M.; Slavin, James A.; Poh, Gangkai; Zurbuchen, Thomas H.

2016-01-01

The strength and time dependence of the electric field in a magnetopause diffusion region relate to the rate of magnetic reconnection between the solar wind and a planetary magnetic field. Here we use approximately 150 milliseconds measurements of energetic electrons from the Mercury Surface, Space Environment, GEochemistry, and Ranging (MESSENGER) spacecraft observed over Mercury's dayside polar cap boundary (PCB) to infer such small-scale changes in magnetic topology and reconnection rates. We provide the first direct measurement of open magnetic topology in flux transfer events at Mercury, structures thought to account for a significant portion of the open magnetic flux transport throughout the magnetosphere. In addition, variations in PCB latitude likely correspond to intermittent bursts of approximately 0.3 to 3 millivolts per meter reconnection electric fields separated by approximately 5 to10 seconds, resulting in average and peak normalized dayside reconnection rates of approximately 0.02 and approximately 0.2, respectively. These data demonstrate that structure in the magnetopause diffusion region at Mercury occurs at the smallest ion scales relevant to reconnection physics.

Diffusion studies with synchrotron Mössbauer spectroscopy

NASA Astrophysics Data System (ADS)

Jackson, J. M.

2011-12-01

Knowledge of diffusion properties is critical for understanding many physical and chemical processes in planetary interiors. For example, diffusion behavior provides constraints on chemical exchange and viscosity. Nuclear resonances open the window for observing diffusion properties under the extreme conditions that exist deep inside the Earth. Synchrotron Mössbauer spectroscopy (viz. nuclear forward scattering) makes use of synchrotron radiation coherently scattered in the forward direction after nuclear resonant excitation. The decay of the forward-scattered radiation is faster when atoms move on the time scale of the excited-state lifetime because of a loss of coherence. Such diffusion-activated processes lead to accelerated decay and line broadening in the measured signal. In the case of the Mössbauer active isotope 57Fe, the nuclear resonance at 14.4 keV has a natural lifetime of 141 ns. Therefore, one can observe diffusion events ranging from approximately one-sixth to 100 times the natural lifetime of 57Fe, which corresponds to diffusion coefficients of 10-16 and 10-13 m2/s, respectively and a two to three order of magnitude range of suitability. In this contribution, we will describe such measurements that access the microscopic details of the diffusion process for iron-bearing phases.

Modeling Bimolecular Reactive Transport With Mixing-Limitation: Theory and Application to Column Experiments

NASA Astrophysics Data System (ADS)

Ginn, T. R.

2018-01-01

The challenge of determining mixing extent of solutions undergoing advective-dispersive-diffusive transport is well known. In particular, reaction extent between displacing and displaced solutes depends on mixing at the pore scale, that is, generally smaller than continuum scale quantification that relies on dispersive fluxes. Here a novel mobile-mobile mass transfer approach is developed to distinguish diffusive mixing from dispersive spreading in one-dimensional transport involving small-scale velocity variations with some correlation, such as occurs in hydrodynamic dispersion, in which short-range ballistic transports give rise to dispersed but not mixed segregation zones, termed here ballisticules. When considering transport of a single solution, this approach distinguishes self-diffusive mixing from spreading, and in the case of displacement of one solution by another, each containing a participant reactant of an irreversible bimolecular reaction, this results in time-delayed diffusive mixing of reactants. The approach generates models for both kinetically controlled and equilibrium irreversible reaction cases, while honoring independently measured reaction rates and dispersivities. The mathematical solution for the equilibrium case is a simple analytical expression. The approach is applied to published experimental data on bimolecular reactions for homogeneous porous media under postasymptotic dispersive conditions with good results.

Thin film growth by 3D multi-particle diffusion limited aggregation model: Anomalous roughening and fractal analysis

NASA Astrophysics Data System (ADS)

Nasehnejad, Maryam; Nabiyouni, G.; Gholipour Shahraki, Mehran

2018-03-01

In this study a 3D multi-particle diffusion limited aggregation method is employed to simulate growth of rough surfaces with fractal behavior in electrodeposition process. A deposition model is used in which the radial motion of the particles with probability P, competes with random motions with probability 1 - P. Thin films growth is simulated for different values of probability P (related to the electric field) and thickness of the layer(related to the number of deposited particles). The influence of these parameters on morphology, kinetic of roughening and the fractal dimension of the simulated surfaces has been investigated. The results show that the surface roughness increases with increasing the deposition time and scaling exponents exhibit a complex behavior which is called as anomalous scaling. It seems that in electrodeposition process, radial motion of the particles toward the growing seeds may be an important mechanism leading to anomalous scaling. The results also indicate that the larger values of probability P, results in smoother topography with more densely packed structure. We have suggested a dynamic scaling ansatz for interface width has a function of deposition time, scan length and probability. Two different methods are employed to evaluate the fractal dimension of the simulated surfaces which are "cube counting" and "roughness" methods. The results of both methods show that by increasing the probability P or decreasing the deposition time, the fractal dimension of the simulated surfaces is increased. All gained values for fractal dimensions are close to 2.5 in the diffusion limited aggregation model.

Natural variability of atmospheric temperatures and geomagnetic intensity over a wide range of time scales.

PubMed

Pelletier, Jon D

2002-02-19

The majority of numerical models in climatology and geomagnetism rely on deterministic finite-difference techniques and attempt to include as many empirical constraints on the many processes and boundary conditions applicable to their very complex systems. Despite their sophistication, many of these models are unable to reproduce basic aspects of climatic or geomagnetic dynamics. We show that a simple stochastic model, which treats the flux of heat energy in the atmosphere by convective instabilities with random advection and diffusive mixing, does a remarkable job at matching the observed power spectrum of historical and proxy records for atmospheric temperatures from time scales of one day to one million years (Myr). With this approach distinct changes in the power-spectral form can be associated with characteristic time scales of ocean mixing and radiative damping. Similarly, a simple model of the diffusion of magnetic intensity in Earth's core coupled with amplification and destruction of the local intensity can reproduce the observed 1/f noise behavior of Earth's geomagnetic intensity from time scales of 1 (Myr) to 100 yr. In addition, the statistics of the fluctuations in the polarity reversal rate from time scales of 1 Myr to 100 Myr are consistent with the hypothesis that reversals are the result of variations in 1/f noise geomagnetic intensity above a certain threshold, suggesting that reversals may be associated with internal fluctuations rather than changes in mantle thermal or magnetic boundary conditions.

Natural variability of atmospheric temperatures and geomagnetic intensity over a wide range of time scales

PubMed Central

Pelletier, Jon D.

2002-01-01

The majority of numerical models in climatology and geomagnetism rely on deterministic finite-difference techniques and attempt to include as many empirical constraints on the many processes and boundary conditions applicable to their very complex systems. Despite their sophistication, many of these models are unable to reproduce basic aspects of climatic or geomagnetic dynamics. We show that a simple stochastic model, which treats the flux of heat energy in the atmosphere by convective instabilities with random advection and diffusive mixing, does a remarkable job at matching the observed power spectrum of historical and proxy records for atmospheric temperatures from time scales of one day to one million years (Myr). With this approach distinct changes in the power-spectral form can be associated with characteristic time scales of ocean mixing and radiative damping. Similarly, a simple model of the diffusion of magnetic intensity in Earth's core coupled with amplification and destruction of the local intensity can reproduce the observed 1/f noise behavior of Earth's geomagnetic intensity from time scales of 1 (Myr) to 100 yr. In addition, the statistics of the fluctuations in the polarity reversal rate from time scales of 1 Myr to 100 Myr are consistent with the hypothesis that reversals are the result of variations in 1/f noise geomagnetic intensity above a certain threshold, suggesting that reversals may be associated with internal fluctuations rather than changes in mantle thermal or magnetic boundary conditions. PMID:11875208

A New Numerical Scheme for Cosmic-Ray Transport

NASA Astrophysics Data System (ADS)

Jiang, Yan-Fei; Oh, S. Peng

2018-02-01

Numerical solutions of the cosmic-ray (CR) magnetohydrodynamic equations are dogged by a powerful numerical instability, which arises from the constraint that CRs can only stream down their gradient. The standard cure is to regularize by adding artificial diffusion. Besides introducing ad hoc smoothing, this has a significant negative impact on either computational cost or complexity and parallel scalings. We describe a new numerical algorithm for CR transport, with close parallels to two-moment methods for radiative transfer under the reduced speed of light approximation. It stably and robustly handles CR streaming without any artificial diffusion. It allows for both isotropic and field-aligned CR streaming and diffusion, with arbitrary streaming and diffusion coefficients. CR transport is handled explicitly, while source terms are handled implicitly. The overall time step scales linearly with resolution (even when computing CR diffusion) and has a perfect parallel scaling. It is given by the standard Courant condition with respect to a constant maximum velocity over the entire simulation domain. The computational cost is comparable to that of solving the ideal MHD equation. We demonstrate the accuracy and stability of this new scheme with a wide variety of tests, including anisotropic streaming and diffusion tests, CR-modified shocks, CR-driven blast waves, and CR transport in multiphase media. The new algorithm opens doors to much more ambitious and hitherto intractable calculations of CR physics in galaxies and galaxy clusters. It can also be applied to other physical processes with similar mathematical structure, such as saturated, anisotropic heat conduction.

Move-by-move dynamics of the advantage in chess matches reveals population-level learning of the game.

PubMed

Ribeiro, Haroldo V; Mendes, Renio S; Lenzi, Ervin K; del Castillo-Mussot, Marcelo; Amaral, Luís A N

2013-01-01

The complexity of chess matches has attracted broad interest since its invention. This complexity and the availability of large number of recorded matches make chess an ideal model systems for the study of population-level learning of a complex system. We systematically investigate the move-by-move dynamics of the white player's advantage from over seventy thousand high level chess matches spanning over 150 years. We find that the average advantage of the white player is positive and that it has been increasing over time. Currently, the average advantage of the white player is 0.17 pawns but it is exponentially approaching a value of 0.23 pawns with a characteristic time scale of 67 years. We also study the diffusion of the move dependence of the white player's advantage and find that it is non-Gaussian, has long-ranged anti-correlations and that after an initial period with no diffusion it becomes super-diffusive. We find that the duration of the non-diffusive period, corresponding to the opening stage of a match, is increasing in length and exponentially approaching a value of 15.6 moves with a characteristic time scale of 130 years. We interpret these two trends as a resulting from learning of the features of the game. Additionally, we find that the exponent [Formula: see text] characterizing the super-diffusive regime is increasing toward a value of 1.9, close to the ballistic regime. We suggest that this trend is due to the increased broadening of the range of abilities of chess players participating in major tournaments.

Move-by-Move Dynamics of the Advantage in Chess Matches Reveals Population-Level Learning of the Game

PubMed Central

Ribeiro, Haroldo V.; Mendes, Renio S.; Lenzi, Ervin K.; del Castillo-Mussot, Marcelo; Amaral, Luís A. N.

2013-01-01

The complexity of chess matches has attracted broad interest since its invention. This complexity and the availability of large number of recorded matches make chess an ideal model systems for the study of population-level learning of a complex system. We systematically investigate the move-by-move dynamics of the white player’s advantage from over seventy thousand high level chess matches spanning over 150 years. We find that the average advantage of the white player is positive and that it has been increasing over time. Currently, the average advantage of the white player is 0.17 pawns but it is exponentially approaching a value of 0.23 pawns with a characteristic time scale of 67 years. We also study the diffusion of the move dependence of the white player’s advantage and find that it is non-Gaussian, has long-ranged anti-correlations and that after an initial period with no diffusion it becomes super-diffusive. We find that the duration of the non-diffusive period, corresponding to the opening stage of a match, is increasing in length and exponentially approaching a value of 15.6 moves with a characteristic time scale of 130 years. We interpret these two trends as a resulting from learning of the features of the game. Additionally, we find that the exponent characterizing the super-diffusive regime is increasing toward a value of 1.9, close to the ballistic regime. We suggest that this trend is due to the increased broadening of the range of abilities of chess players participating in major tournaments. PMID:23382876

Orbital Transfer Vehicle Engine Technology High Velocity Ratio Diffusing Crossover

NASA Technical Reports Server (NTRS)

Lariviere, Brian W.

1992-01-01

High speed, high efficiency head rise multistage pumps require continuous passage diffusing crossovers to effectively convey the pumped fluid from the exit of one impeller to the inlet of the next impeller. On Rocketdyne's Orbital Transfer Vehicle (OTV), the MK49-F, a three stage high pressure liquid hydrogen turbopump, utilizes a 6.23 velocity ratio diffusing crossover. This velocity ratio approaches the diffusion limits for stable and efficient flow over the operating conditions required by the OTV system. The design of the high velocity ratio diffusing crossover was based on advanced analytical techniques anchored by previous tests of stationary two-dimensional diffusers with steady flow. To secure the design and the analytical techniques, tests were required with the unsteady whirling characteristics produced by an impeller. A tester was designed and fabricated using a 2.85 times scale model of the MK49-F turbopumps first stage, including the inducer, impeller, and the diffusing crossover. Water and air tests were completed to evaluate the large scale turbulence, non-uniform velocity, and non-steady velocity on the pump and crossover head and efficiency. Suction performance tests from 80 percent to 124 percent of design flow were completed in water to assess these pump characteristics. Pump and diffuser performance from the water and air tests were compared with the actual MK49-F test data in liquid hydrogen.

Stochastic Analysis of Reaction–Diffusion Processes

PubMed Central

Hu, Jifeng; Kang, Hye-Won

2013-01-01

Reaction and diffusion processes are used to model chemical and biological processes over a wide range of spatial and temporal scales. Several routes to the diffusion process at various levels of description in time and space are discussed and the master equation for spatially discretized systems involving reaction and diffusion is developed. We discuss an estimator for the appropriate compartment size for simulating reaction–diffusion systems and introduce a measure of fluctuations in a discretized system. We then describe a new computational algorithm for implementing a modified Gillespie method for compartmental systems in which reactions are aggregated into equivalence classes and computational cells are searched via an optimized tree structure. Finally, we discuss several examples that illustrate the issues that have to be addressed in general systems. PMID:23719732

Membrane Diffusion Occurs by Continuous-Time Random Walk Sustained by Vesicular Trafficking.

PubMed

Goiko, Maria; de Bruyn, John R; Heit, Bryan

2018-06-19

Diffusion in cellular membranes is regulated by processes that occur over a range of spatial and temporal scales. These processes include membrane fluidity, interprotein and interlipid interactions, interactions with membrane microdomains, interactions with the underlying cytoskeleton, and cellular processes that result in net membrane movement. The complex, non-Brownian diffusion that results from these processes has been difficult to characterize, and moreover, the impact of factors such as membrane recycling on membrane diffusion remains largely unexplored. We have used a careful statistical analysis of single-particle tracking data of the single-pass plasma membrane protein CD93 to show that the diffusion of this protein is well described by a continuous-time random walk in parallel with an aging process mediated by membrane corrals. The overall result is an evolution in the diffusion of CD93: proteins initially diffuse freely on the cell surface but over time become increasingly trapped within diffusion-limiting membrane corrals. Stable populations of freely diffusing and corralled CD93 are maintained by an endocytic/exocytic process in which corralled CD93 is selectively endocytosed, whereas freely diffusing CD93 is replenished by exocytosis of newly synthesized and recycled CD93. This trafficking not only maintained CD93 diffusivity but also maintained the heterogeneous distribution of CD93 in the plasma membrane. These results provide insight into the nature of the biological and biophysical processes that can lead to significantly non-Brownian diffusion of membrane proteins and demonstrate that ongoing membrane recycling is critical to maintaining steady-state diffusion and distribution of proteins in the plasma membrane. Copyright © 2018 Biophysical Society. Published by Elsevier Inc. All rights reserved.

Frequency Dependent Macro-dispersion Induced by Oscillatory Inputs and Spatial Heterogeneity

NASA Astrophysics Data System (ADS)

Rajabi, F.; Battiato, I.

2017-12-01

Elucidating flow and transport processes at the pore scale is the cornerstone of most hydrologic studies in the subsurface. This becomes even more imperative when the system is subject to a cyclic forcing. Such temporal variations with evolving heterogeneity of time scales spanning from days to years can influence transport phenomena at the pore level, e.g. yearly freeze/thaw in the thin active layer of soil above permafrost zone whose thickness increases throughout the thaw season. Moreover, understanding the interactions of different physical phenomena at the pore scale is key to predict the behavior at the continuum scale. Yet, the connection between periodic inputs at the pore scale and macrotransport is to a great extent unknown. In the spirit of homogenization technique, we derived a macrotime continuum-scale equation as well as expressions for the effective transport coefficients. The macrodispersion arises from contributions of molecular diffusion, spatial heterogeneity and time-dependent fluctuations. Moreover, we have quantified the solute spreading by effective dispersion in terms of dimensionless numbers (Pe, Da, and Strouhal), i.e. expressing the interplay of molecular diffusion, advection, reaction and signal frequency. Yet, as every macroscopic model, spatiotemporally averaged models can breakdown when certain criteria are violated. This makes the continuum scale equation a poor approximation for the processes at the pore scale. To this end, we also provide the conditions under which the space-time averaged equations accurately describe pore-scale processes. In addition, this study gives a robust evidence that transverse mixing can in fact benefit from fluctuating boundary forcing due to the interaction of temporal fluctuations and molecular diffusion. Furthermore, it provides a robust quantitative foundation for designing the desired systems since the interplay of geometry and external forcing has been directly connected to each other in terms of dimensionless (St) number. We compare our theoretical framework with data from an experiment performed on several micro-channels with different geometry and different frequencies of injection at the inlet. The proposed formulation is found to provide remarkably good predictions and correctly explain the experimental mixing dynamics.

On the resilience of helical magnetic fields to turbulent diffusion and the astrophysical implications

NASA Astrophysics Data System (ADS)

Blackman, Eric G.; Subramanian, Kandaswamy

2013-02-01

The extent to which large-scale magnetic fields are susceptible to turbulent diffusion is important for interpreting the need for in situ large-scale dynamos in astrophysics and for observationally inferring field strengths compared to kinetic energy. By solving coupled evolution equations for magnetic energy and magnetic helicity in a system initialized with isotropic turbulence and an arbitrarily helical large-scale field, we quantify the decay rate of the latter for a bounded or periodic system. The magnetic energy associated with the non-helical large-scale field decays at least as fast as the kinematically estimated turbulent diffusion rate, but the decay rate of the helical part depends on whether the ratio of its magnetic energy to the turbulent kinetic energy exceeds a critical value given by M1, c = (k1/k2)2, where k1 and k2 are the wavenumbers of the large and forcing scales. Turbulently diffusing helical fields to small scales while conserving magnetic helicity requires a rapid increase in total magnetic energy. As such, only when the helical field is subcritical can it so diffuse. When supercritical, it decays slowly, at a rate determined by microphysical dissipation even in the presence of macroscopic turbulence. In effect, turbulent diffusion of such a large-scale helical field produces small-scale helicity whose amplification abates further turbulent diffusion. Two curious implications are that (1) standard arguments supporting the need for in situ large-scale dynamos based on the otherwise rapid turbulent diffusion of large-scale fields require re-thinking since only the large-scale non-helical field is so diffused in a closed system. Boundary terms could however provide potential pathways for rapid change of the large-scale helical field. (2) Since M1, c ≪ 1 for k1 ≪ k2, the presence of long-lived ordered large-scale helical fields as in extragalactic jets do not guarantee that the magnetic field dominates the kinetic energy.

Adiabatic elimination of inertia of the stochastic microswimmer driven by α -stable noise

NASA Astrophysics Data System (ADS)

Noetel, Joerg; Sokolov, Igor M.; Schimansky-Geier, Lutz

2017-10-01

We consider a microswimmer that moves in two dimensions at a constant speed and changes the direction of its motion due to a torque consisting of a constant and a fluctuating component. The latter will be modeled by a symmetric Lévy-stable (α -stable) noise. The purpose is to develop a kinetic approach to eliminate the angular component of the dynamics to find a coarse-grained description in the coordinate space. By defining the joint probability density function of the position and of the orientation of the particle through the Fokker-Planck equation, we derive transport equations for the position-dependent marginal density, the particle's mean velocity, and the velocity's variance. At time scales larger than the relaxation time of the torque τϕ, the two higher moments follow the marginal density and can be adiabatically eliminated. As a result, a closed equation for the marginal density follows. This equation, which gives a coarse-grained description of the microswimmer's positions at time scales t ≫τϕ , is a diffusion equation with a constant diffusion coefficient depending on the properties of the noise. Hence, the long-time dynamics of a microswimmer can be described as a normal, diffusive, Brownian motion with Gaussian increments.

Adiabatic elimination of inertia of the stochastic microswimmer driven by α-stable noise.

PubMed

Noetel, Joerg; Sokolov, Igor M; Schimansky-Geier, Lutz

2017-10-01

We consider a microswimmer that moves in two dimensions at a constant speed and changes the direction of its motion due to a torque consisting of a constant and a fluctuating component. The latter will be modeled by a symmetric Lévy-stable (α-stable) noise. The purpose is to develop a kinetic approach to eliminate the angular component of the dynamics to find a coarse-grained description in the coordinate space. By defining the joint probability density function of the position and of the orientation of the particle through the Fokker-Planck equation, we derive transport equations for the position-dependent marginal density, the particle's mean velocity, and the velocity's variance. At time scales larger than the relaxation time of the torque τ_{ϕ}, the two higher moments follow the marginal density and can be adiabatically eliminated. As a result, a closed equation for the marginal density follows. This equation, which gives a coarse-grained description of the microswimmer's positions at time scales t≫τ_{ϕ}, is a diffusion equation with a constant diffusion coefficient depending on the properties of the noise. Hence, the long-time dynamics of a microswimmer can be described as a normal, diffusive, Brownian motion with Gaussian increments.

Brain-water diffusion coefficients reflect the severity of inherited prion disease

PubMed Central

Hyare, H.; Wroe, S.; Siddique, D.; Webb, T.; Fox, N. C.; Stevens, J.; Collinge, J.; Yousry, T.; Thornton, J. S.

2010-01-01

Objective: Inherited prion diseases are progressive neurodegenerative conditions, characterized by cerebral spongiosis, gliosis, and neuronal loss, caused by mutations within the prion protein (PRNP) gene. We wished to assess the potential of diffusion-weighted MRI as a biomarker of disease severity in inherited prion diseases. Methods: Twenty-five subjects (mean age 45.2 years) with a known PRNP mutation including 19 symptomatic patients, 6 gene-positive asymptomatic subjects, and 7 controls (mean age 54.1 years) underwent conventional and diffusion-weighted MRI. An index of normalized brain volume (NBV) and region of interest (ROI) mean apparent diffusion coefficient (ADC) for the head of caudate, putamen, and pulvinar nuclei were recorded. ADC histograms were computed for whole brain (WB) and gray matter (GM) tissue fractions. Clinical assessment utilized standardized clinical scores. Mann-Whitney U test and regression analyses were performed. Results: Symptomatic patients exhibited an increased WB mean ADC (p = 0.006) and GM mean ADC (p = 0.024) compared to controls. Decreased NBV and increased mean ADC measures significantly correlated with clinical measures of disease severity. Using a stepwise multivariate regression procedure, GM mean ADC was an independent predictor of Clinician's Dementia Rating score (p = 0.001), Barthel Index of activities of daily living (p = 0.001), and Rankin disability score (p = 0.019). Conclusions: Brain volume loss in inherited prion diseases is accompanied by increased cerebral apparent diffusion coefficient (ADC), correlating with increased disease severity. The association between gray matter ADC and clinical neurologic status suggests this measure may prove a useful biomarker of disease activity in inherited prion diseases. GLOSSARY ADAS-Cog = Alzheimer's Disease Assessment Scale–Cognitive subscale; ADC = apparent diffusion coefficient; ADL = Barthel Activities of Daily Living scale; BET = brain extraction tool; BPRS = Brief Psychiatric Rating Scale; BSE = bovine spongiform encephalopathy; CDR = Clinician's Dementia Rating Scale; CGIS = Clinician's Global Impression of Disease; CI = confidence interval; DWI = diffusion-weighted imaging; FLAIR = fluid-attenuated inversion recovery; FOV = field of view; GM = gray matter; LC = left head of caudate; LP = left putamen; LPu = left pulvinar; MMSE = Mini-Mental State Examination; NBV = normalized brain volume; PH = peak height; PL = peak location; RC = right head of caudate; RP = right putamen; RPu = right pulvinar; ROI = region of interest; sCJD = sporadic Creutzfeldt-Jakob disease; TE = echo time; TI = inversion time; TR = repetition time; vCJD = variant Creutzfeldt-Jakob disease; WB = whole brain; WM = white matter. PMID:20177119

Enhanced reaction kinetics and reactive mixing scale dynamics in mixing fronts under shear flow for arbitrary Damköhler numbers

NASA Astrophysics Data System (ADS)

Bandopadhyay, Aditya; Le Borgne, Tanguy; Méheust, Yves; Dentz, Marco

2017-02-01

Mixing fronts, where fluids of different chemical compositions mix with each other, are known to represent hotspots of chemical reaction in hydrological systems. These fronts are typically subjected to velocity gradients, ranging from the pore scale due to no slip boundary conditions at fluid solid interfaces, to the catchment scale due to permeability variations and complex geometry of the Darcy velocity streamlines. A common trait of these processes is that the mixing interface is strained by shear. Depending on the Péclet number Pe , which represents the ratio of the characteristic diffusion time to the characteristic shear time, and the Damköhler number Da , which represents the ratio of the characteristic diffusion time to the characteristic reaction time, the local reaction rates can be strongly impacted by the dynamics of the mixing interface. So far, this impact has been characterized mostly either in kinetics-limited or in mixing-limited conditions, that is, for either low or high Da. Here the coupling of shear flow and chemical reactivity is investigated for arbitrary Damköhler numbers, for a bimolecular reaction and an initial interface with separated reactants. Approximate analytical expressions for the global production rate and reactive mixing scale are derived based on a reactive lamella approach that allows for a general coupling between stretching enhanced mixing and chemical reactions. While for Pe < Da , reaction kinetics and stretching effects are decoupled, a scenario which we name "weak stretching", for Pe > Da , we uncover a "strong stretching" scenario where new scaling laws emerge from the interplay between reaction kinetics, diffusion, and stretching. The analytical results are validated against numerical simulations. These findings shed light on the effect of flow heterogeneity on the enhancement of chemical reaction and the creation of spatially localized hotspots of reactivity for a broad range of systems ranging from kinetic limited to mixing limited situations.

Fractional Progress Toward Understanding the Fractional Diffusion Limit: The Electromagnetic Response of Spatially Correlated Geomaterials

NASA Astrophysics Data System (ADS)

Weiss, C. J.; Beskardes, G. D.; Everett, M. E.

2016-12-01

In this presentation we review the observational evidence for anomalous electromagnetic diffusion in near-surface geophysical exploration and how such evidence is consistent with a detailed, spatially-correlated geologic medium. To date, the inference of multi-scale geologic correlation is drawn from two independent methods of data analysis. The first of which is analogous to seismic move-out, where the arrival time of an electromagnetic pulse is plotted as a function of transmitter/receiver separation. The "anomalous" diffusion is evident by the fractional-order power law behavior of these arrival times, with an exponent value between unity (pure diffusion) and 2 (lossless wave propagation). The second line of evidence comes from spectral analysis of small-scale fluctuations in electromagnetic profile data which cannot be explained in terms of instrument, user or random error. Rather, the power-law behavior of the spectral content of these signals (i.e., power versus wavenumber) and their increments reveals them to lie in a class of signals with correlations over multiple length scales, a class of signals known formally as fractional Brownian motion. Numerical results over simulated geology with correlated electrical texture - representative of, for example, fractures, sedimentary bedding or metamorphic lineation - are consistent with the (albeit limited, but growing) observational data, suggesting a possible mechanism and modeling approach for a more realistic geology. Furthermore, we show how similar simulated results can arise from a modeling approach where geologic texture is economically captured by a modified diffusion equation containing exotic, but manageable, fractional derivatives. These derivatives arise physically from the generalized convolutional form for the electromagnetic constitutive laws and thus have merit beyond mere mathematical convenience. In short, we are zeroing in on the anomalous, fractional diffusion limit from two converging directions: a zooming down of the macroscopic (fractional derivative) view; and, a heuristic homogenization of the atomistic (brute force discretization) view.

Single file diffusion into a semi-infinite tube.

PubMed

Farrell, Spencer G; Brown, Aidan I; Rutenberg, Andrew D

2015-11-23

We investigate single file diffusion (SFD) of large particles entering a semi-infinite tube, such as luminal diffusion of proteins into microtubules or flagella. While single-file effects have no impact on the evolution of particle density, we report significant single-file effects for individually tracked tracer particle motion. Both exact and approximate ordering statistics of particles entering semi-infinite tubes agree well with our stochastic simulations. Considering initially empty semi-infinite tubes, with particles entering at one end starting from an initial time t = 0, tracked particles are initially super-diffusive after entering the system, but asymptotically diffusive at later times. For finite time intervals, the ratio of the net displacement of individual single-file particles to the average displacement of untracked particles is reduced at early times and enhanced at later times. When each particle is numbered, from the first to enter (n = 1) to the most recent (n = N), we find good scaling collapse of this distance ratio for all n. Experimental techniques that track individual particles, or local groups of particles, such as photo-activation or photobleaching of fluorescently tagged proteins, should be able to observe these single-file effects. However, biological phenomena that depend on local concentration, such as flagellar extension or luminal enzymatic activity, should not exhibit single-file effects.

Full scale evaluation of diffuser ageing with clean water oxygen transfer tests.

PubMed

Krampe, J

2011-01-01

Aeration is a crucial part of the biological wastewater treatment in activated sludge systems and the main energy user of WWTPs. Approximately 50 to 60% of the total energy consumption of a WWTP can be attributed to the aeration system. The performance of the aeration system, and in the case of fine bubble diffused aeration the diffuser performance, has a significant impact on the overall plant efficiency. This paper seeks to isolate the changes of the diffuser performance over time by eliminating all other influencing parameters like sludge retention time, surfactants and reactor layout. To achieve this, different diffusers have been installed and tested in parallel treatment trains in two WWTPs. The diffusers have been performance tested in clean water tests under new conditions and after one year of operation. A set of material property tests describing the diffuser membrane quality was also performed. The results showed a significant drop in the performance of the EPDM diffuser in the first year which resulted in similar oxygen transfer efficiency around 16 g/m3/m for all tested systems. Even though the tested silicone diffusers did not show a drop in performance they had a low efficiency in the initial tests. The material properties indicate that the EPDM performance loss is partly due to the washout of additives.

Observatory enabled discovery of diffuse discharge temperature structure

NASA Astrophysics Data System (ADS)

Bemis, K. G.; Lee, R.; Ivakin, A. N.

2016-12-01

Underwater cabled observatories provide long term but short time and spatial scale measurements of hydrothermal discharge properties. For the first time, an intricate picture of diffuse discharge has been captured at both Axial Volcano (Axial) and the Main Endeavour Field (MEF) on the Juan de Fuca Ridge. This study combines thermistor (3D array, 2D array and spot) and acoustic data to compare the statistical and distribution characteristics of diffuse discharge for narrow crack flow (at ASHES field on Axial) and distributive flow out of a sulfide structure (at Grotto vent in MEF). Two surprising observations seem to apply to both styles of diffuse discharge: (1) thermal variance scales with the mean temperature suggesting coherent flow structures exist in the form of plumes, wakes or boundary layers, and (2) thermal hot spots are persistently localized in space, despite tidal current disruption. Thermal variance was measured at ASHES using a 3D thermistor array (TMPSF) with 10 s sampling over two years and at Grotto using 2D thermistor arrays with 1 hr sampling over several years and a ROV-held CTD (Seabird 39plus) with 0.5 second sampling over several minutes. For locations with temperatures greater than ambient, the variance in temperature scales with the mean temperature. This unusual statistical property is characteristic of self-similar flows like plumes, wakes, and boundary layers and arises from the bounded mixing of a cooling high temperature fluid with a cold ambient fluid. Thus this observation implies an underlying coherence to the diffuse discharge that has not yet been adequately captured or described. A coherent flow like a plume should have a discoverable spatial pattern, albeit one that may vary with the influence of tides. Acoustic observations ( 1m diameter footprint) of the Grotto sulfide edifice found stable local hot spots of diffuse discharge that sway with tides. In contrast, the 3D thermistor array at ASHES sees very localized (single thermistor) hot spots that persist for months. Is this a fundamental difference between two styles of diffuse discharge? Alternate conceptual models of diffuse discharge are used to place localized observations in a spatial context and develop a rigorous understanding of the spatial and temporal pattern of diffuse discharge for both crack and distributive styles.

A coupled model between mechanical deformation and chemical diffusion: An explanation for the preservation of chemical zonation in plagioclase at high temperatures

NASA Astrophysics Data System (ADS)

Zhong, Xin; Vrijmoed, Johannes; Moulas, Evangelos; Tajcmanová, Lucie

2016-04-01

Compositional zoning in metamorphic minerals have been generally recognized as an important geological feature to decipher the metamorphic history of rocks. The observed chemical zoning of, e.g. garnet, is commonly interpreted as disequilibrium between the fractionated inner core and the surrounding matrix. However, chemically zoned minerals were also observed in high grade rocks (T>800 degree C) where the duration of metamorphic processes was independently dated to take several Ma. This implies that temperature may not be the only factor that controls diffusion timescales, and grain scale pressure variation was proposed to be a complementary factor that may significantly contribute to the formation and preservation of chemical zoning in high temperature metamorphic minerals [Tajcmanová 2013, 2015]. Here, a coupled model is developed to simulate viscous deformation and chemical diffusion. The numerical approach considers the conservation of mass, momentum, and a constitutive relation developed from equilibrium thermodynamics. A compressible viscoelastic rheology is applied, which associates the volumetric change triggered by deformation and diffusion to a change of pressure. The numerical model is applied to the chemically zoned plagioclase rim described by [Tajcmanová 2014]. The diffusion process operating during the plagioclase rim formation can lead to a development of a pressure gradient. Such a pressure gradient, if maintained during ongoing viscous relaxation, can lead to the preservation of the observed chemical zonation in minerals. An important dimensionless number, the Deborah number, is defined as the ratio between the Maxwell viscoelastic relaxation time and the characteristic diffusion time. It characterizes the relative influence between the maintenance of grain scale pressure variation and chemical diffusion. Two extreme regimes are shown: the mechanically-controlled regime (high Deborah number) and diffusion-controlled regime (low Deborah number). In the mechanically-controlled regime, the grain scale pressure variation and thus the chemical zonation can be maintained due to slow viscous relaxation. Furthermore, by utilizing experimental flow laws and diffusion coefficients, the Deborah number is estimated in a variety of physical conditions. References Tajcmanová, L., Y. Podladchikov, R. Powell, E. Moulas, J.C. Vrijmoed, and J.A.D. Connolly, 2014. Journal of Metamorphic Geology, 32(2):195-207. Tajcmanová, L., J.C. Vrijmoed, and E. Moulas, 2015. Lithos, 216-217:338-351.

Transient anomalous diffusion in periodic systems: ergodicity, symmetry breaking and velocity relaxation

PubMed Central

Spiechowicz, Jakub; Łuczka, Jerzy; Hänggi, Peter

2016-01-01

We study far from equilibrium transport of a periodically driven inertial Brownian particle moving in a periodic potential. As detected for a SQUID ratchet dynamics, the mean square deviation of the particle position from its average may involve three distinct intermediate, although extended diffusive regimes: initially as superdiffusion, followed by subdiffusion and finally, normal diffusion in the asymptotic long time limit. Even though these anomalies are transient effects, their lifetime can be many, many orders of magnitude longer than the characteristic time scale of the setup and turns out to be extraordinarily sensitive to the system parameters like temperature or the potential asymmetry. In the paper we reveal mechanisms of diffusion anomalies related to ergodicity of the system, symmetry breaking of the periodic potential and ultraslow relaxation of the particle velocity towards its steady state. Similar sequences of the diffusive behaviours could be detected in various systems including, among others, colloidal particles in random potentials, glass forming liquids and granular gases. PMID:27492219

Scale-dependent behavior of the foredune: Implications for barrier island response to storms and sea-level rise

NASA Astrophysics Data System (ADS)

Houser, Chris; Wernette, Phil; Weymer, Bradley A.

2018-02-01

The impact of storm surge on a barrier island tends to be considered from a single cross-shore dimension, dependent on the relative elevations of the storm surge and dune crest. However, the foredune is rarely uniform and can exhibit considerable variation in height and width at a range of length scales. In this study, LiDAR data from barrier islands in Texas and Florida are used to explore how shoreline position and dune morphology vary alongshore, and to determine how this variability is altered or reinforced by storms and post-storm recovery. Wavelet analysis reveals that a power law can approximate historical shoreline change across all scales, but that storm-scale shoreline change ( 10 years) and dune height exhibit similar scale-dependent variations at swash and surf zone scales (< 1000 m). The in-phase nature of the relationship between dune height and storm-scale shoreline change indicates that areas of greater storm-scale shoreline retreat are associated with areas of smaller dunes. It is argued that the decoupling of storm-scale and historical shoreline change at swash and surf zone scales is also associated with the alongshore redistribution of sediment and the tendency of shorelines to evolve to a more diffusive (or straight) pattern with time. The wavelet analysis of the data for post-storm dune recovery is also characterized by red noise at the smallest scales characteristic of diffusive systems, suggesting that it is possible that small-scale variations in dune height can be repaired through alongshore recovery and expansion if there is sufficient time between storms. However, the time required for dune recovery exceeds the time between storms capable of eroding and overwashing the dune. Correlation between historical shoreline retreat and the variance of the dune at swash and surf zone scales suggests that the persistence of the dune is an important control on transgression through island migration or shoreline retreat with relative sea-level rise.

Models of inertial range spectra of interplanetary magnetohydrodynamic turbulence

NASA Technical Reports Server (NTRS)

Zhou, YE; Matthaeus, William H.

1990-01-01

A framework based on turbulence theory is presented to develop approximations for the local turbulence effects that are required in transport models. An approach based on Kolmogoroff-style dimensional analysis is presented as well as one based on a wave-number diffusion picture. Particular attention is given to the case of MHD turbulence with arbitrary cross helicity and with arbitrary ratios of the Alfven time scale and the nonlinear time scale.

Diffusion relaxation times of nonequilibrium isolated small bodies and their solid phase ensembles to equilibrium states

NASA Astrophysics Data System (ADS)

Tovbin, Yu. K.

2017-08-01

The possibility of obtaining analytical estimates in a diffusion approximation of the times needed by nonequilibrium small bodies to relax to their equilibrium states based on knowledge of the mass transfer coefficient is considered. This coefficient is expressed as the product of the self-diffusion coefficient and the thermodynamic factor. A set of equations for the diffusion transport of mixture components is formulated, characteristic scales of the size of microheterogeneous phases are identified, and effective mass transfer coefficients are constructed for them. Allowing for the developed interface of coexisting and immiscible phases along with the porosity of solid phases is discussed. This approach can be applied to the diffusion equalization of concentrations of solid mixture components in many physicochemical systems: the mutual diffusion of components in multicomponent systems (alloys, semiconductors, solid mixtures of inert gases) and the mass transfer of an absorbed mobile component in the voids of a matrix consisting of slow components or a mixed composition of mobile and slow components (e.g., hydrogen in metals, oxygen in oxides, and the transfer of molecules through membranes of different natures, including polymeric).

Plasma diffusion at the magnetopause? The case of lower hybrid drift waves

NASA Technical Reports Server (NTRS)

Treumann, R. A.; Labelle, J.; Pottelette, R.; Gary, S. P.

1990-01-01

The diffusion expected from the quasilinear theory of the lower hybrid drift instability at the Earth's magnetopause is recalculated. The resulting diffusion coefficient is in principle just marginally large enough to explain the thickness of the boundary layer under quiet conditions, based on observational upper limits for the wave intensities. Thus, one possible model for the boundary layer could involve equilibrium between the diffusion arising from lower hybrid waves and various low processes. However, some recent data and simulations seems to indicate that the magnetopause is not consistent with such a soft diffusive equilibrium model. Furthermore, investigation of the nonlinear equations for the lower hybrid waves for magnetopause parameters indicates that the quasilinear state may never arise because coalescence to large wavelengths, followed by collapse once a critical wavelengths is reached, occur on a time scale faster than the quasilinear diffusion. In this case, an inhomogeneous boundary layer is to be expected. More simulations are required over longer time periods to explore whether this nonlinear evolution really takes place at the magnetopause.

Fluctuation correlation models for receptor immobilization

NASA Astrophysics Data System (ADS)

Fourcade, B.

2017-12-01

Nanoscale dynamics with cycles of receptor diffusion and immobilization by cell-external-or-internal factors is a key process in living cell adhesion phenomena at the origin of a plethora of signal transduction pathways. Motivated by modern correlation microscopy approaches, the receptor correlation functions in physical models based on diffusion-influenced reaction is studied. Using analytical and stochastic modeling, this paper focuses on the hybrid regime where diffusion and reaction are not truly separable. The time receptor autocorrelation functions are shown to be indexed by different time scales and their asymptotic expansions are given. Stochastic simulations show that this analysis can be extended to situations with a small number of molecules. It is also demonstrated that this analysis applies when receptor immobilization is coupled to environmental noise.

Reynolds-number dependence of the longitudinal dispersion in turbulent pipe flow.

PubMed

Hawkins, Christopher; Angheluta, Luiza; Krotkiewski, Marcin; Jamtveit, Bjørn

2016-04-01

In Taylor's theory, the longitudinal dispersion in turbulent pipe flows approaches, on long time scales, a diffusive behavior with a constant diffusivity K_{L}, which depends empirically on the Reynolds number Re. We show that the dependence on Re can be determined from the turbulent energy spectrum. By using the intimate connection between the friction factor and the longitudinal dispersion in wall-bounded turbulence, we predict different asymptotic scaling laws of K_{L}(Re) depending on the different turbulent cascades in two-dimensional turbulence. We also explore numerically the K_{L}(Re) dependence in turbulent channel flows with smooth and rough walls using a lattice Boltzmann method.

Parallel STEPS: Large Scale Stochastic Spatial Reaction-Diffusion Simulation with High Performance Computers

PubMed Central

Chen, Weiliang; De Schutter, Erik

2017-01-01

Stochastic, spatial reaction-diffusion simulations have been widely used in systems biology and computational neuroscience. However, the increasing scale and complexity of models and morphologies have exceeded the capacity of any serial implementation. This led to the development of parallel solutions that benefit from the boost in performance of modern supercomputers. In this paper, we describe an MPI-based, parallel operator-splitting implementation for stochastic spatial reaction-diffusion simulations with irregular tetrahedral meshes. The performance of our implementation is first examined and analyzed with simulations of a simple model. We then demonstrate its application to real-world research by simulating the reaction-diffusion components of a published calcium burst model in both Purkinje neuron sub-branch and full dendrite morphologies. Simulation results indicate that our implementation is capable of achieving super-linear speedup for balanced loading simulations with reasonable molecule density and mesh quality. In the best scenario, a parallel simulation with 2,000 processes runs more than 3,600 times faster than its serial SSA counterpart, and achieves more than 20-fold speedup relative to parallel simulation with 100 processes. In a more realistic scenario with dynamic calcium influx and data recording, the parallel simulation with 1,000 processes and no load balancing is still 500 times faster than the conventional serial SSA simulation. PMID:28239346

Parallel STEPS: Large Scale Stochastic Spatial Reaction-Diffusion Simulation with High Performance Computers.

PubMed

Chen, Weiliang; De Schutter, Erik

2017-01-01

Stochastic, spatial reaction-diffusion simulations have been widely used in systems biology and computational neuroscience. However, the increasing scale and complexity of models and morphologies have exceeded the capacity of any serial implementation. This led to the development of parallel solutions that benefit from the boost in performance of modern supercomputers. In this paper, we describe an MPI-based, parallel operator-splitting implementation for stochastic spatial reaction-diffusion simulations with irregular tetrahedral meshes. The performance of our implementation is first examined and analyzed with simulations of a simple model. We then demonstrate its application to real-world research by simulating the reaction-diffusion components of a published calcium burst model in both Purkinje neuron sub-branch and full dendrite morphologies. Simulation results indicate that our implementation is capable of achieving super-linear speedup for balanced loading simulations with reasonable molecule density and mesh quality. In the best scenario, a parallel simulation with 2,000 processes runs more than 3,600 times faster than its serial SSA counterpart, and achieves more than 20-fold speedup relative to parallel simulation with 100 processes. In a more realistic scenario with dynamic calcium influx and data recording, the parallel simulation with 1,000 processes and no load balancing is still 500 times faster than the conventional serial SSA simulation.

Characterizing acid diffusion lengths in chemically amplified resists from measurements of deprotection kinetics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Patil, Abhijit A.; Pandey, Yogendra Narayan; Doxastakis, Manolis

2014-10-01

The acid-catalyzed deprotection of glassy poly(4-hydroxystyrene-co-tertbutyl acrylate) films was studied with infrared absorbance spectroscopy and stochastic simulations. Experimental data were interpreted with a simple description of subdiffusive acid transport coupled to second-order acid loss. This model predicts key attributes of observed deprotection rates, such as fast reaction at short times, slow reaction at long times, and a nonlinear dependence on acid loading. Fickian diffusion is approached by increasing the post-exposure bake temperature or adding plasticizing agents to the polymer resin. These findings demonstrate that acid mobility and overall deprotection kinetics are coupled to glassy matrix dynamics. To complement the analysismore » of bulk kinetics, acid diffusion lengths were calculated from the anomalous transport model and compared with nanopattern line widths. The consistent scaling between experiments and simulations suggests that the anomalous diffusion model could be further developed into a predictive lithography tool.« less

Unsteady Crystal Growth Due to Step-Bunch Cascading

NASA Technical Reports Server (NTRS)

Vekilov, Peter G.; Lin, Hong; Rosenberger, Franz

1997-01-01

Based on our experimental findings of growth rate fluctuations during the crystallization of the protein lysozym, we have developed a numerical model that combines diffusion in the bulk of a solution with diffusive transport to microscopic growth steps that propagate on a finite crystal facet. Nonlinearities in layer growth kinetics arising from step interaction by bulk and surface diffusion, and from step generation by surface nucleation, are taken into account. On evaluation of the model with properties characteristic for the solute transport, and the generation and propagation of steps in the lysozyme system, growth rate fluctuations of the same magnitude and characteristic time, as in the experiments, are obtained. The fluctuation time scale is large compared to that of step generation. Variations of the governing parameters of the model reveal that both the nonlinearity in step kinetics and mixed transport-kinetics control of the crystallization process are necessary conditions for the fluctuations. On a microscopic scale, the fluctuations are associated with a morphological instability of the vicinal face, in which a step bunch triggers a cascade of new step bunches through the microscopic interfacial supersaturation distribution.

A spectral radius scaling semi-implicit iterative time stepping method for reactive flow simulations with detailed chemistry

NASA Astrophysics Data System (ADS)

Xie, Qing; Xiao, Zhixiang; Ren, Zhuyin

2018-09-01

A spectral radius scaling semi-implicit time stepping scheme has been developed for simulating unsteady compressible reactive flows with detailed chemistry, in which the spectral radius in the LUSGS scheme has been augmented to account for viscous/diffusive and reactive terms and a scalar matrix is proposed to approximate the chemical Jacobian using the minimum species destruction timescale. The performance of the semi-implicit scheme, together with a third-order explicit Runge-Kutta scheme and a Strang splitting scheme, have been investigated in auto-ignition and laminar premixed and nonpremixed flames of three representative fuels, e.g., hydrogen, methane, and n-heptane. Results show that the minimum species destruction time scale can well represent the smallest chemical time scale in reactive flows and the proposed scheme can significantly increase the allowable time steps in simulations. The scheme is stable when the time step is as large as 10 μs, which is about three to five orders of magnitude larger than the smallest time scales in various tests considered. For the test flames considered, the semi-implicit scheme achieves second order of accuracy in time. Moreover, the errors in quantities of interest are smaller than those from the Strang splitting scheme indicating the accuracy gain when the reaction and transport terms are solved coupled. Results also show that the relative efficiency of different schemes depends on fuel mechanisms and test flames. When the minimum time scale in reactive flows is governed by transport processes instead of chemical reactions, the proposed semi-implicit scheme is more efficient than the splitting scheme. Otherwise, the relative efficiency depends on the cost in sub-iterations for convergence within each time step and in the integration for chemistry substep. Then, the capability of the compressible reacting flow solver and the proposed semi-implicit scheme is demonstrated for capturing the hydrogen detonation waves. Finally, the performance of the proposed method is demonstrated in a two-dimensional hydrogen/air diffusion flame.

Fluorescence correlation spectroscopy diffusion laws to probe the submicron cell membrane organization.

PubMed

Wawrezinieck, Laure; Rigneault, Hervé; Marguet, Didier; Lenne, Pierre-François

2005-12-01

To probe the complexity of the cell membrane organization and dynamics, it is important to obtain simple physical observables from experiments on live cells. Here we show that fluorescence correlation spectroscopy (FCS) measurements at different spatial scales enable distinguishing between different submicron confinement models. By plotting the diffusion time versus the transverse area of the confocal volume, we introduce the so-called FCS diffusion law, which is the key concept throughout this article. First, we report experimental FCS diffusion laws for two membrane constituents, which are respectively a putative raft marker and a cytoskeleton-hindered transmembrane protein. We find that these two constituents exhibit very distinct behaviors. To understand these results, we propose different models, which account for the diffusion of molecules either in a membrane comprising isolated microdomains or in a meshwork. By simulating FCS experiments for these two types of organization, we obtain FCS diffusion laws in agreement with our experimental observations. We also demonstrate that simple observables derived from these FCS diffusion laws are strongly related to confinement parameters such as the partition of molecules in microdomains and the average confinement time of molecules in a microdomain or a single mesh of a meshwork.

Anisotropic diffusion at the field scale in a 4-year multi-tracer diffusion and retention experiment - I: Insights from the experimental data

NASA Astrophysics Data System (ADS)

Gimmi, Thomas; Leupin, Olivier X.; Eikenberg, Jost; Glaus, Martin A.; Van Loon, Luc R.; Waber, H. Niklaus; Wersin, Paul; Wang, Hao A. O.; Grolimund, Daniel; Borca, Camelia N.; Dewonck, Sarah; Wittebroodt, Charles

2014-01-01

Claystones are considered worldwide as barrier materials for nuclear waste repositories. In the Mont Terri underground research laboratory (URL), a nearly 4-year diffusion and retention (DR) experiment has been performed in Opalinus Clay. It aimed at (1) obtaining data at larger space and time scales than in laboratory experiments and (2) under relevant in situ conditions with respect to pore water chemistry and mechanical stress, (3) quantifying the anisotropy of in situ diffusion, and (4) exploring possible effects of a borehole-disturbed zone. The experiment included two tracer injection intervals in a borehole perpendicular to bedding, through which traced artificial pore water (APW) was circulated, and a pressure monitoring interval. The APW was spiked with neutral tracers (HTO, HDO, H2O-18), anions (Br, I, SeO4), and cations (Na-22, Ba-133, Sr-85, Cs-137, Co-60, Eu-152, stable Cs, and stable Eu). Most tracers were added at the beginning, some were added at a later stage. The hydraulic pressure in the injection intervals was adjusted according to the measured value in the pressure monitoring interval to ensure transport by diffusion only. Concentration time-series in the APW within the borehole intervals were obtained, as well as 2D concentration distributions in the rock at the end of the experiment after overcoring and subsampling which resulted in ∼250 samples and ∼1300 analyses. As expected, HTO diffused the furthest into the rock, followed by the anions (Br, I, SeO4) and by the cationic sorbing tracers (Na-22, Ba-133, Cs, Cs-137, Co-60, Eu-152). The diffusion of SeO4 was slower than that of Br or I, approximately proportional to the ratio of their diffusion coefficients in water. Ba-133 diffused only into ∼0.1 m during the ∼4 a. Stable Cs, added at a higher concentration than Cs-137, diffused further into the rock than Cs-137, consistent with a non-linear sorption behavior. The rock properties (e.g., water contents) were rather homogeneous at the centimeter scale, with no evidence of a borehole-disturbed zone. In situ anisotropy ratios for diffusion, derived for the first time directly from field data, are larger for HTO and Na-22 (∼5) than for anions (∼3-4 for Br and I). The lower ionic strength of the pore water at this location (∼0.22 M) as compared to locations of earlier experiments in the Mont Terri URL (∼0.39 M) had no notable effect on the anion accessible pore fraction for Cl, Br, and I: the value of 0.55 is within the range of earlier data. Detailed transport simulations involving different codes will be presented in a companion paper.

Modes and emergent time scales of embayed beach dynamics

NASA Astrophysics Data System (ADS)

Ratliff, Katherine M.; Murray, A. Brad

2014-10-01

In this study, we use a simple numerical model (the Coastline Evolution Model) to explore alongshore transport-driven shoreline dynamics within generalized embayed beaches (neglecting cross-shore effects). Using principal component analysis (PCA), we identify two primary orthogonal modes of shoreline behavior that describe shoreline variation about its unchanging mean position: the rotation mode, which has been previously identified and describes changes in the mean shoreline orientation, and a newly identified breathing mode, which represents changes in shoreline curvature. Wavelet analysis of the PCA mode time series reveals characteristic time scales of these modes (typically years to decades) that emerge within even a statistically constant white-noise wave climate (without changes in external forcing), suggesting that these time scales can arise from internal system dynamics. The time scales of both modes increase linearly with shoreface depth, suggesting that the embayed beach sediment transport dynamics exhibit a diffusive scaling.

Strain-Rate-Free Diffusion Flames: Initiation, Properties, and Quenching

NASA Technical Reports Server (NTRS)

Fendell, Francis; Rungaldier, Harald; Gokoglu, Suleyman; Schultz, Donald

1997-01-01

For about a half century, the stabilization of a steady planar deflagration on a heat-sink-type flat-flame burner has been of extraordinary service for the theoretical modeling and diagnostic probing of combusting gaseous mixtures. However, most engineering devices and most unwanted fire involve the burning of initially unmixed reactants. The most vigorous burning of initially separated gaseous fuel and oxidizer is the diffusion flame. In this useful idealization (limiting case), the reactants are converted to product at a mathematically thin interface, so no interpenetration of fuel and oxidizer occurs. This limit is of practical importance because it often characterizes the condition of optimal performance (and sometimes environmentally objectionable operation) of a combustor. A steady planar diffusion flame is most closely approached in the laboratory in the counterflow apparatus. The utility of this simple-strain-rate flow for the modeling and probing of diffusion flames was noted by Pandya and Weinberg 35 years ago, though only in the last decade or so has its use become internationally common place. However, typically, as the strain rate a is reduced below about 20 cm(exp -1), and the diffusion-flame limit (reaction rate much faster than the flow rate) is approached, the burning is observed to become unstable in earth gravity. The advantageous steady planar flow is not available in the diffusion-flame limit in earth gravity. This is unfortunate because the typical spatial scale in a counterflow is (k/a)(sup 1/2), where k denotes a characteristic diffusion coefficient; thus, the length scale becomes large, and the reacting flow is particularly amenable to diagnostic probing, as the diffusion-flame limit is approached. The disruption of planar symmetry is owing the fact that, as the strain rate a decreases, the residence time (l/a) of the throughput in the counterflow burner increases. Observationally, when the residence time exceeds about 50 msec, the inevitably present convective (Rayleigh-Benard) instabilities, associated with hot-under-cold (flame-under-fresh-reactant) stratification of fluid in a gravitational field, have time to grow to finite amplitude during transit of the burner.

Diffusive Imaging of Hydraulically Induced and Natural Fracture Systems

NASA Astrophysics Data System (ADS)

Eftekhari, B.; Marder, M. P.; Patzek, T. W.

2017-12-01

Hydraulic fracturing of tight shales continues to provide the US with a major source of energy. Efficiency of gas recovery in shales depends upon the geometry of the resulting network of fractures, the details of which are not yet fully understood. The present research explores how much of the underlying geometry can be deduced from the time dependence of the flow of gas out of the reservoir. We consider both ideal and real gas. In the case of real gas, we calculate production rate for parallel planar hydrofractures embedded in an infinite reservoir. Transport is governed by a nonlinear diffusion equation, which we solve exactly with a scaling curve. The scaling curve production rate declines initially as 1 over square root time, then as an exponential, and finally as 1 over square root of time again at late time. We show that for a given hydraulically fractured well, the onsets of transition between different decline regimes provides a direct estimate of a characteristic spacing of the underlying fracture network. We show that the scaling solution accurately fits the production history of more than 15,000 wells in the Barnett Shale. Almost all of the wells either have not yet transitioned into the late time decline or have been refractured while in exponential decline. However, there are 36 wells which show the late time transition. These allow us to calculate the characteristic spacing, which turns out to have a mode at about 10 m, a minimum at 1.6 m and a maximum at 13.3 m. We estimate that over 30 years these wells will produce on average about 45% more gas because of diffusion from the infinite external reservoir than they would if this contribution is neglected. Finally, we compute the rate at which ideal gas diffuses within an infinite region of rock into a specific absorbing fractal fracture network, which we model using geological constraints and percolation theory. Our solution employs a Brownian walk and the first passage kinetic Monte Carlo algorithm that is robust and efficient. A striking feature of this solution is the presence of a power law decline.

Information filtering via a scaling-based function.

PubMed

Qiu, Tian; Zhang, Zi-Ke; Chen, Guang

2013-01-01

Finding a universal description of the algorithm optimization is one of the key challenges in personalized recommendation. In this article, for the first time, we introduce a scaling-based algorithm (SCL) independent of recommendation list length based on a hybrid algorithm of heat conduction and mass diffusion, by finding out the scaling function for the tunable parameter and object average degree. The optimal value of the tunable parameter can be abstracted from the scaling function, which is heterogeneous for the individual object. Experimental results obtained from three real datasets, Netflix, MovieLens and RYM, show that the SCL is highly accurate in recommendation. More importantly, compared with a number of excellent algorithms, including the mass diffusion method, the original hybrid method, and even an improved version of the hybrid method, the SCL algorithm remarkably promotes the personalized recommendation in three other aspects: solving the accuracy-diversity dilemma, presenting a high novelty, and solving the key challenge of cold start problem.

Scaling of size distributions of C60 and C70 fullerene surface islands

NASA Astrophysics Data System (ADS)

Dubrovskii, V. G.; Berdnikov, Y.; Olyanich, D. A.; Mararov, V. V.; Utas, T. V.; Zotov, A. V.; Saranin, A. A.

2017-06-01

We present experimental data and a theoretical analysis for the size distributions of C60 and C70 surface islands deposited onto In-modified Si(111)√3 × √3-Au surface under different conditions. We show that both fullerene islands feature an analytic Vicsek-Family scaling shape where the scaled size distributions are given by a power law times an incomplete beta-function with the required normalization. The power exponent in this distribution corresponds to the fractal shape of two-dimensional islands, confirmed by the experimentally observed morphologies. Quite interestingly, we do not see any significant difference between C60 and C70 fullerenes in terms of either scaling parameters or temperature dependence of the diffusion constants. In particular, we deduce the activation energy for surface diffusion of ED = 140 ± 10 meV for both types of fullerenes.

Equivalent isotropic scattering formulation for transient short-pulse radiative transfer in anisotropic scattering planar media.

PubMed

Guo, Z; Kumar, S

2000-08-20

An isotropic scaling formulation is evaluated for transient radiative transfer in a one-dimensional planar slab subject to collimated and/or diffuse irradiation. The Monte Carlo method is used to implement the equivalent scattering and exact simulations of the transient short-pulse radiation transport through forward and backward anisotropic scattering planar media. The scaled equivalent isotropic scattering results are compared with predictions of anisotropic scattering in various problems. It is found that the equivalent isotropic scaling law is not appropriate for backward-scattering media in transient radiative transfer. Even for an optically diffuse medium, the differences in temporal transmittance and reflectance profiles between predictions of backward anisotropic scattering and equivalent isotropic scattering are large. Additionally, for both forward and backward anisotropic scattering media, the transient equivalent isotropic results are strongly affected by the change of photon flight time, owing to the change of flight direction associated with the isotropic scaling technique.

Direct measurement of lateral transport in membranes by using time-resolved spatial photometry.

PubMed Central

Kapitza, H G; McGregor, G; Jacobson, K A

1985-01-01

Spatially resolving light detectors allow, with proper calibration, quantitative analysis of the variations in two-dimensional intensity distributions over time. An ultrasensitive microfluorometer was assembled by using as a detector a microchannel plate-intensified video camera. The camera was interfaced with a software-based digital video analysis system to digitize, average, and process images and to directly control the timing of the experiments to minimize exposure of the specimen to light. The detector system has been characterized to allow its use as a photometer. A major application has been to perform fluorescence recovery after photobleaching measurements by using the camera in place of a photomultiplier tube (video-FRAP) with the goal of detecting possible anisotropic diffusion or convective flow. Analysis of the data on macromolecular diffusion in homogenous aqueous glycol solutions yielded diffusion constants in agreement with previous measurements. Results on lipid probe diffusion in dimyristoylphosphatidylcholine multibilayers indicated that at temperatures above the gel-to-liquid crystalline phase transition diffusion is isotropic, and analysis of video-FRAP data yielded diffusion coefficients consistent with those measured previously by using spot photobleaching. However, lipid probes in these multibilayers held just below the main phase transition temperature exhibited markedly anisotropic diffusive fluxes when the bleaching beam was positioned proximate to domain boundaries in the P beta' phase. Lipid probes and lectin receptor complexes diffused isotropically in fibroblast surface membranes with little evidence for diffusion channeled parallel to stress fibers. A second application was to trace the time evolution of cell surface reactions such as patching. The feasibility of following, on the optical scale, the growth of individual receptor clusters induced by the ligand wheat germ agglutinin was demonstrated. PMID:3858869

Direct measurement of lateral transport in membranes by using time-resolved spatial photometry.

PubMed

Kapitza, H G; McGregor, G; Jacobson, K A

1985-06-01

Spatially resolving light detectors allow, with proper calibration, quantitative analysis of the variations in two-dimensional intensity distributions over time. An ultrasensitive microfluorometer was assembled by using as a detector a microchannel plate-intensified video camera. The camera was interfaced with a software-based digital video analysis system to digitize, average, and process images and to directly control the timing of the experiments to minimize exposure of the specimen to light. The detector system has been characterized to allow its use as a photometer. A major application has been to perform fluorescence recovery after photobleaching measurements by using the camera in place of a photomultiplier tube (video-FRAP) with the goal of detecting possible anisotropic diffusion or convective flow. Analysis of the data on macromolecular diffusion in homogenous aqueous glycol solutions yielded diffusion constants in agreement with previous measurements. Results on lipid probe diffusion in dimyristoylphosphatidylcholine multibilayers indicated that at temperatures above the gel-to-liquid crystalline phase transition diffusion is isotropic, and analysis of video-FRAP data yielded diffusion coefficients consistent with those measured previously by using spot photobleaching. However, lipid probes in these multibilayers held just below the main phase transition temperature exhibited markedly anisotropic diffusive fluxes when the bleaching beam was positioned proximate to domain boundaries in the P beta' phase. Lipid probes and lectin receptor complexes diffused isotropically in fibroblast surface membranes with little evidence for diffusion channeled parallel to stress fibers. A second application was to trace the time evolution of cell surface reactions such as patching. The feasibility of following, on the optical scale, the growth of individual receptor clusters induced by the ligand wheat germ agglutinin was demonstrated.

Turbulent transport with intermittency: Expectation of a scalar concentration.

PubMed

Rast, Mark Peter; Pinton, Jean-François; Mininni, Pablo D

2016-04-01

Scalar transport by turbulent flows is best described in terms of Lagrangian parcel motions. Here we measure the Eulerian distance travel along Lagrangian trajectories in a simple point vortex flow to determine the probabilistic impulse response function for scalar transport in the absence of molecular diffusion. As expected, the mean squared Eulerian displacement scales ballistically at very short times and diffusively for very long times, with the displacement distribution at any given time approximating that of a random walk. However, significant deviations in the displacement distributions from Rayleigh are found. The probability of long distance transport is reduced over inertial range time scales due to spatial and temporal intermittency. This can be modeled as a series of trapping events with durations uniformly distributed below the Eulerian integral time scale. The probability of long distance transport is, on the other hand, enhanced beyond that of the random walk for both times shorter than the Lagrangian integral time and times longer than the Eulerian integral time. The very short-time enhancement reflects the underlying Lagrangian velocity distribution, while that at very long times results from the spatial and temporal variation of the flow at the largest scales. The probabilistic impulse response function, and with it the expectation value of the scalar concentration at any point in space and time, can be modeled using only the evolution of the lowest spatial wave number modes (the mean and the lowest harmonic) and an eddy based constrained random walk that captures the essential velocity phase relations associated with advection by vortex motions. Preliminary examination of Lagrangian tracers in three-dimensional homogeneous isotropic turbulence suggests that transport in that setting can be similarly modeled.

Diffusion in translucent media.

PubMed

Shi, Zhou; Genack, Azriel Z

2018-05-10

Diffusion is the result of repeated random scattering. It governs a wide range of phenomena from Brownian motion, to heat flow through window panes, neutron flux in fuel rods, dispersion of light in human tissue, and electronic conduction. It is universally acknowledged that the diffusion approach to describing wave transport fails in translucent samples thinner than the distance between scattering events such as are encountered in meteorology, astronomy, biomedicine, and communications. Here we show in optical measurements and numerical simulations that the scaling of transmission and the intensity profiles of transmission eigenchannels have the same form in translucent as in opaque media. Paradoxically, the similarities in transport across translucent and opaque samples explain the puzzling observations of suppressed optical and ultrasonic delay times relative to predictions of diffusion theory well into the diffusive regime.

Spatially Different Tissue-Scale Diffusivity Shapes ANGUSTIFOLIA3 Gradient in Growing Leaves.

PubMed

Kawade, Kensuke; Tanimoto, Hirokazu; Horiguchi, Gorou; Tsukaya, Hirokazu

2017-09-05

The spatial gradient of signaling molecules is pivotal for establishing developmental patterns of multicellular organisms. It has long been proposed that these gradients could arise from the pure diffusion process of signaling molecules between cells, but whether this simplest mechanism establishes the formation of the tissue-scale gradient remains unclear. Plasmodesmata are unique channel structures in plants that connect neighboring cells for molecular transport. In this study, we measured cellular- and tissue-scale kinetics of molecular transport through plasmodesmata in Arabidopsis thaliana developing leaf primordia by fluorescence recovery assays. These trans-scale measurements revealed biophysical properties of diffusive molecular transport through plasmodesmata and revealed that the tissue-scale diffusivity, but not the cellular-scale diffusivity, is spatially different along the leaf proximal-to-distal axis. We found that the gradient in cell size along the developmental axis underlies this spatially different tissue-scale diffusivity. We then asked how this diffusion-based framework functions in establishing a signaling gradient of endogenous molecules. ANGUSTIFOLIA3 (AN3) is a transcriptional co-activator, and as we have shown here, it forms a long-range signaling gradient along the leaf proximal-to-distal axis to determine a cell-proliferation domain. By genetically engineering AN3 mobility, we assessed each contribution of cell-to-cell movement and tissue growth to the distribution of the AN3 gradient. We constructed a diffusion-based theoretical model using these quantitative data to analyze the AN3 gradient formation and demonstrated that it could be achieved solely by the diffusive molecular transport in a growing tissue. Our results indicate that the spatially different tissue-scale diffusivity is a core mechanism for AN3 gradient formation. This provides evidence that the pure diffusion process establishes the formation of the long-range signaling gradient in leaf development. Copyright © 2017 Biophysical Society. Published by Elsevier Inc. All rights reserved.

Nonlinear Image Denoising Methodologies

DTIC Science & Technology

2002-05-01

53 5.3 A Multiscale Approach to Scale-Space Analysis . . . . . . . . . . . . . . . . 53 5.4...etc. In this thesis, Our approach to denoising is first based on a controlled nonlinear stochastic random walk to achieve a scale space analysis ( as in... stochastic treatment or interpretation of the diffusion. In addition, unless a specific stopping time is known to be adequate, the resulting evolution

Non-uniform lithium-ion migration on micrometre scale for garnet- and NASICON-type solid electrolytes studied by 7Li PGSE-NMR diffusion spectroscopy.

PubMed

Hayamizu, Kikuko; Seki, Shiro; Haishi, Tomoyuki

2018-06-21

The migration behaviours of Li+ in three garnet- and one NASICON-type solid oxide electrolytes were studied on the micrometre scale by pulsed-gradient spin-echo (PGSE) 7Li NMR diffusion spectroscopy to clarify common and specific characteristics of each electrolyte. In these solid electrolytes, clear evidences of grain boundary effects in the diffusion of Li+ were not observed. The Li+ diffusion constants were dependent on parameters such as observation time (Δ) and pulsed field gradient (PFG) strength (g) for all the studied inorganic solid electrolytes. For low Δ values, Li+ ions underwent collisions and diffractions with diffraction distance Rdiffraction [μm]. The apparent Li+ diffusion constants (Dapparent [m2 s-1]) exhibited distributions in a wide range. In this paper, we introduced the apparent diffusion radius, rradius [μm], and compared it with Rdiffraction and mean square displacement (MSD) [μm]; the lengths of these distances were of the micrometre order (10-6 m). The relations between the values of rradius, Rdiffraction and MSD suggested that the migration behaviours of Li+ on the micrometre scale were complicated. Using high Δ and high g values, we obtained an equilibrated value of DLi. The temperature dependences of the number of carrier ions were estimated from the DLi values and ionic conductivities in the four solid oxide electrolytes. For simple comparison and reference, the data of DLi and ionic conductivity of LiPF6 in 1 M solution of propylene carbonate were added.

Coupled information diffusion--pest dynamics models predict delayed benefits of farmer cooperation in pest management programs.

PubMed

Rebaudo, François; Dangles, Olivier

2011-10-01

Worldwide, the theory and practice of agricultural extension system have been dominated for almost half a century by Rogers' "diffusion of innovation theory". In particular, the success of integrated pest management (IPM) extension programs depends on the effectiveness of IPM information diffusion from trained farmers to other farmers, an important assumption which underpins funding from development organizations. Here we developed an innovative approach through an agent-based model (ABM) combining social (diffusion theory) and biological (pest population dynamics) models to study the role of cooperation among small-scale farmers to share IPM information for controlling an invasive pest. The model was implemented with field data, including learning processes and control efficiency, from large scale surveys in the Ecuadorian Andes. Our results predict that although cooperation had short-term costs for individual farmers, it paid in the long run as it decreased pest infestation at the community scale. However, the slow learning process placed restrictions on the knowledge that could be generated within farmer communities over time, giving rise to natural lags in IPM diffusion and applications. We further showed that if individuals learn from others about the benefits of early prevention of new pests, then educational effort may have a sustainable long-run impact. Consistent with models of information diffusion theory, our results demonstrate how an integrated approach combining ecological and social systems would help better predict the success of IPM programs. This approach has potential beyond pest management as it could be applied to any resource management program seeking to spread innovations across populations.

Fixed-scale statistics and the geometry of turbulent dispersion at high Reynolds number via numerical simulation

NASA Astrophysics Data System (ADS)

Hackl, Jason F.

The relative dispersion of one uid particle with respect to another is fundamentally related to the transport and mixing of contaminant species in turbulent flows. The most basic consequence of Kolmogorov's 1941 similarity hypotheses for relative dispersion, the Richardson-Obukhov law that mean-square pair separation distance grows with the cube of time t3 at intermediate times in the inertial subrange, is notoriously difficult to observe in the environment, laboratory, and direct numerical simulations (DNS). Inertial subrange scaling in size parameters like requires careful adjustment for the initial conditions of the dispersion process as well as a very wide range of scales (high Reynolds number) in the flow being studied. However, the statistical evolution of the shapes of clusters of more than two particles has already exhibited statistical invariance at intermediate times in existing DNS. This invariance is identified with inertial-subrange scaling and is more readily observed than inertial-subrange scaling for the seemingly simpler quantity . Results from dispersion of clusters of four particles (called tetrads) in large-scale DNS at grid resolutions up to 40963 and Taylor-scale Reynolds numbers Rlambda from 140 to 1000 are used to explore the question of statistical universality in measures of the size and shape of tetrahedra in homogeneous isotropic turbulence in distinct scaling regimes at very small times (ballistic), intermediate times (inertial) and very late times (diffusive). Derivatives of 1/3 with respect to time normalized by the characteristic time scale at the initial tetrad size r0 constitute a powerful technique in isolating t3 scaling in . This technique is applied to the eigenvalues of a moment-of-inertia-like tensor formed from the separation vectors between particles in the tetrad. Estimates of the proportionality constant g in the Richardson-Obukhov t3 law from DNS at Rlambda ≈ 1000 converge towards the value g ≈ 0.56 reported in previous studies. The exit time taken by a particle pair to first reach successively larger thresholds of fixed separation distance is also brie y discussed and found to have unexplained dependence on initial separation distance for negative moments, but good inertial range scaling for positive moments. The use of diffusion models of relative dispersion in the inertial subrange to connect mean exit time to g is also tested and briefly discussed in these simulations. Mean values and probability density functions of shape parameters including the triangle aspect ratio w, tetrahedron volume-to-gyration radius ratio V2/3/R 2 and normalized moment-of-inertia eigenvalues are all found to approach invariant forms in the inertial subrange for a wider range of initial separations than size parameters such as mean-square gyration radius. These results constitute the clearest evidence to date that turbulence has a tendency to distort and elongate multiparticle configurations more severely in the inertial subrange than it does in the diffusive regime at asymptotically late time. Triangle statistics are found to be independent of initial shape for all time beyond the ballistic regime. The development and testing of different schemes for parallelizing the cubic spline interpolation procedure for particle velocities needed to track particles in DNS is also covered. A "pipeline" method of moving batches of particles from processor to processor is adopted due to its low memory overhead, but there are challenges in achieving good performance scaling.

Study of water diffusion on single-supported bilayer lipid membranes by quasielastic neutron scattering

NASA Astrophysics Data System (ADS)

Bai, M.; Miskowiec, A.; Hansen, F. Y.; Taub, H.; Jenkins, T.; Tyagi, M.; Diallo, S. O.; Mamontov, E.; Herwig, K. W.; Wang, S.-K.

2012-05-01

High-energy-resolution quasielastic neutron scattering has been used to elucidate the diffusion of water molecules in proximity to single bilayer lipid membranes supported on a silicon substrate. By varying sample temperature, level of hydration, and deuteration, we identify three different types of diffusive water motion: bulk-like, confined, and bound. The motion of bulk-like and confined water molecules is fast compared to those bound to the lipid head groups (7-10 H2O molecules per lipid), which move on the same nanosecond time scale as H atoms within the lipid molecules.

Theory and Simulation of Attractive Nanoparticle Transport in Polymer Melts

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yamamoto, Umi; Carrillo, Jan-Michael Y.; Bocharova, Vera

We theoretically study the diffusion of a single attractive nanoparticle (NP) in unentangled and entangled polymer melts based on combining microscopic “core–shell” and “vehicle” mechanisms in a dynamic bond percolation theory framework. A physical picture is constructed which addresses the role of chain length (N), degree of entanglement, nanoparticle size, and NP–polymer attraction strength. The nanoparticle diffusion constant is predicted to initially decrease with N due to the dominance of the core–shell mechanism, then to cross over to the vehicle diffusion regime with a weaker N dependence, and eventually plateau at large enough N. This behavior corresponds to decoupling ofmore » NP diffusivity from the macroscopic melt viscosity, which is reminiscent of repulsive NPs in entangled melts, but here it occurs for a distinct physical reason. Specifically, it reflects a crossover to a transport mechanism whereby nanoparticles adsorb on polymer chains and diffuse using them as “vehicles” over a characteristic desorption time scale. Repetition of random desorption events then leads to Fickian long time NP diffusion. Complementary simulations for a range of chain lengths and low to moderate NP–polymer attraction strengths are also performed. They allow testing of the proposed diffusion mechanisms and qualitatively support the theoretically predicted dynamic crossover behavior. In conclusion, when the desorption time is smaller than or comparable to the onset of entangled polymer dynamics, the NP diffusivity becomes almost chain length independent.« less

Theory and Simulation of Attractive Nanoparticle Transport in Polymer Melts

DOE PAGES

Yamamoto, Umi; Carrillo, Jan-Michael Y.; Bocharova, Vera; ...

2018-03-06

We theoretically study the diffusion of a single attractive nanoparticle (NP) in unentangled and entangled polymer melts based on combining microscopic “core–shell” and “vehicle” mechanisms in a dynamic bond percolation theory framework. A physical picture is constructed which addresses the role of chain length (N), degree of entanglement, nanoparticle size, and NP–polymer attraction strength. The nanoparticle diffusion constant is predicted to initially decrease with N due to the dominance of the core–shell mechanism, then to cross over to the vehicle diffusion regime with a weaker N dependence, and eventually plateau at large enough N. This behavior corresponds to decoupling ofmore » NP diffusivity from the macroscopic melt viscosity, which is reminiscent of repulsive NPs in entangled melts, but here it occurs for a distinct physical reason. Specifically, it reflects a crossover to a transport mechanism whereby nanoparticles adsorb on polymer chains and diffuse using them as “vehicles” over a characteristic desorption time scale. Repetition of random desorption events then leads to Fickian long time NP diffusion. Complementary simulations for a range of chain lengths and low to moderate NP–polymer attraction strengths are also performed. They allow testing of the proposed diffusion mechanisms and qualitatively support the theoretically predicted dynamic crossover behavior. In conclusion, when the desorption time is smaller than or comparable to the onset of entangled polymer dynamics, the NP diffusivity becomes almost chain length independent.« less

Nation-scale adoption of new medicines by doctors: an application of the Bass diffusion model

PubMed Central

2012-01-01

Background The adoption of new medicines is influenced by a complex set of social processes that have been widely examined in terms of individual prescribers’ information-seeking and decision-making behaviour. However, quantitative, population-wide analyses of how long it takes for new healthcare practices to become part of mainstream practice are rare. Methods We applied a Bass diffusion model to monthly prescription volumes of 103 often-prescribed drugs in Australia (monthly time series data totalling 803 million prescriptions between 1992 and 2010), to determine the distribution of adoption rates. Our aim was to test the utility of applying the Bass diffusion model to national-scale prescribing volumes. Results The Bass diffusion model was fitted to the adoption of a broad cross-section of drugs using national monthly prescription volumes from Australia (median R2 = 0.97, interquartile range 0.95 to 0.99). The median time to adoption was 8.2 years (IQR 4.9 to 12.1). The model distinguished two classes of prescribing patterns – those where adoption appeared to be driven mostly by external forces (19 drugs) and those driven mostly by social contagion (84 drugs). Those driven more prominently by internal forces were found to have shorter adoption times (p = 0.02 in a non-parametric analysis of variance by ranks). Conclusion The Bass diffusion model may be used to retrospectively represent the patterns of adoption exhibited in prescription volumes in Australia, and distinguishes between adoption driven primarily by external forces such as regulation, or internal forces such as social contagion. The eight-year delay between the introduction of a new medicine and the adoption of the prescribing practice suggests the presence of system inertia in Australian prescribing practices. PMID:22876867

Tidal influences on vertical diffusion and diurnal variability of ozone in the mesosphere

NASA Technical Reports Server (NTRS)

Bjarnason, Gudmundur G.; Solomon, Susan; Garcia, Rolando R.

1987-01-01

Possible dynamical influences on the diurnal behavior of ozone are investigated. A time dependent one-dimensional photochemical model is developed for this purpose; all model calculations are made at 70 deg N during summer. It is shown that the vertical diffusion can vary as much as 1 order of magnitude within a day as a result of large changes in the zonal wind induced by atmospheric thermal tides. It is found that by introducing a dissipation time scale for turbulence produced by breaking gravity waves, the agreement with Poker Flat echo data is improved. Comparisons of results from photochemical model calculations, where the vertical diffusion is a function of height only, with those in which the vertical diffusion coefficient is changing in time show large differences in the diurnal behavior of ozone between 70 and 90 km. By including the dynamical effect, much better agreement with the Solar Mesosphere Explorers data is obtained. The results are, however, sensitive to the background zonally averaged wind. The influence of including time-varying vertical diffusion coefficient on the OH densities is also large, especially between 80 and 90 km. This suggests that dynamical effects are important in determining the diurnal behavior of the airglow emission from the Meinel bands.

Small-Scale Features in Pulsating Aurora

NASA Technical Reports Server (NTRS)

Jones, Sarah; Jaynes, Allison N.; Knudsen, David J.; Trondsen, Trond; Lessard, Marc

2011-01-01

A field study was conducted from March 12-16, 2002 using a narrow-field intensified CCD camera installed at Churchill, Manitoba. The camera was oriented along the local magnetic zenith where small-scale black auroral forms are often visible. This analysis focuses on such forms occurring within a region of pulsating aurora. The observations show black forms with irregular shape and nonuniform drift with respect to the relatively stationary pulsating patches. The pulsating patches occur within a diffuse auroral background as a modulation of the auroral brightness in a localized region. The images analyzed show a decrease in the brightness of the diffuse background in the region of the pulsating patch at the beginning of the offphase of the modulation. Throughout the off phase the brightness of the diffuse aurora gradually increases back to the average intensity. The time constant for this increase is measured as the first step toward determining the physical process.

Brownian Dynamics simulations of model colloids in channel geometries and external fields

NASA Astrophysics Data System (ADS)

Siems, Ullrich; Nielaba, Peter

2018-04-01

We review the results of Brownian Dynamics simulations of colloidal particles in external fields confined in channels. Super-paramagnetic Brownian particles are well suited two- dimensional model systems for a variety of problems on different length scales, ranging from pedestrian walking through a bottleneck to ions passing ion-channels in living cells. In such systems confinement into channels can have a great influence on the diffusion and transport properties. Especially we will discuss the crossover from single file diffusion in a narrow channel to the diffusion in the extended two-dimensional system. Therefore a new algorithm for computing the mean square displacement (MSD) on logarithmic time scales is presented. In a different study interacting colloidal particles were dragged over a washboard potential and are additionally confined in a two-dimensional micro-channel. In this system kink and anti-kink solitons determine the depinning process of the particles from the periodic potential.

Complimentary aspects of diffusion imaging and fMRI: II. Elucidating contributions to the fMRI signal with diffusion sensitization.

PubMed

Mulkern, Robert V; Haker, Steven J; Maier, Stephan E

2007-07-01

Tissue water molecules reside in different biophysical compartments. For example, water molecules in the vasculature reside for variable periods of time within arteries, arterioles, capillaries, venuoles and veins, and may be within blood cells or blood plasma. Water molecules outside of the vasculature, in the extravascular space, reside, for a time, either within cells or within the interstitial space between cells. Within these different compartments, different types of microscopic motion that water molecules may experience have been identified and discussed. These range from Brownian diffusion to more coherent flow over the time scales relevant to functional magnetic resonance imaging (fMRI) experiments, on the order of several 10s of milliseconds. How these different types of motion are reflected in magnetic resonance imaging (MRI) methods developed for "diffusion" imaging studies has been an ongoing and active area of research. Here we briefly review the ideas that have developed regarding these motions within the context of modern "diffusion" imaging techniques and, in particular, how they have been accessed in attempts to further our understanding of the various contributions to the fMRI signal changes sought in studies of human brain activation.

Twitching motility of bacteria with type-IV pili: Fractal walks, first passage time, and their consequences on microcolonies

NASA Astrophysics Data System (ADS)

Bisht, Konark; Klumpp, Stefan; Banerjee, Varsha; Marathe, Rahul

2017-11-01

A human pathogen, Neisseria gonorrhoeae (NG), moves on surfaces by attaching and retracting polymeric structures called Type IV pili. The tug-of-war between the pili results in a two-dimensional stochastic motion called twitching motility. In this paper, with the help of real-time NG trajectories, we develop coarse-grained models for their description. The fractal properties of these trajectories are determined and their influence on first passage time and formation of bacterial microcolonies is studied. Our main observations are as follows: (i) NG performs a fast ballistic walk on small time scales and a slow diffusive walk over long time scales with a long crossover region; (ii) there exists a characteristic persistent length lp*, which yields the fastest growth of bacterial aggregates or biofilms. Our simulations reveal that lp*˜L0.6 , where L ×L is the surface on which the bacteria move; (iii) the morphologies have distinct fractal characteristics as a consequence of the ballistic and diffusive motion of the constituting bacteria.

Noise-induced phase space transport in two-dimensional Hamiltonian systems.

PubMed

Pogorelov, I V; Kandrup, H E

1999-08-01

First passage time experiments were used to explore the effects of low amplitude noise as a source of accelerated phase space diffusion in two-dimensional Hamiltonian systems, and these effects were then compared with the effects of periodic driving. The objective was to quantify and understand the manner in which "sticky" chaotic orbits that, in the absence of perturbations, are confined near regular islands for very long times, can become "unstuck" much more quickly when subjected to even very weak perturbations. For both noise and periodic driving, the typical escape time scales logarithmically with the amplitude of the perturbation. For white noise, the details seem unimportant: Additive and multiplicative noise typically have very similar effects, and the presence or absence of a friction related to the noise by a fluctuation-dissipation theorem is also largely irrelevant. Allowing for colored noise can significantly decrease the efficacy of the perturbation, but only when the autocorrelation time, which vanishes for white noise, becomes so large that there is little power at frequencies comparable to the natural frequencies of the unperturbed orbit. Similarly, periodic driving is relatively inefficient when the driving frequency is not comparable to these natural frequencies. This suggests that noise-induced extrinsic diffusion, like modulational diffusion associated with periodic driving, is a resonance phenomenon. The logarithmic dependence of the escape time on amplitude reflects the fact that the time required for perturbed and unperturbed orbits to diverge a given distance scales logarithmically in the amplitude of the perturbation.

Multiscale simulations of patchy particle systems combining Molecular Dynamics, Path Sampling and Green's Function Reaction Dynamics

NASA Astrophysics Data System (ADS)

Bolhuis, Peter

Important reaction-diffusion processes, such as biochemical networks in living cells, or self-assembling soft matter, span many orders in length and time scales. In these systems, the reactants' spatial dynamics at mesoscopic length and time scales of microns and seconds is coupled to the reactions between the molecules at microscopic length and time scales of nanometers and milliseconds. This wide range of length and time scales makes these systems notoriously difficult to simulate. While mean-field rate equations cannot describe such processes, the mesoscopic Green's Function Reaction Dynamics (GFRD) method enables efficient simulation at the particle level provided the microscopic dynamics can be integrated out. Yet, many processes exhibit non-trivial microscopic dynamics that can qualitatively change the macroscopic behavior, calling for an atomistic, microscopic description. The recently developed multiscale Molecular Dynamics Green's Function Reaction Dynamics (MD-GFRD) approach combines GFRD for simulating the system at the mesocopic scale where particles are far apart, with microscopic Molecular (or Brownian) Dynamics, for simulating the system at the microscopic scale where reactants are in close proximity. The association and dissociation of particles are treated with rare event path sampling techniques. I will illustrate the efficiency of this method for patchy particle systems. Replacing the microscopic regime with a Markov State Model avoids the microscopic regime completely. The MSM is then pre-computed using advanced path-sampling techniques such as multistate transition interface sampling. I illustrate this approach on patchy particle systems that show multiple modes of binding. MD-GFRD is generic, and can be used to efficiently simulate reaction-diffusion systems at the particle level, including the orientational dynamics, opening up the possibility for large-scale simulations of e.g. protein signaling networks.

Micro- and Nano-scale Diffusion Domains Acting as Kinetic Controls for U(VI) Release to the Hanford 300-Area Aquifer

NASA Astrophysics Data System (ADS)

Stoliker, D. L.; Hay, M. B.; Davis, J. A.; Zachara, J. M.

2008-12-01

The 300-Area of the Hanford reservation, a cold-war era nuclear processing facility, is plagued by long-term elevated concentrations of U(VI) in the underlying aquifer. While the sediment U(VI) concentration is relatively low, it continues to act as a source and sink for the contaminant, allowing for persistent groundwater concentrations well above the maximum contamination limit (MCL). Simple Kd modeling of the attenuation of U(VI) in the aquifer predicted that groundwater U(VI) concentrations would decrease to below the drinking water standard by the year 2002. However, grain-scale morphology of the aquifer material suggests that intra-grain flow paths and mineral coatings, in which sorption complexes and precipitates formed over years of waste disposal, provide a significant kinetic constraint that slows groundwater flushing of the sediments. In order to quantify the impact of diffusion kinetics on the release of U(VI), high-resolution, non-reactive tracer studies were conducted on vadose zone sediments in both column and batch reactors. Systems were equilibrated for long time scales with tritated artificial groundwater and then flushed with flow and stop-flow events included for columns. Previously collected U(VI) release data from batch dissolution/desorption studies is compared with tritium tracer diffusion kinetics as well as porosimetry and detailed microscopy characterization. The micro-scale and nano-scale diffusion regimes, including intra-granular regions as well as mineral coatings, represent a significant potential long-term source of contaminant U(VI). Understanding the physical kinetic limitations coupled with the complex chemistry of U(VI) sorption processes within natural systems is an important step forward in providing information to strengthen field-scale reactive transport simulations.

Application of interleaving models for the description of intrusive layering at the fronts of deep polar water in the Eurasian Basin (Arctic)

NASA Astrophysics Data System (ADS)

Kuzmina, N. P.; Zhurbas, N. V.; Emelianov, M. V.; Pyzhevich, M. L.

2014-09-01

Interleaving models of pure thermohaline and baroclinic frontal zones are applied to describe intrusions at the fronts found in the upper part of the Deep Polar Water (DPW) when the stratification was absolutely stable. It is assumed that differential mixing is the main mechanism of the intrusion formation. Important parameters of the interleaving such as the growth rate, vertical scale, and slope of the most unstable modes relative to the horizontal plane are calculated. It was found that the interleaving model for a pure thermohaline front satisfactory describes the important intrusion parameters observed at the frontal zone. In the case of a baroclinic front, satisfactory agreement over all the interleaving parameters is observed between the model calculations and observations provided that the vertical momentum diffusivity significantly exceeds the corresponding coefficient of mass diffusivity. Under specific (reasonable) constraints of the vertical momentum diffusivity, the most unstable mode has a vertical scale approximately two-three times smaller than the vertical scale of the observed intrusions. A thorough discussion of the results is presented.

Comparison of nanoparticle diffusion using fluorescence correlation spectroscopy and differential dynamic microscopy within concentrated polymer solutions

NASA Astrophysics Data System (ADS)

Shokeen, Namita; Issa, Christopher; Mukhopadhyay, Ashis

2017-12-01

We studied the diffusion of nanoparticles (NPs) within aqueous entangled solutions of polyethylene oxide (PEO) by using two different optical techniques. Fluorescence correlation spectroscopy, a method widely used to investigate nanoparticle dynamics in polymer solution, was used to measure the long-time diffusion coefficient (D) of 25 nm radius particles within high molecular weight, Mw = 600 kg/mol PEO in water solutions. Differential dynamic microscopy (DDM) was used to determine the wave-vector dependent dynamics of NPs within the same polymer solutions. Our results showed good agreement between the two methods, including demonstration of normal diffusion and almost identical diffusion coefficients obtained by both techniques. The research extends the scope of DDM to study the dynamics and rheological properties of soft matter at a nanoscale. The measured diffusion coefficients followed a scaling theory, which can be explained by the coupling between polymer dynamics and NP motion.

Structural Measurements from Images of Noble Gas Diffusion

NASA Astrophysics Data System (ADS)

Cadman, Robert V.; Kadlecek, Stephen J.; Emami, Kiarash; MacDuffie Woodburn, John; Vahdat, Vahid; Ishii, Masaru; Rizi, Rahim R.

2009-03-01

Magnetic resonance imaging of externally polarized noble gases such as ^3He has been used for pulmonary imaging for more than a decade. Because gas diffusion is impeded by the alveoli, the diffusion coefficient of gas in the lung, measured on a time scale of milliseconds, is reduced compared to that of the same gas mixture in the absence of restrictions. When the alveolar walls decay, as in emphysema, diffusivity in the lung increases. In this paper, the relationship between diffusion measurements and the size of the restricting structures will be discussed. The simple case of diffusion in an impermeable cylinder, a structure similar to the upper respiratory airways in mammals, has been studied. A procedure will be presented by which airways of order 2 mm in diameter may be accurately measured; demonstration experiments with plastic tubes will also be presented. The additional developments needed before this technique becomes practical will be briefly discussed.

Relativistic analysis of stochastic kinematics

NASA Astrophysics Data System (ADS)

Giona, Massimiliano

2017-10-01

The relativistic analysis of stochastic kinematics is developed in order to determine the transformation of the effective diffusivity tensor in inertial frames. Poisson-Kac stochastic processes are initially considered. For one-dimensional spatial models, the effective diffusion coefficient measured in a frame Σ moving with velocity w with respect to the rest frame of the stochastic process is inversely proportional to the third power of the Lorentz factor γ (w ) =(1-w2/c2) -1 /2 . Subsequently, higher-dimensional processes are analyzed and it is shown that the diffusivity tensor in a moving frame becomes nonisotropic: The diffusivities parallel and orthogonal to the velocity of the moving frame scale differently with respect to γ (w ) . The analysis of discrete space-time diffusion processes permits one to obtain a general transformation theory of the tensor diffusivity, confirmed by several different simulation experiments. Several implications of the theory are also addressed and discussed.

Dynamics of Phenanthrenequinone on Carbon Nano-Onion Surfaces Probed by Quasielastic Neutron Scattering

DOE Office of Scientific and Technical Information (OSTI.GOV)

Anjos, Daniela M; Mamontov, Eugene; Brown, Gilbert M

We used quasielastic neutron scattering (QENS) to study the dynamics of phenanthrenequinone (PQ) on the surface of onion-like carbon (OLC), or so called carbon onions, as a function of surface coverage and temperature. For both the high- and low-coverage samples, we observed two diffusion processes; a faster process and nearly an order of magnitude slower process. On the high-coverage surface, the slow diffusion process is of long-range translational character, whereas the fast diffusion process is spatially localized on the length scale of ~ 4.7 . On the low-coverage surface, both diffusion processes are spatially localized; on the same length scalemore » of ~ 4.7 for the fast diffusion and a somewhat larger length scale for the slow diffusion. Arrhenius temperature dependence is observed except for the long-range diffusion on the high-coverage surface. We attribute the fast diffusion process to the generic localized in-cage dynamics of PQ molecules, and the slow diffusion process to the long-range translational dynamics of PQ molecules, which, depending on the coverage, may be either spatially restricted, or long-range. On the low-coverage surface, uniform surface coverage is not attained, and the PQ molecules experience the effect of spatial constraints on their long-range translational dynamics. Unexpectedly, the dynamics of PQ molecules on OLC as a function of temperature and surface coverage bears qualitative resemblance to the dynamics of water molecules on oxide surfaces, including practically temperature-independent residence times for the low-coverage surface. The dynamics features that we observed may be universal across different classes of surface adsorbates.« less

A geometrical multi-scale numerical method for coupled hygro-thermo-mechanical problems in photovoltaic laminates.

PubMed

Lenarda, P; Paggi, M

A comprehensive computational framework based on the finite element method for the simulation of coupled hygro-thermo-mechanical problems in photovoltaic laminates is herein proposed. While the thermo-mechanical problem takes place in the three-dimensional space of the laminate, moisture diffusion occurs in a two-dimensional domain represented by the polymeric layers and by the vertical channel cracks in the solar cells. Therefore, a geometrical multi-scale solution strategy is pursued by solving the partial differential equations governing heat transfer and thermo-elasticity in the three-dimensional space, and the partial differential equation for moisture diffusion in the two dimensional domains. By exploiting a staggered scheme, the thermo-mechanical problem is solved first via a fully implicit solution scheme in space and time, with a specific treatment of the polymeric layers as zero-thickness interfaces whose constitutive response is governed by a novel thermo-visco-elastic cohesive zone model based on fractional calculus. Temperature and relative displacements along the domains where moisture diffusion takes place are then projected to the finite element model of diffusion, coupled with the thermo-mechanical problem by the temperature and crack opening dependent diffusion coefficient. The application of the proposed method to photovoltaic modules pinpoints two important physical aspects: (i) moisture diffusion in humidity freeze tests with a temperature dependent diffusivity is a much slower process than in the case of a constant diffusion coefficient; (ii) channel cracks through Silicon solar cells significantly enhance moisture diffusion and electric degradation, as confirmed by experimental tests.

Real-time ab initio KMC simulation of the self-assembly and sintering of bimetallic epitaxial nanoclusters: Au + Ag on Ag(100).

PubMed

Han, Yong; Liu, Da-Jiang; Evans, James W

2014-08-13

Far-from-equilibrium shape and structure evolution during formation and post-assembly sintering of bimetallic nanoclusters is extremely sensitive to the periphery diffusion and intermixing kinetics. Precise characterization of the many distinct local-environment-dependent diffusion barriers is achieved for epitaxial nanoclusters using density functional theory to assess interaction energies both with atoms at adsorption sites and at transition states. Kinetic Monte Carlo simulation incorporating these barriers then captures structure evolution on the appropriate time scale for two-dimensional core-ring and intermixed Au-Ag nanoclusters on Ag(100).

Real-Time Ab Initio KMC Simulation of the Self-Assembly and Sintering of Bimetallic Epitaxial Nanoclusters: Au + Ag on Ag(100)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Han, Yong; Liu, Da-Jiang; Evans, James W

2014-08-13

Far-from-equilibrium shape and structure evolution during formation and post-assembly sintering of bimetallic nanoclusters is extremely sensitive to the periphery diffusion and intermixing kinetics. Precise characterization of the many distinct local-environment-dependent diffusion barriers is achieved for epitaxial nanoclusters using density functional theory to assess interaction energies both with atoms at adsorption sites and at transition states. Kinetic Monte Carlo simulation incorporating these barriers then captures structure evolution on the appropriate time scale for two-dimensional core-ring and intermixed Au-Ag nanoclusters on Ag(100).

Parametric spatiotemporal oscillation in reaction-diffusion systems.

PubMed

Ghosh, Shyamolina; Ray, Deb Shankar

2016-03-01

We consider a reaction-diffusion system in a homogeneous stable steady state. On perturbation by a time-dependent sinusoidal forcing of a suitable scaling parameter the system exhibits parametric spatiotemporal instability beyond a critical threshold frequency. We have formulated a general scheme to calculate the threshold condition for oscillation and the range of unstable spatial modes lying within a V-shaped region reminiscent of Arnold's tongue. Full numerical simulations show that depending on the specificity of nonlinearity of the models, the instability may result in time-periodic stationary patterns in the form of standing clusters or spatially localized breathing patterns with characteristic wavelengths. Our theoretical analysis of the parametric oscillation in reaction-diffusion system is corroborated by full numerical simulation of two well-known chemical dynamical models: chlorite-iodine-malonic acid and Briggs-Rauscher reactions.

Fluorescence Correlation Spectroscopy to Study Diffusion of Polymer Chains within Layered Hydrogen-Bonded Polymer Films

NASA Astrophysics Data System (ADS)

Pristinski, Denis; Kharlampieva, Evguenia; Sukhishvili, Svetlana

2002-03-01

Fluorescence Correlation Spectroscopy (FCS) has been used to probe molecular motions within polymer multilayers formed by hydrogen-bonding sequential self-assembly. Polyethylene glycol (PEG) molecules were end-labeled with the fluorescent tags, and self-assembled with polymethacrylic acid (PMAA) using layer-by-layer deposition. We have found that molecules included in the top adsorbed layer have significant mobility at the millisecond time scale, probably due to translational diffusion. However, their dynamics deviate from classical Brownian motion with a single diffusion time. Possible reasons for the deviation are discussed. We found that motions were significantly slowed with increasing depth within the PEG/PMAA multilayer. This phenomena occured in a narrow pH range around 4.0 in which intermolecular interactions were relatively weak.

Parametric spatiotemporal oscillation in reaction-diffusion systems

NASA Astrophysics Data System (ADS)

Ghosh, Shyamolina; Ray, Deb Shankar

2016-03-01

We consider a reaction-diffusion system in a homogeneous stable steady state. On perturbation by a time-dependent sinusoidal forcing of a suitable scaling parameter the system exhibits parametric spatiotemporal instability beyond a critical threshold frequency. We have formulated a general scheme to calculate the threshold condition for oscillation and the range of unstable spatial modes lying within a V-shaped region reminiscent of Arnold's tongue. Full numerical simulations show that depending on the specificity of nonlinearity of the models, the instability may result in time-periodic stationary patterns in the form of standing clusters or spatially localized breathing patterns with characteristic wavelengths. Our theoretical analysis of the parametric oscillation in reaction-diffusion system is corroborated by full numerical simulation of two well-known chemical dynamical models: chlorite-iodine-malonic acid and Briggs-Rauscher reactions.

Diffusion in an expanding medium: Fokker-Planck equation, Green's function, and first-passage properties

NASA Astrophysics Data System (ADS)

Yuste, S. B.; Abad, E.; Escudero, C.

2016-09-01

We present a classical, mesoscopic derivation of the Fokker-Planck equation for diffusion in an expanding medium. To this end, we take a conveniently generalized Chapman-Kolmogorov equation as the starting point. We obtain an analytical expression for the Green's function (propagator) and investigate both analytically and numerically how this function and the associated moments behave. We also study first-passage properties in expanding hyperspherical geometries. We show that in all cases the behavior is determined to a great extent by the so-called Brownian conformal time τ (t ) , which we define via the relation τ ˙=1 /a2 , where a (t ) is the expansion scale factor. If the medium expansion is driven by a power law [a (t ) ∝tγ with γ >0 ] , then we find interesting crossover effects in the mixing effectiveness of the diffusion process when the characteristic exponent γ is varied. Crossover effects are also found at the level of the survival probability and of the moments of the first passage-time distribution with two different regimes separated by the critical value γ =1 /2 . The case of an exponential scale factor is analyzed separately both for expanding and contracting media. In the latter situation, a stationary probability distribution arises in the long-time limit.

Lagrangian and Eulerian statistics obtained from direct numerical simulations of homogeneous turbulence

NASA Technical Reports Server (NTRS)

Squires, Kyle D.; Eaton, John K.

1991-01-01

Direct numerical simulation is used to study dispersion in decaying isotropic turbulence and homogeneous shear flow. Both Lagrangian and Eulerian data are presented allowing direct comparison, but at fairly low Reynolds number. The quantities presented include properties of the dispersion tensor, isoprobability contours of particle displacement, Lagrangian and Eulerian velocity autocorrelations and time scale ratios, and the eddy diffusivity tensor. The Lagrangian time microscale is found to be consistently larger than the Eulerian microscale, presumably due to the advection of the small scales by the large scales in the Eulerian reference frame.

Nonlinear dynamics of capacitive charging and desalination by porous electrodes.

PubMed

Biesheuvel, P M; Bazant, M Z

2010-03-01

The rapid and efficient exchange of ions between porous electrodes and aqueous solutions is important in many applications, such as electrical energy storage by supercapacitors, water desalination and purification by capacitive deionization, and capacitive extraction of renewable energy from a salinity difference. Here, we present a unified mean-field theory for capacitive charging and desalination by ideally polarizable porous electrodes (without Faradaic reactions or specific adsorption of ions) valid in the limit of thin double layers (compared to typical pore dimensions). We illustrate the theory for the case of a dilute, symmetric, binary electrolyte using the Gouy-Chapman-Stern (GCS) model of the double layer, for which simple formulae are available for salt adsorption and capacitive charging of the diffuse part of the double layer. We solve the full GCS mean-field theory numerically for realistic parameters in capacitive deionization, and we derive reduced models for two limiting regimes with different time scales: (i) in the "supercapacitor regime" of small voltages and/or early times, the porous electrode acts like a transmission line, governed by a linear diffusion equation for the electrostatic potential, scaled to the RC time of a single pore, and (ii) in the "desalination regime" of large voltages and long times, the porous electrode slowly absorbs counterions, governed by coupled, nonlinear diffusion equations for the pore-averaged potential and salt concentration.

Nonlinear dynamics of capacitive charging and desalination by porous electrodes

NASA Astrophysics Data System (ADS)

Biesheuvel, P. M.; Bazant, M. Z.

2010-03-01

The rapid and efficient exchange of ions between porous electrodes and aqueous solutions is important in many applications, such as electrical energy storage by supercapacitors, water desalination and purification by capacitive deionization, and capacitive extraction of renewable energy from a salinity difference. Here, we present a unified mean-field theory for capacitive charging and desalination by ideally polarizable porous electrodes (without Faradaic reactions or specific adsorption of ions) valid in the limit of thin double layers (compared to typical pore dimensions). We illustrate the theory for the case of a dilute, symmetric, binary electrolyte using the Gouy-Chapman-Stern (GCS) model of the double layer, for which simple formulae are available for salt adsorption and capacitive charging of the diffuse part of the double layer. We solve the full GCS mean-field theory numerically for realistic parameters in capacitive deionization, and we derive reduced models for two limiting regimes with different time scales: (i) in the “supercapacitor regime” of small voltages and/or early times, the porous electrode acts like a transmission line, governed by a linear diffusion equation for the electrostatic potential, scaled to the RC time of a single pore, and (ii) in the “desalination regime” of large voltages and long times, the porous electrode slowly absorbs counterions, governed by coupled, nonlinear diffusion equations for the pore-averaged potential and salt concentration.

Postcoalescence evolution of growth stress in polycrystalline films.

PubMed

González-González, A; Polop, C; Vasco, E

2013-02-01

The growth stress generated once grains coalesce in Volmer-Weber-type thin films is investigated by time-multiscale simulations comprising complementary modules of (i) finite-element modeling to address the interactions between grains happening at atomic vibration time scales (~0.1 ps), (ii) dynamic scaling to account for the surface stress relaxation via morphology changes at surface diffusion time scales (~μs-ms), and (iii) the mesoscopic rate equation approach to simulate the bulk stress relaxation at deposition time scales (~sec-h). On the basis of addressing the main experimental evidence reported so far on the topic dealt with, the simulation results provide key findings concerning the interplay between anisotropic grain interactions at complementary space scales, deposition conditions (such as flux and mobility), and mechanisms of stress accommodation-relaxation, which underlies the origin, nature and spatial distribution, and the flux dependence of the postcoalescence growth stress.

Classical transport in disordered systems

NASA Astrophysics Data System (ADS)

Papaioannou, Antonios

This thesis reports on the manifestation of structural disorder on molecular transport and it consists of two parts. Part I discusses the relations between classical transport and the underlying structural complexity of the system. Both types of molecular diffusion, namely Gaussian and non- Gaussian are presented and the relevant time regimes are discussed. In addition the concept of structural universality is introduced and connected with the diffusion metrics. One of the most robust techniques for measuring molecular mean square displacements is magnetic resonance. This method requires encoding and subsequently reading out after an experimentally controlled time, a phase φ to the spins using magnetic field gradients. The main limitation for probing short diffusion lengths L(t) ˜ 1micro m with magnetic resonance is the requirement to encode and decode the phase φ in very short time intervals. Therefore, to probe such displacements a special probe was developed equipped with a gradient coil capable of delivering magnetic field gradients of approximately 90 G/cmA . The design of the probe is reported. Part I also includes a discussion of experiments of transport in two qualitatively different disordered phantoms and reports on a direct observation of universality in one-dimension. The results reveal the universal power law scaling of the diffusion coefficient at the long-time regime and illustrate the essence of structural universality by experimentally determining the structure correlation function of the phantoms. In addition, the scaling of the diffusive permeability of the phantoms with respect to the pore size is investigated. Additional work presented includes a detailed study of adsorption of methane gas in Vycor disordered glass. The techniques described in Part I of this thesis are widely used for measuring structural parameters of porous media, such as the surface-to-volume ratio or diffusive permeability. Part II of this thesis discusses the biophysical application of diffusion in disordered systems in the field of bioengineering. Elastin-based bioengineered scaffolds, which are mainly used for tissue and bone regeneration, must be able to deliver nutrients to the native tissue. It is therefore essential to quantitatively assess their structural parameters such as their surface-to-volume ratio and diffusive permeability. Part II focuses on a detailed study of structure and dynamics of elastin, the principle protein component found in tissues and one of the main components for scaffold engineering, using NMR 13C-MAS techniques. Lastly, the second half of Part II, discusses preliminary experiments of diffusion in elastin-based films.

Variable diffusion in stock market fluctuations

NASA Astrophysics Data System (ADS)

Hua, Jia-Chen; Chen, Lijian; Falcon, Liberty; McCauley, Joseph L.; Gunaratne, Gemunu H.

2015-02-01

We analyze intraday fluctuations in several stock indices to investigate the underlying stochastic processes using techniques appropriate for processes with nonstationary increments. The five most actively traded stocks each contains two time intervals during the day where the variance of increments can be fit by power law scaling in time. The fluctuations in return within these intervals follow asymptotic bi-exponential distributions. The autocorrelation function for increments vanishes rapidly, but decays slowly for absolute and squared increments. Based on these results, we propose an intraday stochastic model with linear variable diffusion coefficient as a lowest order approximation to the real dynamics of financial markets, and to test the effects of time averaging techniques typically used for financial time series analysis. We find that our model replicates major stylized facts associated with empirical financial time series. We also find that ensemble averaging techniques can be used to identify the underlying dynamics correctly, whereas time averages fail in this task. Our work indicates that ensemble average approaches will yield new insight into the study of financial markets' dynamics. Our proposed model also provides new insight into the modeling of financial markets dynamics in microscopic time scales.

A model for including thermal conduction in molecular dynamics simulations

NASA Technical Reports Server (NTRS)

Wu, Yue; Friauf, Robert J.

1989-01-01

A technique is introduced for including thermal conduction in molecular dynamics simulations for solids. A model is developed to allow energy flow between the computational cell and the bulk of the solid when periodic boundary conditions cannot be used. Thermal conduction is achieved by scaling the velocities of atoms in a transitional boundary layer. The scaling factor is obtained from the thermal diffusivity, and the results show good agreement with the solution for a continuous medium at long times. The effects of different temperature and size of the system, and of variations in strength parameter, atomic mass, and thermal diffusivity were investigated. In all cases, no significant change in simulation results has been found.

Nitric oxide kinetics in the afterglow of a diffuse plasma filament

NASA Astrophysics Data System (ADS)

Burnette, D.; Montello, A.; Adamovich, I. V.; Lempert, W. R.

2014-08-01

A suite of laser diagnostics is used to study kinetics of vibrational energy transfer and plasma chemical reactions in a nanosecond pulse, diffuse filament electric discharge and afterglow in N2 and dry air at 100 Torr. Laser-induced fluorescence of NO and two-photon absorption laser-induced fluorescence of O and N atoms are used to measure absolute, time-resolved number densities of these species after the discharge pulse, and picosecond coherent anti-Stokes Raman spectroscopy is used to measure time-resolved rotational temperature and ground electronic state N2(v = 0-4) vibrational level populations. The plasma filament diameter, determined from plasma emission and NO planar laser-induced fluorescence images, remains nearly constant after the discharge pulse, over a few hundred microseconds, and does not exhibit expansion on microsecond time scale. Peak temperature in the discharge and the afterglow is low, T ≈ 370 K, in spite of significant vibrational nonequilibrium, with peak N2 vibrational temperature of Tv ≈ 2000 K. Significant vibrational temperature rise in the afterglow is likely caused by the downward N2-N2 vibration-vibration (V-V) energy transfer. Simple kinetic modeling of time-resolved N, O, and NO number densities in the afterglow, on the time scale longer compared to relaxation and quenching time of excited species generated in the plasma, is in good agreement with the data. In nitrogen, the N atom density after the discharge pulse is controlled by three-body recombination and radial diffusion. In air, N, NO and O concentrations are dominated by the reverse Zel'dovich reaction, N + NO → N2 + O, and ozone formation reaction, O + O2 + M → O3 + M, respectively. The effect of vibrationally excited nitrogen molecules and excited N atoms on NO formation kinetics is estimated to be negligible. The results suggest that NO formation in the nanosecond pulse discharge is dominated by reactions of excited electronic states of nitrogen, occurring on microsecond time scale.

Breakthrough behavior of granular ferric hydroxide (GFH) fixed-bed adsorption filters: modeling and experimental approaches.

PubMed

Sperlich, Alexander; Werner, Arne; Genz, Arne; Amy, Gary; Worch, Eckhard; Jekel, Martin

2005-03-01

Breakthrough curves (BTC) for the adsorption of arsenate and salicylic acid onto granulated ferric hydroxide (GFH) in fixed-bed adsorbers were experimentally determined and modeled using the homogeneous surface diffusion model (HSDM). The input parameters for the HSDM, the Freundlich isotherm constants and mass transfer coefficients for film and surface diffusion, were experimentally determined. The BTC for salicylic acid revealed a shape typical for trace organic compound adsorption onto activated carbon, and model results agreed well with the experimental curves. Unlike salicylic acid, arsenate BTCs showed a non-ideal shape with a leveling off at c/c0 approximately 0.6. Model results based on the experimentally derived parameters over-predicted the point of arsenic breakthrough for all simulated curves, lab-scale or full-scale, and were unable to catch the shape of the curve. The use of a much lower surface diffusion coefficient D(S) for modeling led to an improved fit of the later stages of the BTC shape, pointing on a time-dependent D(S). The mechanism for this time dependence is still unknown. Surface precipitation was discussed as one possible removal mechanism for arsenate besides pure adsorption interfering the determination of Freundlich constants and D(S). Rapid small-scale column tests (RSSCT) proved to be a powerful experimental alternative to the modeling procedure for arsenic.

Turbulent diffusion of chemically reacting flows: Theory and numerical simulations

NASA Astrophysics Data System (ADS)

Elperin, T.; Kleeorin, N.; Liberman, M.; Lipatnikov, A. N.; Rogachevskii, I.; Yu, R.

2017-11-01

The theory of turbulent diffusion of chemically reacting gaseous admixtures developed previously [T. Elperin et al., Phys. Rev. E 90, 053001 (2014), 10.1103/PhysRevE.90.053001] is generalized for large yet finite Reynolds numbers and the dependence of turbulent diffusion coefficient on two parameters, the Reynolds number and Damköhler number (which characterizes a ratio of turbulent and reaction time scales), is obtained. Three-dimensional direct numerical simulations (DNSs) of a finite-thickness reaction wave for the first-order chemical reactions propagating in forced, homogeneous, isotropic, and incompressible turbulence are performed to validate the theoretically predicted effect of chemical reactions on turbulent diffusion. It is shown that the obtained DNS results are in good agreement with the developed theory.

Study of translational dynamics in molten polymer by variation of gradient pulse-width of PGSE.

PubMed

Stepišnik, Janez; Lahajnar, Gojmir; Zupančič, Ivan; Mohorič, Aleš

2013-11-01

Pulsed gradient spin echo is a method of measuring molecular translation. Changing Δ makes it sensitive to diffusion spectrum. Spin translation effects the buildup of phase structure during the application of gradient pulses as well. The time scale of the self-diffusion measurement shortens if this is taken into account. The method of diffusion spectrometry with variable δ is also less sensitive to artifacts caused by spin relaxation and internal gradient fields. Here the method is demonstrated in the case of diffusion spectrometry of molten polyethylene. The results confirm a model of constraint release in a system of entangled polymer chains as a sort of tube Rouse motion. Copyright © 2013 Elsevier Inc. All rights reserved.

Turbulent diffusion of chemically reacting flows: Theory and numerical simulations.

PubMed

Elperin, T; Kleeorin, N; Liberman, M; Lipatnikov, A N; Rogachevskii, I; Yu, R

2017-11-01

The theory of turbulent diffusion of chemically reacting gaseous admixtures developed previously [T. Elperin et al., Phys. Rev. E 90, 053001 (2014)PLEEE81539-375510.1103/PhysRevE.90.053001] is generalized for large yet finite Reynolds numbers and the dependence of turbulent diffusion coefficient on two parameters, the Reynolds number and Damköhler number (which characterizes a ratio of turbulent and reaction time scales), is obtained. Three-dimensional direct numerical simulations (DNSs) of a finite-thickness reaction wave for the first-order chemical reactions propagating in forced, homogeneous, isotropic, and incompressible turbulence are performed to validate the theoretically predicted effect of chemical reactions on turbulent diffusion. It is shown that the obtained DNS results are in good agreement with the developed theory.

Modeling Sediment Detention Ponds Using Reactor Theory and Advection-Diffusion Concepts

NASA Astrophysics Data System (ADS)

Wilson, Bruce N.; Barfield, Billy J.

1985-04-01

An algorithm is presented to model the sedimentation process in detention ponds. This algorithm is based on a mass balance for an infinitesimal layer that couples reactor theory concepts with advection-diffusion processes. Reactor theory concepts are used to (1) determine residence time of sediment particles and to (2) mix influent sediment with previously stored flow. Advection-diffusion processes are used to model the (1) settling characteristics of sediment and the (2) vertical diffusion of sediment due to turbulence. Predicted results of the model are compared to those observed on two pilot scale ponds for a total of 12 runs. The average percent error between predicted and observed trap efficiency was 5.2%. Overall, the observed sedimentology values were predicted with reasonable accuracy.

Approximate Seismic Diffusive Models of Near-Receiver Geology: Applications from Lab Scale to Field

NASA Astrophysics Data System (ADS)

King, Thomas; Benson, Philip; De Siena, Luca; Vinciguerra, Sergio

2017-04-01

This paper presents a novel and simple method of seismic envelope analysis that can be applied at multiple scales, e.g. field, m to km scale and laboratory, mm to cm scale, and utilises the diffusive approximation of the seismic wavefield (Wegler, 2003). Coefficient values for diffusion and attenuation are obtained from seismic coda energies and are used to describe the rate at which seismic energy is scattered and attenuated into the local medium around a receiver. Values are acquired by performing a linear least squares inversion of coda energies calculated in successive time windows along a seismic trace. Acoustic emission data were taken from piezoelectric transducers (PZT) with typical resonance frequency of 1-5MHz glued around rock samples during deformation laboratory experiments carried out using a servo-controlled triaxial testing machine, where a shear/damage zone is generated under compression after the nucleation, growth and coalescence of microcracks. Passive field data were collected from conventional geophones during the 2004-2008 eruption of Mount St. Helens volcano (MSH), USA where a sudden reawakening of the volcanic activity and a new dome growth has occurred. The laboratory study shows a strong correlation between variations of the coefficients over time and the increase of differential stress as the experiment progresses. The field study links structural variations present in the near-surface geology, including those seen in previous geophysical studies of the area, to these same coefficients. Both studies show a correlation between frequency and structural feature size, i.e. landslide slip-planes and microcracks, with higher frequencies being much more sensitive to smaller scale features and vice-versa.

Feynman-Kac equation for anomalous processes with space- and time-dependent forces

NASA Astrophysics Data System (ADS)

Cairoli, Andrea; Baule, Adrian

2017-04-01

Functionals of a stochastic process Y(t) model many physical time-extensive observables, for instance particle positions, local and occupation times or accumulated mechanical work. When Y(t) is a normal diffusive process, their statistics are obtained as the solution of the celebrated Feynman-Kac equation. This equation provides the crucial link between the expected values of diffusion processes and the solutions of deterministic second-order partial differential equations. When Y(t) is non-Brownian, e.g. an anomalous diffusive process, generalizations of the Feynman-Kac equation that incorporate power-law or more general waiting time distributions of the underlying random walk have recently been derived. A general representation of such waiting times is provided in terms of a Lévy process whose Laplace exponent is directly related to the memory kernel appearing in the generalized Feynman-Kac equation. The corresponding anomalous processes have been shown to capture nonlinear mean square displacements exhibiting crossovers between different scaling regimes, which have been observed in numerous experiments on biological systems like migrating cells or diffusing macromolecules in intracellular environments. However, the case where both space- and time-dependent forces drive the dynamics of the generalized anomalous process has not been solved yet. Here, we present the missing derivation of the Feynman-Kac equation in such general case by using the subordination technique. Furthermore, we discuss its extension to functionals explicitly depending on time, which are of particular relevance for the stochastic thermodynamics of anomalous diffusive systems. Exact results on the work fluctuations of a simple non-equilibrium model are obtained. An additional aim of this paper is to provide a pedagogical introduction to Lévy processes, semimartingales and their associated stochastic calculus, which underlie the mathematical formulation of anomalous diffusion as a subordinated process.

Critical time scales for advection-diffusion-reaction processes

NASA Astrophysics Data System (ADS)

Ellery, Adam J.; Simpson, Matthew J.; McCue, Scott W.; Baker, Ruth E.

2012-04-01

The concept of local accumulation time (LAT) was introduced by Berezhkovskii and co-workers to give a finite measure of the time required for the transient solution of a reaction-diffusion equation to approach the steady-state solution [A. M. Berezhkovskii, C. Sample, and S. Y. Shvartsman, Biophys. J.BIOJAU0006-349510.1016/j.bpj.2010.07.045 99, L59 (2010); A. M. Berezhkovskii, C. Sample, and S. Y. Shvartsman, Phys. Rev. EPLEEE81539-375510.1103/PhysRevE.83.051906 83, 051906 (2011)]. Such a measure is referred to as a critical time. Here, we show that LAT is, in fact, identical to the concept of mean action time (MAT) that was first introduced by McNabb [A. McNabb and G. C. Wake, IMA J. Appl. Math.IJAMDM0272-496010.1093/imamat/47.2.193 47, 193 (1991)]. Although McNabb's initial argument was motivated by considering the mean particle lifetime (MPLT) for a linear death process, he applied the ideas to study diffusion. We extend the work of these authors by deriving expressions for the MAT for a general one-dimensional linear advection-diffusion-reaction problem. Using a combination of continuum and discrete approaches, we show that MAT and MPLT are equivalent for certain uniform-to-uniform transitions; these results provide a practical interpretation for MAT by directly linking the stochastic microscopic processes to a meaningful macroscopic time scale. We find that for more general transitions, the equivalence between MAT and MPLT does not hold. Unlike other critical time definitions, we show that it is possible to evaluate the MAT without solving the underlying partial differential equation (pde). This makes MAT a simple and attractive quantity for practical situations. Finally, our work explores the accuracy of certain approximations derived using MAT, showing that useful approximations for nonlinear kinetic processes can be obtained, again without treating the governing pde directly.

The Role of Triplet Exciton Diffusion in Light-Upconverting Polymer Glasses.

PubMed

Raišys, Steponas; Kazlauskas, Karolis; Juršėnas, Saulius; Simon, Yoan C

2016-06-22

Light upconversion (UC) via triplet-triplet annihilation (TTA) by using noncoherent photoexcitation at subsolar irradiance power densities is extremely attractive, particularly for enhanced solar energy harvesting. Unfortunately, practical TTA-UC application is hampered by low UC efficiency of upconverting polymer glasses, which is commonly attributed to poor exciton diffusion of the triplet excitons across emitter molecules. The present study addresses this issue by systematically evaluating triplet exciton diffusion coefficients and diffusion lengths (LD) in a UC model system based on platinum-octaethylporphyrin-sensitized poly(methyl methacrylate)/diphenylanthracene (emitter) films as a function of emitter concentration (15-40 wt %). For this evaluation time-resolved photoluminescence bulk-quenching technique followed by Stern-Volmer-type quenching analysis of experimental data was employed. The key finding is that although increasing emitter concentration in the disordered PMMA/DPA/PtOEP films improves triplet exciton diffusion, and thus LD, this does not result in enhanced UC quantum yield. Conversely, improved LD accompanied by the accelerated decay of UC intensity on millisecond time scale degrades TTA-UC performance at high emitter loadings (>25 wt %) and suggests that diffusion-enhanced nonradiative decay of triplet excitons is the major limiting factor.

Understanding quantum tunneling using diffusion Monte Carlo simulations

NASA Astrophysics Data System (ADS)

Inack, E. M.; Giudici, G.; Parolini, T.; Santoro, G.; Pilati, S.

2018-03-01

In simple ferromagnetic quantum Ising models characterized by an effective double-well energy landscape the characteristic tunneling time of path-integral Monte Carlo (PIMC) simulations has been shown to scale as the incoherent quantum-tunneling time, i.e., as 1 /Δ2 , where Δ is the tunneling gap. Since incoherent quantum tunneling is employed by quantum annealers (QAs) to solve optimization problems, this result suggests that there is no quantum advantage in using QAs with respect to quantum Monte Carlo (QMC) simulations. A counterexample is the recently introduced shamrock model (Andriyash and Amin, arXiv:1703.09277), where topological obstructions cause an exponential slowdown of the PIMC tunneling dynamics with respect to incoherent quantum tunneling, leaving open the possibility for potential quantum speedup, even for stoquastic models. In this work we investigate the tunneling time of projective QMC simulations based on the diffusion Monte Carlo (DMC) algorithm without guiding functions, showing that it scales as 1 /Δ , i.e., even more favorably than the incoherent quantum-tunneling time, both in a simple ferromagnetic system and in the more challenging shamrock model. However, a careful comparison between the DMC ground-state energies and the exact solution available for the transverse-field Ising chain indicates an exponential scaling of the computational cost required to keep a fixed relative error as the system size increases.

On the asymptotic behavior of a subcritical convection-diffusion equation with nonlocal diffusion

NASA Astrophysics Data System (ADS)

Cazacu, Cristian M.; Ignat, Liviu I.; Pazoto, Ademir F.

2017-08-01

In this paper we consider a subcritical model that involves nonlocal diffusion and a classical convective term. In spite of the nonlocal diffusion, we obtain an Oleinik type estimate similar to the case when the diffusion is local. First we prove that the entropy solution can be obtained by adding a small viscous term μ uxx and letting μ\\to 0 . Then, by using uniform Oleinik estimates for the viscous approximation we are able to prove the well-posedness of the entropy solutions with L 1-initial data. Using a scaling argument and hyperbolic estimates given by Oleinik’s inequality, we obtain the first term in the asymptotic behavior of the nonnegative solutions. Finally, the large time behavior of changing sign solutions is proved using the classical flux-entropy method and estimates for the nonlocal operator.

Time scale of random sequential adsorption.

PubMed

Erban, Radek; Chapman, S Jonathan

2007-04-01

A simple multiscale approach to the diffusion-driven adsorption from a solution to a solid surface is presented. The model combines two important features of the adsorption process: (i) The kinetics of the chemical reaction between adsorbing molecules and the surface and (ii) geometrical constraints on the surface made by molecules which are already adsorbed. The process (i) is modeled in a diffusion-driven context, i.e., the conditional probability of adsorbing a molecule provided that the molecule hits the surface is related to the macroscopic surface reaction rate. The geometrical constraint (ii) is modeled using random sequential adsorption (RSA), which is the sequential addition of molecules at random positions on a surface; one attempt to attach a molecule is made per one RSA simulation time step. By coupling RSA with the diffusion of molecules in the solution above the surface the RSA simulation time step is related to the real physical time. The method is illustrated on a model of chemisorption of reactive polymers to a virus surface.

A fractional reaction-diffusion description of supply and demand

NASA Astrophysics Data System (ADS)

Benzaquen, Michael; Bouchaud, Jean-Philippe

2018-02-01

We suggest that the broad distribution of time scales in financial markets could be a crucial ingredient to reproduce realistic price dynamics in stylised Agent-Based Models. We propose a fractional reaction-diffusion model for the dynamics of latent liquidity in financial markets, where agents are very heterogeneous in terms of their characteristic frequencies. Several features of our model are amenable to an exact analytical treatment. We find in particular that the impact is a concave function of the transacted volume (aka the "square-root impact law"), as in the normal diffusion limit. However, the impact kernel decays as t-β with β = 1/2 in the diffusive case, which is inconsistent with market efficiency. In the sub-diffusive case the decay exponent β takes any value in [0, 1/2], and can be tuned to match the empirical value β ≈ 1/4. Numerical simulations confirm our theoretical results. Several extensions of the model are suggested. Contribution to the Topical Issue "Continuous Time Random Walk Still Trendy: Fifty-year History, Current State and Outlook", edited by Ryszard Kutner and Jaume Masoliver.

Effect of thermal diffusion on the stability of strongly tilted mantle plume tails

NASA Astrophysics Data System (ADS)

Kerr, R. C.; MéRiaux, C.; Lister, J. R.

2008-09-01

The effect of thermal diffusion on the stability of strongly tilted mantle plume tails is explored by investigating experimentally and numerically the gravitational instability of a rising horizontal cylindrical region of buoyant viscous fluid. At large viscosity ratios, we find that the instability is unaffected by diffusion when the Rayleigh number Ra is greater than about 300. When Ra is less than 300, diffusion significantly increases the time for instability, as the rising fluid region needs to grow substantially by entrainment before it becomes unstable. When Ra is less than about 140 and the rise height available H is less than about 40 times the cylinder radius, the rising region of fluid is unable to grow sufficiently and instability is prevented. When our results are applied to the Earth, we predict that thermal diffusion will stabilize plume tails in both the upper and lower mantle. We also predict that some of the buoyancy flux in mantle plumes is lost during ascent to form downstream thermal wakes in any larger-scale mantle flow.

Quantitative Characterization of Tissue Microstructure with Temporal Diffusion Spectroscopy

PubMed Central

Xu, Junzhong; Does, Mark D.; Gore, John C.

2009-01-01

The signals recorded by diffusion-weighted magnetic resonance imaging (DWI) are dependent on the micro-structural properties of biological tissues, so it is possible to obtain quantitative structural information non-invasively from such measurements. Oscillating gradient spin echo (OGSE) methods have the ability to probe the behavior of water diffusion over different time scales and the potential to detect variations in intracellular structure. To assist in the interpretation of OGSE data, analytical expressions have been derived for diffusion-weighted signals with OGSE methods for restricted diffusion in some typical structures, including parallel planes, cylinders and spheres, using the theory of temporal diffusion spectroscopy. These analytical predictions have been confirmed with computer simulations. These expressions suggest how OGSE signals from biological tissues should be analyzed to characterize tissue microstructure, including how to estimate cell nuclear sizes. This approach provides a model to interpret diffusion data obtained from OGSE measurements that can be used for applications such as monitoring tumor response to treatment in vivo. PMID:19616979

A living mesoscopic cellular automaton made of skin scales.

PubMed

Manukyan, Liana; Montandon, Sophie A; Fofonjka, Anamarija; Smirnov, Stanislav; Milinkovitch, Michel C

2017-04-12

In vertebrates, skin colour patterns emerge from nonlinear dynamical microscopic systems of cell interactions. Here we show that in ocellated lizards a quasi-hexagonal lattice of skin scales, rather than individual chromatophore cells, establishes a green and black labyrinthine pattern of skin colour. We analysed time series of lizard scale colour dynamics over four years of their development and demonstrate that this pattern is produced by a cellular automaton (a grid of elements whose states are iterated according to a set of rules based on the states of neighbouring elements) that dynamically computes the colour states of individual mesoscopic skin scales to produce the corresponding macroscopic colour pattern. Using numerical simulations and mathematical derivation, we identify how a discrete von Neumann cellular automaton emerges from a continuous Turing reaction-diffusion system. Skin thickness variation generated by three-dimensional morphogenesis of skin scales causes the underlying reaction-diffusion dynamics to separate into microscopic and mesoscopic spatial scales, the latter generating a cellular automaton. Our study indicates that cellular automata are not merely abstract computational systems, but can directly correspond to processes generated by biological evolution.

A living mesoscopic cellular automaton made of skin scales

NASA Astrophysics Data System (ADS)

Manukyan, Liana; Montandon, Sophie A.; Fofonjka, Anamarija; Smirnov, Stanislav; Milinkovitch, Michel C.

2017-04-01

In vertebrates, skin colour patterns emerge from nonlinear dynamical microscopic systems of cell interactions. Here we show that in ocellated lizards a quasi-hexagonal lattice of skin scales, rather than individual chromatophore cells, establishes a green and black labyrinthine pattern of skin colour. We analysed time series of lizard scale colour dynamics over four years of their development and demonstrate that this pattern is produced by a cellular automaton (a grid of elements whose states are iterated according to a set of rules based on the states of neighbouring elements) that dynamically computes the colour states of individual mesoscopic skin scales to produce the corresponding macroscopic colour pattern. Using numerical simulations and mathematical derivation, we identify how a discrete von Neumann cellular automaton emerges from a continuous Turing reaction-diffusion system. Skin thickness variation generated by three-dimensional morphogenesis of skin scales causes the underlying reaction-diffusion dynamics to separate into microscopic and mesoscopic spatial scales, the latter generating a cellular automaton. Our study indicates that cellular automata are not merely abstract computational systems, but can directly correspond to processes generated by biological evolution.

Asymptotic properties of blow-up solutions in reaction-diffusion equations with nonlocal boundary flux

NASA Astrophysics Data System (ADS)

Liu, Bingchen; Dong, Mengzhen; Li, Fengjie

2018-04-01

This paper deals with a reaction-diffusion problem with coupled nonlinear inner sources and nonlocal boundary flux. Firstly, we propose the critical exponents on nonsimultaneous blow-up under some conditions on the initial data. Secondly, we combine the scaling technique and the Green's identity method to determine four kinds of simultaneous blow-up rates. Thirdly, the lower and the upper bounds of blow-up time are derived by using Sobolev-type differential inequalities.

On the Role of Built-in Electric Fields on the Ignition of Oxide Coated NanoAluminum: Ion Mobility versus Fickian Diffusion

DTIC Science & Technology

2010-01-01

on Al ion diffu- sion can be computed using the Nernst –Planck equation . The Nernst –Plank equation is given in Eq. 4,22 J = − D dC dx − zFDC RT d dx...The use of the bulk diffusion equation is reason- able since during the time scales considered the movement of only the atoms initially on the surface

Anomalous diffusion due to hindering by mobile obstacles undergoing Brownian motion or Orstein-Ulhenbeck processes.

PubMed

Berry, Hugues; Chaté, Hugues

2014-02-01

In vivo measurements of the passive movements of biomolecules or vesicles in cells consistently report "anomalous diffusion," where mean-squared displacements scale as a power law of time with exponent α<1 (subdiffusion). While the detailed mechanisms causing such behaviors are not always elucidated, movement hindrance by obstacles is often invoked. However, our understanding of how hindered diffusion leads to subdiffusion is based on diffusion amidst randomly located immobile obstacles. Here, we have used Monte Carlo simulations to investigate transient subdiffusion due to mobile obstacles with various modes of mobility. Our simulations confirm that the anomalous regimes rapidly disappear when the obstacles move by Brownian motion. By contrast, mobile obstacles with more confined displacements, e.g., Orstein-Ulhenbeck motion, are shown to preserve subdiffusive regimes. The mean-squared displacement of tracked protein displays convincing power laws with anomalous exponent α that varies with the density of Orstein-Ulhenbeck (OU) obstacles or the relaxation time scale of the OU process. In particular, some of the values we observed are significantly below the universal value predicted for immobile obstacles in two dimensions. Therefore, our results show that subdiffusion due to mobile obstacles with OU type of motion may account for the large variation range exhibited by experimental measurements in living cells and may explain that some experimental estimates are below the universal value predicted for immobile obstacles.

Fluctuating magnetic moments in liquid metals.

PubMed

Patty, Mark; Schoen, Keary; Montfrooij, Wouter

2006-02-01

We reanalyze literature data on neutron scattering by liquid metals and show that there is an additional broad (in energy) quasielastic mode present that is absent in x-ray scattering. This mode cannot be accounted for by the standard coherent and incoherent scattering mechanisms. We argue that this mode indicates that nonmagnetic liquid metals possess a magnetic moment which fluctuates on a picosecond time scale. This time scale is the same as the time scale of the cage-diffusion process in which an ion rattles around in the cage formed by its neighbors. We find that these fluctuating magnetic moments are present in liquid Hg, Al, Ga, and Pb and possibly also in the alkali metals.

Time-lapse videos for physics education: specific examples

NASA Astrophysics Data System (ADS)

Vollmer, Michael; Möllmann, Klaus-Peter

2018-05-01

There are many physics experiments with long time scales such that they are usually neither shown in the physics class room nor in student labs. However, they can be easily recorded with time-lapse cameras and the respective time-lapse videos allow qualitative and/or quantitative analysis of the underlying physics. Here, we present some examples from thermal physics (melting, evaporation, cooling) as well as diffusion processes

Field-scale forward and back diffusion through low-permeability zones

NASA Astrophysics Data System (ADS)

Yang, Minjune; Annable, Michael D.; Jawitz, James W.

2017-07-01

Understanding the effects of back diffusion of groundwater contaminants from low-permeability zones to aquifers is critical to making site management decisions related to remedial actions. Here, we combine aquifer and aquitard data to develop recommended site characterization strategies using a three-stage classification of plume life cycle based on the solute origins: aquifer source zone dissolution, source zone dissolution combined with back diffusion from an aquitard, and only back diffusion. We use measured aquitard concentration profile data from three field sites to identify signature shapes that are characteristic of these three stages. We find good fits to the measured data with analytical solutions that include the effects of advection and forward and back diffusion through low-permeability zones, and linearly and exponentially decreasing flux resulting from source dissolution in the aquifer. Aquifer contaminant time series data at monitoring wells from a mature site were well described using analytical solutions representing the combined case of source zone and back diffusion, while data from a site where the source had been isolated were well described solely by back diffusion. The modeling approach presented in this study is designed to enable site managers to implement appropriate remediation technologies at a proper timing for high- and low-permeability zones, considering estimated plume life cycle.

Field-scale forward and back diffusion through low-permeability zones.

PubMed

Yang, Minjune; Annable, Michael D; Jawitz, James W

2017-07-01

Understanding the effects of back diffusion of groundwater contaminants from low-permeability zones to aquifers is critical to making site management decisions related to remedial actions. Here, we combine aquifer and aquitard data to develop recommended site characterization strategies using a three-stage classification of plume life cycle based on the solute origins: aquifer source zone dissolution, source zone dissolution combined with back diffusion from an aquitard, and only back diffusion. We use measured aquitard concentration profile data from three field sites to identify signature shapes that are characteristic of these three stages. We find good fits to the measured data with analytical solutions that include the effects of advection and forward and back diffusion through low-permeability zones, and linearly and exponentially decreasing flux resulting from source dissolution in the aquifer. Aquifer contaminant time series data at monitoring wells from a mature site were well described using analytical solutions representing the combined case of source zone and back diffusion, while data from a site where the source had been isolated were well described solely by back diffusion. The modeling approach presented in this study is designed to enable site managers to implement appropriate remediation technologies at a proper timing for high- and low-permeability zones, considering estimated plume life cycle. Copyright © 2017 Elsevier B.V. All rights reserved.

Measurement of nanoscale three-dimensional diffusion in the interior of living cells by STED-FCS.

PubMed

Lanzanò, Luca; Scipioni, Lorenzo; Di Bona, Melody; Bianchini, Paolo; Bizzarri, Ranieri; Cardarelli, Francesco; Diaspro, Alberto; Vicidomini, Giuseppe

2017-07-06

The observation of molecular diffusion at different spatial scales, and in particular below the optical diffraction limit (<200 nm), can reveal details of the subcellular topology and its functional organization. Stimulated-emission depletion microscopy (STED) has been previously combined with fluorescence correlation spectroscopy (FCS) to investigate nanoscale diffusion (STED-FCS). However, stimulated-emission depletion fluorescence correlation spectroscopy has only been used successfully to reveal functional organization in two-dimensional space, such as the plasma membrane, while, an efficient implementation for measurements in three-dimensional space, such as the cellular interior, is still lacking. Here we integrate the STED-FCS method with two analytical approaches, the recent separation of photons by lifetime tuning and the fluorescence lifetime correlation spectroscopy, to simultaneously probe diffusion in three dimensions at different sub-diffraction scales. We demonstrate that this method efficiently provides measurement of the diffusion of EGFP at spatial scales tunable from the diffraction size down to ∼80 nm in the cytoplasm of living cells.The measurement of molecular diffusion at sub-diffraction scales has been achieved in 2D space using STED-FCS, but an implementation for 3D diffusion is lacking. Here the authors present an analytical approach to probe diffusion in 3D space using STED-FCS and measure the diffusion of EGFP at different spatial scales.

Multidiffusion mechanisms for noble gases (He, Ne, Ar) in silicate glasses and melts in the transition temperature domain: Implications for glass polymerization

NASA Astrophysics Data System (ADS)

Amalberti, Julien; Burnard, Pete; Laporte, Didier; Tissandier, Laurent; Neuville, Daniel R.

2016-01-01

Noble gases are ideal probes to study the structure of silicate glasses and melts as the modifications of the silicate network induced by the incorporation of noble gases are negligible. In addition, there are systematic variations in noble gas atomic radii and several noble gas isotopes with which the influence of the network itself on diffusion may be investigated. Noble gases are therefore ideally suited to constrain the time scales of magma degassing and cooling. In order to document noble gas diffusion behavior in silicate glass, we measured the diffusivities of three noble gases (4He, 20Ne and 40Ar) and the isotopic diffusivities of two Ar isotopes (36Ar and 40Ar) in two synthetic basaltic glasses (G1 and G2; 20Ne and 36Ar were only measured in sample G1). These new diffusion results are used to re-interpret time scales of the acquisition of fractionated atmospheric noble gas signatures in pumices. The noble gas bearing glasses were synthesized by exposing the liquids to high noble gas partial pressures at high temperature and pressure (1750-1770 K and 1.2 GPa) in a piston-cylinder apparatus. Diffusivities were measured by step heating the glasses between 423 and 1198 K and measuring the fraction of gas released at each temperature step by noble gas mass spectrometry. In addition we measured the viscosity of G1 between 996 and 1072 K in order to determine the precise glass transition temperature and to estimate network relaxation time scales. The results indicate that, to a first order, that the smaller the size of the diffusing atom, the greater its diffusivity at a given temperature: D(He) > D(Ne) > D(Ar) at constant T. Significantly, the diffusivities of the noble gases in the glasses investigated do not display simple Arrhenian behavior: there are well-defined departures from Arrhenian behavior which occur at lower temperatures for He than for Ne or Ar. We propose that the non-Arrhenian behavior of noble gases can be explained by structural modifications of the silicate network itself as the glass transition temperature is approached: as the available free volume (available site for diffusive jumps) is modified, noble gas diffusion is no longer solely temperature-activated but also becomes sensitive to the kinetics of network rearrangements. The non-Arrhenian behavior of noble gas diffusion close to Tg is well described by a modified Vogel-Tammann-Fulcher (VTF) equation: Finally, our step heating diffusion experiments suggest that at T close to Tg, noble gas isotopes may suffer kinetic fractionation at a degree larger than that predicted by Graham's law. In the case of 40Ar and 36Ar, the traditional assumption based on Graham's law is that the ratio D40Ar/D36Ar should be equal to 0.95 (the square root of the ratio of the mass of 36Ar over the mass of 40Ar). In our experiment with glass G1, D40Ar/D36Ar rapidly decreased with decreasing temperature, from near unity (0.98 ± 0.14) at T > 1040 K to 0.76 when close to Tg (T = 1003 K). Replicate experiments are needed to confirm the strong kinetic fractionation of heavy noble gases close to the transition temperature.

Transient ensemble dynamics in time-independent galactic potentials

NASA Astrophysics Data System (ADS)

Mahon, M. Elaine; Abernathy, Robert A.; Bradley, Brendan O.; Kandrup, Henry E.

1995-07-01

This paper summarizes a numerical investigation of the short-time, possibly transient, behaviour of ensembles of stochastic orbits evolving in fixed non-integrable potentials, with the aim of deriving insights into the structure and evolution of galaxies. The simulations involved three different two-dimensional potentials, quite different in appearance. However, despite these differences, ensembles in all three potentials exhibit similar behaviour. This suggests that the conclusions inferred from the simulations are robust, relying only on basic topological properties, e.g., the existence of KAM tori and cantori. Generic ensembles of initial conditions, corresponding to stochastic orbits, exhibit a rapid coarse-grained approach towards a near-invariant distribution on a time-scale <>t_H, although various irregularities associated with external and/or internal irregularities can drastically accelerate this process. A principal tool in the analysis is the notion of a local Liapounov exponent, which provides a statistical characterization of the overall instability of stochastic orbits over finite time intervals. In particular, there is a precise sense in which confined stochastic orbits are less unstable, with smaller local Liapounov exponents, than are unconfined stochastic orbits.

IMPLEMENTATION OF FIRST-PASSAGE TIME APPROACH FOR OBJECT KINETIC MONTE CARLO SIMULATIONS OF IRRADIATION

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nandipati, Giridhar; Setyawan, Wahyu; Heinisch, Howard L.

2014-06-30

The objective of the work is to implement a first-passage time (FPT) approach to deal with very fast 1D diffusing SIA clusters in KSOME (kinetic simulations of microstructural evolution) [1] to achieve longer time-scales during irradiation damage simulations. The goal is to develop FPT-KSOME, which has the same flexibility as KSOME.

Linking basin-scale and pore-scale gas hydrate distribution patterns in diffusion-dominated marine hydrate systems: DIFFUSION-DRIVEN HYDRATE GROWTH IN SANDS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nole, Michael; Daigle, Hugh; Cook, Ann E.

The goal of this study is to computationally determine the potential distribution patterns of diffusion-driven methane hydrate accumulations in coarse-grained marine sediments. Diffusion of dissolved methane in marine gas hydrate systems has been proposed as a potential transport mechanism through which large concentrations of hydrate can preferentially accumulate in coarse-grained sediments over geologic time. Using one-dimensional compositional reservoir simulations, we examine hydrate distribution patterns at the scale of individual sand layers (1 to 20 m thick) that are deposited between microbially active fine-grained material buried through the gas hydrate stability zone (GHSZ). We then extrapolate to two- dimensional and basin-scalemore » three-dimensional simulations, where we model dipping sands and multilayered systems. We find that properties of a sand layer including pore size distribution, layer thickness, dip, and proximity to other layers in multilayered systems all exert control on diffusive methane fluxes toward and within a sand, which in turn impact the distribution of hydrate throughout a sand unit. In all of these simulations, we incorporate data on physical properties and sand layer geometries from the Terrebonne Basin gas hydrate system in the Gulf of Mexico. We demonstrate that diffusion can generate high hydrate saturations (upward of 90%) at the edges of thin sands at shallow depths within the GHSZ, but that it is ineffective at producing high hydrate saturations throughout thick (greater than 10 m) sands buried deep within the GHSZ. As a result, we find that hydrate in fine-grained material can preserve high hydrate saturations in nearby thin sands with burial.« less

Linking basin-scale and pore-scale gas hydrate distribution patterns in diffusion-dominated marine hydrate systems: DIFFUSION-DRIVEN HYDRATE GROWTH IN SANDS

DOE PAGES

Nole, Michael; Daigle, Hugh; Cook, Ann E.; ...

2017-02-01

The goal of this study is to computationally determine the potential distribution patterns of diffusion-driven methane hydrate accumulations in coarse-grained marine sediments. Diffusion of dissolved methane in marine gas hydrate systems has been proposed as a potential transport mechanism through which large concentrations of hydrate can preferentially accumulate in coarse-grained sediments over geologic time. Using one-dimensional compositional reservoir simulations, we examine hydrate distribution patterns at the scale of individual sand layers (1 to 20 m thick) that are deposited between microbially active fine-grained material buried through the gas hydrate stability zone (GHSZ). We then extrapolate to two- dimensional and basin-scalemore » three-dimensional simulations, where we model dipping sands and multilayered systems. We find that properties of a sand layer including pore size distribution, layer thickness, dip, and proximity to other layers in multilayered systems all exert control on diffusive methane fluxes toward and within a sand, which in turn impact the distribution of hydrate throughout a sand unit. In all of these simulations, we incorporate data on physical properties and sand layer geometries from the Terrebonne Basin gas hydrate system in the Gulf of Mexico. We demonstrate that diffusion can generate high hydrate saturations (upward of 90%) at the edges of thin sands at shallow depths within the GHSZ, but that it is ineffective at producing high hydrate saturations throughout thick (greater than 10 m) sands buried deep within the GHSZ. As a result, we find that hydrate in fine-grained material can preserve high hydrate saturations in nearby thin sands with burial.« less

Time and length scales within a fire and implications for numerical simulation

DOE Office of Scientific and Technical Information (OSTI.GOV)

TIESZEN,SHELDON R.

2000-02-02

A partial non-dimensionalization of the Navier-Stokes equations is used to obtain order of magnitude estimates of the rate-controlling transport processes in the reacting portion of a fire plume as a function of length scale. Over continuum length scales, buoyant times scales vary as the square root of the length scale; advection time scales vary as the length scale, and diffusion time scales vary as the square of the length scale. Due to the variation with length scale, each process is dominant over a given range. The relationship of buoyancy and baroclinc vorticity generation is highlighted. For numerical simulation, first principlesmore » solution for fire problems is not possible with foreseeable computational hardware in the near future. Filtered transport equations with subgrid modeling will be required as two to three decades of length scale are captured by solution of discretized conservation equations. By whatever filtering process one employs, one must have humble expectations for the accuracy obtainable by numerical simulation for practical fire problems that contain important multi-physics/multi-length-scale coupling with up to 10 orders of magnitude in length scale.« less

Normal and tumoral melanocytes exhibit q-Gaussian random search patterns.

PubMed

da Silva, Priscila C A; Rosembach, Tiago V; Santos, Anésia A; Rocha, Márcio S; Martins, Marcelo L

2014-01-01

In multicellular organisms, cell motility is central in all morphogenetic processes, tissue maintenance, wound healing and immune surveillance. Hence, failures in its regulation potentiates numerous diseases. Here, cell migration assays on plastic 2D surfaces were performed using normal (Melan A) and tumoral (B16F10) murine melanocytes in random motility conditions. The trajectories of the centroids of the cell perimeters were tracked through time-lapse microscopy. The statistics of these trajectories was analyzed by building velocity and turn angle distributions, as well as velocity autocorrelations and the scaling of mean-squared displacements. We find that these cells exhibit a crossover from a normal to a super-diffusive motion without angular persistence at long time scales. Moreover, these melanocytes move with non-Gaussian velocity distributions. This major finding indicates that amongst those animal cells supposedly migrating through Lévy walks, some of them can instead perform q-Gaussian walks. Furthermore, our results reveal that B16F10 cells infected by mycoplasmas exhibit essentially the same diffusivity than their healthy counterparts. Finally, a q-Gaussian random walk model was proposed to account for these melanocytic migratory traits. Simulations based on this model correctly describe the crossover to super-diffusivity in the cell migration tracks.

Homogenization of Large-Scale Movement Models in Ecology

USGS Publications Warehouse

Garlick, M.J.; Powell, J.A.; Hooten, M.B.; McFarlane, L.R.

2011-01-01

A difficulty in using diffusion models to predict large scale animal population dispersal is that individuals move differently based on local information (as opposed to gradients) in differing habitat types. This can be accommodated by using ecological diffusion. However, real environments are often spatially complex, limiting application of a direct approach. Homogenization for partial differential equations has long been applied to Fickian diffusion (in which average individual movement is organized along gradients of habitat and population density). We derive a homogenization procedure for ecological diffusion and apply it to a simple model for chronic wasting disease in mule deer. Homogenization allows us to determine the impact of small scale (10-100 m) habitat variability on large scale (10-100 km) movement. The procedure generates asymptotic equations for solutions on the large scale with parameters defined by small-scale variation. The simplicity of this homogenization procedure is striking when compared to the multi-dimensional homogenization procedure for Fickian diffusion,and the method will be equally straightforward for more complex models. ?? 2010 Society for Mathematical Biology.

Molecular binoculars: how to spatially resolve environmental fluctuations by following two or more single-molecule spectral trails at a time.

PubMed

Lubchenko, Vassiliy; Silbey, Robert J

2013-10-24

We propose a novel type of spectral diffusion experiment that enables one to decouple spatial characteristics of the environmental fluctuations, such as their concentration, from the interaction with the chromophore. Traditional hole broadening experiments do not allow for such decoupling in the common case when the chromophore-environment interaction is scale invariant. Here we propose to simultaneously follow the spectral trails of a small number of nearby chromophores--two or more--which thereby sense a highly overlapping set of the fluctuations. To this end, we estimate the combined probability distribution for the frequencies of a set of chromophores contained within the same sample. The present setup introduces a new length scale, i.e., the interchromophore distance, which breaks the aforementioned scale invariance and enables one to determine independently the concentration of the environmental fluctuations and their coupling to the chromophores, by monitoring the time after which spectral diffusion of distinct chromophores becomes uncorrelated. We illustrate these results with structural excitations in low temperature glasses.

Raman Spectroscopy of Isotopic Water Diffusion in Ultraviscous, Glassy, and Gel States in Aerosol by Use of Optical Tweezers.

PubMed

Davies, James F; Wilson, Kevin R

2016-02-16

The formation of ultraviscous, glassy, and amorphous gel states in aqueous aerosol following the loss of water results in nonequilibrium dynamics due to the extended time scales for diffusive mixing. Existing techniques for measuring water diffusion by isotopic exchange are limited by contact of samples with the substrate, and methods applied to infer diffusion coefficients from mass transport in levitated droplets requires analysis by complex coupled differential equations to derive diffusion coefficients. We present a new technique that combines contactless levitation with aerosol optical tweezers with isotopic exchange (D2O/H2O) to measure the water diffusion coefficient over a broad range (Dw ≈ 10(-12)-10(-17) m(2)·s(-1)) in viscous organic liquids (citric acid, sucrose, and shikimic acid) and inorganic gels (magnesium sulfate, MgSO4). For the organic liquids in binary and ternary mixtures, Dw depends on relative humidity and follows a simple compositional Vignes relationship. In MgSO4 droplets, water diffusivity decreases sharply with water activity and is consistent with predictions from percolation theory. These measurements show that, by combining micrometer-sized particle levitation (a contactless measurement with rapid mixing times) with an established probe of water diffusion, Dw can be simply and directly quantified for amorphous and glassy states that are inaccessible to existing methods.

Raman Spectroscopy of Isotopic Water Diffusion in Ultraviscous, Glassy, and Gel States in Aerosol by Use of Optical Tweezers

DOE PAGES

Davies, James F.; Wilson, Kevin R.

2016-01-11

The formation of ultraviscous, glassy, and amorphous gel states in aqueous aerosol following the loss of water results in nonequilibrium dynamics due to the extended time scales for diffusive mixing. Existing techniques for measuring water diffusion by isotopic exchange are limited by contact of samples with the substrate, and methods applied to infer diffusion coefficients from mass transport in levitated droplets requires analysis by complex coupled differential equations to derive diffusion coefficients. Here, we present a new technique that combines contactless levitation with aerosol optical tweezers with isotopic exchange (D 2O/H 2O) to measure the water diffusion coefficient over amore » broad range (D w ≈ 10 -12-10 -17 m 2s -1) in viscous organic liquids (citric acid, sucrose, and shikimic acid) and inorganic gels (magnesium sulfate, MgSO 4). For the organic liquids in binary and ternary mixtures, D w depends on relative humidity and follows a simple compositional Vignes relationship. In MgSO 4 droplets, water diffusivity decreases sharply with water activity and is consistent with predictions from percolation theory. These measurements show that, by combining micrometer-sized particle levitation (a contactless measurement with rapid mixing times) with an established probe of water diffusion, D w can be simply and directly quantified for amorphous and glassy states that are inaccessible to existing methods.« less

Vertical eddy diffusivity as a control parameter in the tropical Pacific

NASA Astrophysics Data System (ADS)

Martinez Avellaneda, N.; Cornuelle, B.

2011-12-01

Ocean models suffer from errors in the treatment of turbulent sub-grid-scale motions responsible for mixing and energy dissipation. Unrealistic small-scale physics in models can have large-scale consequences, such as biases in the upper ocean temperature, a symptom of poorly-simulated upwelling, currents and air-sea interactions. This is of special importance in the tropical Pacific Ocean (TP), which is home to energetic air-sea interactions that affect global climate. It has been shown in a number of studies that the simulated ENSO variability is highly dependent on the state of the ocean (e.g.: background mixing). Moreover, the magnitude of the vertical numerical diffusion is of primary importance in properly reproducing the Pacific equatorial thermocline. This work is part of a NASA-funded project to estimate the space- and time-varying ocean mixing coefficients in an eddy-permitting (1/3dgr) model of the TP to obtain an improved estimate of its time-varying circulation and its underlying dynamics. While an estimation procedure for the TP (26dgr S - 30dgr N) in underway using the MIT general circulation model, complementary adjoint-based sensitivity studies have been carried out for the starting ocean state from Forget (2010). This analysis aids the interpretation of the estimated mixing coefficients and possible error compensation. The focus of the sensitivity tests is the Equatorial Undercurrent and sub-thermocline jets (i.e., Tsuchiya Jets), which have been thought to have strong dependence on vertical diffusivity and should provide checks on the estimated mixing parameters. In order to build intuition for the vertical diffusivity adjoint results in the TP, adjoint and forward perturbed simulations were carried out for an idealized sharp thermocline in a rectangular domain.

Aminopolymer Mobility and Support Interactions in Silica-PEI Composites for CO 2 Capture Applications: A Quasielastic Neutron Scattering Study

DOE PAGES

Holewinski, Adam; Sakwa-Novak, Miles A.; Carrillo, Jan-Michael Y.; ...

2017-05-30

Composite gas sorbents, formed from an active polymer phase and a porous support, are promising materials for the separation of acid gases from a variety of gas streams. Significant changes in sorption performance (capacity, rate, stability etc.) can be achieved by tuning the properties of the polymer and the nature of interactions between polymer and support. We utilize quasielastic neutron scattering (QENS) and coarse-grained molecular dynamics (MD) simulations to characterize the dynamic behavior of the most commonly reported polymer in such materials, poly(ethylenimine) (PEI), both in bulk form and when supported in a mesoporous silica framework. The polymer chain dynamicsmore » (rotational and translational diffusion) are characterized using two neutron backscattering spectrometers that have overlapping time scales, ranging from picoseconds to a few nanoseconds. Two modes of motion are detected for the PEI molecule in QENS. At low energy transfers, a “slow process” on the time scale of ~200 ps is found and attributed to jump-mediated, center-of-mass diffusion. Second, a “fast process” at ~20 ps scale is also found and is attributed to a locally confined, jump-diffusion. Characteristic data (time scale and spectral weight) of these processes are compared to those characterized by MD, and reasonable agreement is found. For the nanopore-confined PEI, we observe a significant reduction in the time scale of polymer motion as compared to the bulk. The impacts of silica surface functionalization and of polymer fill fraction in the silica pores (controlling the portion of polymer molecules in contact with the pore walls), are both studied in detail. Hydrophobic functionalization of the silica leads to an increase of the PEI mobility above that in native silanol-terminated silica, but the dynamics are still slower than those in bulk PEI. Sorbents with faster PEI dynamics are also found to be more efficient for CO 2 capture, possibly because sorption sites are more accessible than those in systems with slower PEI dynamics. Therefore, this work supports the existence of a link between the affinity of the support for PEI and the accessibility of active sorbent functional groups.« less

Upper Bound on Diffusivity

NASA Astrophysics Data System (ADS)

Hartman, Thomas; Hartnoll, Sean A.; Mahajan, Raghu

2017-10-01

The linear growth of operators in local quantum systems leads to an effective light cone even if the system is nonrelativistic. We show that the consistency of diffusive transport with this light cone places an upper bound on the diffusivity: D ≲v2τeq. The operator growth velocity v defines the light cone, and τeq is the local equilibration time scale, beyond which the dynamics of conserved densities is diffusive. We verify that the bound is obeyed in various weakly and strongly interacting theories. In holographic models, this bound establishes a relation between the hydrodynamic and leading nonhydrodynamic quasinormal modes of planar black holes. Our bound relates transport data—including the electrical resistivity and the shear viscosity—to the local equilibration time, even in the absence of a quasiparticle description. In this way, the bound sheds light on the observed T -linear resistivity of many unconventional metals, the shear viscosity of the quark-gluon plasma, and the spin transport of unitary fermions.

Statistics of actin-propelled trajectories in noisy environments

NASA Astrophysics Data System (ADS)

Wen, Fu-Lai; Chen, Hsuan-Yi; Leung, Kwan-tai

2016-06-01

Actin polymerization is ubiquitously utilized to power the locomotion of eukaryotic cells and pathogenic bacteria in living systems. Inevitably, actin polymerization and depolymerization proceed in a fluctuating environment that renders the locomotion stochastic. Previously, we have introduced a deterministic model that manages to reproduce actin-propelled trajectories in experiments, but not to address fluctuations around them. To remedy this, here we supplement the deterministic model with noise terms. It enables us to compute the effects of fluctuating actin density and forces on the trajectories. Specifically, the mean-squared displacement (MSD) of the trajectories is computed and found to show a super-ballistic scaling with an exponent 3 in the early stage, followed by a crossover to a normal, diffusive scaling of exponent 1 in the late stage. For open-end trajectories such as straights and S-shaped curves, the time of crossover matches the decay time of orientational order of the velocities along trajectories, suggesting that it is the spreading of velocities that leads to the crossover. We show that the super-ballistic scaling of MSD arises from the initial, linearly increasing correlation of velocities, before time translational symmetry is established. When the spreading of velocities reaches a steady state in the long-time limit, short-range correlation then yields a diffusive scaling in MSD. In contrast, close-loop trajectories like circles exhibit localized periodic motion, which inhibits spreading. The initial super-ballistic scaling of MSD arises from velocity correlation that both linearly increases and oscillates in time. Finally, we find that the above statistical features of the trajectories transcend the nature of noises, be it additive or multiplicative, and generalize to other self-propelled systems that are not necessarily actin based.

Evidence of Hierarchy in the Complex Fractured System of Geropotamos (Crete, Greece), as Extracted from Transient Electromagnetic Responses

NASA Astrophysics Data System (ADS)

Vallianatos, Filippos; Kouli, Maria; Kalisperi, Despina

2018-03-01

The essential goals of this paper are to test the transient electromagnetic (TEM) response in a fractured geological complex medium and to better understand the physics introduced by associating a roughness parameter β to the geological formation. An anomalous fractional diffusion approach is incorporated to describe the electromagnetic induction in rough multi-scaled geological structures. The multi-scaling characteristics of Geropotamos basin in Crete are revealed through the analysis of transient step-off response of an EM loop antenna. The semi-empirical parameters derived from late-time TEM measurements are correlated with the multi-scale heterogeneities of the medium. Certain interesting properties of the late-time slope γ(β) and the power law of near surface resistivity distribution, as extracted from TEM inversion for different depth, are presented. The analysis of the parameter γ(β) which scales the induced voltage in the loop in the late stage of the electromagnetic response leads to a different view of the EM geophysical data interpretation. We show that it is strongly correlated with areas of high fracture density within the geological formations of the Geropotamos area. For that reason, it is proposed as a local multi-scaling empirical index. The results of this paper suggest that anomalous diffusion could be a viable physical mechanism for the fractal transport of charge carriers, explaining observed late-time TEM responses across a variety of natural geological settings.

Computing eddy-driven effective diffusivity using Lagrangian particles

DOE PAGES

Wolfram, Phillip J.; Ringler, Todd D.

2017-08-14

A novel method to derive effective diffusivity from Lagrangian particle trajectory data sets is developed and then analyzed relative to particle-derived meridional diffusivity for eddy-driven mixing in an idealized circumpolar current. Quantitative standard dispersion- and transport-based mixing diagnostics are defined, compared and contrasted to motivate the computation and use of effective diffusivity derived from Lagrangian particles. We compute the effective diffusivity by first performing scalar transport on Lagrangian control areas using stored trajectories computed from online Lagrangian In-situ Global High-performance particle Tracking (LIGHT) using the Model for Prediction Across Scales Ocean (MPAS-O). Furthermore, the Lagrangian scalar transport scheme is comparedmore » against an Eulerian scalar transport scheme. Spatially-variable effective diffusivities are computed from resulting time-varying cumulative concentrations that vary as a function of cumulative area. The transport-based Eulerian and Lagrangian effective diffusivity diagnostics are found to be qualitatively consistent with the dispersion-based diffusivity. All diffusivity estimates show a region of increased subsurface diffusivity within the core of an idealized circumpolar current and results are within a factor of two of each other. The Eulerian and Lagrangian effective diffusivities are most similar; smaller and more spatially diffused values are obtained with the dispersion-based diffusivity computed with particle clusters.« less

Computing eddy-driven effective diffusivity using Lagrangian particles

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wolfram, Phillip J.; Ringler, Todd D.

A novel method to derive effective diffusivity from Lagrangian particle trajectory data sets is developed and then analyzed relative to particle-derived meridional diffusivity for eddy-driven mixing in an idealized circumpolar current. Quantitative standard dispersion- and transport-based mixing diagnostics are defined, compared and contrasted to motivate the computation and use of effective diffusivity derived from Lagrangian particles. We compute the effective diffusivity by first performing scalar transport on Lagrangian control areas using stored trajectories computed from online Lagrangian In-situ Global High-performance particle Tracking (LIGHT) using the Model for Prediction Across Scales Ocean (MPAS-O). Furthermore, the Lagrangian scalar transport scheme is comparedmore » against an Eulerian scalar transport scheme. Spatially-variable effective diffusivities are computed from resulting time-varying cumulative concentrations that vary as a function of cumulative area. The transport-based Eulerian and Lagrangian effective diffusivity diagnostics are found to be qualitatively consistent with the dispersion-based diffusivity. All diffusivity estimates show a region of increased subsurface diffusivity within the core of an idealized circumpolar current and results are within a factor of two of each other. The Eulerian and Lagrangian effective diffusivities are most similar; smaller and more spatially diffused values are obtained with the dispersion-based diffusivity computed with particle clusters.« less

Effects of geometry and fluid elasticity during polymeric droplet pinch-off in microfluidic environments

NASA Astrophysics Data System (ADS)

Steinhaus, Ben; Shen, Amy; Sureshkumar, Radhakrishna

2006-11-01

We investigate the effects of fluid elasticity and channel geometry on polymeric droplet pinch-off by performing systematic experiments using viscoelastic polymer solutions which possess practically shear rate-independent viscosity (Boger fluids). Four different geometric sizes (width and depth are scaled up proportionally at the ratio of 0.5, 1, 2, 20) are used to study the effect of the length scale, which in turn influences the ratio of elastic to viscous forces as well as the Rayleigh time scale associated with the interfacial instability of a cylindrical column of liquid. We observe a power law relationship between the dimensionless (scaled with respect to the Rayleigh time scale) capillary pinch-off time, T, and the elasticity number, E, defined as the ratio of the fluid relaxation time to the time scale of viscous diffusion. In general, T increases dramatically with increasing E. The inhibition of ``bead-on-a-string'' formation is observed for flows with effective Deborah number, De, defined as the ratio of the fluid relaxation time to the Rayleigh time scale becomes greater than 10. For sufficiently large values of De, the Rayleigh instability may be modified substantially by fluid elasticity.

Large-scale magnetic fields at high Reynolds numbers in magnetohydrodynamic simulations.

PubMed

Hotta, H; Rempel, M; Yokoyama, T

2016-03-25

The 11-year solar magnetic cycle shows a high degree of coherence in spite of the turbulent nature of the solar convection zone. It has been found in recent high-resolution magnetohydrodynamics simulations that the maintenance of a large-scale coherent magnetic field is difficult with small viscosity and magnetic diffusivity (≲10 (12) square centimenters per second). We reproduced previous findings that indicate a reduction of the energy in the large-scale magnetic field for lower diffusivities and demonstrate the recovery of the global-scale magnetic field using unprecedentedly high resolution. We found an efficient small-scale dynamo that suppresses small-scale flows, which mimics the properties of large diffusivity. As a result, the global-scale magnetic field is maintained even in the regime of small diffusivities-that is, large Reynolds numbers. Copyright © 2016, American Association for the Advancement of Science.

Fractal diffusion in high temperature polymer electrolyte fuel cell membranes

NASA Astrophysics Data System (ADS)

Hopfenmüller, Bernhard; Zorn, Reiner; Holderer, Olaf; Ivanova, Oxana; Lehnert, Werner; Lüke, Wiebke; Ehlers, Georg; Jalarvo, Niina; Schneider, Gerald J.; Monkenbusch, Michael; Richter, Dieter

2018-05-01

The performance of fuel cells depends largely on the proton diffusion in the proton conducting membrane, the core of a fuel cell. High temperature polymer electrolyte fuel cells are based on a polymer membrane swollen with phosphoric acid as the electrolyte, where proton conduction takes place. We studied the proton diffusion in such membranes with neutron scattering techniques which are especially sensitive to the proton contribution. Time of flight spectroscopy and backscattering spectroscopy have been combined to cover a broad dynamic range. In order to selectively observe the diffusion of protons potentially contributing to the ion conductivity, two samples were prepared, where in one of the samples the phosphoric acid was used with hydrogen replaced by deuterium. The scattering data from the two samples were subtracted in a suitable way after measurement. Thereby subdiffusive behavior of the proton diffusion has been observed and interpreted in terms of a model of fractal diffusion. For this purpose, a scattering function for fractal diffusion has been developed. The fractal diffusion dimension dw and the Hausdorff dimension df have been determined on the length scales covered in the neutron scattering experiments.

Development and pilot line production of lithium doped silicon solar cells

NASA Technical Reports Server (NTRS)

Payne, P. A.

1972-01-01

Scaling up the BCl3 without O2 diffusion beyond 30 to 40 cells was investigated by using a 100 cell capacity diffusion boat which held the cells vertically. Sheet resistances and I-V curves were uniform with 10 to 20 cells spaced along the entire boat, so the quantity was increased to 40 and then 60 cells per diffusion. There was no change in cell output and uniformity going from 20 to 40 cells per diffusion; however only half the lithium cells fabricated from slices diffused in the 60 cell diffusion had efficiencies of 11% or better. Although uniform sheet resistances and I-V characteristic curves were obtained with up to 60 cells in the BCl3 with O2 diffusion, the short circuit currents were approximately 15% lower than the anticipated 135 to 140 mA. Consequently, work on this diffusion process has been aimed solely at increasing the short circuit current. The diffusion temperature was lowered from 1055 to 1000 and 950 C, and at each of these temperatures variations in diffusion time were investigated. At 1000 C short circuit currents were approximately 10 mA higher, 130 rather than 120 mA average.

Scaling of coupled dilatancy-diffusion processes in space and time

NASA Astrophysics Data System (ADS)

Main, I. G.; Bell, A. F.; Meredith, P. G.; Brantut, N.; Heap, M.

2012-04-01

Coupled dilatancy-diffusion processes resulting from microscopically brittle damage due to precursory cracking have been observed in the laboratory and suggested as a mechanism for earthquake precursors. One reason precursors have proven elusive may be the scaling in space: recent geodetic and seismic data placing strong limits on the spatial extent of the nucleation zone for recent earthquakes. Another may be the scaling in time: recent laboratory results on axi-symmetric samples show both a systematic decrease in circumferential extensional strain at failure and a delayed and a sharper acceleration of acoustic emission event rate as strain rate is decreased. Here we examine the scaling of such processes in time from laboratory to field conditions using brittle creep (constant stress loading) to failure tests, in an attempt to bridge part of the strain rate gap to natural conditions, and discuss the implications for forecasting the failure time. Dilatancy rate is strongly correlated to strain rate, and decreases to zero in the steady-rate creep phase at strain rates around 10-9 s-1 for a basalt from Mount Etna. The data are well described by a creep model based on the linear superposition of transient (decelerating) and accelerating micro-crack growth due to stress corrosion. The model produces good fits to the failure time in retrospect using the accelerating acoustic emission event rate, but in prospective tests on synthetic data with the same properties we find failure-time forecasting is subject to systematic epistemic and aleatory uncertainties that degrade predictability. The next stage is to use the technology developed to attempt failure forecasting in real time, using live streamed data and a public web-based portal to quantify the prospective forecast quality under such controlled laboratory conditions.

Reduced xenon diffusion for quantitative lung study--the role of SF(6)

NASA Technical Reports Server (NTRS)

Mair, R. W.; Hoffmann, D.; Sheth, S. A.; Wong, G. P.; Butler, J. P.; Patz, S.; Topulos, G. P.; Walsworth, R. L.

2000-01-01

The large diffusion coefficients of gases result in significant spin motion during the application of gradient pulses that typically last a few milliseconds in most NMR experiments. In restricted environments, such as the lung, this rapid gas diffusion can lead to violations of the narrow pulse approximation, a basic assumption of the standard Stejskal-Tanner NMR method of diffusion measurement. We therefore investigated the effect of a common, biologically inert buffer gas, sulfur hexafluoride (SF(6)), on (129)Xe NMR and diffusion. We found that the contribution of SF(6) to (129)Xe T(1) relaxation in a 1:1 xenon/oxygen mixture is negligible up to 2 bar of SF(6) at standard temperature. We also measured the contribution of SF(6) gas to (129)Xe T(2) relaxation, and found it to scale inversely with pressure, with this contribution approximately equal to 1 s for 1 bar SF(6) pressure and standard temperature. Finally, we found the coefficient of (129)Xe diffusion through SF(6) to be approximately 4.6 x 10(-6) m(2)s(-1) for 1 bar pressure of SF(6) and standard temperature, which is only 1.2 times smaller than the (129)Xe self diffusion coefficient for 1 bar (129)Xe pressure and standard temperature. From these measurements we conclude that SF(6) will not sufficiently reduce (129)Xe diffusion to allow accurate surface-area/volume ratio measurements in human alveoli using time-dependent gas diffusion NMR.

Numerical Study of Microstructural Evolution During Homogenization of Al-Si-Mg-Fe-Mn Alloys

NASA Astrophysics Data System (ADS)

Priya, Pikee; Johnson, David R.; Krane, Matthew J. M.

2016-09-01

Microstructural evolution during homogenization of Al-Si-Mg-Fe-Mn alloys occurs in two stages at different length scales: while holding at the homogenization temperature (diffusion on the scale of the secondary dendrite arm spacing (SDAS) in micrometers) and during quenching to room temperature (dispersoid precipitation at the nanometer to submicron scale). Here a numerical study estimates microstructural changes during both stages. A diffusion-based model developed to simulate evolution at the SDAS length scale predicts homogenization times and microstructures matching experiments. That model is coupled with a Kampmann Wagner Neumann-based precipitate nucleation and growth model to study the effect of temperature, composition, as-cast microstructure, and cooling rates during posthomogenization quenching on microstructural evolution. A homogenization schedule of 853 K (580 °C) for 8 hours, followed by cooling at 250 K/h, is suggested to optimize microstructures for easier extrusion, consisting of minimal α-Al(FeMn)Si, no β-AlFeSi, and Mg2Si dispersoids <1 μm size.

A Simple Parameterization of Mixing of Passive Scalars in Turbulent Flows

NASA Astrophysics Data System (ADS)

Nithianantham, Ajithshanthar; Venayagamoorthy, Karan

2015-11-01

A practical model for quantifying the turbulent diascalar diffusivity is proposed as Ks = 1 . 1γ'LTk 1 / 2 , where LT is defined as the Thorpe length scale, k is the turbulent kinetic energy and γ' is one-half of the mechanical to scalar time scale ratio, which was shown by previous researchers to be approximately 0 . 7 . The novelty of the proposed model lies in the use of LT, which is a widely used length scale in stably stratified flows (almost exclusively used in oceanography), for quantifying turbulent mixing in unstratified flows. LT can be readily obtained in the field using a Conductivity, Temperature and Depth (CTD) profiler. The turbulent kinetic energy is mostly contained in the large scales of the flow field and hence can be measured in the field or modeled in numerical simulations. Comparisons using DNS data show remarkably good agreement between the predicted and exact diffusivities. Office of Naval Research and National Science Foundation.

Information Filtering via a Scaling-Based Function

PubMed Central

Qiu, Tian; Zhang, Zi-Ke; Chen, Guang

2013-01-01

Finding a universal description of the algorithm optimization is one of the key challenges in personalized recommendation. In this article, for the first time, we introduce a scaling-based algorithm (SCL) independent of recommendation list length based on a hybrid algorithm of heat conduction and mass diffusion, by finding out the scaling function for the tunable parameter and object average degree. The optimal value of the tunable parameter can be abstracted from the scaling function, which is heterogeneous for the individual object. Experimental results obtained from three real datasets, Netflix, MovieLens and RYM, show that the SCL is highly accurate in recommendation. More importantly, compared with a number of excellent algorithms, including the mass diffusion method, the original hybrid method, and even an improved version of the hybrid method, the SCL algorithm remarkably promotes the personalized recommendation in three other aspects: solving the accuracy-diversity dilemma, presenting a high novelty, and solving the key challenge of cold start problem. PMID:23696829

Memory beyond memory in heart beating, a sign of a healthy physiological condition.

PubMed

Allegrini, P; Grigolini, P; Hamilton, P; Palatella, L; Raffaelli, G

2002-04-01

We describe two types of memory and illustrate each using artificial and actual heartbeat data sets. The first type of memory, yielding anomalous diffusion, implies the inverse power-law nature of the waiting time distribution and the second the correlation among distinct times, and consequently also the occurrence of many pseudoevents, namely, not genuinely random events. Using the method of diffusion entropy analysis, we establish the scaling that would be determined by the real events alone. We prove that the heart beating of healthy patients reveals the existence of many more pseudoevents than in the patients with congestive heart failure.

Inward propagating chemical waves in Taylor vortices.

PubMed

Thompson, Barnaby W; Novak, Jan; Wilson, Mark C T; Britton, Melanie M; Taylor, Annette F

2010-04-01

Advection-reaction-diffusion (ARD) waves in the Belousov-Zhabotinsky reaction in steady Taylor-Couette vortices have been visualized using magnetic-resonance imaging and simulated using an adapted Oregonator model. We show how propagating wave behavior depends on the ratio of advective, chemical and diffusive time scales. In simulations, inward propagating spiral flamelets are observed at high Damköhler number (Da). At low Da, the reaction distributes itself over several vortices and then propagates inwards as contracting ring pulses--also observed experimentally.

Monte Carlo Study of Cosmic-Ray Propagation in the Galaxy and Diffuse Gamma-Ray Production

NASA Astrophysics Data System (ADS)

Huang, C.-Y.; Pohl, M.

This talk present preliminary results for the time-dependent cosmic-ray propagation in the Galaxy by a fully 3-dimensional Monte Carlo simulation. The distribution of cosmic-rays (both protons and helium nuclei) in the Galaxy is studied on various spatial scales for both constant and variable cosmic-ray sources. The continuous diffuse gamma-ray emission produced by cosmic-rays during the propagation is evaluated. The results will be compared with calculations made with other propagation models.

Benchmarking urban flood models of varying complexity and scale using high resolution terrestrial LiDAR data

NASA Astrophysics Data System (ADS)

Fewtrell, Timothy J.; Duncan, Alastair; Sampson, Christopher C.; Neal, Jeffrey C.; Bates, Paul D.

2011-01-01

This paper describes benchmark testing of a diffusive and an inertial formulation of the de St. Venant equations implemented within the LISFLOOD-FP hydraulic model using high resolution terrestrial LiDAR data. The models are applied to a hypothetical flooding scenario in a section of Alcester, UK which experienced significant surface water flooding in the June and July floods of 2007 in the UK. The sensitivity of water elevation and velocity simulations to model formulation and grid resolution are analyzed. The differences in depth and velocity estimates between the diffusive and inertial approximations are within 10% of the simulated value but inertial effects persist at the wetting front in steep catchments. Both models portray a similar scale dependency between 50 cm and 5 m resolution which reiterates previous findings that errors in coarse scale topographic data sets are significantly larger than differences between numerical approximations. In particular, these results confirm the need to distinctly represent the camber and curbs of roads in the numerical grid when simulating surface water flooding events. Furthermore, although water depth estimates at grid scales coarser than 1 m appear robust, velocity estimates at these scales seem to be inconsistent compared to the 50 cm benchmark. The inertial formulation is shown to reduce computational cost by up to three orders of magnitude at high resolutions thus making simulations at this scale viable in practice compared to diffusive models. For the first time, this paper highlights the utility of high resolution terrestrial LiDAR data to inform small-scale flood risk management studies.

Comparison of LFM-test particle simulations and radial diffusion models of radiation belt electron injection into the slot region

NASA Astrophysics Data System (ADS)

Chu, F.; Hudson, M.; Kress, B.

2008-12-01

The physics-based Lyon-Fedder-Mobarry (LFM) code simulates Earth's magnetospheric topology and dynamics by solving the equations of ideal MHD using input solar wind parameters at the upstream boundary. Comparison with electron phase space density evolution during storms using a radial diffusion code, as well as spacecraft measurements where available, will tell us when diffusion is insufficiently accurate for radiation belt simulation, for example, during CME-shock injection events like March 24, 1991, which occurred on MeV electron drift time scales of minutes (Li et al., 1993). The 2004 July and 2004 November storms, comparable in depth of penetration into the slot region to the Halloween 2003 storm, have been modeled with both approaches. The November 8, 2004 storm was preceded by a Storm Sudden Commencement produced by a CME-shock followed by minimum Dst = -373 nT, while the July 23 to July 28 storm interval had milder consecutive drops in Dst, corresponding to multiple CME shocks and southward IMF Bz turnings. We have run the November and July storms with LFM using ACE data as upstream input, running the July storm with lower temporal resolution over a longer time interval. The November storm was different because the SCC shock was unusually intense, therefore the possibility of drift time scale acceleration by the associated magnetosonic impulse produced by the shock exists, as in March 1991 and also Halloween 2003 events (Kress et al., 2007). It can then take a short time (minutes) for electrons to be transported to low L shell while conserving their first invariant, resulting in a peak in energy and phase space density in the slot region. Radial diffusion suffices for some storm periods like the July 2004 sequence of three storms, while the guiding center test particle simulation in MHD fields is necessary to describe prompt injections which occur faster than diffusive time scales, for which November 2004 is a likely candidate. Earlier examples have been studied, including the Kress et al., 2007 study of the Halloween 2003 storm and Li et al., 1993 study of the March 24, 1991 injection event with MHD simulation carried out by Elkington et al. (2002) for this event. Radial diffusion remains the best approach for extended relatively quiet periods like the two month interval following the March 1991 prompt injection. Strong shocks will inject particles into lower L shell within a few minutes violating the third adiabatic invariant, so the diffusion mechanism cannot be adopted for sudden commencements, when Dst increases then decreases drastically; however particle tracing in time-dependent MHD fields will give an accurate estimation, so radial diffusion and particle tracing in MHD fields complement each other in radiation belt studies. Elkington, S. R., M.K. Hudson, M.J. Wiltberger, J.G. Lyon (2002) JASTP, 64, p. 607-615; Kress B. T., M. K. Hudson, M. D. Looper, J. Albert, J. G. Lyon, C. C. Goodrich (2007), J. Geophys. Res., 112, A09215, doi:10.1029/2006JA012218; Li, X., I. Roth, M. Temerin, J. R. Wygant, M. K. Hudson, and J. B. Blake (1993), Geophys. Res. Lett., 20, p. 2423-2426.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Han, Chang W.; Iddir, Hakim; Uzun, Alper

To address the challenge of fast, direct atomic-scale visualization of the diffusion of atoms and clusters on surfaces, we used aberration-corrected scanning transmission electron microscopy (STEM) with high scan speeds (as little as ~0.1 s per frame) to visualize the diffusion of (1) a heavy atom (Ir) on the surface of a support consisting of light atoms, MgO(100), and (2) an Ir 3 cluster on MgO(110). Sequential Z-contrast images elucidate the diffusion mechanisms, including the hopping of Ir1 and the rotational migration of Ir 3 as two Ir atoms remain anchored to the surface. Density functional theory (DFT) calculations providedmore » estimates of the diffusion energy barriers and binding energies of the iridium species to the surfaces. The results show how the combination of fast-scan STEM and DFT calculations allow real-time visualization and fundamental understanding of surface diffusion phenomena pertaining to supported catalysts and other materials.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dubey, P., E-mail: purushd@barc.gov.in; Sharma, V. K.; Mitra, S.

Synthetic hydroxyapatite (HAp) is an important material in biomedical engineering due to its excellent biocompatibility and bioactivity. Here we report dynamics of cetyltrimethylammonium bromide (CTAB) in HAp composite, prepared by co-precipitation method, as studied by quasielastic neutron scattering (QENS) technique. It is found that the observed dynamics involved two time scales associated with fast torsional motion and segmental motion of the CTAB monomers. In addition to segmental motion of the hydrogen atoms, few undergo torsional motion as well. Torsional dynamics was described by a 2-fold jump diffusion model. The segmental dynamics of CTAB has been described assumimg the hydrogen atomsmore » undergoing diffusion inside a sphere of confined volume. While the diffusivity is found to increase with temperature, the spherical volumes within which the hydrogen atoms are undergoing diffusion remain almost unchanged.« less

A Mass Diffusion Model for Dry Snow Utilizing a Fabric Tensor to Characterize Anisotropy

NASA Astrophysics Data System (ADS)

Shertzer, Richard H.; Adams, Edward E.

2018-03-01

A homogenization algorithm for randomly distributed microstructures is applied to develop a mass diffusion model for dry snow. Homogenization is a multiscale approach linking constituent behavior at the microscopic level—among ice and air—to the macroscopic material—snow. Principles of continuum mechanics at the microscopic scale describe water vapor diffusion across an ice grain's surface to the air-filled pore space. Volume averaging and a localization assumption scale up and down, respectively, between microscopic and macroscopic scales. The model yields a mass diffusivity expression at the macroscopic scale that is, in general, a second-order tensor parameterized by both bulk and microstructural variables. The model predicts a mass diffusivity of water vapor through snow that is less than that through air. Mass diffusivity is expected to decrease linearly with ice volume fraction. Potential anisotropy in snow's mass diffusivity is captured due to the tensor representation. The tensor is built from directional data assigned to specific, idealized microstructural features. Such anisotropy has been observed in the field and laboratories in snow morphologies of interest such as weak layers of depth hoar and near-surface facets.

The effect of physical back-diffusion of 13CO2 tracer on the coupling between photosynthesis and soil CO2 efflux in grassland.

PubMed

Burri, Susanne; Sturm, Patrick; Baur, Thomas; Barthel, Matti; Knohl, Alexander; Buchmann, Nina

2014-01-01

Pulse labelling experiments provide a common tool to study short-term processes in the plant-soil system and investigate below-ground carbon allocation as well as the coupling of soil CO(2) efflux to photosynthesis. During the first hours after pulse labelling, the measured isotopic signal of soil CO(2) efflux is a combination of both physical tracer diffusion into and out of the soil as well as biological tracer release via root and microbial respiration. Neglecting physical back-diffusion can lead to misinterpretation regarding time lags between photosynthesis and soil CO(2) efflux in grassland or any ecosystem type where the above-ground plant parts cannot be labelled in gas-tight chambers separated from the soil. We studied the effects of physical (13)CO(2) tracer back-diffusion in pulse labelling experiments in grassland, focusing on the isotopic signature of soil CO(2) efflux. Having accounted for back-diffusion, the estimated time lag for first tracer appearance in soil CO(2) efflux changed from 0 to 1.81±0.56 h (mean±SD) and the time lag for maximum tracer appearance from 2.67±0.39 to 9.63±3.32 h (mean±SD). Thus, time lags were considerably longer when physical tracer diffusion was considered. Using these time lags after accounting for physical back-diffusion, high nocturnal soil CO(2) efflux rates could be related to daytime rates of gross primary productivity (R(2)=0.84). Moreover, pronounced diurnal patterns in the δ(13)C of soil CO(2) efflux were found during the decline of the tracer over 3 weeks. Possible mechanisms include diurnal changes in the relative contributions of autotrophic and heterotrophic soil respiration as well as their respective δ(13)C values. Thus, after accounting for physical back-diffusion, we were able to quantify biological time lags in the coupling of photosynthesis and soil CO(2) efflux in grassland at the diurnal time scale.

Multiscale models and stochastic simulation methods for computing rare but key binding events in cell biology

DOE Office of Scientific and Technical Information (OSTI.GOV)

Guerrier, C.; Holcman, D., E-mail: david.holcman@ens.fr; Mathematical Institute, Oxford OX2 6GG, Newton Institute

The main difficulty in simulating diffusion processes at a molecular level in cell microdomains is due to the multiple scales involving nano- to micrometers. Few to many particles have to be simulated and simultaneously tracked while there are exploring a large portion of the space for binding small targets, such as buffers or active sites. Bridging the small and large spatial scales is achieved by rare events representing Brownian particles finding small targets and characterized by long-time distribution. These rare events are the bottleneck of numerical simulations. A naive stochastic simulation requires running many Brownian particles together, which is computationallymore » greedy and inefficient. Solving the associated partial differential equations is also difficult due to the time dependent boundary conditions, narrow passages and mixed boundary conditions at small windows. We present here two reduced modeling approaches for a fast computation of diffusing fluxes in microdomains. The first approach is based on a Markov mass-action law equations coupled to a Markov chain. The second is a Gillespie's method based on the narrow escape theory for coarse-graining the geometry of the domain into Poissonian rates. The main application concerns diffusion in cellular biology, where we compute as an example the distribution of arrival times of calcium ions to small hidden targets to trigger vesicular release.« less

Chemical ageing and transformation of diffusivity in semi-solid multi-component organic aerosol particles

NASA Astrophysics Data System (ADS)

Pfrang, C.; Shiraiwa, M.; Pöschl, U.

2011-04-01

Recent experimental evidence underlines the importance of reduced diffusivity in amorphous semi-solid or glassy atmospheric aerosols. This paper investigates the impact of diffusivity on the ageing of multi-component reactive organic particles representative of atmospheric cooking aerosols. We apply and extend the recently developed KM-SUB model in a study of a 12-component mixture containing oleic and palmitoleic acids. We demonstrate that changes in the diffusivity may explain the evolution of chemical loss rates in ageing semi-solid particles, and we resolve surface and bulk processes under transient reaction conditions considering diffusivities altered by oligomerisation. This new model treatment allows prediction of the ageing of mixed organic multi-component aerosols over atmospherically relevant time scales and conditions. We illustrate the impact of changing diffusivity on the chemical half-life of reactive components in semi-solid particles, and we demonstrate how solidification and crust formation at the particle surface can affect the chemical transformation of organic aerosols.

Surface diffusion of cyclic hydrocarbons on nickel

NASA Astrophysics Data System (ADS)

Silverwood, I. P.; Armstrong, J.

2018-08-01

Surface diffusion of adsorbates is difficult to measure on realistic systems, yet it is of fundamental interest in catalysis and coating reactions. quasielastic neutron scattering (QENS) was used to investigate the diffusion of cyclohexane and benzene adsorbed on a nickel metal sponge catalyst. Molecular dynamics simulations of benzene on a model (111) nickel surface showed localised motion with diffusion by intermittent jumps. The experimental data was therefore fitted to the Singwi-Sjölander model and activation energies for diffusion of 4.0 kJ mol-1 for benzene and 4.3 kJ mol-1 for cyclohexane were calculated for the two dimensional model. Limited motion out-of plane was seen in the dynamics simulations and is discussed, although the resolution of the scattering experiment is insufficient to quantify this. Good agreement is seen between the use of a perfect crystal as a model for a disordered system over short time scales, suggesting that simple models are adequate to describe diffusion over polycrystalline metal surfaces on the timescale of QENS measurement.

Non-kinematic Flux-transport Dynamos Including the Effects of Diffusivity Quenching

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ichimura, Chiaki; Yokoyama, Takaaki

2017-04-10

Turbulent magnetic diffusivity is quenched when strong magnetic fields suppress turbulent motion in a phenomenon known as diffusivity quenching. Diffusivity quenching can provide a mechanism for amplifying magnetic field and influencing global velocity fields through Lorentz force feedback. To investigate this effect, we conducted mean field flux-transport dynamo simulations that included the effects of diffusivity quenching in a non-kinematic regime. We found that toroidal magnetic field strength is amplified by up to approximately 1.5 times in the convection zone as a result of diffusivity quenching. This amplification is much weaker than that in kinematic cases as a result of Lorentzmore » force feedback on the system’s differential rotation. While amplified toroidal fields lead to the suppression of equatorward meridional flow locally near the base of the convection zone, large-scale equatorward transport of magnetic flux via meridional flow, which is the essential process of the flux-transport dynamo, is sustainable in our calculations.« less

Glasslike Membrane Protein Diffusion in a Crowded Membrane.

PubMed

Munguira, Ignacio; Casuso, Ignacio; Takahashi, Hirohide; Rico, Felix; Miyagi, Atsushi; Chami, Mohamed; Scheuring, Simon

2016-02-23

Many functions of the plasma membrane depend critically on its structure and dynamics. Observation of anomalous diffusion in vivo and in vitro using fluorescence microscopy and single particle tracking has advanced our concept of the membrane from a homogeneous fluid bilayer with freely diffusing proteins to a highly organized crowded and clustered mosaic of lipids and proteins. Unfortunately, anomalous diffusion could not be related to local molecular details given the lack of direct and unlabeled molecular observation capabilities. Here, we use high-speed atomic force microscopy and a novel analysis methodology to analyze the pore forming protein lysenin in a highly crowded environment and document coexistence of several diffusion regimes within one membrane. We show the formation of local glassy phases, where proteins are trapped in neighbor-formed cages for time scales up to 10 s, which had not been previously experimentally reported for biological membranes. Furthermore, around solid-like patches and immobile molecules a slower glass phase is detected leading to protein trapping and creating a perimeter of decreased membrane diffusion.

Atomic scale modeling of defect production and microstructure evolution in irradiated metals

DOE Office of Scientific and Technical Information (OSTI.GOV)

Diaz de la Rubia, T.; Soneda, N.; Shimomura, Y.

1997-04-01

Irradiation effects in materials depend in a complex way on the form of the as-produced primary damage state and its spatial and temporal evolution. Thus, while collision cascades produce defects on a time scale of tens of picosecond, diffusion occurs over much longer time scales, of the order of seconds, and microstructure evolution over even longer time scales. In this report the authors present work aimed at describing damage production and evolution in metals across all the relevant time and length scales. They discuss results of molecular dynamics simulations of displacement cascades in Fe and V. They show that interstitialmore » clusters are produced in cascades above 5 keV, but not vacancy clusters. Next, they discuss the development of a kinetic Monte Carlo model that enables calculations of damage evolution over much longer time scales (1000`s of s) than the picosecond lifetime of the cascade. They demonstrate the applicability of the method by presenting predictions on the fraction of freely migrating defects in {alpha}Fe during irradiation at 600 K.« less

SMALL-SCALE ANISOTROPIES OF COSMIC RAYS FROM RELATIVE DIFFUSION

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ahlers, Markus; Mertsch, Philipp

2015-12-10

The arrival directions of multi-TeV cosmic rays show significant anisotropies at small angular scales. It has been argued that this small-scale structure can naturally arise from cosmic ray scattering in local turbulent magnetic fields that distort a global dipole anisotropy set by diffusion. We study this effect in terms of the power spectrum of cosmic ray arrival directions and show that the strength of small-scale anisotropies is related to properties of relative diffusion. We provide a formalism for how these power spectra can be inferred from simulations and motivate a simple analytic extension of the ensemble-averaged diffusion equation that canmore » account for the effect.« less

Chemistry resolved kinetic flow modeling of TATB based explosives

NASA Astrophysics Data System (ADS)

Vitello, Peter; Fried, Laurence E.; William, Howard; Levesque, George; Souers, P. Clark

2012-03-01

Detonation waves in insensitive, TATB-based explosives are believed to have multiple time scale regimes. The initial burn rate of such explosives has a sub-microsecond time scale. However, significant late-time slow release in energy is believed to occur due to diffusion limited growth of carbon. In the intermediate time scale concentrations of product species likely change from being in equilibrium to being kinetic rate controlled. We use the thermo-chemical code CHEETAH linked to an ALE hydrodynamics code to model detonations. We term our model chemistry resolved kinetic flow, since CHEETAH tracks the time dependent concentrations of individual species in the detonation wave and calculates EOS values based on the concentrations. We present here two variants of our new rate model and comparison with hot, ambient, and cold experimental data for PBX 9502.

Brownian dynamics of confined rigid bodies

DOE Office of Scientific and Technical Information (OSTI.GOV)

Delong, Steven; Balboa Usabiaga, Florencio; Donev, Aleksandar, E-mail: donev@courant.nyu.edu

2015-10-14

We introduce numerical methods for simulating the diffusive motion of rigid bodies of arbitrary shape immersed in a viscous fluid. We parameterize the orientation of the bodies using normalized quaternions, which are numerically robust, space efficient, and easy to accumulate. We construct a system of overdamped Langevin equations in the quaternion representation that accounts for hydrodynamic effects, preserves the unit-norm constraint on the quaternion, and is time reversible with respect to the Gibbs-Boltzmann distribution at equilibrium. We introduce two schemes for temporal integration of the overdamped Langevin equations of motion, one based on the Fixman midpoint method and the othermore » based on a random finite difference approach, both of which ensure that the correct stochastic drift term is captured in a computationally efficient way. We study several examples of rigid colloidal particles diffusing near a no-slip boundary and demonstrate the importance of the choice of tracking point on the measured translational mean square displacement (MSD). We examine the average short-time as well as the long-time quasi-two-dimensional diffusion coefficient of a rigid particle sedimented near a bottom wall due to gravity. For several particle shapes, we find a choice of tracking point that makes the MSD essentially linear with time, allowing us to estimate the long-time diffusion coefficient efficiently using a Monte Carlo method. However, in general, such a special choice of tracking point does not exist, and numerical techniques for simulating long trajectories, such as the ones we introduce here, are necessary to study diffusion on long time scales.« less

Anomalous diffusion on the Hanoi networks

NASA Astrophysics Data System (ADS)

Boettcher, S.; Gonçalves, B.

2008-11-01

Diffusion is modeled on the recently proposed Hanoi networks by studying the mean-square displacement of random walks with time, langr2rang~t2/dw. It is found that diffusion —the quintessential mode of transport throughout Nature— proceeds faster than ordinary, in one case with an exact, anomalous exponent dw=2- log2(phi)=1.30576... . It is an instance of a physical exponent containing the "golden ratio"\\phi=(1+\\sqrt{5})/2 that is intimately related to Fibonacci sequences and since Euclid's time has been found to be fundamental throughout geometry, architecture, art, and Nature itself. It originates from a singular renormalization group fixed point with a subtle boundary layer, for whose resolution phi is the main protagonist. The origin of this rare singularity is easily understood in terms of the physics of the process. Yet, the connection between network geometry and the emergence of phi in this context remains elusive. These results provide an accurate test of recently proposed universal scaling forms for first passage times.

Chemistry Resolved Kinetic Flow Modeling of TATB Based Explosives

NASA Astrophysics Data System (ADS)

Vitello, Peter; Fried, Lawrence; Howard, Mike; Levesque, George; Souers, Clark

2011-06-01

Detonation waves in insensitive, TATB based explosives are believed to have multi-time scale regimes. The initial burn rate of such explosives has a sub-microsecond time scale. However, significant late-time slow release in energy is believed to occur due to diffusion limited growth of carbon. In the intermediate time scale concentrations of product species likely change from being in equilibrium to being kinetic rate controlled. We use the thermo-chemical code CHEETAH linked to ALE hydrodynamics codes to model detonations. We term our model chemistry resolved kinetic flow as CHEETAH tracks the time dependent concentrations of individual species in the detonation wave and calculate EOS values based on the concentrations. A validation suite of model simulations compared to recent high fidelity metal push experiments at ambient and cold temperatures has been developed. We present here a study of multi-time scale kinetic rate effects for these experiments. Prepared by LLNL under Contract DE-AC52-07NA27344.

Diffusion of rod-like nanoparticles in non-adhesive and adhesive porous polymeric gels

NASA Astrophysics Data System (ADS)

Wang, Jiuling; Yang, Yiwei; Yu, Miaorong; Hu, Guoqing; Gan, Yong; Gao, Huajian; Shi, Xinghua

2018-03-01

It is known that rod-like nanoparticles (NPs) can achieve higher diffusivity than their spherical counterparts in biological porous media such as mucus and tumor interstitial matrix, but the underlying mechanisms still remain elusive. Here, we present a joint experimental and theoretical study to show that the aspect ratio (AR) of NPs and their adhesive interactions with the host medium play key roles in such anomalous diffusion behaviors of nanorods. In an adhesive polymer solution/gel (e.g., mucus), hopping diffusion enables nanorods to achieve higher diffusivity than spherical NPs with diameters equal to the minor axis of the rods, and there exists an optimal AR that leads to maximum diffusivity. In contrast, the diffusivity of nanorods decreases monotonically with increasing AR in a non-adhesive polymer solution/gel (e.g., hydroxyethyl cellulose, HEC). Our theoretical model, which captures all the experimental observations, generalizes the so-called obstruction-scaling model by incorporating the effects of the NPs/matrix interaction via the mean first passage time (MFPT) theory. This work reveals the physical origin of the anomalous diffusion behaviors of rod-like NPs in biological gels and may provide guidelines for a range of applications that involve NPs diffusion in complex porous media.

A new scaling for the rotational diffusion of molecular probes in polymer solutions.

PubMed

Qing, Jing; Chen, Anpu; Zhao, Nanrong

2017-12-13

In the present work, we propose a new scaling form for the rotational diffusion coefficient of molecular probes in semi-dilute polymer solutions, based on a theoretical study. The mean-field theory for depletion effect and semi-empirical scaling equation for the macroscopic viscosity of polymer solutions are properly incorporated to specify the space-dependent concentration and viscosity profiles in the vicinity of the probe surface. Following the scheme of classical fluid mechanics, we numerically evaluate the shear torque exerted on the probes, which then allows us to further calculate the rotational diffusion coefficient D r . Particular attention is given to the scaling behavior of the retardation factor R rot ≡ D/D r with D being the diffusion coefficient in pure solvent. We find that R rot has little relevance to the macroscopic viscosity of the polymer solution, while it can be well featured by the characteristic length scale r h /δ, i.e. the ratio between the hydrodynamic radius of the probe r h and the depletion thickness δ. Correspondingly, we obtain a novel scaling form for the rotational retardation factor, following R rot = exp[a(r h /δ) b ] with rather robust parameters of a ≃ 0.51 and b ≃ 0.56. We apply the theory to an extensive calculation for various probes in specific polymer solutions of poly(ethylene glycol) (PEG) and dextran. Our theoretical results show good agreements with the experimental data, and clearly demonstrate the validity of the new scaling form. In addition, the difference of the scaling behavior between translational and rotational diffusions is clarified, from which we conclude that the depletion effect plays a more significant role on the local rotational diffusion rather than the long-range translation diffusion.

Coupled Protein Diffusion and Folding in the Cell

PubMed Central

Guo, Minghao; Gelman, Hannah; Gruebele, Martin

2014-01-01

When a protein unfolds in the cell, its diffusion coefficient is affected by its increased hydrodynamic radius and by interactions of exposed hydrophobic residues with the cytoplasmic matrix, including chaperones. We characterize protein diffusion by photobleaching whole cells at a single point, and imaging the concentration change of fluorescent-labeled protein throughout the cell as a function of time. As a folded reference protein we use green fluorescent protein. The resulting region-dependent anomalous diffusion is well characterized by 2-D or 3-D diffusion equations coupled to a clustering algorithm that accounts for position-dependent diffusion. Then we study diffusion of a destabilized mutant of the enzyme phosphoglycerate kinase (PGK) and of its stable control inside the cell. Unlike the green fluorescent protein control's diffusion coefficient, PGK's diffusion coefficient is a non-monotonic function of temperature, signaling ‘sticking’ of the protein in the cytosol as it begins to unfold. The temperature-dependent increase and subsequent decrease of the PGK diffusion coefficient in the cytosol is greater than a simple size-scaling model suggests. Chaperone binding of the unfolding protein inside the cell is one plausible candidate for even slower diffusion of PGK, and we test the plausibility of this hypothesis experimentally, although we do not rule out other candidates. PMID:25436502

Coupled protein diffusion and folding in the cell.

PubMed

Guo, Minghao; Gelman, Hannah; Gruebele, Martin

2014-01-01

When a protein unfolds in the cell, its diffusion coefficient is affected by its increased hydrodynamic radius and by interactions of exposed hydrophobic residues with the cytoplasmic matrix, including chaperones. We characterize protein diffusion by photobleaching whole cells at a single point, and imaging the concentration change of fluorescent-labeled protein throughout the cell as a function of time. As a folded reference protein we use green fluorescent protein. The resulting region-dependent anomalous diffusion is well characterized by 2-D or 3-D diffusion equations coupled to a clustering algorithm that accounts for position-dependent diffusion. Then we study diffusion of a destabilized mutant of the enzyme phosphoglycerate kinase (PGK) and of its stable control inside the cell. Unlike the green fluorescent protein control's diffusion coefficient, PGK's diffusion coefficient is a non-monotonic function of temperature, signaling 'sticking' of the protein in the cytosol as it begins to unfold. The temperature-dependent increase and subsequent decrease of the PGK diffusion coefficient in the cytosol is greater than a simple size-scaling model suggests. Chaperone binding of the unfolding protein inside the cell is one plausible candidate for even slower diffusion of PGK, and we test the plausibility of this hypothesis experimentally, although we do not rule out other candidates.

Entangled time in flocking: Multi-time-scale interaction reveals emergence of inherent noise

PubMed Central

Murakami, Hisashi

2018-01-01

Collective behaviors that seem highly ordered and result in collective alignment, such as schooling by fish and flocking by birds, arise from seamless shuffling (such as super-diffusion) and bustling inside groups (such as Lévy walks). However, such noisy behavior inside groups appears to preclude the collective behavior: intuitively, we expect that noisy behavior would lead to the group being destabilized and broken into small sub groups, and high alignment seems to preclude shuffling of neighbors. Although statistical modeling approaches with extrinsic noise, such as the maximum entropy approach, have provided some reasonable descriptions, they ignore the cognitive perspective of the individuals. In this paper, we try to explain how the group tendency, that is, high alignment, and highly noisy individual behavior can coexist in a single framework. The key aspect of our approach is multi-time-scale interaction emerging from the existence of an interaction radius that reflects short-term and long-term predictions. This multi-time-scale interaction is a natural extension of the attraction and alignment concept in many flocking models. When we apply this method in a two-dimensional model, various flocking behaviors, such as swarming, milling, and schooling, emerge. The approach also explains the appearance of super-diffusion, the Lévy walk in groups, and local equilibria. At the end of this paper, we discuss future developments, including extending our model to three dimensions. PMID:29689074

The effects of noise on binocular rivalry waves: a stochastic neural field model

NASA Astrophysics Data System (ADS)

Webber, Matthew A.; Bressloff, Paul C.

2013-03-01

We analyze the effects of extrinsic noise on traveling waves of visual perception in a competitive neural field model of binocular rivalry. The model consists of two one-dimensional excitatory neural fields, whose activity variables represent the responses to left-eye and right-eye stimuli, respectively. The two networks mutually inhibit each other, and slow adaptation is incorporated into the model by taking the network connections to exhibit synaptic depression. We first show how, in the absence of any noise, the system supports a propagating composite wave consisting of an invading activity front in one network co-moving with a retreating front in the other network. Using a separation of time scales and perturbation methods previously developed for stochastic reaction-diffusion equations, we then show how extrinsic noise in the activity variables leads to a diffusive-like displacement (wandering) of the composite wave from its uniformly translating position at long time scales, and fluctuations in the wave profile around its instantaneous position at short time scales. We use our analysis to calculate the first-passage-time distribution for a stochastic rivalry wave to travel a fixed distance, which we find to be given by an inverse Gaussian. Finally, we investigate the effects of noise in the depression variables, which under an adiabatic approximation lead to quenched disorder in the neural fields during propagation of a wave.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wolfram, Phillip J.; Ringler, Todd D.

Meridional diffusivity is assessed in this paper for a baroclinically unstable jet in a high-latitudeIdealized Circumpolar Current (ICC) using the Model for Prediction Across Scales-Ocean (MPAS-O) and the online Lagrangian In-situ Global High-performance particle Tracking (LIGHT) diagnostic via space-time dispersion of particle clusters over 120 monthly realizations of O(10 6) particles on 11 potential density surfaces. Diffusivity in the jet reaches values of O(6000 m 2 s -1) and is largest near the critical layer supporting mixing suppression and critical layer theory. Values in the vicinity of the shelf break are suppressed to O(100 m 2 s -1) due tomore » the presence of westward slope front currents. Diffusivity attenuates less rapidly with depth in the jet than both eddy velocity and kinetic energy scalings would suggest. Removal of the mean flow via high-pass filtering shifts the nonlinear parameter (ratio of the eddy velocity to eddy phase speed) into the linear wave regime by increasing the eddy phase speed via the depth-mean flow. Low-pass filtering, in contrast, quantifies the effect of mean shear. Diffusivity is decomposed into mean flow shear, linear waves, and the residual nonhomogeneous turbulence components, where turbulence dominates and eddy-produced filamentation strained by background mean shear enhances mixing, accounting for ≥ 80% of the total diffusivity relative to mean shear [O(100 m 2 s -1)], linear waves [O(1000 m 2 s -1)], and undecomposed full diffusivity [O(6000 m 2 s -1)]. Finally, diffusivity parameterizations accounting for both the nonhomogeneous turbulence residual and depth variability are needed.« less

Zonal flow evolution and overstability in accretion discs

NASA Astrophysics Data System (ADS)

Vanon, R.; Ogilvie, G. I.

2017-04-01

This work presents a linear analytical calculation on the stability and evolution of a compressible, viscous self-gravitating (SG) Keplerian disc with both horizontal thermal diffusion and a constant cooling time-scale when an axisymmetric structure is present and freely evolving. The calculation makes use of the shearing sheet model and is carried out for a range of cooling times. Although the solutions to the inviscid problem with no cooling or diffusion are well known, it is non-trivial to predict the effect caused by the introduction of cooling and of small diffusivities; this work focuses on perturbations of intermediate wavelengths, therefore representing an extension to the classical stability analysis on thermal and viscous instabilities. For density wave modes, the analysis can be simplified by means of a regular perturbation analysis; considering both shear and thermal diffusivities, the system is found to be overstable for intermediate and long wavelengths for values of the Toomre parameter Q ≲ 2; a non-SG instability is also detected for wavelengths ≳18H, where H is the disc scale-height, as long as γ ≲ 1.305. The regular perturbation analysis does not, however, hold for the entropy and potential vorticity slow modes as their ideal growth rates are degenerate. To understand their evolution, equations for the axisymmetric structure's amplitudes in these two quantities are analytically derived and their instability regions obtained. The instability appears boosted by increasing the value of the adiabatic index and of the Prandtl number, while it is quenched by efficient cooling.

A theoretical model for the collective motion of proteins by means of principal component analysis

NASA Astrophysics Data System (ADS)

Kamberaj, Hiqmet

2011-02-01

A coarse grained model in the frame work of principal component analysis is presented. We used a bath of harmonic oscillators approach, based on classical mechanics, to derive the generalized Langevin equations of motion for the collective coordinates. The dynamics of the protein collective coordinates derived from molecular dynamics simulations have been studied for the Bovine Pancreatic Trypsin Inhibitor. We analyzed the stability of the method by studying structural fluctuations of the C a atoms obtained from a 20 ns molecular dynamics simulation. Subsequently, the dynamics of the collective coordinates of protein were characterized by calculating the dynamical friction coefficient and diffusion coefficients along with time-dependent correlation functions of collective coordinates. A dual diffusion behavior was observed with a fast relaxation time of short diffusion regime 0.2-0.4 ps and slow relaxation time of long diffusion about 1-2 ps. In addition, we observed a power law decay of dynamical friction coefficient with exponent for the first five collective coordinates varying from -0.746 to -0.938 for the real part and from -0.528 to -0.665 for its magnitude. It was found that only the first ten collective coordinates are responsible for configuration transitions occurring on time scale longer than 50 ps.

An assessment of optical and biogeochemical multi-decadal trends in the Sargasso Sea

NASA Astrophysics Data System (ADS)

Allen, J. G.; Siegel, D.; Nelson, N. B.

2016-02-01

Observations of optical and biogeochemical data, made as part of the Bermuda Bio-Optics Project (BBOP) at the Bermuda Atlantic Time-series Study (BATS) site in the Sargasso Sea, allow for the examination of temporal trends in vertical light attenuation and their potential controls. Trends in both the magnitude and spectral slope of the diffuse attenuation coefficient should reflect changes in chlorophyll and chromophoric dissolved organic matter (CDOM) concentrations in the Sargasso Sea. The length and methodological consistency of this time series provides an excellent opportunity to extend analyses of seasonal cycles of apparent optical properties to interannual and multi-year time scales. Here, we characterize changes in the size and shape of diffuse attenuation coefficient spectra and compare them to temperature, chlorophyll a concentration, and to discrete measurements of phytoplankton and CDOM absorption. The time series analyses reveal up to a 1.2% annual increase of the magnitude of the diffuse attenuation coefficient over the upper 70 m of the water column while showing no significant change in the spectral slope of diffuse attenuation over the course of the study. These observations indicate that increases in phytoplankton pigment concentration rather than changes in CDOM are the primary driver for the attenuation trends on multi-year timescales for this region.

Proposing an Educational Scaling-and-Diffusion Model for Inquiry-Based Learning Designs

ERIC Educational Resources Information Center

Hung, David; Lee, Shu-Shing

2015-01-01

Education cannot adopt the linear model of scaling used by the medical sciences. "Gold standards" cannot be replicated without considering process-in-learning, diversity, and student-variedness in classrooms. This article proposes a nuanced model of educational scaling-and-diffusion, describing the scaling (top-down supports) and…

Dynamics of associating networks

NASA Astrophysics Data System (ADS)

Tang, Shengchang; Habicht, Axel; Wang, Muzhou; Li, Shuaili; Seiffert, Sebastian; Olsen, Bradley

Associating polymers offer important technological solutions to renewable and self-healing materials, conducting electrolytes for energy storage and transport, and vehicles for cell and protein deliveries. The interplay between polymer topologies and association chemistries warrants new interesting physics from associating networks, yet poses significant challenges to study these systems over a wide range of time and length scales. In a series of studies, we explored self-diffusion mechanisms of associating polymers above the percolation threshold, by combining experimental measurements using forced Rayleigh scattering and analytical insights from a two-state model. Despite the differences in molecular structures, a universal super-diffusion phenomenon is observed when diffusion of molecular species is hindered by dissociation kinetics. The molecular dissociation rate can be used to renormalize shear rheology data, which yields an unprecedented time-temperature-concentration superposition. The obtained shear rheology master curves provide experimental evidence of the relaxation hierarchy in associating networks.

Following fluctuating signs: Anomalous active superdiffusion of swimmers in anisotropic media

NASA Astrophysics Data System (ADS)

Toner, John; Löwen, Hartmut; Wensink, Henricus H.

2016-06-01

Active (i.e., self-propelled or swimming) particles moving through an isotropic fluid exhibit conventional diffusive behavior. We report anomalous diffusion of an active particle moving in an anisotropic nematic background. While the translational motion parallel to the nematic director shows ballistic behavior, the long-time transverse motion is superdiffusive, with an anomalous scaling proportional to t lnt of the mean-square displacement with time t . This behavior is predicted by an analytical theory that we present here and is corroborated by numerical simulation of active particle diffusion in a simple lattice model for a nematic liquid crystal. It is universal for any collection of self-propelled elements (e.g., bacteria or active rods) moving in a nematic background, provided only that the swimmers are sufficiently dilute that their interactions with each other can be neglected and that they do not perform hairpin turns.

Atomistic modeling of dropwise condensation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sikarwar, B. S., E-mail: bssikarwar@amity.edu; Singh, P. L.; Muralidhar, K.

The basic aim of the atomistic modeling of condensation of water is to determine the size of the stable cluster and connect phenomena occurring at atomic scale to the macroscale. In this paper, a population balance model is described in terms of the rate equations to obtain the number density distribution of the resulting clusters. The residence time is taken to be large enough so that sufficient time is available for all the adatoms existing in vapor-phase to loose their latent heat and get condensed. The simulation assumes clusters of a given size to be formed from clusters of smallermore » sizes, but not by the disintegration of the larger clusters. The largest stable cluster size in the number density distribution is taken to be representative of the minimum drop radius formed in a dropwise condensation process. A numerical confirmation of this result against predictions based on a thermodynamic model has been obtained. Results show that the number density distribution is sensitive to the surface diffusion coefficient and the rate of vapor flux impinging on the substrate. The minimum drop radius increases with the diffusion coefficient and the impinging vapor flux; however, the dependence is weak. The minimum drop radius predicted from thermodynamic considerations matches the prediction of the cluster model, though the former does not take into account the effect of the surface properties on the nucleation phenomena. For a chemically passive surface, the diffusion coefficient and the residence time are dependent on the surface texture via the coefficient of friction. Thus, physical texturing provides a means of changing, within limits, the minimum drop radius. The study reveals that surface texturing at the scale of the minimum drop radius does not provide controllability of the macro-scale dropwise condensation at large timescales when a dynamic steady-state is reached.« less

Scaling oxygen microprofiles at the sediment interface of deep stratified waters

NASA Astrophysics Data System (ADS)

Schwefel, Robert; Hondzo, Miki; Wüest, Alfred; Bouffard, Damien

2017-02-01

Dissolved oxygen microprofiles at the sediment-water interface of Lake Geneva were measured concurrently with velocities 0.25 to 2 m above the sediment. The measurements and scaling analyses indicate dissolved oxygen fluctuations and turbulent fluxes in exceedance of molecular diffusion in the proximity of the sediment-water interface. The measurements allowed the parameterization of the turbulent diffusion as a function of the dimensionless height above the sediment and the turbulence above the sediment-water interface. Turbulent diffusion depended strongly on the friction velocity and differed from formulations reported in the literature that are based on concepts of turbulent and developed wall-bounded flows. The dissolved oxygen microprofiles and proposed parameterization of turbulent diffusion enable a foundation for the similarity scaling of oxygen microprofiles in proximity to the sediment. The proposed scaling allows the estimation of diffusive boundary layer thickness, oxygen flux, and oxygen microprofile distribution in the near-sediment boundary layer.

Water of Hydration Dynamics in Minerals Gypsum and Bassanite: Ultrafast 2D IR Spectroscopy of Rocks.

PubMed

Yan, Chang; Nishida, Jun; Yuan, Rongfeng; Fayer, Michael D

2016-08-03

Water of hydration plays an important role in minerals, determining their crystal structures and physical properties. Here ultrafast nonlinear infrared (IR) techniques, two-dimensional infrared (2D IR) and polarization selective pump-probe (PSPP) spectroscopies, were used to measure the dynamics and disorder of water of hydration in two minerals, gypsum (CaSO4·2H2O) and bassanite (CaSO4·0.5H2O). 2D IR spectra revealed that water arrangement in freshly precipitated gypsum contained a small amount of inhomogeneity. Following annealing at 348 K, water molecules became highly ordered; the 2D IR spectrum became homogeneously broadened (motional narrowed). PSPP measurements observed only inertial orientational relaxation. In contrast, water in bassanite's tubular channels is dynamically disordered. 2D IR spectra showed a significant amount of inhomogeneous broadening caused by a range of water configurations. At 298 K, water dynamics cause spectral diffusion that sampled a portion of the inhomogeneous line width on the time scale of ∼30 ps, while the rest of inhomogeneity is static on the time scale of the measurements. At higher temperature, the dynamics become faster. Spectral diffusion accelerates, and a portion of the lower temperature spectral diffusion became motionally narrowed. At sufficiently high temperature, all of the dynamics that produced spectral diffusion at lower temperatures became motionally narrowed, and only homogeneous broadening and static inhomogeneity were observed. Water angular motions in bassanite exhibit temperature-dependent diffusive orientational relaxation in a restricted cone of angles. The experiments were made possible by eliminating the vast amount of scattered light produced by the granulated powder samples using phase cycling methods.

Diffusive mass transport in agglomerated glassy fallout from a near-surface nuclear test

NASA Astrophysics Data System (ADS)

Weisz, David G.; Jacobsen, Benjamin; Marks, Naomi E.; Knight, Kim B.; Isselhardt, Brett H.; Matzel, Jennifer E.

2018-02-01

Aerodynamically-shaped glassy fallout is formed when vapor phase constituents from the nuclear device are incorporated into molten carriers (i.e. fallout precursor materials derived from soil or other near-field environmental debris). The effects of speciation and diffusive transport of condensing constituents are not well defined in models of fallout formation. Previously we reported observations of diffuse micrometer scale layers enriched in Na, Fe, Ca, and 235U, and depleted in Al and Ti, at the interfaces of agglomerated fallout objects. Here, we derive the timescales of uranium mass transport in such fallout as it cools from 2500 K to 1500 K by applying a 1-dimensional planar diffusion model to the observed 235U/30Si variation at the interfaces. By modeling the thermal transport between the fireball and the carrier materials, the time of mass transport is calculated to be <0.6 s, <1 s, <2 s, and <3.5 s for fireball yields of 0.1 kt, 1 kt, 10 kt, and 100 kt respectively. Based on the calculated times of mass transport, a maximum temperature of deposition of uranium onto the carrier material of ∼2200 K is inferred (1σ uncertainty of ∼200 K). We also determine that the occurrence of micrometer scale layers of material enriched in relatively volatile Na-species as well as more refractory Ca-species provides evidence for an oxygen-rich fireball based on the vapor pressure of the two species under oxidizing conditions. These results represent the first application of diffusion-based modeling to derive material transport, thermal environments, and oxidation-speciation in near-surface nuclear detonation environments.

Diffusive mass transport in agglomerated glassy fallout from a near-surface nuclear test

DOE PAGES

Weisz, David G.; Jacobsen, Benjamin; Marks, Naomi E.; ...

2017-12-15

Aerodynamically-shaped glassy fallout is formed when vapor phase constituents from the nuclear device are incorporated into molten carriers (i.e. fallout precursor materials derived from soil or other near-field environmental debris). The effects of speciation and diffusive transport of condensing constituents are not well defined in models of fallout formation. Previously we reported observations of diffuse micrometer scale layers enriched in Na, Fe, Ca, and 235U, and depleted in Al and Ti, at the interfaces of agglomerated fallout objects. Here in this paper, we derive the timescales of uranium mass transport in such fallout as it cools from 2500 K tomore » 1500 K by applying a 1-dimensional planar diffusion model to the observed 235U/ 30Si variation at the interfaces. By modeling the thermal transport between the fireball and the carrier materials, the time of mass transport is calculated to be <0.6 s, <1 s, <2 s, and <3.5 s for fireball yields of 0.1 kt, 1 kt, 10 kt, and 100 kt respectively. Based on the calculated times of mass transport, a maximum temperature of deposition of uranium onto the carrier material of ~2200 K is inferred (1σ uncertainty of ~200 K). We also determine that the occurrence of micrometer scale layers of material enriched in relatively volatile Na-species as well as more refractory Ca-species provides evidence for an oxygen-rich fireball based on the vapor pressure of the two species under oxidizing conditions. These results represent the first application of diffusion-based modeling to derive material transport, thermal environments, and oxidation-speciation in near-surface nuclear detonation environments.« less

Diffusive mass transport in agglomerated glassy fallout from a near-surface nuclear test

DOE Office of Scientific and Technical Information (OSTI.GOV)

Weisz, David G.; Jacobsen, Benjamin; Marks, Naomi E.

Aerodynamically-shaped glassy fallout is formed when vapor phase constituents from the nuclear device are incorporated into molten carriers (i.e. fallout precursor materials derived from soil or other near-field environmental debris). The effects of speciation and diffusive transport of condensing constituents are not well defined in models of fallout formation. Previously we reported observations of diffuse micrometer scale layers enriched in Na, Fe, Ca, and 235U, and depleted in Al and Ti, at the interfaces of agglomerated fallout objects. Here in this paper, we derive the timescales of uranium mass transport in such fallout as it cools from 2500 K tomore » 1500 K by applying a 1-dimensional planar diffusion model to the observed 235U/ 30Si variation at the interfaces. By modeling the thermal transport between the fireball and the carrier materials, the time of mass transport is calculated to be <0.6 s, <1 s, <2 s, and <3.5 s for fireball yields of 0.1 kt, 1 kt, 10 kt, and 100 kt respectively. Based on the calculated times of mass transport, a maximum temperature of deposition of uranium onto the carrier material of ~2200 K is inferred (1σ uncertainty of ~200 K). We also determine that the occurrence of micrometer scale layers of material enriched in relatively volatile Na-species as well as more refractory Ca-species provides evidence for an oxygen-rich fireball based on the vapor pressure of the two species under oxidizing conditions. These results represent the first application of diffusion-based modeling to derive material transport, thermal environments, and oxidation-speciation in near-surface nuclear detonation environments.« less

The relationship of dynamical heterogeneity to the Adam-Gibbs and random first-order transition theories of glass formation.

PubMed

Starr, Francis W; Douglas, Jack F; Sastry, Srikanth

2013-03-28

We carefully examine common measures of dynamical heterogeneity for a model polymer melt and test how these scales compare with those hypothesized by the Adam and Gibbs (AG) and random first-order transition (RFOT) theories of relaxation in glass-forming liquids. To this end, we first analyze clusters of highly mobile particles, the string-like collective motion of these mobile particles, and clusters of relative low mobility. We show that the time scale of the high-mobility clusters and strings is associated with a diffusive time scale, while the low-mobility particles' time scale relates to a structural relaxation time. The difference of the characteristic times for the high- and low-mobility particles naturally explains the well-known decoupling of diffusion and structural relaxation time scales. Despite the inherent difference of dynamics between high- and low-mobility particles, we find a high degree of similarity in the geometrical structure of these particle clusters. In particular, we show that the fractal dimensions of these clusters are consistent with those of swollen branched polymers or branched polymers with screened excluded-volume interactions, corresponding to lattice animals and percolation clusters, respectively. In contrast, the fractal dimension of the strings crosses over from that of self-avoiding walks for small strings, to simple random walks for longer, more strongly interacting, strings, corresponding to flexible polymers with screened excluded-volume interactions. We examine the appropriateness of identifying the size scales of either mobile particle clusters or strings with the size of cooperatively rearranging regions (CRR) in the AG and RFOT theories. We find that the string size appears to be the most consistent measure of CRR for both the AG and RFOT models. Identifying strings or clusters with the "mosaic" length of the RFOT model relaxes the conventional assumption that the "entropic droplets" are compact. We also confirm the validity of the entropy formulation of the AG theory, constraining the exponent values of the RFOT theory. This constraint, together with the analysis of size scales, enables us to estimate the characteristic exponents of RFOT.

Confined Mobility of TonB and FepA in Escherichia coli Membranes

PubMed Central

Lill, Yoriko; Jordan, Lorne D.; Smallwood, Chuck R.; Newton, Salete M.; Lill, Markus A.; Klebba, Phillip E.; Ritchie, Ken

2016-01-01

The important process of nutrient uptake in Escherichia coli, in many cases, involves transit of the nutrient through a class of beta-barrel proteins in the outer membrane known as TonB-dependent transporters (TBDTs) and requires interaction with the inner membrane protein TonB. Here we have imaged the mobility of the ferric enterobactin transporter FepA and TonB by tracking them in the membranes of live E. coli with single-molecule resolution at time-scales ranging from milliseconds to seconds. We employed simple simulations to model/analyze the lateral diffusion in the membranes of E.coli, to take into account both the highly curved geometry of the cell and artifactual effects expected due to finite exposure time imaging. We find that both molecules perform confined lateral diffusion in their respective membranes in the absence of ligand with FepA confined to a region 0.180−0.007+0.006 μm in radius in the outer membrane and TonB confined to a region 0.266−0.009+0.007 μm in radius in the inner membrane. The diffusion coefficient of these molecules on millisecond time-scales was estimated to be 21−5+9 μm2/s and 5.4−0.8+1.5 μm2/s for FepA and TonB, respectively, implying that each molecule is free to diffuse within its domain. Disruption of the inner membrane potential, deletion of ExbB/D from the inner membrane, presence of ligand or antibody to FepA and disruption of the MreB cytoskeleton was all found to further restrict the mobility of both molecules. Results are analyzed in terms of changes in confinement size and interactions between the two proteins. PMID:27935943

Confined Mobility of TonB and FepA in Escherichia coli Membranes.

PubMed

Lill, Yoriko; Jordan, Lorne D; Smallwood, Chuck R; Newton, Salete M; Lill, Markus A; Klebba, Phillip E; Ritchie, Ken

2016-01-01

The important process of nutrient uptake in Escherichia coli, in many cases, involves transit of the nutrient through a class of beta-barrel proteins in the outer membrane known as TonB-dependent transporters (TBDTs) and requires interaction with the inner membrane protein TonB. Here we have imaged the mobility of the ferric enterobactin transporter FepA and TonB by tracking them in the membranes of live E. coli with single-molecule resolution at time-scales ranging from milliseconds to seconds. We employed simple simulations to model/analyze the lateral diffusion in the membranes of E.coli, to take into account both the highly curved geometry of the cell and artifactual effects expected due to finite exposure time imaging. We find that both molecules perform confined lateral diffusion in their respective membranes in the absence of ligand with FepA confined to a region [Formula: see text] μm in radius in the outer membrane and TonB confined to a region [Formula: see text] μm in radius in the inner membrane. The diffusion coefficient of these molecules on millisecond time-scales was estimated to be [Formula: see text] μm2/s and [Formula: see text] μm2/s for FepA and TonB, respectively, implying that each molecule is free to diffuse within its domain. Disruption of the inner membrane potential, deletion of ExbB/D from the inner membrane, presence of ligand or antibody to FepA and disruption of the MreB cytoskeleton was all found to further restrict the mobility of both molecules. Results are analyzed in terms of changes in confinement size and interactions between the two proteins.

Principle of Parsimony, Fake Science, and Scales

NASA Astrophysics Data System (ADS)

Yeh, T. C. J.; Wan, L.; Wang, X. S.

2017-12-01

Considering difficulties in predicting exact motions of water molecules, and the scale of our interests (bulk behaviors of many molecules), Fick's law (diffusion concept) has been created to predict solute diffusion process in space and time. G.I. Taylor (1921) demonstrated that random motion of the molecules reach the Fickian regime in less a second if our sampling scale is large enough to reach ergodic condition. Fick's law is widely accepted for describing molecular diffusion as such. This fits the definition of the parsimony principle at the scale of our concern. Similarly, advection-dispersion or convection-dispersion equation (ADE or CDE) has been found quite satisfactory for analysis of concentration breakthroughs of solute transport in uniformly packed soil columns. This is attributed to the solute is often released over the entire cross-section of the column, which has sampled many pore-scale heterogeneities and met the ergodicity assumption. Further, the uniformly packed column contains a large number of stationary pore-size heterogeneity. The solute thus reaches the Fickian regime after traveling a short distance along the column. Moreover, breakthrough curves are concentrations integrated over the column cross-section (the scale of our interest), and they meet the ergodicity assumption embedded in the ADE and CDE. To the contrary, scales of heterogeneity in most groundwater pollution problems evolve as contaminants travel. They are much larger than the scale of our observations and our interests so that the ergodic and the Fickian conditions are difficult. Upscaling the Fick's law for solution dispersion, and deriving universal rules of the dispersion to the field- or basin-scale pollution migrations are merely misuse of the parsimony principle and lead to a fake science ( i.e., the development of theories for predicting processes that can not be observed.) The appropriate principle of parsimony for these situations dictates mapping of large-scale heterogeneities as detailed as possible and adapting the Fick's law for effects of small-scale heterogeneity resulting from our inability to characterize them in detail.

The Relation Between Capillary Transit Times and Hemoglobin Saturation Heterogeneity. Part 1: Theoretical Models

PubMed Central

Lücker, Adrien; Secomb, Timothy W.; Weber, Bruno; Jenny, Patrick

2018-01-01

Capillary dysfunction impairs oxygen supply to parenchymal cells and often occurs in Alzheimer's disease, diabetes and aging. Disturbed capillary flow patterns have been shown to limit the efficacy of oxygen extraction and can be quantified using capillary transit time heterogeneity (CTH). However, the transit time of red blood cells (RBCs) through the microvasculature is not a direct measure of their capacity for oxygen delivery. Here we examine the relation between CTH and capillary outflow saturation heterogeneity (COSH), which is the heterogeneity of blood oxygen content at the venous end of capillaries. Models for the evolution of hemoglobin saturation heterogeneity (HSH) in capillary networks were developed and validated using a computational model with moving RBCs. Two representative situations were selected: a Krogh cylinder geometry with heterogeneous hemoglobin saturation (HS) at the inflow, and a parallel array of four capillaries. The heterogeneity of HS after converging capillary bifurcations was found to exponentially decrease with a time scale of 0.15–0.21 s due to diffusive interaction between RBCs. Similarly, the HS difference between parallel capillaries also drops exponentially with a time scale of 0.12–0.19 s. These decay times are substantially smaller than measured RBC transit times and only weakly depend on the distance between microvessels. This work shows that diffusive interaction strongly reduces COSH on a small spatial scale. Therefore, we conclude that CTH influences COSH yet does not determine it. The second part of this study will focus on simulations in microvascular networks from the rodent cerebral cortex. Actual estimates of COSH and CTH will then be given. PMID:29755365

The Relation Between Capillary Transit Times and Hemoglobin Saturation Heterogeneity. Part 1: Theoretical Models.

PubMed

Lücker, Adrien; Secomb, Timothy W; Weber, Bruno; Jenny, Patrick

2018-01-01

Capillary dysfunction impairs oxygen supply to parenchymal cells and often occurs in Alzheimer's disease, diabetes and aging. Disturbed capillary flow patterns have been shown to limit the efficacy of oxygen extraction and can be quantified using capillary transit time heterogeneity (CTH). However, the transit time of red blood cells (RBCs) through the microvasculature is not a direct measure of their capacity for oxygen delivery. Here we examine the relation between CTH and capillary outflow saturation heterogeneity (COSH), which is the heterogeneity of blood oxygen content at the venous end of capillaries. Models for the evolution of hemoglobin saturation heterogeneity (HSH) in capillary networks were developed and validated using a computational model with moving RBCs. Two representative situations were selected: a Krogh cylinder geometry with heterogeneous hemoglobin saturation (HS) at the inflow, and a parallel array of four capillaries. The heterogeneity of HS after converging capillary bifurcations was found to exponentially decrease with a time scale of 0.15-0.21 s due to diffusive interaction between RBCs. Similarly, the HS difference between parallel capillaries also drops exponentially with a time scale of 0.12-0.19 s. These decay times are substantially smaller than measured RBC transit times and only weakly depend on the distance between microvessels. This work shows that diffusive interaction strongly reduces COSH on a small spatial scale. Therefore, we conclude that CTH influences COSH yet does not determine it. The second part of this study will focus on simulations in microvascular networks from the rodent cerebral cortex. Actual estimates of COSH and CTH will then be given.

Some consequences of shear on galactic dynamos with helicity fluxes

NASA Astrophysics Data System (ADS)

Zhou, Hongzhe; Blackman, Eric G.

2017-08-01

Galactic dynamo models sustained by supernova (SN) driven turbulence and differential rotation have revealed that the sustenance of large-scale fields requires a flux of small-scale magnetic helicity to be viable. Here we generalize a minimalist analytic version of such galactic dynamos to explore some heretofore unincluded contributions from shear on the total turbulent energy and turbulent correlation time, with the helicity fluxes maintained by either winds, diffusion or magnetic buoyancy. We construct an analytic framework for modelling the turbulent energy and correlation time as a function of SN rate and shear. We compare our prescription with previous approaches that include only rotation. The solutions depend separately on the rotation period and the eddy turnover time and not just on their ratio (the Rossby number). We consider models in which these two time-scales are allowed to be independent and also a case in which they are mutually dependent on radius when a radial-dependent SN rate model is invoked. For the case of a fixed rotation period (or a fixed radius), we show that the influence of shear is dramatic for low Rossby numbers, reducing the correlation time of the turbulence, which, in turn, strongly reduces the saturation value of the dynamo compared to the case when the shear is ignored. We also show that even in the absence of winds or diffusive fluxes, magnetic buoyancy may be able to sustain sufficient helicity fluxes to avoid quenching.

Accelerated Cartesian expansion (ACE) based framework for the rapid evaluation of diffusion, lossy wave, and Klein-Gordon potentials

DOE PAGES

Baczewski, Andrew David; Vikram, Melapudi; Shanker, Balasubramaniam; ...

2010-08-27

Diffusion, lossy wave, and Klein–Gordon equations find numerous applications in practical problems across a range of diverse disciplines. The temporal dependence of all three Green’s functions are characterized by an infinite tail. This implies that the cost complexity of the spatio-temporal convolutions, associated with evaluating the potentials, scales as O(N s 2N t 2), where N s and N t are the number of spatial and temporal degrees of freedom, respectively. In this paper, we discuss two new methods to rapidly evaluate these spatio-temporal convolutions by exploiting their block-Toeplitz nature within the framework of accelerated Cartesian expansions (ACE). The firstmore » scheme identifies a convolution relation in time amongst ACE harmonics and the fast Fourier transform (FFT) is used for efficient evaluation of these convolutions. The second method exploits the rank deficiency of the ACE translation operators with respect to time and develops a recursive numerical compression scheme for the efficient representation and evaluation of temporal convolutions. It is shown that the cost of both methods scales as O(N sN tlog 2N t). Furthermore, several numerical results are presented for the diffusion equation to validate the accuracy and efficacy of the fast algorithms developed here.« less

Magnetic Reconnection Dynamics in the Presence of Low-energy Ion Component: PIC Simulations of Hidden Particle Population

NASA Astrophysics Data System (ADS)

Khotyaintsev, Y. V.; Divin, A. V.; Toledo Redondo, S.; Andre, M.; Vaivads, A.; Markidis, S.; Lapenta, G.

2015-12-01

Magnetospheric and astrophysical plasmas are rarely in the state of thermal equilibrium. Plasma distribution functions may contain beams, supra-thermal tails, multiple ion and electron populations which are not thermalized over long time scales due to the lack of collisions between particles. In particular, the equatorial region of the dayside Earth's magnetosphere is often populated by plasma containing hot and cold ion components of comparable densities [Andre and Cully, 2012], and such ion distribution alters properties of the magnetic reconnection regions at the magnetopause [Toledo-Redondo et. al., 2015]. Motivated by these recent findings and also by fact that this region is one of the targets of the recently launched MMS mission, we performed 2D PIC simulations of magnetic reconnection in collisionless plasma with hot and cold ion components. We used a standard Harris current sheet, to which a uniform cold ion background is added. We found that introduction of the cold component modifies the structure of reconnection diffusion region. Diffusion region displays three-scale structure, with the cold Ion Diffusion Region (cIDR) scale appearing in-between the Electron Diffusion Region (EDR) and Ion Diffusion Region (IDR) scales. Structure and strength of the Hall magnetic field depends weakly on cold ion temperature or density, and is rather controlled by the conditions (B, n) upstream the reconnection region. The cold ions are accelerated predominantly transverse to the magnetic field by the Hall electric fields inside the IDR, leading to a large ion pressure anisotropy, which is unstable to ion Weibel-type or mirror-type mode. On the opposite, acceleration of cold ions is mostly field-aligned at the reconnection jet fronts downstream the X-line, producing intense ion phase-space holes there. Despite comparable reconnection rates produced , we find that the overall evolution of reconnection in presence of cold ion population is more dynamic compared to the case with a single hot ion component.

Double diffusivity model under stochastic forcing

NASA Astrophysics Data System (ADS)

Chattopadhyay, Amit K.; Aifantis, Elias C.

2017-05-01

The "double diffusivity" model was proposed in the late 1970s, and reworked in the early 1980s, as a continuum counterpart to existing discrete models of diffusion corresponding to high diffusivity paths, such as grain boundaries and dislocation lines. It was later rejuvenated in the 1990s to interpret experimental results on diffusion in polycrystalline and nanocrystalline specimens where grain boundaries and triple grain boundary junctions act as high diffusivity paths. Technically, the model pans out as a system of coupled Fick-type diffusion equations to represent "regular" and "high" diffusivity paths with "source terms" accounting for the mass exchange between the two paths. The model remit was extended by analogy to describe flow in porous media with double porosity, as well as to model heat conduction in media with two nonequilibrium local temperature baths, e.g., ion and electron baths. Uncoupling of the two partial differential equations leads to a higher-ordered diffusion equation, solutions of which could be obtained in terms of classical diffusion equation solutions. Similar equations could also be derived within an "internal length" gradient (ILG) mechanics formulation applied to diffusion problems, i.e., by introducing nonlocal effects, together with inertia and viscosity, in a mechanics based formulation of diffusion theory. While being remarkably successful in studies related to various aspects of transport in inhomogeneous media with deterministic microstructures and nanostructures, its implications in the presence of stochasticity have not yet been considered. This issue becomes particularly important in the case of diffusion in nanopolycrystals whose deterministic ILG-based theoretical calculations predict a relaxation time that is only about one-tenth of the actual experimentally verified time scale. This article provides the "missing link" in this estimation by adding a vital element in the ILG structure, that of stochasticity, that takes into account all boundary layer fluctuations. Our stochastic-ILG diffusion calculation confirms rapprochement between theory and experiment, thereby benchmarking a new generation of gradient-based continuum models that conform closer to real-life fluctuating environments.

Establishing the kinetics of ballistic-to-diffusive transition using directional statistics

NASA Astrophysics Data System (ADS)

Liu, Pai; Heinson, William R.; Sumlin, Benjamin J.; Shen, Kuan-Yu; Chakrabarty, Rajan K.

2018-04-01

We establish the kinetics of ballistic-to-diffusive (BD) transition observed in two-dimensional random walk using directional statistics. Directional correlation is parameterized using the walker's turning angle distribution, which follows the commonly adopted wrapped Cauchy distribution (WCD) function. During the BD transition, the concentration factor (ρ) governing the WCD shape is observed to decrease from its initial value. We next analytically derive the relationship between effective ρ and time, which essentially quantifies the BD transition rate. The prediction of our kinetic expression agrees well with the empirical datasets obtained from correlated random walk simulation. We further connect our formulation with the conventionally used scaling relationship between the walker's mean-square displacement and time.

Mathematical modeling of synthesis gas fueled electrochemistry and transport including H2/CO co-oxidation and surface diffusion in solid oxide fuel cell

NASA Astrophysics Data System (ADS)

Bao, Cheng; Jiang, Zeyi; Zhang, Xinxin

2015-10-01

Fuel flexibility is a significant advantage of solid oxide fuel cell (SOFC). A comprehensive macroscopic framework is proposed for synthesis gas (syngas) fueled electrochemistry and transport in SOFC anode with two main novelties, i.e. analytical H2/CO electrochemical co-oxidation, and correction of gas species concentration at triple phase boundary considering competitive absorption and surface diffusion. Staring from analytical approximation of the decoupled charge and mass transfer, we present analytical solutions of two defined variables, i.e. hydrogen current fraction and enhancement factor. Giving explicit answer (rather than case-by-case numerical calculation) on how many percent of the current output contributed by H2 or CO and on how great the water gas shift reaction plays role on, this approach establishes at the first time an adaptive superposition mechanism of H2-fuel and CO-fuel electrochemistry for syngas fuel. Based on the diffusion equivalent circuit model, assuming series-connected resistances of surface diffusion and bulk diffusion, the model predicts well at high fuel utilization by keeping fixed porosity/tortuosity ratio. The model has been validated by experimental polarization behaviors in a wide range of operation on a button cell for H2-H2O-CO-CO2-N2 fuel systems. The framework could be helpful to narrow the gap between macro-scale and meso-scale SOFC modeling.

Fractal diffusion in high temperature polymer electrolyte fuel cell membranes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hopfenmuller, Bernhard; Zorn, Reiner; Holderer, Olaf

In this paper, the performance of fuel cells depends largely on the proton diffusion in the proton conducting membrane, the core of a fuel cell. High temperature polymer electrolyte fuel cells are based on a polymer membrane swollen with phosphoric acid as the electrolyte, where proton conduction takes place. We studied the proton diffusion in such membranes with neutron scattering techniques which are especially sensitive to the proton contribution. Time of flight spectroscopy and backscattering spectroscopy have been combined to cover a broad dynamic range. In order to selectively observe the diffusion of protons potentially contributing to the ion conductivity,more » two samples were prepared, where in one of the samples the phosphoric acid was used with hydrogen replaced by deuterium. The scattering data from the two samples were subtracted in a suitable way after measurement. Thereby subdiffusive behavior of the proton diffusion has been observed and interpreted in terms of a model of fractal diffusion. For this purpose, a scattering function for fractal diffusion has been developed. The fractal diffusion dimension d w and the Hausdorff dimension d f have been determined on the length scales covered in the neutron scattering experiments.« less

Fractal diffusion in high temperature polymer electrolyte fuel cell membranes

DOE PAGES

Hopfenmuller, Bernhard; Zorn, Reiner; Holderer, Olaf; ...

2018-05-29

In this paper, the performance of fuel cells depends largely on the proton diffusion in the proton conducting membrane, the core of a fuel cell. High temperature polymer electrolyte fuel cells are based on a polymer membrane swollen with phosphoric acid as the electrolyte, where proton conduction takes place. We studied the proton diffusion in such membranes with neutron scattering techniques which are especially sensitive to the proton contribution. Time of flight spectroscopy and backscattering spectroscopy have been combined to cover a broad dynamic range. In order to selectively observe the diffusion of protons potentially contributing to the ion conductivity,more » two samples were prepared, where in one of the samples the phosphoric acid was used with hydrogen replaced by deuterium. The scattering data from the two samples were subtracted in a suitable way after measurement. Thereby subdiffusive behavior of the proton diffusion has been observed and interpreted in terms of a model of fractal diffusion. For this purpose, a scattering function for fractal diffusion has been developed. The fractal diffusion dimension d w and the Hausdorff dimension d f have been determined on the length scales covered in the neutron scattering experiments.« less

Detecting recurrent gene mutation in interaction network context using multi-scale graph diffusion.

PubMed

Babaei, Sepideh; Hulsman, Marc; Reinders, Marcel; de Ridder, Jeroen

2013-01-23

Delineating the molecular drivers of cancer, i.e. determining cancer genes and the pathways which they deregulate, is an important challenge in cancer research. In this study, we aim to identify pathways of frequently mutated genes by exploiting their network neighborhood encoded in the protein-protein interaction network. To this end, we introduce a multi-scale diffusion kernel and apply it to a large collection of murine retroviral insertional mutagenesis data. The diffusion strength plays the role of scale parameter, determining the size of the network neighborhood that is taken into account. As a result, in addition to detecting genes with frequent mutations in their genomic vicinity, we find genes that harbor frequent mutations in their interaction network context. We identify densely connected components of known and putatively novel cancer genes and demonstrate that they are strongly enriched for cancer related pathways across the diffusion scales. Moreover, the mutations in the clusters exhibit a significant pattern of mutual exclusion, supporting the conjecture that such genes are functionally linked. Using multi-scale diffusion kernel, various infrequently mutated genes are found to harbor significant numbers of mutations in their interaction network neighborhood. Many of them are well-known cancer genes. The results demonstrate the importance of defining recurrent mutations while taking into account the interaction network context. Importantly, the putative cancer genes and networks detected in this study are found to be significant at different diffusion scales, confirming the necessity of a multi-scale analysis.

Simulation of Bacillus subtilis biofilm growth on agar plate by diffusion-reaction based continuum model

NASA Astrophysics Data System (ADS)

Zhang, Xianlong; Wang, Xiaoling; Nie, Kai; Li, Mingpeng; Sun, Qingping

2016-08-01

Various species of bacteria form highly organized spatially-structured aggregates known as biofilms. To understand how microenvironments impact biofilm growth dynamics, we propose a diffusion-reaction continuum model to simulate the formation of Bacillus subtilis biofilm on an agar plate. The extended finite element method combined with level set method are employed to perform the simulation, numerical results show the quantitative relationship between colony morphologies and nutrient depletion over time. Considering that the production of polysaccharide in wild-type cells may enhance biofilm spreading on the agar plate, we inoculate mutant colony incapable of producing polysaccharide to verify our results. Predictions of the glutamate source biofilm’s shape parameters agree with the experimental mutant colony better than that of glycerol source biofilm, suggesting that glutamate is rate limiting nutrient for Bacillus subtilis biofilm growth on agar plate, and the diffusion-limited is a better description to the experiment. In addition, we find that the diffusion time scale is of the same magnitude as growth process, and the common-employed quasi-steady approximation is not applicable here.

Simulation of Bacillus subtilis biofilm growth on agar plate by diffusion-reaction based continuum model.

PubMed

Zhang, Xianlong; Wang, Xiaoling; Nie, Kai; Li, Mingpeng; Sun, Qingping

2016-07-19

Various species of bacteria form highly organized spatially-structured aggregates known as biofilms. To understand how microenvironments impact biofilm growth dynamics, we propose a diffusion-reaction continuum model to simulate the formation of Bacillus subtilis biofilm on an agar plate. The extended finite element method combined with level set method are employed to perform the simulation, numerical results show the quantitative relationship between colony morphologies and nutrient depletion over time. Considering that the production of polysaccharide in wild-type cells may enhance biofilm spreading on the agar plate, we inoculate mutant colony incapable of producing polysaccharide to verify our results. Predictions of the glutamate source biofilm's shape parameters agree with the experimental mutant colony better than that of glycerol source biofilm, suggesting that glutamate is rate limiting nutrient for Bacillus subtilis biofilm growth on agar plate, and the diffusion-limited is a better description to the experiment. In addition, we find that the diffusion time scale is of the same magnitude as growth process, and the common-employed quasi-steady approximation is not applicable here.

Lamination and mixing in laminar flows driven by Lorentz body forces

NASA Astrophysics Data System (ADS)

Rossi, L.; Doorly, D.; Kustrin, D.

2012-01-01

We present a new approach to the design of mixers. This approach relies on a sequence of tailored flows coupled with a new procedure to quantify the local degree of striation, called lamination. Lamination translates to the distance over which the molecular diffusion needs to act to finalise mixing. A novel in situ mixing is achieved by the tailored sequence of flows. This sequence is shown with the property that material lines and lamination grow exponentially, according to processes akin to the well-known baker's map. The degree of mixing (stirring coefficient) likewise shows exponential growth before the saturation of the stirring rate. Such saturation happens when the typical striations' thickness is smaller than the diffusion's length scale. Moreover, without molecular diffusion, the predicted striations' thickness would be smaller than the size of an atom of hydrogen within 40 flow turnover times. In fact, we conclude that about 3 minutes, i.e. 15 turnover times, are sufficient to mix species with very low diffusivities, e.g. suspensions of virus, bacteria, human cells, and DNA.

Unity and diversity in mixing: Stretching, diffusion, breakup, and aggregation in chaotic flows

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ottino, J.M.

1991-05-01

Experiments and theory have produced a reasonably good qualitative understanding of the evolution of chaotic mixing of passive tracers, especially in two-dimensional time-periodic flow fields. Such an understanding forms a fabric for the evolution of breakup, aggregation, and diffusion-controlled reactions in more complex flows. These systems can be viewed as a population of microstructures'' whose behavior is dictated by iterations of a chaotic flow; microstructures break, diffuse, and aggregate, causing the population to evolve in space and time. This paper presents simple physical models for such processes. Self-similarity is common to all the problems; examples arise in the context ofmore » the distribution of stretchings within chaotic flows, in the asymptotic evolution of diffusion-reaction processes at striation thickness scales, in the equilibrium distribution of drop sizes generated upon mixing of immiscible fluids, in the equations describing mean-field kinetics of coagulation, in the sequence of actions necessary for the destruction of islands in two-dimensional flow, and in the fractal structure of clusters produced upon aggregation in chaotic flows.« less

Chemistry Resolved Kinetic Flow Modeling of TATB Based Explosives

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vitello, P A; Fried, L E; Howard, W M

2011-07-21

Detonation waves in insensitive, TATB based explosives are believed to have multi-time scale regimes. The initial burn rate of such explosives has a sub-microsecond time scale. However, significant late-time slow release in energy is believed to occur due to diffusion limited growth of carbon. In the intermediate time scale concentrations of product species likely change from being in equilibrium to being kinetic rate controlled. They use the thermo-chemical code CHEETAH linked to an ALE hydrodynamics code to model detonations. They term their model chemistry resolved kinetic flow as CHEETAH tracks the time dependent concentrations of individual species in the detonationmore » wave and calculates EOS values based on the concentrations. A HE-validation suite of model simulations compared to experiments at ambient, hot, and cold temperatures has been developed. They present here a new rate model and comparison with experimental data.« less

Convergence of lateral dynamic measurements in the plasma membrane of live cells from single particle tracking and STED-FCS

NASA Astrophysics Data System (ADS)

Lagerholm, B. Christoffer; Andrade, Débora M.; Clausen, Mathias P.; Eggeling, Christian

2017-02-01

Fluorescence correlation spectroscopy (FCS) in combination with the super-resolution imaging method STED (STED-FCS), and single-particle tracking (SPT) are able to directly probe the lateral dynamics of lipids and proteins in the plasma membrane of live cells at spatial scales much below the diffraction limit of conventional microscopy. However, a major disparity in interpretation of data from SPT and STED-FCS remains, namely the proposed existence of a very fast (unhindered) lateral diffusion coefficient, ⩾5 µm2 s-1, in the plasma membrane of live cells at very short length scales, ≈⩽ 100 nm, and time scales, ≈1-10 ms. This fast diffusion coefficient has been advocated in several high-speed SPT studies, for lipids and membrane proteins alike, but the equivalent has not been detected in STED-FCS measurements. Resolving this ambiguity is important because the assessment of membrane dynamics currently relies heavily on SPT for the determination of heterogeneous diffusion. A possible systematic error in this approach would thus have vast implications in this field. To address this, we have re-visited the analysis procedure for SPT data with an emphasis on the measurement errors and the effect that these errors have on the measurement outputs. We subsequently demonstrate that STED-FCS and SPT data, following careful consideration of the experimental errors of the SPT data, converge to a common interpretation which for the case of a diffusing phospholipid analogue in the plasma membrane of live mouse embryo fibroblasts results in an unhindered, intra-compartment, diffusion coefficient of  ≈0.7-1.0 µm2 s-1, and a compartment size of about 100-150 nm.

Convergence of lateral dynamic measurements in the plasma membrane of live cells from single particle tracking and STED-FCS

PubMed Central

Lagerholm, B Christoffer; Andrade, Débora M; Clausen, Mathias P; Eggeling, Christian

2017-01-01

Abstract Fluorescence correlation spectroscopy (FCS) in combination with the super-resolution imaging method STED (STED-FCS), and single-particle tracking (SPT) are able to directly probe the lateral dynamics of lipids and proteins in the plasma membrane of live cells at spatial scales much below the diffraction limit of conventional microscopy. However, a major disparity in interpretation of data from SPT and STED-FCS remains, namely the proposed existence of a very fast (unhindered) lateral diffusion coefficient, ⩾5 µm2 s−1, in the plasma membrane of live cells at very short length scales, ≈⩽ 100 nm, and time scales, ≈1–10 ms. This fast diffusion coefficient has been advocated in several high-speed SPT studies, for lipids and membrane proteins alike, but the equivalent has not been detected in STED-FCS measurements. Resolving this ambiguity is important because the assessment of membrane dynamics currently relies heavily on SPT for the determination of heterogeneous diffusion. A possible systematic error in this approach would thus have vast implications in this field. To address this, we have re-visited the analysis procedure for SPT data with an emphasis on the measurement errors and the effect that these errors have on the measurement outputs. We subsequently demonstrate that STED-FCS and SPT data, following careful consideration of the experimental errors of the SPT data, converge to a common interpretation which for the case of a diffusing phospholipid analogue in the plasma membrane of live mouse embryo fibroblasts results in an unhindered, intra-compartment, diffusion coefficient of  ≈0.7–1.0 µm2 s−1, and a compartment size of about 100–150 nm. PMID:28458397

Similarities between principal components of protein dynamics and random diffusion

NASA Astrophysics Data System (ADS)

Hess, Berk

2000-12-01

Principal component analysis, also called essential dynamics, is a powerful tool for finding global, correlated motions in atomic simulations of macromolecules. It has become an established technique for analyzing molecular dynamics simulations of proteins. The first few principal components of simulations of large proteins often resemble cosines. We derive the principal components for high-dimensional random diffusion, which are almost perfect cosines. This resemblance between protein simulations and noise implies that for many proteins the time scales of current simulations are too short to obtain convergence of collective motions.

Scaling characteristics of one-dimensional fractional diffusion processes in the presence of power-law distributed random noise

NASA Astrophysics Data System (ADS)

Nezhadhaghighi, Mohsen Ghasemi

2017-08-01

Here, we present results of numerical simulations and the scaling characteristics of one-dimensional random fluctuations with heavy-tailed probability distribution functions. Assuming that the distribution function of the random fluctuations obeys Lévy statistics with a power-law scaling exponent, we investigate the fractional diffusion equation in the presence of μ -stable Lévy noise. We study the scaling properties of the global width and two-point correlation functions and then compare the analytical and numerical results for the growth exponent β and the roughness exponent α . We also investigate the fractional Fokker-Planck equation for heavy-tailed random fluctuations. We show that the fractional diffusion processes in the presence of μ -stable Lévy noise display special scaling properties in the probability distribution function (PDF). Finally, we numerically study the scaling properties of the heavy-tailed random fluctuations by using the diffusion entropy analysis. This method is based on the evaluation of the Shannon entropy of the PDF generated by the random fluctuations, rather than on the measurement of the global width of the process. We apply the diffusion entropy analysis to extract the growth exponent β and to confirm the validity of our numerical analysis.

Scaling characteristics of one-dimensional fractional diffusion processes in the presence of power-law distributed random noise.

PubMed

Nezhadhaghighi, Mohsen Ghasemi

2017-08-01

Here, we present results of numerical simulations and the scaling characteristics of one-dimensional random fluctuations with heavy-tailed probability distribution functions. Assuming that the distribution function of the random fluctuations obeys Lévy statistics with a power-law scaling exponent, we investigate the fractional diffusion equation in the presence of μ-stable Lévy noise. We study the scaling properties of the global width and two-point correlation functions and then compare the analytical and numerical results for the growth exponent β and the roughness exponent α. We also investigate the fractional Fokker-Planck equation for heavy-tailed random fluctuations. We show that the fractional diffusion processes in the presence of μ-stable Lévy noise display special scaling properties in the probability distribution function (PDF). Finally, we numerically study the scaling properties of the heavy-tailed random fluctuations by using the diffusion entropy analysis. This method is based on the evaluation of the Shannon entropy of the PDF generated by the random fluctuations, rather than on the measurement of the global width of the process. We apply the diffusion entropy analysis to extract the growth exponent β and to confirm the validity of our numerical analysis.

Diffusive real-time dynamics of a particle with Berry curvature

NASA Astrophysics Data System (ADS)

Misaki, Kou; Miyashita, Seiji; Nagaosa, Naoto

2018-02-01

We study theoretically the influence of Berry phase on the real-time dynamics of the single particle focusing on the diffusive dynamics, i.e., the time dependence of the distribution function. Our model can be applied to the real-time dynamics of intraband relaxation and diffusion of optically excited excitons, trions, or particle-hole pair. We found that the dynamics at the early stage is deeply influenced by the Berry curvature in real space (B ), momentum space (Ω ), and also the crossed space between these two (C ). For example, it is found that Ω induces the rotation of the wave packet and causes the time dependence of the mean square displacement of the particle to be linear in time t at the initial stage; it is qualitatively different from the t3 dependence in the absence of the Berry curvature. It is also found that Ω and C modify the characteristic time scale of the thermal equilibration of momentum distribution. Moreover, the dynamics under various combinations of B ,Ω , and C shows singular behaviors such as the critical slowing down or speeding up of the momentum equilibration and the reversals of the direction of rotations. The relevance of our model for time-resolved experiments in transition metal dichalcogenides is also discussed.

Effects of Small-Scale Bathymetric Roughness on the Global Internal Wave Field

DTIC Science & Technology

2008-09-30

Navy. Much of the interest stems from the suggestion by Munk and Wunsch (1998) that the strength of the meridional overturning circulation is controlled... meridional overturning circulation . Journal of Physical Oceanography 32, 3578-3595. St. Laurent, L.C., 1999. Diapycnal advection by double diffusion...waves generated by flows over the rough seafloor. On the time scales of internal waves, mesoscale eddies and the general circulation can be regarded as

Reaction-diffusion on the fully-connected lattice: A+A\\rightarrow A

NASA Astrophysics Data System (ADS)

Turban, Loïc; Fortin, Jean-Yves

2018-04-01

Diffusion-coagulation can be simply described by a dynamic where particles perform a random walk on a lattice and coalesce with probability unity when meeting on the same site. Such processes display non-equilibrium properties with strong fluctuations in low dimensions. In this work we study this problem on the fully-connected lattice, an infinite-dimensional system in the thermodynamic limit, for which mean-field behaviour is expected. Exact expressions for the particle density distribution at a given time and survival time distribution for a given number of particles are obtained. In particular, we show that the time needed to reach a finite number of surviving particles (vanishing density in the scaling limit) displays strong fluctuations and extreme value statistics, characterized by a universal class of non-Gaussian distributions with singular behaviour.

Collective motion of macroscopic spheres floating on capillary ripples: Dynamic heterogeneity and dynamic criticality

NASA Astrophysics Data System (ADS)

Sanlı, Ceyda; Saitoh, Kuniyasu; Luding, Stefan; van der Meer, Devaraj

2014-09-01

When a densely packed monolayer of macroscopic spheres floats on chaotic capillary Faraday waves, a coexistence of large scale convective motion and caging dynamics typical for glassy systems is observed. We subtract the convective mean flow using a coarse graining (homogenization) method and reveal subdiffusion for the caging time scales followed by a diffusive regime at later times. We apply the methods developed to study dynamic heterogeneity and show that the typical time and length scales of the fluctuations due to rearrangements of observed particle groups significantly increase when the system approaches its largest experimentally accessible packing concentration. To connect the system to the dynamic criticality literature, we fit power laws to our results. The resultant critical exponents are consistent with those found in densely packed suspensions of colloids.

Collective motion of macroscopic spheres floating on capillary ripples: dynamic heterogeneity and dynamic criticality.

PubMed

Sanlı, Ceyda; Saitoh, Kuniyasu; Luding, Stefan; van der Meer, Devaraj

2014-09-01

When a densely packed monolayer of macroscopic spheres floats on chaotic capillary Faraday waves, a coexistence of large scale convective motion and caging dynamics typical for glassy systems is observed. We subtract the convective mean flow using a coarse graining (homogenization) method and reveal subdiffusion for the caging time scales followed by a diffusive regime at later times. We apply the methods developed to study dynamic heterogeneity and show that the typical time and length scales of the fluctuations due to rearrangements of observed particle groups significantly increase when the system approaches its largest experimentally accessible packing concentration. To connect the system to the dynamic criticality literature, we fit power laws to our results. The resultant critical exponents are consistent with those found in densely packed suspensions of colloids.

ELECTROCHEMICAL CHROMIC ACID REGENERATION PROCESS: FITTING OF MEMBRANE TRANSPORT PROPERTIES. (R827125)

EPA Science Inventory

Abstract

A mathematical model was developed to predict changes in contaminant concentrations with time, and to estimate contaminant fluxes due to migration, diffusion, and convection in a laboratory-scale batch electrolysis cell for the regeneration of contaminated har...

Homogenization of a Directed Dispersal Model for Animal Movement in a Heterogeneous Environment.

PubMed

Yurk, Brian P

2016-10-01

The dispersal patterns of animals moving through heterogeneous environments have important ecological and epidemiological consequences. In this work, we apply the method of homogenization to analyze an advection-diffusion (AD) model of directed movement in a one-dimensional environment in which the scale of the heterogeneity is small relative to the spatial scale of interest. We show that the large (slow) scale behavior is described by a constant-coefficient diffusion equation under certain assumptions about the fast-scale advection velocity, and we determine a formula for the slow-scale diffusion coefficient in terms of the fast-scale parameters. We extend the homogenization result to predict invasion speeds for an advection-diffusion-reaction (ADR) model with directed dispersal. For periodic environments, the homogenization approximation of the solution of the AD model compares favorably with numerical simulations. Invasion speed approximations for the ADR model also compare favorably with numerical simulations when the spatial period is sufficiently small.

Pore and Continuum Scale Study of the Effect of Subgrid Transport Heterogeneity on Redox Reaction Rates

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Yuanyuan; Liu, Chongxuan; Zhang, Changyong

2015-08-01

A micromodel system with a pore structure for heterogeneous flow and transport was used to investigate the effect of subgrid transport heterogeneity on redox reaction rates. Hematite reductive dissolution by injecting a reduced form of flavin mononucleotide (FMNH2) at variable flow rates was used as an example to probe the variations of redox reaction rates in different subgrid transport domains. Experiments, pore-scale simulations, and macroscopic modeling were performed to measure and simulate in-situ hematite reduction and to evaluate the scaling behavior of the redox reaction rates from the pore to macroscopic scales. The results indicated that the measured pore-scale ratesmore » of hematite reduction were consistent with the predictions from a pore scale reactive transport model. A general trend is that hematite reduction followed reductant transport pathways, starting from the advection-dominated pores toward the interior of diffusion-dominated domains. Two types of diffusion domains were considered in the micromodel: a micropore diffusion domain, which locates inside solid grains or aggregates where reactant transport is limited by diffusion; and a macropore diffusion domain, which locates at wedged, dead-end pore spaces created by the grain-grain contacts. The rate of hematite reduction in the advection-dominated domain was faster than those in the diffusion-controlled domains, and the rate in the macropore diffusion domain was faster than that in the micropore domain. The reduction rates in the advection and macropore diffusion domains increased with increasing flow rate, but were affected by different mechanisms. The rate increase in the advection domain was controlled by the mass action effect as a faster flow supplied more reactants, and the rate increase in the macropore domain was more affected by the rate of mass exchange with the advection domain, which increased with increasing flow rate. The hematite reduction rate in the micropore domain was, however, not affected by the flow rate because molecular diffusion limits reductant supply to the micropore domain interior. Domain-based macroscopic models were evaluated to scale redox reaction rates from the pore to macroscopic scales. A single domain model, which ignores subgrid transport heterogeneity deviated significantly from the pore-scale results. Further analysis revealed that the rate expression for hematite reduction was not scalable from the pore to porous media using the single domain model. A three-domain model, which effectively considers subgrid reactive diffusion in the micropore and macropore domains, significantly improved model description. Overall this study revealed the importance of subgrid transport heterogeneity in the manifestation of redox reaction rates in porous media and in scaling reactions from the pore to porous media. The research also supported that the domain-based scaling approach can be used to directly scale redox reactions in porous media with subgrid transport heterogeneity.« less

Multi-scale analysis of collective behavior in 2D self-propelled particle models of swarms: An Advection-Diffusion with Memory Approach

NASA Astrophysics Data System (ADS)

Raghib, Michael; Levin, Simon; Kevrekidis, Ioannis

2010-05-01

Self-propelled particle models (SPP's) are a class of agent-based simulations that have been successfully used to explore questions related to various flavors of collective motion, including flocking, swarming, and milling. These models typically consist of particle configurations, where each particle moves with constant speed, but changes its orientation in response to local averages of the positions and orientations of its neighbors found within some interaction region. These local averages are based on `social interactions', which include avoidance of collisions, attraction, and polarization, that are designed to generate configurations that move as a single object. Errors made by the individuals in the estimates of the state of the local configuration are modeled as a random rotation of the updated orientation resulting from the social rules. More recently, SPP's have been introduced in the context of collective decision-making, where the main innovation consists of dividing the population into naïve and `informed' individuals. Whereas naïve individuals follow the classical collective motion rules, members of the informed sub-population update their orientations according to a weighted average of the social rules and a fixed `preferred' direction, shared by all the informed individuals. Collective decision-making is then understood in terms of the ability of the informed sub-population to steer the whole group along the preferred direction. Summary statistics of collective decision-making are defined in terms of the stochastic properties of the random walk followed by the centroid of the configuration as the particles move about, in particular the scaling behavior of the mean squared displacement (msd). For the region of parameters where the group remains coherent , we note that there are two characteristic time scales, first there is an anomalous transient shared by both purely naïve and informed configurations, i.e. the scaling exponent lies between 1 and 2. The long-time behavior of the msd of the centroid walk scales linearly with time for naïve groups (diffusion), but shows a sharp transition to quadratic scaling (advection) for informed ones. These observations suggest that the mesoscopic variables of interest are the magnitude of the drift, the diffusion coefficient and the time-scales at which the anomalous and the asymptotic behavior respectively dominate transport, the latter being linked to the time scale at which the group reaches a decision. In order to estimate these summary statistics from the msd, we assumed that the configuration centroid follows an uncoupled Continuous Time Random Walk (CTRW) with smooth jump and waiting time pdf's. The mesoscopic transport equation for this type of random walk corresponds to an Advection-Diffusion Equation with Memory (ADEM). The introduction of the memory, and thus non-Markovian effects, is necessary in order to correctly account for the two time scales present. Although we were not able to calculate the memory directly from the individual-level rules, we show that it can estimated from a single, relatively short, simulation run using a Mittag-Leffler function as template. With this function it is possible to predict accurately the behavior of the msd, as well as the full pdf for the position of the centroid. The resulting ADEM is self-consistent in the sense that transport parameters estimated from the memory via a Kubo relationship coincide with those estimated from the moments of the jump size pdf of the associated CTRW for a large number of group sizes, proportions of informed individuals, and degrees of bias along the preferred direction. We also discuss the phase diagrams for the transport coefficients estimated from this method, where we notice velocity-precision trade-offs, where precision is a measure of the deviation of realized group orientations with respect to the informed direction. We also note that the time scale to collective decision is invariant with respect to group size, and depends only on the proportion of informed individuals and the strength of the coupling along the informed direction.

Improvement of gray-scale representation of horizontally scanning holographic display using error diffusion.

PubMed

Matsumoto, Yuji; Takaki, Yasuhiro

2014-06-15

Horizontally scanning holography can enlarge both screen size and viewing zone angle. A microelectromechanical-system spatial light modulator, which can generate only binary images, is used to generate hologram patterns. Thus, techniques to improve gray-scale representation in reconstructed images should be developed. In this study, the error diffusion technique was used for the binarization of holograms. When the Floyd-Steinberg error diffusion coefficients were used, gray-scale representation was improved. However, the linearity in the gray-scale representation was not satisfactory. We proposed the use of a correction table and showed that the linearity was greatly improved.

Radionuclide Transport in Fracture-Granite Interface Zones

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hu, Q; Mori, A

In situ radionuclide migration experiments, followed by excavation and sample characterization, were conducted in a water-conducting shear zone at the Grimsel Test Site (GTS) in Switzerland to study diffusion paths of radionuclides in fractured granite. In this work, we employed a micro-scale mapping technique that interfaces laser ablation sampling with inductively coupled plasma-mass spectrometry (LA/ICP-MS) to measure the fine-scale (micron-range) distribution of actinides ({sup 234}U, {sup 235}U, and {sup 237}Np) in the fracture-granite interface zones. Long-lived {sup 234}U, {sup 235}U, and {sup 237}Np were detected in flow channels, as well as in the adjacent rock matrix, using the sensitive, feature-basedmore » mapping of the LA/ICP-MS technique. The injected sorbing actinides are mainly located within the advective flowing fractures and the immediately adjacent regions. The water-conducting fracture studied in this work is bounded on one side by mylonite and the other by granitic matrix regions. These actinides did not penetrate into the mylonite side as much as the relatively higher-porosity granite matrix, most likely due to the low porosity, hydraulic conductivity, and diffusivity of the fracture wall (a thickness of about 0.4 mm separates the mylonite region from the fracture) and the mylonite region itself. Overall, the maximum penetration depth detected with this technique for the more diffusive {sup 237}Np over the field experimental time scale of about 60 days was about 10 mm in the granitic matrix, illustrating the importance of matrix diffusion in retarding radionuclide transport from the advective fractures. Laboratory tests and numerical modeling of radionuclide diffusion into granitic matrix was conducted to complement and help interpret the field results. Measured apparent diffusivity of multiple tracers in granite provided consistent predictions for radionuclide transport in the fractured granitic rock.« less

A priori analysis of differential diffusion for model development for scale-resolving simulations

NASA Astrophysics Data System (ADS)

Hunger, Franziska; Dietzsch, Felix; Gauding, Michael; Hasse, Christian

2018-01-01

The present study analyzes differential diffusion and the mechanisms responsible for it with regard to the turbulent/nonturbulent interface (TNTI) with special focus on model development for scale-resolving simulations. In order to analyze differences between resolved and subfilter phenomena, direct numerical simulation (DNS) data are compared with explicitly filtered data. The DNS database stems from a temporally evolving turbulent plane jet transporting two passive scalars with Schmidt numbers of unity and 0.25 presented by Hunger et al. [F. Hunger et al., J. Fluid Mech. 802, R5 (2016), 10.1017/jfm.2016.471]. The objective of this research is twofold: (i) to compare the position of the turbulent-nonturbulent interface between the original DNS data and the filtered data and (ii) to analyze differential diffusion and the impact of the TNTI with regard to scale resolution in the filtered DNS data. For the latter, differential diffusion quantities are studied, clearly showing the decrease of differential diffusion at the resolved scales with increasing filter width. A transport equation for the scalar differences is evaluated. Finally, the existence of large scalar gradients, gradient alignment, and the diffusive fluxes being the physical mechanisms responsible for the separation of the two scalars are compared between the resolved and subfilter scales.

Effects of a temperature-dependent rheology on large scale continental extension

NASA Technical Reports Server (NTRS)

Sonder, Leslie J.; England, Philip C.

1988-01-01

The effects of a temperature-dependent rheology on large-scale continental extension are investigated using a thin viscous sheet model. A vertically-averaged rheology is used that is consistent with laboratory experiments on power-law creep of olivine and that depends exponentially on temperature. Results of the calculations depend principally on two parameters: the Peclet number, which describes the relative rates of advection and diffusion of heat, and a dimensionless activation energy, which controls the temperature dependence of the rheology. At short times following the beginning of extension, deformation occurs with negligible change in temperature, so that only small changes in lithospheric strength occur due to attenuation of the lithosphere. However, after a certain critical time interval, thermal diffusion lowers temperatures in the lithosphere, strongly increasing lithospheric strength and slowing the rate of extension. This critical time depends principally on the Peclet number and is short compared with the thermal time constant of the lithosphere. The strength changes cause the locus of high extensional strain rates to shift with time from regions of high strain to regions of low strain. Results of the calculations are compared with observations from the Aegean, where maximum extensional strains are found in the south, near Crete, but maximum present-day strain rates are largest about 300 km further north.

Carbon diffusion paths and segregation at high-angle tilt grain boundaries in α-Fe studied by using a kinetic activation-relation technique

NASA Astrophysics Data System (ADS)

Restrepo, Oscar A.; Mousseau, Normand; Trochet, Mickaël; El-Mellouhi, Fedwa; Bouhali, Othmane; Becquart, Charlotte S.

2018-02-01

Carbon diffusion and segregation in iron is fundamental to steel production but is also associated with corrosion. Using the kinetic activation-relaxation technique (k-ART), a kinetic Monte Carlo (KMC) algorithm with an on-the-fly catalog that allows to obtain diffusion properties over large time scales taking into account long-range elastic effects coupled with an EAM force field, we study the motion of a carbon impurity in four Fe systems with high-angle grain boundaries (GB), focusing on the impact of these extended defects on the long-time diffusion of C. Short and long-time stability of the various GBs is first analyzed, which allows us to conclude that the Σ 3 (1 1 1 ) θ =109 .53∘<110 > GB is unstable, with Fe migration barriers of ˜0.1 eV or less, and C acts as a pinning center. Focusing on three stable GBs, in all cases, these extended defects trap C in energy states lower than found in the crystal. Yet, contrary to general understanding, we show, through simulations extending to 0.1 s, that even tough C diffusion takes place predominantly in the GB, it is not necessarily faster than in the bulk and can even be slower by one to two orders of magnitude depending on the GB type. Analysis of the energy landscape provided by k-ART also shows that the free cavity volume around the impurity is not a strong predictor of diffusion barrier height. Overall, results show rather complex diffusion kinetics intimately dependent on the local environment.

Can Disorder Enhance Incoherent Exciton Diffusion?

PubMed

Lee, Elizabeth M Y; Tisdale, William A; Willard, Adam P

2015-07-30

Recent experiments aimed at probing the dynamics of excitons have revealed that semiconducting films composed of disordered molecular subunits, unlike expectations for their perfectly ordered counterparts, can exhibit a time-dependent diffusivity in which the effective early time diffusion constant is larger than that of the steady state. This observation has led to speculation about what role, if any, microscopic disorder may play in enhancing exciton transport properties. In this article, we present the results of a model study aimed at addressing this point. Specifically, we introduce a general model, based upon Förster theory, for incoherent exciton diffusion in a material composed of independent molecular subunits with static energetic disorder. Energetic disorder leads to heterogeneity in molecule-to-molecule transition rates, which we demonstrate has two important consequences related to exciton transport. First, the distribution of local site-specific hopping rates is broadened in a manner that results in a decrease in average exciton diffusivity relative to that in a perfectly ordered film. Second, since excitons prefer to make transitions that are downhill in energy, the steady state distribution of exciton energies is biased toward low-energy molecular subunits, those that exhibit reduced diffusivity relative to a perfectly ordered film. These effects combine to reduce the net diffusivity in a manner that is time dependent and grows more pronounced as disorder is increased. Notably, however, we demonstrate that the presence of energetic disorder can give rise to a population of molecular subunits with exciton transfer rates exceeding those of subunits in an energetically uniform material. Such enhancements may play an important role in processes that are sensitive to molecular-scale fluctuations in exciton density field.

Vertical length scale selection for pancake vortices in strongly stratified viscous fluids

NASA Astrophysics Data System (ADS)

Godoy-Diana, Ramiro; Chomaz, Jean-Marc; Billant, Paul

2004-04-01

The evolution of pancake dipoles of different aspect ratio is studied in a stratified tank experiment. Two cases are reported here for values of the dipole initial aspect ratio alpha_0 = L_v/L_h (where L_v and L_h are vertical and horizontal length scales, respectively) of alpha_0 = 0.4 (case I) and alpha_0 = 1.2 (case II). In the first case, the usual decay scenario is observed where the dipole diffuses slowly with a growing thickness and a decaying circulation. In case II, we observed a regime where the thickness of the dipole decreases and the circulation in the horizontal mid-plane of the vortices remains constant. We show that this regime where the vertical length scale decreases can be explained by the shedding of two boundary layers at the top and bottom of the dipole that literally peel off vorticity layers. Horizontal advection and vertical diffusion cooperate in this regime and the decrease towards the viscous vertical length scale delta = L_hRe(-1/2) occurs on a time scale alpha_0 Re(1/2) T_A, T_A being the advection time L_h/U. From a scaling analysis of the equations for a stratified viscous fluid in the Boussinesq approximation, two dominant balances depending on the parameter R = ReF_h(2) are discussed, where F_h = U/NL_h is the horizontal Froude number and Re = UL_h/nu is the Reynolds number, U, N and nu being, respectively, the translation speed of the dipole, the Brunt Väisälä frequency and the kinematic viscosity. When R≫ 1 the vertical length scale is determined by buoyancy effects to be of order L_b = U/N. The experiments presented in this paper pertain to the case of small R, where viscous effects govern the selection of the vertical length scale. We show that if initially L_v ≤ delta, the flow diffuses on the vertical (case I), while if L_v ≫ delta (case II), vertically sheared horizontal advection decreases the vertical length scale down to delta. This viscous regime may explain results from experiments and numerical simulations on the late evolution of stratified flows where the decay is observed to be independent of the buoyancy frequency N.

Constraints on the Longevity of the 2010 Eyjaföll Eruption Cloud From Analog Experiments and Modeling

NASA Astrophysics Data System (ADS)

Carazzo, G.; Jellinek, M.

2010-12-01

The prolonged disruption of global air travel as a result of the 2010 Eyjafjöll eruption in Iceland underscores the value of discerning the dynamics of volcanic ash-clouds in the atmosphere. Understanding the longevity of these clouds is a particularly long standing problem that bears not only on volcanic hazards to humans but also on the nature and time scale of volcanic forcings on climate change. Since early work on the subject, the common practice to tackle the problem of cloud longevity has been to account for the dynamics of sedimentation by individual particle settling. We use 1D modeling and analog experiments of a turbulent particle-laden umbrella cloud to show that this classical view can be misleading and that the residence times of these ash-clouds in the atmosphere depends strongly on the collective behavior of the solid fraction. Diffusive convection driven by the differential diffusion of constituents altering the cloud density (ash, temperature, sulfur dioxide) may enhance particle scavenging and extend the cloud longevity over time scales orders of magnitude longer than currently expected (i.e., years rather than days for powerful eruptions). Records of this behavior can be found in real-time measurements of stratospheric post-volcanic aerosols following the 1974 Fuego, the 1982 El Chichon, the 1991 Hudson and Pinatubo events, and more recently, from the 14 April 2010 Eyjafjöll eruption. The importance of diffusive convection in volcanic ash-clouds depends strongly on particle size distribution and concentration. For the 2010 Eyjafjöll eruption, we predict that particles larger than 10 microns should settle individually as commonly assumed, but particles smaller than 1 micron should diffuse slowly in layers extending the cloud longevity to several weeks rather than days. These predictions are found to be in good agreement with a number of satellite and ground-based lidar data on ash size and mass estimates performed at different locations across Europe.

Radiative Extinction of Gaseous Spherical Diffusion Flames in Microgravity

NASA Technical Reports Server (NTRS)

Santa, K. J.; Chao, B. H.; Sunderland, P. B.; Urban, D. L.; Stocker, D. P.; Axelbaum, R. L.

2007-01-01

Radiative extinction of spherical diffusion flames was investigated experimentally and numerically. The experiments involved microgravity spherical diffusion flames burning ethylene and propane at 0.98 bar. Both normal (fuel flowing into oxidizer) and inverse (oxidizer flowing into fuel) flames were studied, with nitrogen supplied to either the fuel or the oxygen. Flame conditions were chosen to ensure that the flames extinguished within the 2.2 s of available test time; thus extinction occurred during unsteady flame conditions. Diagnostics included color video and thin-filament pyrometry. The computations, which simulated flow from a porous sphere into a quiescent environment, included detailed chemistry, transport and radiation, and yielded transient results. Radiative extinction was observed experimentally and simulated numerically. Extinction time, peak temperature, and radiative loss fraction were found to be independent of flow rate except at very low flow rates. Radiative heat loss was dominated by the combustion products downstream of the flame and was found to scale with flame surface area, not volume. For large transient flames the heat release rate also scaled with surface area and thus the radiative loss fraction was largely independent of flow rate. Peak temperatures at extinction onset were about 1100 K, which is significantly lower than for kinetic extinction. One observation of this work is that while radiative heat losses can drive transient extinction, this is not because radiative losses are increasing with time (flame size) but rather because the heat release rate is falling off as the temperature drops.

Design and Testing of Scaled Ejector-Diffusers for Jet Engine Test Facility Applications.

DTIC Science & Technology

1983-09-01

the test cell such that the exhaust will be vented into an augmenting tube which acts as an ejector -diffuser assembly. 11 The kinetic energy of the...OF STANDARDS-1963-A ..’I -Dy , - 77 *4********* Z 7.77- NAVAL POSTGRADUATE SCHOOL Monterey, California W I THESIS DESIGN AND TESTING OF SCALED EJECTOR ...PERIOD COVERED Design and Testing of Scaled Ejector - "flglfeerls Thesis~ Diffusers for Jet Engine Test Facility Spebr18 S. PERFORMING ORG. REPORT

Reverse flexing as a physical/mechanical treatment to mitigate fouling of fine bubble diffusers.

PubMed

Odize, Victory O; Novak, John; De Clippeleir, Haydee; Al-Omari, Ahmed; Smeraldi, Joshua D; Murthy, Sudhir; Rosso, Diego

2017-10-01

Achieving energy neutrality has shifted focus towards aeration system optimization, due to the high energy consumption of aeration processes in modern advanced wastewater treatment plants. A study on fine bubble diffuser fouling and mitigation, quantified by dynamic wet pressure (DWP), oxygen transfer efficiency and alpha was carried out in Blue Plains, Washington, DC. Four polyurethane fine bubble diffusers were installed in a pilot reactor column fed with high rate activated sludge from a full scale system. A mechanical cleaning method, reverse flexing (RF), was used to treat two diffusers (RF1, RF2), while two diffusers were kept as a control (i.e., no reverse flexing). There was a 45% increase in DWP of the control diffuser after 17 months of operation, an indication of fouling. RF treated diffusers (RF1 and RF2) did not show significant increase in DWP, and in comparison to the control diffuser prevented about 35% increase in DWP. Hence, reverse flexing potentially saves blower energy, by reducing the pressure burden on the air blower which increases blower energy requirement. However, no significant impact of the RF treatment in preventing a decrease in alpha-fouling (αF) of the fine pore diffusers, over time in operation was observed.

Atomistic modeling of water diffusion in hydrolytic biomaterials.

PubMed

Gautieri, Alfonso; Mezzanzanica, Andrea; Motta, Alberto; Redealli, Alberto; Vesentini, Simone

2012-04-01

One of the most promising applications of hydrolytically degrading biomaterials is their use as drug release carriers. These uses, however, require that the degradation and diffusion of drug are reliably predicted, which is complex to achieve through present experimental methods. Atomistic modeling can help in the knowledge-based design of degrading biomaterials with tuned drug delivery properties, giving insights on the small molecules diffusivity at intermediate states of the degradation process. We present here an atomistic-based approach to investigate the diffusion of water (through which hydrolytic degradation occurs) in degrading bulk models of poly(lactic acid) or PLA. We determine the water diffusion coefficient for different swelling states of the polymeric matrix (from almost dry to pure water) and for different degrees of degradation. We show that water diffusivity is highly influenced by the swelling degree, while little or not influenced by the degradation state. This approach, giving water diffusivity for different states of the matrix, can be combined with diffusion-reaction analytical methods in order to predict the degradation path on longer time scales. Furthermore, atomistic approach can be used to investigate diffusion of other relevant small molecules, eventually leading to the a priori knowledge of degradable biomaterials transport properties, helping the design of the drug delivery systems.

Coupling between diffusion and orientation of pentacene molecules on an organic surface.

PubMed

Rotter, Paul; Lechner, Barbara A J; Morherr, Antonia; Chisnall, David M; Ward, David J; Jardine, Andrew P; Ellis, John; Allison, William; Eckhardt, Bruno; Witte, Gregor

2016-04-01

The realization of efficient organic electronic devices requires the controlled preparation of molecular thin films and heterostructures. As top-down structuring methods such as lithography cannot be applied to van der Waals bound materials, surface diffusion becomes a structure-determining factor that requires microscopic understanding. Scanning probe techniques provide atomic resolution, but are limited to observations of slow movements, and therefore constrained to low temperatures. In contrast, the helium-3 spin-echo (HeSE) technique achieves spatial and time resolution on the nm and ps scale, respectively, thus enabling measurements at elevated temperatures. Here we use HeSE to unveil the intricate motion of pentacene admolecules diffusing on a chemisorbed monolayer of pentacene on Cu(110) that serves as a stable, well-ordered organic model surface. We find that pentacene moves along rails parallel and perpendicular to the surface molecules. The experimental data are explained by admolecule rotation that enables a switching between diffusion directions, which extends our molecular level understanding of diffusion in complex organic systems.

Using Measurements of Topography to Infer Rates of Crater Degradation and Surface Evolution on the Moon and Mercury

NASA Astrophysics Data System (ADS)

Fassett, C.; Crowley, M. C.; Leight, C.; Dyar, M. D.; Minton, D.; Hirabayashi, M.; Thomson, B. J.; Watters, W. A.

2017-12-01

Observations of how the topography of impact craters vary with age enable estimates for how fast the surface of airless bodies evolve. Fresh simple craters form with a depth/diameter (d/D) ratio of 0.21, sharp rims, and steep interior slopes. These fresh craters then are eroded and infilled, reducing d/D, and topographically muting their appearance. On the Moon and Mercury, the dominant mechanism responsible for this erosion likely includes the cumulative effects of numerous later small primary and secondary impact craters. The resulting topographic evolution can be modeled as a diffusive process, similar to how hillslopes evolve on Earth. However, the topographic diffusivity (κ) forced by impact cratering is dependent on both scale and time, so diffusion is anomalous, rather than classical. A key finding of this study is how the diffusivity and hence erosion rate is different on the Moon and Mercury. On the Moon, based on measurements of >13000 craters in the 800 m ≤ D ≤ 5 km size range on the lunar maria, the average diffusivity at 1 km scale is estimated as 5.5m2/Myr. With this diffusivity, D 1 km craters are reduced to 52% of their original depth over 3 Ga. Larger craters have relative depths that are much less reduced over an equivalent period, and smaller craters are much more eroded, even accounting for some scale-dependence of diffusivity (κ ∝ D0.9). In fact, the smallest craters are sufficiently degraded to become unrecognizable. The rate of topographic diffusion is the critical control on how a crater population reaches saturation equilibrium. On Mercury, d/D for 204 craters with 2.5 km ≤ D ≤ 5 km on the smooth plains were measured with MDIS stereo topography and MLA data. For these craters, the median d/D was 0.13. Craters in this same size range on the lunar maria are much less modified than those on Mercury when measured with the same techniques on data resampled to a resolution equivalent to the Mercury data, and their d/D is nearly indistinguishable from the fresh crater value. This difference in crater degradation is remarkable given that Mercury's smooth plains and the lunar maria likely have average ages that are comparable ( 3.3-3.8 Ga), if not identical. These results imply crater degradation is faster by a factor of at least two on Mercury than on the Moon, suggesting more rapid landform evolution on Mercury at all scales.

Quantifying residual, eddy, and mean flow effects on mixing in an idealized circumpolar current

DOE PAGES

Wolfram, Phillip J.; Ringler, Todd D.

2017-07-13

Meridional diffusivity is assessed in this paper for a baroclinically unstable jet in a high-latitudeIdealized Circumpolar Current (ICC) using the Model for Prediction Across Scales-Ocean (MPAS-O) and the online Lagrangian In-situ Global High-performance particle Tracking (LIGHT) diagnostic via space-time dispersion of particle clusters over 120 monthly realizations of O(10 6) particles on 11 potential density surfaces. Diffusivity in the jet reaches values of O(6000 m 2 s -1) and is largest near the critical layer supporting mixing suppression and critical layer theory. Values in the vicinity of the shelf break are suppressed to O(100 m 2 s -1) due tomore » the presence of westward slope front currents. Diffusivity attenuates less rapidly with depth in the jet than both eddy velocity and kinetic energy scalings would suggest. Removal of the mean flow via high-pass filtering shifts the nonlinear parameter (ratio of the eddy velocity to eddy phase speed) into the linear wave regime by increasing the eddy phase speed via the depth-mean flow. Low-pass filtering, in contrast, quantifies the effect of mean shear. Diffusivity is decomposed into mean flow shear, linear waves, and the residual nonhomogeneous turbulence components, where turbulence dominates and eddy-produced filamentation strained by background mean shear enhances mixing, accounting for ≥ 80% of the total diffusivity relative to mean shear [O(100 m 2 s -1)], linear waves [O(1000 m 2 s -1)], and undecomposed full diffusivity [O(6000 m 2 s -1)]. Finally, diffusivity parameterizations accounting for both the nonhomogeneous turbulence residual and depth variability are needed.« less

Evaluation of scaling invariance embedded in short time series.

PubMed

Pan, Xue; Hou, Lei; Stephen, Mutua; Yang, Huijie; Zhu, Chenping

2014-01-01

Scaling invariance of time series has been making great contributions in diverse research fields. But how to evaluate scaling exponent from a real-world series is still an open problem. Finite length of time series may induce unacceptable fluctuation and bias to statistical quantities and consequent invalidation of currently used standard methods. In this paper a new concept called correlation-dependent balanced estimation of diffusion entropy is developed to evaluate scale-invariance in very short time series with length ~10(2). Calculations with specified Hurst exponent values of 0.2,0.3,...,0.9 show that by using the standard central moving average de-trending procedure this method can evaluate the scaling exponents for short time series with ignorable bias (≤0.03) and sharp confidential interval (standard deviation ≤0.05). Considering the stride series from ten volunteers along an approximate oval path of a specified length, we observe that though the averages and deviations of scaling exponents are close, their evolutionary behaviors display rich patterns. It has potential use in analyzing physiological signals, detecting early warning signals, and so on. As an emphasis, the our core contribution is that by means of the proposed method one can estimate precisely shannon entropy from limited records.

Evaluation of Scaling Invariance Embedded in Short Time Series

PubMed Central

Pan, Xue; Hou, Lei; Stephen, Mutua; Yang, Huijie; Zhu, Chenping

2014-01-01

Scaling invariance of time series has been making great contributions in diverse research fields. But how to evaluate scaling exponent from a real-world series is still an open problem. Finite length of time series may induce unacceptable fluctuation and bias to statistical quantities and consequent invalidation of currently used standard methods. In this paper a new concept called correlation-dependent balanced estimation of diffusion entropy is developed to evaluate scale-invariance in very short time series with length . Calculations with specified Hurst exponent values of show that by using the standard central moving average de-trending procedure this method can evaluate the scaling exponents for short time series with ignorable bias () and sharp confidential interval (standard deviation ). Considering the stride series from ten volunteers along an approximate oval path of a specified length, we observe that though the averages and deviations of scaling exponents are close, their evolutionary behaviors display rich patterns. It has potential use in analyzing physiological signals, detecting early warning signals, and so on. As an emphasis, the our core contribution is that by means of the proposed method one can estimate precisely shannon entropy from limited records. PMID:25549356

Insights into the role of wettability in cathode catalyst layer of proton exchange membrane fuel cell; pore scale immiscible flow and transport processes

NASA Astrophysics Data System (ADS)

Fathi, H.; Raoof, A.; Mansouri, S. H.

2017-05-01

The production of liquid water in cathode catalyst layer, CCL, is a significant barrier to increase the efficiency of proton exchange membrane fuel cell. Here we present, for the first time, a direct three-dimensional pore-scale modelling to look at the complex immiscible two-phase flow in CCL. After production of the liquid water at the surface of CCL agglomerates due to the electrochemical reactions, water spatial distribution affects transport of oxygen through the CCL as well as the rate of reaction at the agglomerate surfaces. To explore the wettability effects, we apply hydrophilic and hydrophobic properties using different surface contact angles. Effective diffusivity is calculated under several water saturation levels. Results indicate larger diffusive transport values for hydrophilic domain compared to the hydrophobic media where the liquid water preferentially floods the larger pores. However, hydrophobic domain showed more available surface area and higher oxygen consumption rate at the reaction sites under various saturation levels, which is explained by the effect of wettability on pore-scale distribution of water. Hydrophobic domain, with a contact angle of 150, reveals efficient water removal where only 28% of the pore space stays saturated. This condition contributes to the enhanced available reaction surface area and oxygen diffusivity.

A small-angle neutron scattering study of the kinetics of phase separation in a supersaturated Ni-12.5 at. pct Si alloy

NASA Astrophysics Data System (ADS)

Polat, S.; Chen, Haydn; Epperson, J. E.

1989-04-01

The kinetic behavior of precipitation in a supersaturated Ni-12.5 at. pct Si alloy single crystal has been studied by the small-angle neutron scattering (SANS) technique to supplement earlier transmission electron microscopy (TEM) and wide-angle X-ray diffraction (XRD) work. The SANS measurements performed at room temperature on quenched specimens subjected to isothermal anneals at 400, 450, 505, and 550 °C for various amounts of time have revealed the presence of an interference peak in the scattering function. The particle size, determined according to the Guinier approximation, is found to grow in accordance with the diffusion controlled model put forth by Lifshitz and Slyozov, and independently by Wagner. The activation energy for solute diffusion is determined using the rate constants governing the growth of particle size and the variation of the mean interparticle distance. Results are in agreement with the values given in the literature. Transition from an earlier growth stage has been observed, and enhanced diffusion is noted at temperatures below 505 °C; both observations are consistent with the previous X-ray results. The dynamical scaling law appears to be followed by the data obtained in the coarsening stage. A disruption of scaling occurs at the point when the particle growth changes from a parabolic rate behavior to a cubic coarsening rate. Dynamical scaling offers the potential for projecting the service lifetimes for components from experimental measurements carried out over a much shorter time interval. Discrepancies in the size parameters determined by different techniques are discussed.

Dynamic scaling for the growth of non-equilibrium fluctuations during thermophoretic diffusion in microgravity

DOE PAGES

Cerbino, Roberto; Sun, Yifei; Donev, Aleksandar; ...

2015-09-30

Diffusion processes are widespread in biological and chemical systems, where they play a fundamental role in the exchange of substances at the cellular level and in determining the rate of chemical reactions. Recently, the classical picture that portrays diffusion as random uncorrelated motion of molecules has been revised, when it was shown that giant non-equilibrium fluctuations develop during diffusion processes. Under microgravity conditions and at steady-state, non-equilibrium fluctuations exhibit scale invariance and their size is only limited by the boundaries of the system. Here in this work, we investigate the onset of non-equilibrium concentration fluctuations induced by thermophoretic diffusion inmore » microgravity, a regime not accessible to analytical calculations but of great relevance for the understanding of several natural and technological processes. A combination of state of the art simulations and experiments allows us to attain a fully quantitative description of the development of fluctuations during transient diffusion in microgravity. Both experiments and simulations show that during the onset the fluctuations exhibit scale invariance at large wave vectors. In a broader range of wave vectors simulations predict a spinodal-like growth of fluctuations, where the amplitude and length-scale of the dominant mode are determined by the thickness of the diffuse layer.« less

Dynamic scaling for the growth of non-equilibrium fluctuations during thermophoretic diffusion in microgravity

PubMed Central

Cerbino, Roberto; Sun, Yifei; Donev, Aleksandar; Vailati, Alberto

2015-01-01

Diffusion processes are widespread in biological and chemical systems, where they play a fundamental role in the exchange of substances at the cellular level and in determining the rate of chemical reactions. Recently, the classical picture that portrays diffusion as random uncorrelated motion of molecules has been revised, when it was shown that giant non-equilibrium fluctuations develop during diffusion processes. Under microgravity conditions and at steady-state, non-equilibrium fluctuations exhibit scale invariance and their size is only limited by the boundaries of the system. In this work, we investigate the onset of non-equilibrium concentration fluctuations induced by thermophoretic diffusion in microgravity, a regime not accessible to analytical calculations but of great relevance for the understanding of several natural and technological processes. A combination of state of the art simulations and experiments allows us to attain a fully quantitative description of the development of fluctuations during transient diffusion in microgravity. Both experiments and simulations show that during the onset the fluctuations exhibit scale invariance at large wave vectors. In a broader range of wave vectors simulations predict a spinodal-like growth of fluctuations, where the amplitude and length-scale of the dominant mode are determined by the thickness of the diffuse layer. PMID:26419420

Dynamic scaling for the growth of non-equilibrium fluctuations during thermophoretic diffusion in microgravity.

PubMed

Cerbino, Roberto; Sun, Yifei; Donev, Aleksandar; Vailati, Alberto

2015-09-30

Diffusion processes are widespread in biological and chemical systems, where they play a fundamental role in the exchange of substances at the cellular level and in determining the rate of chemical reactions. Recently, the classical picture that portrays diffusion as random uncorrelated motion of molecules has been revised, when it was shown that giant non-equilibrium fluctuations develop during diffusion processes. Under microgravity conditions and at steady-state, non-equilibrium fluctuations exhibit scale invariance and their size is only limited by the boundaries of the system. In this work, we investigate the onset of non-equilibrium concentration fluctuations induced by thermophoretic diffusion in microgravity, a regime not accessible to analytical calculations but of great relevance for the understanding of several natural and technological processes. A combination of state of the art simulations and experiments allows us to attain a fully quantitative description of the development of fluctuations during transient diffusion in microgravity. Both experiments and simulations show that during the onset the fluctuations exhibit scale invariance at large wave vectors. In a broader range of wave vectors simulations predict a spinodal-like growth of fluctuations, where the amplitude and length-scale of the dominant mode are determined by the thickness of the diffuse layer.

Statistical properties of the anomalous scaling exponent estimator based on time-averaged mean-square displacement

NASA Astrophysics Data System (ADS)

Sikora, Grzegorz; Teuerle, Marek; Wyłomańska, Agnieszka; Grebenkov, Denis

2017-08-01

The most common way of estimating the anomalous scaling exponent from single-particle trajectories consists of a linear fit of the dependence of the time-averaged mean-square displacement on the lag time at the log-log scale. We investigate the statistical properties of this estimator in the case of fractional Brownian motion (FBM). We determine the mean value, the variance, and the distribution of the estimator. Our theoretical results are confirmed by Monte Carlo simulations. In the limit of long trajectories, the estimator is shown to be asymptotically unbiased, consistent, and with vanishing variance. These properties ensure an accurate estimation of the scaling exponent even from a single (long enough) trajectory. As a consequence, we prove that the usual way to estimate the diffusion exponent of FBM is correct from the statistical point of view. Moreover, the knowledge of the estimator distribution is the first step toward new statistical tests of FBM and toward a more reliable interpretation of the experimental histograms of scaling exponents in microbiology.