The precise time-dependent solution of the Fokker–Planck equation with anomalous diffusion

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

Guo, Ran; Du, Jiulin, E-mail: jiulindu@aliyun.com

2015-08-15

We study the time behavior of the Fokker–Planck equation in Zwanzig’s rule (the backward-Ito’s rule) based on the Langevin equation of Brownian motion with an anomalous diffusion in a complex medium. The diffusion coefficient is a function in momentum space and follows a generalized fluctuation–dissipation relation. We obtain the precise time-dependent analytical solution of the Fokker–Planck equation and at long time the solution approaches to a stationary power-law distribution in nonextensive statistics. As a test, numerically we have demonstrated the accuracy and validity of the time-dependent solution. - Highlights: • The precise time-dependent solution of the Fokker–Planck equation with anomalousmore » diffusion is found. • The anomalous diffusion satisfies a generalized fluctuation–dissipation relation. • At long time the time-dependent solution approaches to a power-law distribution in nonextensive statistics. • Numerically we have demonstrated the accuracy and validity of the time-dependent solution.« less

Modeling anomalous radial transport in kinetic transport codes

NASA Astrophysics Data System (ADS)

Bodi, K.; Krasheninnikov, S. I.; Cohen, R. H.; Rognlien, T. D.

2009-11-01

Anomalous transport is typically the dominant component of the radial transport in magnetically confined plasmas, where the physical origin of this transport is believed to be plasma turbulence. A model is presented for anomalous transport that can be used in continuum kinetic edge codes like TEMPEST, NEO and the next-generation code being developed by the Edge Simulation Laboratory. The model can also be adapted to particle-based codes. It is demonstrated that the model with a velocity-dependent diffusion and convection terms can match a diagonal gradient-driven transport matrix as found in contemporary fluid codes, but can also include off-diagonal effects. The anomalous transport model is also combined with particle drifts and a particle/energy-conserving Krook collision operator to study possible synergistic effects with neoclassical transport. For the latter study, a velocity-independent anomalous diffusion coefficient is used to mimic the effect of long-wavelength ExB turbulence.

Macromolecule diffusion and confinement in prokaryotic cells.

PubMed

Mika, Jacek T; Poolman, Bert

2011-02-01

We review recent observations on the mobility of macromolecules and their spatial organization in live bacterial cells. We outline the major fluorescence microscopy-based methods to determine the mobility and thus the diffusion coefficients (D) of molecules, which is not trivial in small cells. The extremely high macromolecule crowding of prokaryotes is used to rationalize the reported lower diffusion coefficients as compared to eukaryotes, and we speculate on the nature of the barriers for diffusion observed for proteins (and mRNAs) in vivo. Building on in vitro experiments and modeling studies, we evaluate the size dependence of diffusion coefficients for macromolecules in vivo, in case of both water-soluble and integral membrane proteins. We comment on the possibilities of anomalous diffusion and provide examples where the macromolecule mobility may be limiting biological processes. Copyright © 2010 Elsevier Ltd. All rights reserved.

Fractal analysis of lateral movement in biomembranes.

PubMed

Gmachowski, Lech

2018-04-01

Lateral movement of a molecule in a biomembrane containing small compartments (0.23-μm diameter) and large ones (0.75 μm) is analyzed using a fractal description of its walk. The early time dependence of the mean square displacement varies from linear due to the contribution of ballistic motion. In small compartments, walking molecules do not have sufficient time or space to develop an asymptotic relation and the diffusion coefficient deduced from the experimental records is lower than that measured without restrictions. The model makes it possible to deduce the molecule step parameters, namely the step length and time, from data concerning confined and unrestricted diffusion coefficients. This is also possible using experimental results for sub-diffusive transport. The transition from normal to anomalous diffusion does not affect the molecule step parameters. The experimental literature data on molecular trajectories recorded at a high time resolution appear to confirm the modeled value of the mean free path length of DOPE for Brownian and anomalous diffusion. Although the step length and time give the proper values of diffusion coefficient, the DOPE speed calculated as their quotient is several orders of magnitude lower than the thermal speed. This is interpreted as a result of intermolecular interactions, as confirmed by lateral diffusion of other molecules in different membranes. The molecule step parameters are then utilized to analyze the problem of multiple visits in small compartments. The modeling of the diffusion exponent results in a smooth transition to normal diffusion on entering a large compartment, as observed in experiments.

Anomalous versus slowed-down Brownian diffusion in the ligand-binding equilibrium.

PubMed

Soula, Hédi; Caré, Bertrand; Beslon, Guillaume; Berry, Hugues

2013-11-05

Measurements of protein motion in living cells and membranes consistently report transient anomalous diffusion (subdiffusion) that converges back to a Brownian motion with reduced diffusion coefficient at long times after the anomalous diffusion regime. Therefore, slowed-down Brownian motion could be considered the macroscopic limit of transient anomalous diffusion. On the other hand, membranes are also heterogeneous media in which Brownian motion may be locally slowed down due to variations in lipid composition. Here, we investigate whether both situations lead to a similar behavior for the reversible ligand-binding reaction in two dimensions. We compare the (long-time) equilibrium properties obtained with transient anomalous diffusion due to obstacle hindrance or power-law-distributed residence times (continuous-time random walks) to those obtained with space-dependent slowed-down Brownian motion. Using theoretical arguments and Monte Carlo simulations, we show that these three scenarios have distinctive effects on the apparent affinity of the reaction. Whereas continuous-time random walks decrease the apparent affinity of the reaction, locally slowed-down Brownian motion and local hindrance by obstacles both improve it. However, only in the case of slowed-down Brownian motion is the affinity maximal when the slowdown is restricted to a subregion of the available space. Hence, even at long times (equilibrium), these processes are different and exhibit irreconcilable behaviors when the area fraction of reduced mobility changes. Copyright © 2013 Biophysical Society. Published by Elsevier Inc. All rights reserved.

Nature of self-diffusion in two-dimensional fluids

NASA Astrophysics Data System (ADS)

Choi, Bongsik; Han, Kyeong Hwan; Kim, Changho; Talkner, Peter; Kidera, Akinori; Lee, Eok Kyun

2017-12-01

Self-diffusion in a two-dimensional simple fluid is investigated by both analytical and numerical means. We investigate the anomalous aspects of self-diffusion in two-dimensional fluids with regards to the mean square displacement, the time-dependent diffusion coefficient, and the velocity autocorrelation function (VACF) using a consistency equation relating these quantities. We numerically confirm the consistency equation by extensive molecular dynamics simulations for finite systems, corroborate earlier results indicating that the kinematic viscosity approaches a finite, non-vanishing value in the thermodynamic limit, and establish the finite size behavior of the diffusion coefficient. We obtain the exact solution of the consistency equation in the thermodynamic limit and use this solution to determine the large time asymptotics of the mean square displacement, the diffusion coefficient, and the VACF. An asymptotic decay law of the VACF resembles the previously known self-consistent form, 1/(t\\sqrt{{ln}t}), however with a rescaled time.

Peclet number as affected by molecular diffusion controls transient anomalous transport in alluvial aquifer-aquitard complexes

USGS Publications Warehouse

Zhang, Yong; Green, Christopher T.; Tick, Geoffrey R.

2015-01-01

This study evaluates the role of the Peclet number as affected by molecular diffusion in transient anomalous transport, which is one of the major knowledge gaps in anomalous transport, by combining Monte Carlo simulations and stochastic model analysis. Two alluvial settings containing either short- or long-connected hydrofacies are generated and used as media for flow and transport modeling. Numerical experiments show that 1) the Peclet number affects both the duration of the power-law segment of tracer breakthrough curves (BTCs) and the transition rate from anomalous to Fickian transport by determining the solute residence time for a given low-permeability layer, 2) mechanical dispersion has a limited contribution to the anomalous characteristics of late-time transport as compared to molecular diffusion due to an almost negligible velocity in floodplain deposits, and 3) the initial source dimensions only enhance the power-law tail of the BTCs at short travel distances. A tempered stable stochastic (TSS) model is then applied to analyze the modeled transport. Applications show that the time-nonlocal parameters in the TSS model relate to the Peclet number, Pe. In particular, the truncation parameter in the TSS model increases nonlinearly with a decrease in Pe due to the decrease of the mean residence time, and the capacity coefficient increases with an increase in molecular diffusion which is probably due to the increase in the number of immobile particles. The above numerical experiments and stochastic analysis therefore reveal that the Peclet number as affected by molecular diffusion controls transient anomalous transport in alluvial aquifer–aquitard complexes.

Levitation effect: Distinguishing anomalous from linear regime of guests sorbed in zeolites through the decay of intermediate scattering function and wavevector dependence of self-diffusivity.

PubMed

Ghorai, Pradip Kr; Yashonath, S

2005-03-10

Previous work investigating the dependence of self-diffusivity, D, on the size of the guest diffusing within the porous solid such as zeolite has reported the existence of an anomalous maximum in the diffusion coefficient (J. Phys. Chem. 1994, 98, 6368). Two distinct regimes of dependence of D on sigma(gg), diameter of the guest were reported. D proportional to 1/sigma(gg)2, often referred to as linear regime (LR), is found when sigma(gg) is smaller than sigma(v), the diameter of the void. A maximum in D has been observed when sigma(gg) is comparable to sigma(v) and this regime is referred to as anomalous regime (AR). Here we report the intermediate scattering function for a particle from LR and AR in zeolite faujasite. A particle from LR exhibits a biexponential decay while a particle from AR exhibits a single-exponential decay at small k. Variation with k of the full width at half-maximum of the self-part of the dynamic structure factor is nonmonotonic for a particle in the linear regime. In contrast, this variation is monotonic for a particle in the anomalous regime. These results can be understood in terms of the existence of energetic barrier at the bottleneck, the 12-ring window, in the path of diffusion. They provide additional signatures for the linear regime and anomalous regimes and therefore for levitation effect (LE).

Peclet number as affected by molecular diffusion controls transient anomalous transport in alluvial aquifer-aquitard complexes.

PubMed

Zhang, Yong; Green, Christopher T; Tick, Geoffrey R

2015-01-01

This study evaluates the role of the Peclet number as affected by molecular diffusion in transient anomalous transport, which is one of the major knowledge gaps in anomalous transport, by combining Monte Carlo simulations and stochastic model analysis. Two alluvial settings containing either short- or long-connected hydrofacies are generated and used as media for flow and transport modeling. Numerical experiments show that 1) the Peclet number affects both the duration of the power-law segment of tracer breakthrough curves (BTCs) and the transition rate from anomalous to Fickian transport by determining the solute residence time for a given low-permeability layer, 2) mechanical dispersion has a limited contribution to the anomalous characteristics of late-time transport as compared to molecular diffusion due to an almost negligible velocity in floodplain deposits, and 3) the initial source dimensions only enhance the power-law tail of the BTCs at short travel distances. A tempered stable stochastic (TSS) model is then applied to analyze the modeled transport. Applications show that the time-nonlocal parameters in the TSS model relate to the Peclet number, Pe. In particular, the truncation parameter in the TSS model increases nonlinearly with a decrease in Pe due to the decrease of the mean residence time, and the capacity coefficient increases with an increase in molecular diffusion which is probably due to the increase in the number of immobile particles. The above numerical experiments and stochastic analysis therefore reveal that the Peclet number as affected by molecular diffusion controls transient anomalous transport in alluvial aquifer-aquitard complexes. Copyright © 2015 Elsevier B.V. All rights reserved.

Fractional order analysis of Sephadex gel structures: NMR measurements reflecting anomalous diffusion

NASA Astrophysics Data System (ADS)

Magin, Richard L.; Akpa, Belinda S.; Neuberger, Thomas; Webb, Andrew G.

2011-12-01

We report the appearance of anomalous water diffusion in hydrophilic Sephadex gels observed using pulse field gradient (PFG) nuclear magnetic resonance (NMR). The NMR diffusion data was collected using a Varian 14.1 Tesla imaging system with a home-built RF saddle coil. A fractional order analysis of the data was used to characterize heterogeneity in the gels for the dynamics of water diffusion in this restricted environment. Several recent studies of anomalous diffusion have used the stretched exponential function to model the decay of the NMR signal, i.e., exp[-( bD) α], where D is the apparent diffusion constant, b is determined the experimental conditions (gradient pulse separation, durations and strength), and α is a measure of structural complexity. In this work, we consider a different case where the spatial Laplacian in the Bloch-Torrey equation is generalized to a fractional order model of diffusivity via a complexity parameter, β, a space constant, μ, and a diffusion coefficient, D. This treatment reverts to the classical result for the integer order case. The fractional order decay model was fit to the diffusion-weighted signal attenuation for a range of b-values (0 < b < 4000 s mm -2). Throughout this range of b values, the parameters β, μ and D, were found to correlate with the porosity and tortuosity of the gel structure.

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

Nature of self-diffusion in two-dimensional fluids

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

Choi, Bongsik; Han, Kyeong Hwan; Kim, Changho

Self-diffusion in a two-dimensional simple fluid is investigated by both analytical and numerical means. We investigate the anomalous aspects of self-diffusion in two-dimensional fluids with regards to the mean square displacement, the time-dependent diffusion coefficient, and the velocity autocorrelation function (VACF) using a consistency equation relating these quantities. Here, we numerically confirm the consistency equation by extensive molecular dynamics simulations for finite systems, corroborate earlier results indicating that the kinematic viscosity approaches a finite, non-vanishing value in the thermodynamic limit, and establish the finite size behavior of the diffusion coefficient. We obtain the exact solution of the consistency equation in the thermodynamic limit and use this solution to determine the large time asymptotics of the mean square displacement, the diffusion coefficient, and the VACF. An asymptotic decay law of the VACF resembles the previously known self-consistent form, 1/(more » $$t\\sqrt{In t)}$$ however with a rescaled time.« less

Nature of self-diffusion in two-dimensional fluids

DOE PAGES

Choi, Bongsik; Han, Kyeong Hwan; Kim, Changho; ...

2017-12-18

Self-diffusion in a two-dimensional simple fluid is investigated by both analytical and numerical means. We investigate the anomalous aspects of self-diffusion in two-dimensional fluids with regards to the mean square displacement, the time-dependent diffusion coefficient, and the velocity autocorrelation function (VACF) using a consistency equation relating these quantities. Here, we numerically confirm the consistency equation by extensive molecular dynamics simulations for finite systems, corroborate earlier results indicating that the kinematic viscosity approaches a finite, non-vanishing value in the thermodynamic limit, and establish the finite size behavior of the diffusion coefficient. We obtain the exact solution of the consistency equation in the thermodynamic limit and use this solution to determine the large time asymptotics of the mean square displacement, the diffusion coefficient, and the VACF. An asymptotic decay law of the VACF resembles the previously known self-consistent form, 1/(more » $$t\\sqrt{In t)}$$ however with a rescaled time.« less

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.

Crossover from anomalous to normal diffusion in porous media

NASA Astrophysics Data System (ADS)

Aarão Reis, F. D. A.; di Caprio, Dung

2014-06-01

Random walks (RW) of particles adsorbed in the internal walls of porous deposits produced by ballistic-type growth models are studied. The particles start at the external surface of the deposits and enter their pores in order to simulate an external flux of a species towards a porous solid. For short times, the walker concentration decays as a stretched exponential of the depth z, but a crossover to long-time normal diffusion is observed in most samples. The anomalous concentration profile remains at long times in very porous solids if the walker steps are restricted to nearest neighbors and is accompanied with subdiffusion features. These findings are correlated with a decay of the explored area with z. The study of RW of tracer particles left at the internal part of the solid rules out an interpretation by diffusion equations with position-dependent coefficients. A model of RW in a tube of decreasing cross section explains those results by showing long crossovers from an effective subdiffusion regime to an asymptotic normal diffusion. The crossover position and density are analytically calculated for a tube with area decreasing exponentially with z and show good agreement with numerical data. The anomalous decay of the concentration profile is interpreted as a templating effect of the tube shape on the total number of diffusing particles at each depth, while the volumetric concentration in the actually explored porous region may not have significant decay. These results may explain the anomalous diffusion of metal atoms in porous deposits observed in recent works. They also confirm the difficulty in interpreting experimental or computational data on anomalous transport reported in recent works, particularly if only the concentration profiles are measured.

Anomalous diffusion in the evolution of soccer championship scores: Real data, mean-field analysis, and an agent-based model

NASA Astrophysics Data System (ADS)

da Silva, Roberto; Vainstein, Mendeli H.; Gonçalves, Sebastián; Paula, Felipe S. F.

2013-08-01

Statistics of soccer tournament scores based on the double round robin system of several countries are studied. Exploring the dynamics of team scoring during tournament seasons from recent years we find evidences of superdiffusion. A mean-field analysis results in a drift velocity equal to that of real data but in a different diffusion coefficient. Along with the analysis of real data we present the results of simulations of soccer tournaments obtained by an agent-based model which successfully describes the final scoring distribution [da Silva , Comput. Phys. Commun.CPHCBZ0010-465510.1016/j.cpc.2012.10.030 184, 661 (2013)]. Such model yields random walks of scores over time with the same anomalous diffusion as observed in real data.

Implementation of an anomalous radial transport model for continuum kinetic edge codes

NASA Astrophysics Data System (ADS)

Bodi, K.; Krasheninnikov, S. I.; Cohen, R. H.; Rognlien, T. D.

2007-11-01

Radial plasma transport in magnetic fusion devices is often dominated by plasma turbulence compared to neoclassical collisional transport. Continuum kinetic edge codes [such as the (2d,2v) transport version of TEMPEST and also EGK] compute the collisional transport directly, but there is a need to model the anomalous transport from turbulence for long-time transport simulations. Such a model is presented and results are shown for its implementation in the TEMPEST gyrokinetic edge code. The model includes velocity-dependent convection and diffusion coefficients expressed as a Hermite polynominals in velocity. The specification of the Hermite coefficients can be set, e.g., by specifying the ratio of particle and energy transport as in fluid transport codes. The anomalous transport terms preserve the property of no particle flux into unphysical regions of velocity space. TEMPEST simulations are presented showing the separate control of particle and energy anomalous transport, and comparisons are made with neoclassical transport also included.

Anomalous Diffusion of Water in Lamellar Membranes Formed by Pluronic Polymers

NASA Astrophysics Data System (ADS)

Zhang, Zhe; Ohl, Michael; Han, Youngkyu; Smith, Gregory; Do, Changwoo; Biology; Soft-Matter Division, Oak Ridge National Laboratory Team; Julich CenterNeutron Science Team

Water diffusion is playing an important role in polymer systems. We calculated the water diffusion coefficient at different layers along z-direction which is perpendicular to the lamellar membrane formed by Pluronic block copolymers (L62: (EO6-PO34-EO6)) with the molecular dynamics simulation trajectories. Water molecules at bulk layers are following the normal diffusion, while that at hydration layers formed by polyethylene oxide (PEO) and hydrophobic layers formed by polypropylene oxide (PPO) are following anomalous diffusion. We find that although the subdiffusive regimes at PEO layers and PPO layers are the same, which is the fractional Brownian motion, however, the dynamics are different, i.e. diffusion at the PEO layers is much faster than that at the PPO layers, and meanwhile it exhibits a normal diffusive approximation within a short time period which is governed by the localized free self-diffusion, but becomes subdiffusive after t >8 ps, which is governed by the viscoelastic medium. The Scientific User Facilities Division, Office of Basic Energy Sciences, U.S. Department of Energy; and Zhe Zhang gratefully acknowledges financial support from Julich Center for Neutron Science.

Electron transport in the stochastic fields of the reversed-field pinch

NASA Astrophysics Data System (ADS)

Kim, Myung-Hee; Punjabi, Alkesh

1996-08-01

We employ the Monte Carlo method for the calculation of anomalous transport developed by Punjabi and Boozer to calculate the particle diffusion coefficient for electrons in the stochastic magnetic fields of the reversed-field pinch (RFP). in the Monte Carlo calculations represented here, the transport mechanism is the loss of magnetic surfaces due to resistive perturbations. The equilibrium magnetic fields are represented by the Bessel function model for the RFP. The diffusion coefficient D is calculated as a function of a, the amplitude of the perturbation. We see three regimes as the amplitude of the tearing modes is increased: the Rechester—Rosenbluth regime where D scales as a2 the anomalous regime where D scales more rapidly than a2 and the Mynick—Krornmes regime where D scales more slowly than a2. Inclusion of the effects of loop voltage on the particle drift orbits in the RFP does not affect the intervals in the amplitude a where these regimes operate.

Fractional Diffusion Equations and Anomalous Diffusion

NASA Astrophysics Data System (ADS)

Evangelista, Luiz Roberto; Kaminski Lenzi, Ervin

2018-01-01

Preface; 1. Mathematical preliminaries; 2. A survey of the fractional calculus; 3. From normal to anomalous diffusion; 4. Fractional diffusion equations: elementary applications; 5. Fractional diffusion equations: surface effects; 6. Fractional nonlinear diffusion equation; 7. Anomalous diffusion: anisotropic case; 8. Fractional Schrödinger equations; 9. Anomalous diffusion and impedance spectroscopy; 10. The Poisson–Nernst–Planck anomalous (PNPA) models; References; Index.

Interpretation of diffusion coefficients in nanostructured materials from random walk numerical simulation.

PubMed

Anta, Juan A; Mora-Seró, Iván; Dittrich, Thomas; Bisquert, Juan

2008-08-14

We make use of the numerical simulation random walk (RWNS) method to compute the "jump" diffusion coefficient of electrons in nanostructured materials via mean-square displacement. First, a summary of analytical results is given that relates the diffusion coefficient obtained from RWNS to those in the multiple-trapping (MT) and hopping models. Simulations are performed in a three-dimensional lattice of trap sites with energies distributed according to an exponential distribution and with a step-function distribution centered at the Fermi level. It is observed that once the stationary state is reached, the ensemble of particles follow Fermi-Dirac statistics with a well-defined Fermi level. In this stationary situation the diffusion coefficient obeys the theoretical predictions so that RWNS effectively reproduces the MT model. Mobilities can be also computed when an electrical bias is applied and they are observed to comply with the Einstein relation when compared with steady-state diffusion coefficients. The evolution of the system towards the stationary situation is also studied. When the diffusion coefficients are monitored along simulation time a transition from anomalous to trap-limited transport is observed. The nature of this transition is discussed in terms of the evolution of electron distribution and the Fermi level. All these results will facilitate the use of RW simulation and related methods to interpret steady-state as well as transient experimental techniques.

Scale-invariant Green-Kubo relation for time-averaged diffusivity

NASA Astrophysics Data System (ADS)

Meyer, Philipp; Barkai, Eli; Kantz, Holger

2017-12-01

In recent years it was shown both theoretically and experimentally that in certain systems exhibiting anomalous diffusion the time- and ensemble-averaged mean-squared displacement are remarkably different. The ensemble-averaged diffusivity is obtained from a scaling Green-Kubo relation, which connects the scale-invariant nonstationary velocity correlation function with the transport coefficient. Here we obtain the relation between time-averaged diffusivity, usually recorded in single-particle tracking experiments, and the underlying scale-invariant velocity correlation function. The time-averaged mean-squared displacement is given by 〈δ2¯〉 ˜2 DνtβΔν -β , where t is the total measurement time and Δ is the lag time. Here ν is the anomalous diffusion exponent obtained from ensemble-averaged measurements 〈x2〉 ˜tν , while β ≥-1 marks the growth or decline of the kinetic energy 〈v2〉 ˜tβ . Thus, we establish a connection between exponents that can be read off the asymptotic properties of the velocity correlation function and similarly for the transport constant Dν. We demonstrate our results with nonstationary scale-invariant stochastic and deterministic models, thereby highlighting that systems with equivalent behavior in the ensemble average can differ strongly in their time average. If the averaged kinetic energy is finite, β =0 , the time scaling of 〈δ2¯〉 and 〈x2〉 are identical; however, the time-averaged transport coefficient Dν is not identical to the corresponding ensemble-averaged diffusion constant.

Infinite densities for Lévy walks.

PubMed

Rebenshtok, A; Denisov, S; Hänggi, P; Barkai, E

2014-12-01

Motion of particles in many systems exhibits a mixture between periods of random diffusive-like events and ballistic-like motion. In many cases, such systems exhibit strong anomalous diffusion, where low-order moments 〈|x(t)|(q)〉 with q below a critical value q(c) exhibit diffusive scaling while for q>q(c) a ballistic scaling emerges. The mixed dynamics constitutes a theoretical challenge since it does not fall into a unique category of motion, e.g., the known diffusion equations and central limit theorems fail to describe both aspects. In this paper we resolve this problem by resorting to the concept of infinite density. Using the widely applicable Lévy walk model, we find a general expression for the corresponding non-normalized density which is fully determined by the particles velocity distribution, the anomalous diffusion exponent α, and the diffusion coefficient K(α). We explain how infinite densities play a central role in the description of dynamics of a large class of physical processes and discuss how they can be evaluated from experimental or numerical data.

Anomalously Fast Diffusion of Targeted Carbon Nanotubes in Cellular Spheroids.

PubMed

Wang, Yichun; Bahng, Joong Hwan; Che, Quantong; Han, Jishu; Kotov, Nicholas A

2015-08-25

Understanding transport of carbon nanotubes (CNTs) and other nanocarriers within tissues is essential for biomedical imaging and drug delivery using these carriers. Compared to traditional cell cultures in animal studies, three-dimensional tissue replicas approach the complexity of the actual organs and enable high temporal and spatial resolution of the carrier permeation. We investigated diffusional transport of CNTs in highly uniform spheroids of hepatocellular carcinoma and found that apparent diffusion coefficients of CNTs in these tissue replicas are anomalously high and comparable to diffusion rates of similarly charged molecules with molecular weights 10000× lower. Moreover, diffusivity of CNTs in tissues is enhanced after functionalization with transforming growth factor β1. This unexpected trend contradicts predictions of the Stokes-Einstein equation and previously obtained empirical dependences of diffusivity on molecular mass for permeants in gas, liquid, solid or gel. It is attributed to the planar diffusion (gliding) of CNTs along cellular membranes reducing effective dimensionality of diffusional space. These findings indicate that nanotubes and potentially similar nanostructures are capable of fast and deep permeation into the tissue, which is often difficult to realize with anticancer agents.

What is the alternative to the Alexander-Orbach relation?

NASA Astrophysics Data System (ADS)

Sokolov, Igor M.

2016-03-01

The Alexander-Orbach (AO) relation d w = 2d f /d s connecting the fractal dimension of a random walk’s (RW) trajectory d w or the exponent of anomalous diffusion α = 2/d w on a fractal structure with the fractal and spectral dimension of the structure itself plays a key role in discussion of dynamical properties of complex systems including living cells and single biomolecules. This relation however does not hold universally and breaks down for some structures like diffusion limited aggregates and Eden trees. We show that the alternative to the AO relation is the explicit dependence of the coefficient of the anomalous diffusion on the system’s size, i.e. the absence of its thermodynamical limit. The prerequisite for its breakdown is the dependence of the local structure of possible steps of the RW on the system’s size. The discussion is illustrated by the examples of diffusion on a Koch curve (AO-conform) and on a Cantor dust (violating AO relation).

Comparisons of anomalous and collisional radial transport with a continuum kinetic edge code

NASA Astrophysics Data System (ADS)

Bodi, K.; Krasheninnikov, S.; Cohen, R.; Rognlien, T.

2009-05-01

Modeling of anomalous (turbulence-driven) radial transport in controlled-fusion plasmas is necessary for long-time transport simulations. Here the focus is continuum kinetic edge codes such as the (2-D, 2-V) transport version of TEMPEST, NEO, and the code being developed by the Edge Simulation Laboratory, but the model also has wider application. Our previously developed anomalous diagonal transport matrix model with velocity-dependent convection and diffusion coefficients allows contact with typical fluid transport models (e.g., UEDGE). Results are presented that combine the anomalous transport model and collisional transport owing to ion drift orbits utilizing a Krook collision operator that conserves density and energy. Comparison is made of the relative magnitudes and possible synergistic effects of the two processes for typical tokamak device parameters.

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.

Spin transport study in a Rashba spin-orbit coupling system

PubMed Central

Mei, Fuhong; Zhang, Shan; Tang, Ning; Duan, Junxi; Xu, Fujun; Chen, Yonghai; Ge, Weikun; Shen, Bo

2014-01-01

One of the most important topics in spintronics is spin transport. In this work, spin transport properties of two-dimensional electron gas in AlxGa1-xN/GaN heterostructure were studied by helicity-dependent photocurrent measurements at room temperature. Spin-related photocurrent was detected under normal incidence of a circularly polarized laser with a Gaussian distribution. On one hand, spin polarized electrons excited by the laser generate a diffusive spin polarization current, which leads to a vortex charge current as a result of anomalous circular photogalvanic effect. On the other hand, photo-induced spin polarized electrons driven by a longitudinal electric field give rise to a transverse current via anomalous Hall Effect. Both of these effects originated from the Rashba spin-orbit coupling. By analyzing spin-related photocurrent varied with laser position, the contributions of the two effects were differentiated and the ratio of the spin diffusion coefficient to photo-induced anomalous spin Hall mobility Ds/μs = 0.08 V was extracted at room temperature. PMID:24504193

Relationship between the anomalous diffusion and the fractal dimension of the environment

NASA Astrophysics Data System (ADS)

Zhokh, Alexey; Trypolskyi, Andrey; Strizhak, Peter

2018-03-01

In this letter, we provide an experimental study highlighting a relation between the anomalous diffusion and the fractal dimension of the environment using the methanol anomalous transport through the porous solid pellets with various pores geometries and different chemical compositions. The anomalous diffusion exponent was derived from the non-integer order of the time-fractional diffusion equation that describes the methanol anomalous transport through the solid media. The surface fractal dimension was estimated from the nitrogen adsorption isotherms using the Frenkel-Halsey-Hill method. Our study shows that decreasing the fractal dimension leads to increasing the anomalous diffusion exponent, whereas the anomalous diffusion constant is independent on the fractal dimension. We show that the obtained results are in a good agreement with the anomalous diffusion model on a fractal mesh.

Dual control of flow field heterogeneity and immobile porosity on non-Fickian transport in Berea sandstone

NASA Astrophysics Data System (ADS)

Gjetvaj, Filip; Russian, Anna; Gouze, Philippe; Dentz, Marco

2015-10-01

Both flow field heterogeneity and mass transfer between mobile and immobile domains have been studied separately for explaining observed anomalous transport. Here we investigate non-Fickian transport using high-resolution 3-D X-ray microtomographic images of Berea sandstone containing microporous cement with pore size below the setup resolution. Transport is computed for a set of representative elementary volumes and results from advection and diffusion in the resolved macroporosity (mobile domain) and diffusion in the microporous phase (immobile domain) where the effective diffusion coefficient is calculated from the measured local porosity using a phenomenological model that includes a porosity threshold (ϕθ) below which diffusion is null and the exponent n that characterizes tortuosity-porosity power-law relationship. We show that both flow field heterogeneity and microporosity trigger anomalous transport. Breakthrough curve (BTC) tailing is positively correlated to microporosity volume and mobile-immobile interface area. The sensitivity analysis showed that the BTC tailing increases with the value of ϕθ, due to the increase of the diffusion path tortuosity until the volume of the microporosity becomes negligible. Furthermore, increasing the value of n leads to an increase in the standard deviation of the distribution of effective diffusion coefficients, which in turn results in an increase of the BTC tailing. Finally, we propose a continuous time random walk upscaled model where the transition time is the sum of independently distributed random variables characterized by specific distributions. It allows modeling a 1-D equivalent macroscopic transport honoring both the control of the flow field heterogeneity and the multirate mass transfer between mobile and immobile domains.

Kubo conductivity of a strongly magnetized two-dimensional plasma.

NASA Technical Reports Server (NTRS)

Montgomery, D.; Tappert, F.

1971-01-01

The Kubo formula is used to evaluate the bulk electrical conductivity of a two-dimensional guiding-center plasma in a strong dc magnetic field. The particles interact only electrostatically. An ?anomalous' electrical conductivity is derived for this system, which parallels a recent result of Taylor and McNamara for the coefficient of spatial diffusion.

Anomalous transport in the crowded world of biological cells

NASA Astrophysics Data System (ADS)

Höfling, Felix; Franosch, Thomas

2013-04-01

A ubiquitous observation in cell biology is that the diffusive motion of macromolecules and organelles is anomalous, and a description simply based on the conventional diffusion equation with diffusion constants measured in dilute solution fails. This is commonly attributed to macromolecular crowding in the interior of cells and in cellular membranes, summarizing their densely packed and heterogeneous structures. The most familiar phenomenon is a sublinear, power-law increase of the mean-square displacement (MSD) as a function of the lag time, but there are other manifestations like strongly reduced and time-dependent diffusion coefficients, persistent correlations in time, non-Gaussian distributions of spatial displacements, heterogeneous diffusion and a fraction of immobile particles. After a general introduction to the statistical description of slow, anomalous transport, we summarize some widely used theoretical models: Gaussian models like fractional Brownian motion and Langevin equations for visco-elastic media, the continuous-time random walk model, and the Lorentz model describing obstructed transport in a heterogeneous environment. Particular emphasis is put on the spatio-temporal properties of the transport in terms of two-point correlation functions, dynamic scaling behaviour, and how the models are distinguished by their propagators even if the MSDs are identical. Then, we review the theory underlying commonly applied experimental techniques in the presence of anomalous transport like single-particle tracking, fluorescence correlation spectroscopy (FCS) and fluorescence recovery after photobleaching (FRAP). We report on the large body of recent experimental evidence for anomalous transport in crowded biological media: in cyto- and nucleoplasm as well as in cellular membranes, complemented by in vitro experiments where a variety of model systems mimic physiological crowding conditions. Finally, computer simulations are discussed which play an important role in testing the theoretical models and corroborating the experimental findings. The review is completed by a synthesis of the theoretical and experimental progress identifying open questions for future investigation.

Anomalous Extracellular Diffusion in Rat Cerebellum

PubMed Central

Xiao, Fanrong; Hrabe, Jan; Hrabetova, Sabina

2015-01-01

Extracellular space (ECS) is a major channel transporting biologically active molecules and drugs in the brain. Diffusion-mediated transport of these substances is hindered by the ECS structure but the microscopic basis of this hindrance is not fully understood. One hypothesis proposes that the hindrance originates in large part from the presence of dead-space (DS) microdomains that can transiently retain diffusing molecules. Because previous theoretical and modeling work reported an initial period of anomalous diffusion in similar environments, we expected that brain regions densely populated by DS microdomains would exhibit anomalous extracellular diffusion. Specifically, we targeted granular layers (GL) of rat and turtle cerebella that are populated with large and geometrically complex glomeruli. The integrative optical imaging (IOI) method was employed to evaluate diffusion of fluorophore-labeled dextran (MW 3000) in GL, and the IOI data analysis was adapted to quantify the anomalous diffusion exponent dw from the IOI records. Diffusion was significantly anomalous in rat GL, where dw reached 4.8. In the geometrically simpler turtle GL, dw was elevated but not robustly anomalous (dw = 2.6). The experimental work was complemented by numerical Monte Carlo simulations of anomalous ECS diffusion in several three-dimensional tissue models containing glomeruli-like structures. It demonstrated that both the duration of transiently anomalous diffusion and the anomalous exponent depend on the size of model glomeruli and the degree of their wrapping. In conclusion, we have found anomalous extracellular diffusion in the GL of rat cerebellum. This finding lends support to the DS microdomain hypothesis. Transiently anomalous diffusion also has a profound effect on the spatiotemporal distribution of molecules released into the ECS, especially at diffusion distances on the order of a few cell diameters, speeding up short-range diffusion-mediated signals in less permeable structures. PMID:25954895

Normal and Anomalous Diffusion: An Analytical Study Based on Quantum Collision Dynamics and Boltzmann Transport Theory.

PubMed

Mahakrishnan, Sathiya; Chakraborty, Subrata; Vijay, Amrendra

2016-09-15

Diffusion, an emergent nonequilibrium transport phenomenon, is a nontrivial manifestation of the correlation between the microscopic dynamics of individual molecules and their statistical behavior observed in experiments. We present a thorough investigation of this viewpoint using the mathematical tools of quantum scattering, within the framework of Boltzmann transport theory. In particular, we ask: (a) How and when does a normal diffusive transport become anomalous? (b) What physical attribute of the system is conceptually useful to faithfully rationalize large variations in the coefficient of normal diffusion, observed particularly within the dynamical environment of biological cells? To characterize the diffusive transport, we introduce, analogous to continuous phase transitions, the curvature of the mean square displacement as an order parameter and use the notion of quantum scattering length, which measures the effective interactions between the diffusing molecules and the surrounding, to define a tuning variable, η. We show that the curvature signature conveniently differentiates the normal diffusion regime from the superdiffusion and subdiffusion regimes and the critical point, η = ηc, unambiguously determines the coefficient of normal diffusion. To solve the Boltzmann equation analytically, we use a quantum mechanical expression for the scattering amplitude in the Boltzmann collision term and obtain a general expression for the effective linear collision operator, useful for a variety of transport studies. We also demonstrate that the scattering length is a useful dynamical characteristic to rationalize experimental observations on diffusive transport in complex systems. We assess the numerical accuracy of the present work with representative experimental results on diffusion processes in biological systems. Furthermore, we advance the idea of temperature-dependent effective voltage (of the order of 1 μV or less in a biological environment, for example) as a dynamical cause of the perpetual molecular movement, which eventually manifests as an ordered motion, called the diffusion.

Transport in sheared stochastic magnetic fields

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

Vanden Eijnden, E.; Balescu, R.

1997-02-01

The transport of test particles in a stochastic magnetic field with a sheared component is studied. Two stages in the particle dynamics are distinguished depending on whether the collisional effects perpendicular to the main field are negligible or not. Whenever the perpendicular collisions are unimportant, the particles show a subdiffusive behavior which is slower in the presence of shear. The particle dynamics is then inhomogeneous and non-Markovian and no diffusion coefficient may be properly defined. When the perpendicular collision frequency is small, this subdiffusive stage may be very long. In the truly asymptotic stage, however, the perpendicular collisions must bemore » accounted for and the particle motion eventually becomes diffusive. Here again, however, the shear is shown to reduce the anomalous diffusion coefficient of the system. {copyright} {ital 1997 American Institute of Physics.}« less

Fractional calculus applied to the analysis of spectral electrical conductivity of clay-water system.

PubMed

Korosak, Dean; Cvikl, Bruno; Kramer, Janja; Jecl, Renata; Prapotnik, Anita

2007-06-16

The analysis of the low-frequency conductivity spectra of the clay-water mixtures is presented. The frequency dependence of the conductivity is shown to follow the power-law with the exponent n=0.67 before reaching the frequency-independent part. When scaled with the value of the frequency-independent part of the spectrum the conductivity spectra for samples at different water content values are shown to fit to a single master curve. It is argued that the observed conductivity dispersion is a consequence of the anomalously diffusing ions in the clay-water system. The fractional Langevin equation is then used to describe the stochastic dynamics of the single ion. The results indicate that the experimentally observed dielectric properties originate in anomalous ion transport in clay-water system characterized with time-dependent diffusion coefficient.

A fractal derivative model for the characterization of anomalous diffusion in magnetic resonance imaging

NASA Astrophysics Data System (ADS)

Liang, Yingjie; Ye, Allen Q.; Chen, Wen; Gatto, Rodolfo G.; Colon-Perez, Luis; Mareci, Thomas H.; Magin, Richard L.

2016-10-01

Non-Gaussian (anomalous) diffusion is wide spread in biological tissues where its effects modulate chemical reactions and membrane transport. When viewed using magnetic resonance imaging (MRI), anomalous diffusion is characterized by a persistent or 'long tail' behavior in the decay of the diffusion signal. Recent MRI studies have used the fractional derivative to describe diffusion dynamics in normal and post-mortem tissue by connecting the order of the derivative with changes in tissue composition, structure and complexity. In this study we consider an alternative approach by introducing fractal time and space derivatives into Fick's second law of diffusion. This provides a more natural way to link sub-voxel tissue composition with the observed MRI diffusion signal decay following the application of a diffusion-sensitive pulse sequence. Unlike previous studies using fractional order derivatives, here the fractal derivative order is directly connected to the Hausdorff fractal dimension of the diffusion trajectory. The result is a simpler, computationally faster, and more direct way to incorporate tissue complexity and microstructure into the diffusional dynamics. Furthermore, the results are readily expressed in terms of spectral entropy, which provides a quantitative measure of the overall complexity of the heterogeneous and multi-scale structure of biological tissues. As an example, we apply this new model for the characterization of diffusion in fixed samples of the mouse brain. These results are compared with those obtained using the mono-exponential, the stretched exponential, the fractional derivative, and the diffusion kurtosis models. Overall, we find that the order of the fractal time derivative, the diffusion coefficient, and the spectral entropy are potential biomarkers to differentiate between the microstructure of white and gray matter. In addition, we note that the fractal derivative model has practical advantages over the existing models from the perspective of computational accuracy and efficiency.

Anomalous extracellular diffusion in rat cerebellum.

PubMed

Xiao, Fanrong; Hrabe, Jan; Hrabetova, Sabina

2015-05-05

Extracellular space (ECS) is a major channel transporting biologically active molecules and drugs in the brain. Diffusion-mediated transport of these substances is hindered by the ECS structure but the microscopic basis of this hindrance is not fully understood. One hypothesis proposes that the hindrance originates in large part from the presence of dead-space (DS) microdomains that can transiently retain diffusing molecules. Because previous theoretical and modeling work reported an initial period of anomalous diffusion in similar environments, we expected that brain regions densely populated by DS microdomains would exhibit anomalous extracellular diffusion. Specifically, we targeted granular layers (GL) of rat and turtle cerebella that are populated with large and geometrically complex glomeruli. The integrative optical imaging (IOI) method was employed to evaluate diffusion of fluorophore-labeled dextran (MW 3000) in GL, and the IOI data analysis was adapted to quantify the anomalous diffusion exponent dw from the IOI records. Diffusion was significantly anomalous in rat GL, where dw reached 4.8. In the geometrically simpler turtle GL, dw was elevated but not robustly anomalous (dw = 2.6). The experimental work was complemented by numerical Monte Carlo simulations of anomalous ECS diffusion in several three-dimensional tissue models containing glomeruli-like structures. It demonstrated that both the duration of transiently anomalous diffusion and the anomalous exponent depend on the size of model glomeruli and the degree of their wrapping. In conclusion, we have found anomalous extracellular diffusion in the GL of rat cerebellum. This finding lends support to the DS microdomain hypothesis. Transiently anomalous diffusion also has a profound effect on the spatiotemporal distribution of molecules released into the ECS, especially at diffusion distances on the order of a few cell diameters, speeding up short-range diffusion-mediated signals in less permeable structures. Copyright © 2015 Biophysical Society. Published by Elsevier Inc. All rights reserved.

A Physical Interpretation of the Phenomenological Coefficients of Membrane Permeability

PubMed Central

Kedem, O.; Katchalsky, A.

1961-01-01

A "translation" of the phenomenological permeability coefficients into friction and distribution coefficients amenable to physical interpretation is presented. Expressions are obtained for the solute permeability coefficient ω and the reflection coefficient σ for both non-electrolytic and electrolytic permeants. An analysis of the coefficients is given for loose membranes as well as for dense natural membranes where transport may go through capillaries or by solution in the lipoid parts of the membrane. Water diffusion and filtration and the relation between these and capillary pore radius of the membrane are discussed. For the permeation of ions through the charged membranes equations are developed for the case of zero electrical current in the membrane. The correlation of σ with ω and Lp for electrolytes resembles that for non-electrolytes. In this case ω and σ depend markedly on ion concentration and on the charge density of the membrane. The reflection coefficient may assume negative values indicating anomalous osmosis. An analysis of the phenomena of anomalous osmosis was carried out for the model of Teorell and Meyer and Sievers and the results agree with the experimental data of Loeb and of Grim and Sollner. A set of equations and reference curves are presented for the evaluation of ω and σ in the transport of polyvalent ions through charged membranes. PMID:13752127

General PFG signal attenuation expressions for anisotropic anomalous diffusion by modified-Bloch equations

NASA Astrophysics Data System (ADS)

Lin, Guoxing

2018-05-01

Anomalous diffusion exists widely in polymer and biological systems. Pulsed-field gradient (PFG) anomalous diffusion is complicated, especially in the anisotropic case where limited research has been reported. A general PFG signal attenuation expression, including the finite gradient pulse (FGPW) effect for free general anisotropic fractional diffusion { 0 < α , β ≤ 2 } based on the fractional derivative, has not been obtained, where α and β are time and space derivative orders. It is essential to derive a general PFG signal attenuation expression including the FGPW effect for PFG anisotropic anomalous diffusion research. In this paper, two recently developed modified-Bloch equations, the fractal differential modified-Bloch equation and the fractional integral modified-Bloch equation, were extended to obtain general PFG signal attenuation expressions for anisotropic anomalous diffusion. Various cases of PFG anisotropic anomalous diffusion were investigated, including coupled and uncoupled anisotropic anomalous diffusion. The continuous-time random walk (CTRW) simulation was also carried out to support the theoretical results. The theory and the CTRW simulation agree with each other. The obtained signal attenuation expressions and the three-dimensional fractional modified-Bloch equations are important for analyzing PFG anisotropic anomalous diffusion in NMR and MRI.

Effects of Anomalous Cosmic Rays on the Structure of the Outer Heliosphere

NASA Astrophysics Data System (ADS)

Guo, Xiaocheng; Florinski, Vladimir; Wang, Chi

2018-06-01

Based on Voyager 1 observations, some anomalous cosmic rays (ACRs) may have crossed the heliopause and escaped into the interstellar medium, providing a mechanism of energy transfer between the inner and outer heliosheaths that is not included in conventional magnetohydrodynamics (MHD) models. In this paper, we study the effect of energetic particles’ escape through the heliopause on the size and shape of the heliosphere using a simple model that includes diffusive transport of cosmic rays. We show that the presence of ACRs significantly changes the heliosphere structure, including the location of the heliopause and termination shock. It was found that the heliopause would contract for certain values of the ACR diffusion coefficients when the diffusive particles’ pressure is comparable to the pressure of the plasma background. The difference in Voyager 1 and 2 observations of energetic particles during their respective termination shock crossings is interpreted here as due to the differences in diffusion environments during the different phases of the solar cycle. The shorter period of enhanced ACR intensities upstream of the shock measured by Voyager 2 may have been caused by weaker radial diffusive transport compared with the time of Voyager 1 crossing. We conclude that ACR diffusive effects could be prominent and should be included in MHD models of the heliosphere.

Spin diffusion in disordered organic semiconductors

NASA Astrophysics Data System (ADS)

Li, Ling; Gao, Nan; Lu, Nianduan; Liu, Ming; Bässler, Heinz

2015-12-01

An analytical theory for spin diffusion in disordered organic semiconductors is derived. It is based on percolation theory and variable range hopping in a disordered energy landscape with a Gaussian density of states. It describes universally the dependence of the spin diffusion on temperature, carrier density, material disorder, magnetic field, and electric field at the arbitrary magnitude of the Hubbard energy of charge pairs. It is found that, compared to the spin transport carried by carriers hopping, the spin exchange will hinder the spin diffusion process at low carrier density, even under the condition of a weak electric field. Importantly, under the influence of a bias voltage, anomalous spreading of the spin packet will lead to an abnormal temperature dependence of the spin diffusion coefficient and diffusion length. This explains the recent experimental data for spin diffusion length observed in Alq3.

Strongly anomalous diffusion in sheared magnetic configurations

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

Vanden Eijnden, E.; Balescu, R.

1996-03-01

The statistical behavior of magnetic lines in a sheared magnetic configuration with reference surface {ital x}=0 is investigated within the framework of the kinetic theory. A Liouville equation is associated with the equations of motion of the stochastic magnetic lines. After averaging over an ensemble of realizations, it yields a convection-diffusion equation within the quasilinear approximation. The diffusion coefficients are space dependent and peaked around the reference surface {ital x}=0. Due to the shear, the diffusion of lines away from the reference surface is slowed down. The behavior of the lines is asymptotically strongly non-Gaussian. The reference surface acts likemore » an attractor around which the magnetic lines spread with an effective subdiffusive behavior. Comparison is also made with more usual treatments based on the study of the first two moments equations. For sheared systems, it is explicitly shown that the Corrsin approximation assumed in the latter approach is no longer valid. It is also concluded that the diffusion coefficients cannot be derived from the mean square displacement of the magnetic lines in an inhomogeneous medium. {copyright} {ital 1996 American Institute of Physics.}« less

Anomalous heat conduction and anomalous diffusion in nonlinear lattices, single walled nanotubes, and billiard gas channels.

PubMed

Li, Baowen; Wang, Jiao; Wang, Lei; Zhang, Gang

2005-03-01

We study anomalous heat conduction and anomalous diffusion in low-dimensional systems ranging from nonlinear lattices, single walled carbon nanotubes, to billiard gas channels. We find that in all discussed systems, the anomalous heat conductivity can be connected with the anomalous diffusion, namely, if energy diffusion is sigma(2)(t)=2Dt(alpha) (01) implies an anomalous heat conduction with a divergent thermal conductivity (beta>0), and more interestingly, a subdiffusion (alpha<1) implies an anomalous heat conduction with a convergent thermal conductivity (beta<0), consequently, the system is a thermal insulator in the thermodynamic limit. Existing numerical data support our theoretical prediction.

Non-equilibrium dynamics in disordered materials: Ab initio molecular dynamics simulations

NASA Astrophysics Data System (ADS)

Ohmura, Satoshi; Nagaya, Kiyonobu; Shimojo, Fuyuki; Yao, Makoto

2015-08-01

The dynamic properties of liquid B2O3 under pressure and highly-charged bromophenol molecule are studied by using molecular dynamics (MD) simulations based on density functional theory (DFT). Diffusion properties of covalent liquids under high pressure are very interesting in the sense that they show unexpected pressure dependence. It is found from our simulation that the magnitude relation of diffusion coefficients for boron and oxygen in liquid B2O3 shows the anomalous pressure dependence. The simulation clarified the microscopic origin of the anomalous diffusion properties. Our simulation also reveals the dissociation mechanism in the coulomb explosion of the highly-charged bromophenol molecule. When the charge state n is 6, hydrogen atom in the hydroxyl group dissociates at times shorter than 20 fs while all hydrogen atoms dissociate when n is 8. After the hydrogen dissociation, the carbon ring breaks at about 100 fs. There is also a difference on the mechanism of the ring breaking depending on charge states, in which the ring breaks with expanding (n = 6) or shrink (n = 8).

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

Ohmura, Satoshi; Nagaya, Kiyonobu; Yao, Makoto

The dynamic properties of liquid B{sub 2}O{sub 3} under pressure and highly-charged bromophenol molecule are studied by using molecular dynamics (MD) simulations based on density functional theory (DFT). Diffusion properties of covalent liquids under high pressure are very interesting in the sense that they show unexpected pressure dependence. It is found from our simulation that the magnitude relation of diffusion coefficients for boron and oxygen in liquid B{sub 2}O{sub 3} shows the anomalous pressure dependence. The simulation clarified the microscopic origin of the anomalous diffusion properties. Our simulation also reveals the dissociation mechanism in the coulomb explosion of the highly-chargedmore » bromophenol molecule. When the charge state n is 6, hydrogen atom in the hydroxyl group dissociates at times shorter than 20 fs while all hydrogen atoms dissociate when n is 8. After the hydrogen dissociation, the carbon ring breaks at about 100 fs. There is also a difference on the mechanism of the ring breaking depending on charge states, in which the ring breaks with expanding (n = 6) or shrink (n = 8)« less

Self-crowding of AMPA receptors in the excitatory postsynaptic density can effectuate anomalous receptor sub-diffusion.

PubMed

Gupta, Rahul

2018-02-01

AMPA receptors (AMPARs) and their associations with auxiliary transmembrane proteins are bulky structures with large steric-exclusion volumes. Hence, self-crowding of AMPARs, depending on the local density, may affect their lateral diffusion in the postsynaptic membrane as well as in the highly crowded postsynaptic density (PSD) at excitatory synapses. Earlier theoretical studies considered only the roles of transmembrane obstacles and the AMPAR-binding submembranous scaffold proteins in shaping receptor diffusion within PSD. Using lattice model of diffusion, the present study investigates the additional impacts of self-crowding on the anomalousity and effective diffusion coefficient (Deff) of AMPAR diffusion. A recursive algorithm for avoiding false self-blocking during diffusion simulation is also proposed. The findings suggest that high density of AMPARs in the obstacle-free membrane itself engenders strongly anomalous diffusion and severe decline in Deff. Adding transmembrane obstacles to the membrane accentuates the anomalousity arising from self-crowding due to the reduced free diffusion space. Contrarily, enhanced AMPAR-scaffold binding, either through increase in binding strength or scaffold density or both, ameliorates the anomalousity resulting from self-crowding. However, binding has differential impacts on Deff depending on the receptor density. Increase in binding causes consistent decrease in Deff for low and moderate receptor density. For high density, binding increases Deff as long as it reduces anomalousity associated with intense self-crowding. Given a sufficiently strong binding condition when diffusion acquires normal behavior, further increase in binding causes decrease in Deff. Supporting earlier experimental observations are mentioned and implications of present findings to the experimental observations on AMPAR diffusion are also drawn.

Drift turbulence, particle transport, and anomalous dissipation at the reconnecting magnetopause

NASA Astrophysics Data System (ADS)

Le, A.; Daughton, W.; Ohia, O.; Chen, L.-J.; Liu, Y.-H.; Wang, S.; Nystrom, W. D.; Bird, R.

2018-06-01

Using fully kinetic 3D simulations, the reconnection dynamics of asymmetric current sheets are examined at the Earth's magnetopause. The plasma parameters are selected to model MMS magnetopause diffusion region crossings with guide fields of 0.1, 0.4, and 1 of the reconnecting magnetosheath field. In each case, strong drift-wave fluctuations are observed in the lower-hybrid frequency range at the steep density gradient across the magnetospheric separatrix. These fluctuations give rise to cross-field electron particle transport. In addition, this turbulent mixing leads to significantly enhanced electron parallel heating in comparison to 2D simulations. We study three different methods of quantifying the anomalous dissipation produced by the drift fluctuations, based on spatial averaging, temporal averaging, and temporal averaging followed by integrating along magnetic field lines. A comparison of different methods reveals complications in identifying and measuring the anomalous dissipation. Nevertheless, the anomalous dissipation from short wavelength drift fluctuations appears weak for each case, and the reconnection rates observed in 3D are nearly the same as in 2D models. The 3D simulations feature a number of interesting new features that are consistent with recent MMS observations, including cold beams of magnetosheath electrons that penetrate into the hotter magnetospheric inflow, the related observation of decreasing temperature in regions of increasing total density, and an effective turbulent diffusion coefficient that agrees with predictions from quasi-linear theory.

Revisiting point FRAP to quantitatively characterize anomalous diffusion in live cells.

PubMed

Daddysman, Matthew K; Fecko, Christopher J

2013-02-07

Fluorescence recovery after photobleaching (FRAP) is widely used to interrogate diffusion and binding of proteins in live cells. Herein, we apply two-photon excited FRAP with a diffraction limited bleaching and observation volume to study anomalous diffusion of unconjugated green fluorescence protein (GFP) in vitro and in cells. Experiments performed on dilute solutions of GFP reveal that reversible fluorophore bleaching can be mistakenly interpreted as anomalous diffusion. We derive a reaction-diffusion FRAP model that includes reversible photobleaching, and demonstrate that it properly accounts for these photophysics. We then apply this model to investigate the diffusion of GFP in HeLa cells and polytene cells of Drosophila larval salivary glands. GFP exhibits anomalous diffusion in the cytoplasm of both cell types and in HeLa nuclei. Polytene nuclei contain optically resolvable chromosomes, permitting FRAP experiments that focus separately on chromosomal or interchrosomal regions. We find that GFP exhibits anomalous diffusion in chromosomal regions but diffuses normally in regions devoid of chromatin. This observation indicates that obstructed transport through chromatin and not crowding by macromolecules is a source of anomalous diffusion in polytene nuclei. This behavior is likely true in other cells, so it will be important to account for this type of transport physics and for reversible photobleaching to properly interpret future FRAP experiments on DNA-binding proteins.

The Shape of Protein Crowders is a Major Determinant of Protein Diffusion

PubMed Central

Balbo, Jessica; Mereghetti, Paolo; Herten, Dirk-Peter; Wade, Rebecca C.

2013-01-01

As a model for understanding how molecular crowding influences diffusion and transport of proteins in cellular environments, we combined experimental and theoretical approaches to study the diffusion of proteins in highly concentrated protein solutions. Bovine serum albumin and γ-Globulin were chosen as molecular crowders and as tracers. These two proteins are representatives of the main types of plasma protein and have different shapes and sizes. Solutions consisting of one or both proteins were studied. The self-diffusion coefficients of the fluorescently labeled tracer proteins were measured by means of fluorescence correlation spectroscopy at a total protein concentration of up to 400 g/L. γ-Globulin is found to have a stronger influence as a crowder on the tracer self-diffusion coefficient than Bovine serum albumin. Brownian dynamics simulations show that the excluded volume and the shape of the crowding protein have a significantly stronger influence on translational and rotational diffusion coefficients, as well as transient oligomerization, than hydrodynamic or direct interactions. Anomalous subdiffusion, which is not observed at the experimental fluorescence correlation spectroscopy timescales (>100 μs), appears only at very short timescales (<1 μs) in the simulations due to steric effects of the proteins. We envision that the combined experimental and computational approach employed here can be developed to unravel the different biophysical contributions to protein motion and interaction in cellular environments by systematically varying protein properties such as molecular weight, size, shape, and electrostatic interactions. PMID:23561534

Self-crowding of AMPA receptors in the excitatory postsynaptic density can effectuate anomalous receptor sub-diffusion

PubMed Central

Gupta, Rahul

2018-01-01

AMPA receptors (AMPARs) and their associations with auxiliary transmembrane proteins are bulky structures with large steric-exclusion volumes. Hence, self-crowding of AMPARs, depending on the local density, may affect their lateral diffusion in the postsynaptic membrane as well as in the highly crowded postsynaptic density (PSD) at excitatory synapses. Earlier theoretical studies considered only the roles of transmembrane obstacles and the AMPAR-binding submembranous scaffold proteins in shaping receptor diffusion within PSD. Using lattice model of diffusion, the present study investigates the additional impacts of self-crowding on the anomalousity and effective diffusion coefficient (Deff) of AMPAR diffusion. A recursive algorithm for avoiding false self-blocking during diffusion simulation is also proposed. The findings suggest that high density of AMPARs in the obstacle-free membrane itself engenders strongly anomalous diffusion and severe decline in Deff. Adding transmembrane obstacles to the membrane accentuates the anomalousity arising from self-crowding due to the reduced free diffusion space. Contrarily, enhanced AMPAR-scaffold binding, either through increase in binding strength or scaffold density or both, ameliorates the anomalousity resulting from self-crowding. However, binding has differential impacts on Deff depending on the receptor density. Increase in binding causes consistent decrease in Deff for low and moderate receptor density. For high density, binding increases Deff as long as it reduces anomalousity associated with intense self-crowding. Given a sufficiently strong binding condition when diffusion acquires normal behavior, further increase in binding causes decrease in Deff. Supporting earlier experimental observations are mentioned and implications of present findings to the experimental observations on AMPAR diffusion are also drawn. PMID:29444074

Computational analysis of the roles of biochemical reactions in anomalous diffusion dynamics

NASA Astrophysics Data System (ADS)

Naruemon, Rueangkham; Charin, Modchang

2016-04-01

Most biochemical processes in cells are usually modeled by reaction-diffusion (RD) equations. In these RD models, the diffusive process is assumed to be Gaussian. However, a growing number of studies have noted that intracellular diffusion is anomalous at some or all times, which may result from a crowded environment and chemical kinetics. This work aims to computationally study the effects of chemical reactions on the diffusive dynamics of RD systems by using both stochastic and deterministic algorithms. Numerical method to estimate the mean-square displacement (MSD) from a deterministic algorithm is also investigated. Our computational results show that anomalous diffusion can be solely due to chemical reactions. The chemical reactions alone can cause anomalous sub-diffusion in the RD system at some or all times. The time-dependent anomalous diffusion exponent is found to depend on many parameters, including chemical reaction rates, reaction orders, and chemical concentrations. Project supported by the Thailand Research Fund and Mahidol University (Grant No. TRG5880157), the Thailand Center of Excellence in Physics (ThEP), CHE, Thailand, and the Development Promotion of Science and Technology.

Cooper Pair-Like Systems at High Temperature and their Role on Fluctuations Near the Critical Temperature

NASA Astrophysics Data System (ADS)

Ausloos, M.; Dorbolo, S.

A logarithmic behavior is hidden in the linear temperature regime of the electrical resistivity R(T) of some YBCO sample below 2Tc where "pairs" break apart, fluctuations occur and "a gap is opening". An anomalous effect also occurs near 200 K in the normal state Hall coefficient. In a simulation of oxygen diffusion in planar 123 YBCO, an anomalous behavior is found in the oxygen-vacancy motion near such a temperature. We claim that the behavior of the specific heat above and near the critical temperature should be reexamined in order to show the influence and implications of fluctuations and dimensionality on the nature of the phase transition and on the true onset temperature.

Anomalous Seebeck coefficient observed in silicon nanowire micro thermoelectric generator

NASA Astrophysics Data System (ADS)

Hashimoto, S.; Asada, S.; Xu, T.; Oba, S.; Himeda, Y.; Yamato, R.; Matsukawa, T.; Matsuki, T.; Watanabe, T.

2017-07-01

We have found experimentally an anomalous thermoelectric characteristic of an n-type Si nanowire micro thermoelectric generator (μTEG). The μTEG is fabricated on a silicon-on-insulator wafer by electron beam lithography and dry etching, and its surface is covered with a thermally grown silicon dioxide film. The observed thermoelectric current is opposite to what is expected from the Seebeck coefficient of n-type Si. The result is understandable by considering a potential barrier in the nanowire. Upon the application of the temperature gradient across the nanowire, the potential barrier impedes the diffusion of thermally activated majority carriers into the nanowire, and it rather stimulates the injection of thermally generated minority carriers. The most plausible origin of the potential barrier is negative charges trapped at the interface between the Si nanowire and the oxide film. We practically confirmed that the normal Seebeck coefficient of the n-type Si nanowire is recovered after the hydrogen forming gas annealing. This implies that the interface traps are diminished by the hydrogen termination of bonding defects. The present results show the importance of the surface inactivation treatment of μTEGs to suppress the potential barrier and unfavorable contribution of minority carriers.

Langevin equation with fluctuating diffusivity: A two-state model

NASA Astrophysics Data System (ADS)

Miyaguchi, Tomoshige; Akimoto, Takuma; Yamamoto, Eiji

2016-07-01

Recently, anomalous subdiffusion, aging, and scatter of the diffusion coefficient have been reported in many single-particle-tracking experiments, though the origins of these behaviors are still elusive. Here, as a model to describe such phenomena, we investigate a Langevin equation with diffusivity fluctuating between a fast and a slow state. Namely, the diffusivity follows a dichotomous stochastic process. We assume that the sojourn time distributions of these two states are given by power laws. It is shown that, for a nonequilibrium ensemble, the ensemble-averaged mean-square displacement (MSD) shows transient subdiffusion. In contrast, the time-averaged MSD shows normal diffusion, but an effective diffusion coefficient transiently shows aging behavior. The propagator is non-Gaussian for short time and converges to a Gaussian distribution in a long-time limit; this convergence to Gaussian is extremely slow for some parameter values. For equilibrium ensembles, both ensemble-averaged and time-averaged MSDs show only normal diffusion and thus we cannot detect any traces of the fluctuating diffusivity with these MSDs. Therefore, as an alternative approach to characterizing the fluctuating diffusivity, the relative standard deviation (RSD) of the time-averaged MSD is utilized and it is shown that the RSD exhibits slow relaxation as a signature of the long-time correlation in the fluctuating diffusivity. Furthermore, it is shown that the RSD is related to a non-Gaussian parameter of the propagator. To obtain these theoretical results, we develop a two-state renewal theory as an analytical tool.

Diffusion control for a tempered anomalous diffusion system using fractional-order PI controllers.

PubMed

Juan Chen; Zhuang, Bo; Chen, YangQuan; Cui, Baotong

2017-05-09

This paper is concerned with diffusion control problem of a tempered anomalous diffusion system based on fractional-order PI controllers. The contribution of this paper is to introduce fractional-order PI controllers into the tempered anomalous diffusion system for mobile actuators motion and spraying control. For the proposed control force, convergence analysis of the system described by mobile actuator dynamical equations is presented based on Lyapunov stability arguments. Moreover, a new Centroidal Voronoi Tessellation (CVT) algorithm based on fractional-order PI controllers, henceforth called FOPI-based CVT algorithm, is provided together with a modified simulation platform called Fractional-Order Diffusion Mobile Actuator-Sensor 2-Dimension Fractional-Order Proportional Integral (FO-Diff-MAS2D-FOPI). Finally, extensive numerical simulations for the tempered anomalous diffusion process are presented to verify the effectiveness of our proposed fractional-order PI controllers. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Nonlinear anomalous diffusion equation and fractal dimension: exact generalized Gaussian solution.

PubMed

Pedron, I T; Mendes, R S; Malacarne, L C; Lenzi, E K

2002-04-01

In this work we incorporate, in a unified way, two anomalous behaviors, the power law and stretched exponential ones, by considering the radial dependence of the N-dimensional nonlinear diffusion equation partial differential rho/ partial differential t=nabla.(Knablarho(nu))-nabla.(muFrho)-alpharho, where K=Dr(-theta), nu, theta, mu, and D are real parameters, F is the external force, and alpha is a time-dependent source. This equation unifies the O'Shaughnessy-Procaccia anomalous diffusion equation on fractals (nu=1) and the spherical anomalous diffusion for porous media (theta=0). An exact spherical symmetric solution of this nonlinear Fokker-Planck equation is obtained, leading to a large class of anomalous behaviors. Stationary solutions for this Fokker-Planck-like equation are also discussed by introducing an effective potential.

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).

Cusping, transport and variance of solutions to generalized Fokker-Planck equations

NASA Astrophysics Data System (ADS)

Carnaffan, Sean; Kawai, Reiichiro

2017-06-01

We study properties of solutions to generalized Fokker-Planck equations through the lens of the probability density functions of anomalous diffusion processes. In particular, we examine solutions in terms of their cusping, travelling wave behaviours, and variance, within the framework of stochastic representations of generalized Fokker-Planck equations. We give our analysis in the cases of anomalous diffusion driven by the inverses of the stable, tempered stable and gamma subordinators, demonstrating the impact of changing the distribution of waiting times in the underlying anomalous diffusion model. We also analyse the cases where the underlying anomalous diffusion contains a Lévy jump component in the parent process, and when a diffusion process is time changed by an uninverted Lévy subordinator. On the whole, we present a combination of four criteria which serve as a theoretical basis for model selection, statistical inference and predictions for physical experiments on anomalously diffusing systems. We discuss possible applications in physical experiments, including, with reference to specific examples, the potential for model misclassification and how combinations of our four criteria may be used to overcome this issue.

Anisotropy of anomalous diffusion improves the accuracy of differentiating low- and high-grade cerebral gliomas.

PubMed

Xu, Boyan; Su, Lu; Wang, Zhenxiong; Fan, Yang; Gong, Gaolang; Zhu, Wenzhen; Gao, Peiyi; Gao, Jia-Hong

2018-04-17

Anomalous diffusion model has been introduced and shown to be beneficial in clinical applications. However, only the directionally averaged values of anomalous diffusion parameters were investigated, and the anisotropy of anomalous diffusion remains unexplored. The aim of this study was to demonstrate the feasibility of using anisotropy of anomalous diffusion for differentiating low- and high-grade cerebral gliomas. Diffusion MRI images were acquired from brain tumor patients and analyzed using the fractional motion (FM) model. Twenty-two patients with histopathologically confirmed gliomas were selected. An anisotropy metric for the FM-related parameters, including the Noah exponent (α) and the Hurst exponent (H), was introduced and their values were statistically compared between the low- and high-grade gliomas. Additionally, multivariate logistic regression analysis was performed to assess the combination of the anisotropy metric and the directionally averaged value for each parameter. The diagnostic performances for grading gliomas were evaluated using a receiver operating characteristic (ROC) analysis. The Hurst exponent H was more anisotropic in high-grade than in low-grade gliomas (P = 0.015), while no significant difference was observed for the anisotropy of α. The ROC analysis revealed that larger areas under the ROC curves were produced for the combination of α (1) and the combination of H (0.813) compared with the directionally averaged α (0.979) and H (0.594), indicating an improved performance for tumor differentiation. The anisotropy of anomalous diffusion can provide distinctive information and benefit the differentiation of low- and high-grade gliomas. The utility of anisotropic anomalous diffusion may have an improved effect for investigating pathological changes in tissues. Copyright © 2018 Elsevier Inc. All rights reserved.

Kubo number and magnetic field line diffusion coefficient for anisotropic magnetic turbulence.

PubMed

Pommois, P; Veltri, P; Zimbardo, G

2001-06-01

The magnetic field line diffusion coefficients Dx and D(y) are obtained by numerical simulations in the case that all the magnetic turbulence correlation lengths l(x), l(y), and l(z) are different. We find that the variety of numerical results can be organized in terms of the Kubo number, the definition of which is extended from R=(deltaB/B(0))(l(parallel)/l(perpendicular)) to R=(deltaB/B(0))(l(z)/l(x)), for l(x) > or = l(y). Here, l(parallel) (l(perpendicular)) is the correlation length along (perpendicular to) the average field B(0)=B(0)ê(z). We have anomalous, non-Gaussian transport for R less, similar 0.1, in which case the mean square deviation scales nonlinearly with time. For R greater, similar 1 we have several Gaussian regimes: an almost quasilinear regime for 0.1 less, similar R less, similar 1, an intermediate, transition regime for 1 less, similar R less, similar 10, and a percolative regime for R greater, similar 10. An analytical form of the diffusion coefficient is proposed, D(i)=D(deltaBl(z)/B(0)l(x))(mu)(l(i)/l(x))(nu)l(2)(x)/l(z), which well describes the numerical simulation results in the quasilinear, intermediate, and percolative regimes.

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.

Effect of Greenhouse Gases Dissolved in Seawater

PubMed Central

Matsunaga, Shigeki

2015-01-01

A molecular dynamics simulation has been performed on the greenhouse gases carbon dioxide and methane dissolved in a sodium chloride aqueous solution, as a simple model of seawater. A carbon dioxide molecule is also treated as a hydrogen carbonate ion. The structure, coordination number, diffusion coefficient, shear viscosity, specific heat, and thermal conductivity of the solutions have been discussed. The anomalous behaviors of these properties, especially the negative pressure dependence of thermal conductivity, have been observed in the higher-pressure region. PMID:26729101

Effect of Greenhouse Gases Dissolved in Seawater.

PubMed

Matsunaga, Shigeki

2015-12-30

A molecular dynamics simulation has been performed on the greenhouse gases carbon dioxide and methane dissolved in a sodium chloride aqueous solution, as a simple model of seawater. A carbon dioxide molecule is also treated as a hydrogen carbonate ion. The structure, coordination number, diffusion coefficient, shear viscosity, specific heat, and thermal conductivity of the solutions have been discussed. The anomalous behaviors of these properties, especially the negative pressure dependence of thermal conductivity, have been observed in the higher-pressure region.

Rad4 recognition-at-a-distance: Physical basis of conformation-specific anomalous diffusion of DNA repair proteins.

PubMed

Kong, Muwen; Van Houten, Bennett

2017-08-01

Since Robert Brown's first observations of random walks by pollen particles suspended in solution, the concept of diffusion has been subject to countless theoretical and experimental studies in diverse fields from finance and social sciences, to physics and biology. Diffusive transport of macromolecules in cells is intimately linked to essential cellular functions including nutrient uptake, signal transduction, gene expression, as well as DNA replication and repair. Advancement in experimental techniques has allowed precise measurements of these diffusion processes. Mathematical and physical descriptions and computer simulations have been applied to model complicated biological systems in which anomalous diffusion, in addition to simple Brownian motion, was observed. The purpose of this review is to provide an overview of the major physical models of anomalous diffusion and corresponding experimental evidence on the target search problem faced by DNA-binding proteins, with an emphasis on DNA repair proteins and the role of anomalous diffusion in DNA target recognition. Copyright © 2016 Elsevier Ltd. All rights reserved.

Variable-order fractional MSD function to describe the evolution of protein lateral diffusion ability in cell membranes

NASA Astrophysics Data System (ADS)

Yin, Deshun; Qu, Pengfei

2018-02-01

Protein lateral diffusion is considered anomalous in the plasma membrane. And this diffusion is related to membrane microstructure. In order to better describe the property of protein lateral diffusion and find out the inner relationship between protein lateral diffusion and membrane microstructure, this article applies variable-order fractional mean square displacement (f-MSD) function for characterizing the anomalous diffusion. It is found that the variable order can reflect the evolution of diffusion ability. The results of numerical simulation demonstrate variable-order f-MSD function can predict the tendency of anomalous diffusion during the process of confined diffusion. It is also noted that protein lateral diffusion ability during the processes of confined and hop diffusion can be split into three parts. In addition, the comparative analyses reveal that the variable order is related to the confinement-domain size and microstructure of compartment boundary too.

General pulsed-field gradient signal attenuation expression based on a fractional integral modified-Bloch equation

NASA Astrophysics Data System (ADS)

Lin, Guoxing

2018-10-01

Anomalous diffusion has been investigated in many polymer and biological systems. The analysis of PFG anomalous diffusion relies on the ability to obtain the signal attenuation expression. However, the general analytical PFG signal attenuation expression based on the fractional derivative has not been previously reported. Additionally, the reported modified-Bloch equations for PFG anomalous diffusion in the literature yielded different results due to their different forms. Here, a new integral type modified-Bloch equation based on the fractional derivative for PFG anomalous diffusion is proposed, which is significantly different from the conventional differential type modified-Bloch equation. The merit of the integral type modified-Bloch equation is that the original properties of the contributions from linear or nonlinear processes remain unchanged at the instant of the combination. From the modified-Bloch equation, the general solutions are derived, which includes the finite gradient pulse width (FGPW) effect. The numerical evaluation of these PFG signal attenuation expressions can be obtained either by the Adomian decomposition, or a direct integration method that is fast and practicable. The theoretical results agree with the continuous-time random walk (CTRW) simulations performed in this paper. Additionally, the relaxation effect in PFG anomalous diffusion is found to be different from that in PFG normal diffusion. The new modified-Bloch equations and their solutions provide a fundamental tool to analyze PFG anomalous diffusion in nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI).

Numerical schemes for anomalous diffusion of single-phase fluids in porous media

NASA Astrophysics Data System (ADS)

Awotunde, Abeeb A.; Ghanam, Ryad A.; Al-Homidan, Suliman S.; Tatar, Nasser-eddine

2016-10-01

Simulation of fluid flow in porous media is an indispensable part of oil and gas reservoir management. Accurate prediction of reservoir performance and profitability of investment rely on our ability to model the flow behavior of reservoir fluids. Over the years, numerical reservoir simulation models have been based mainly on solutions to the normal diffusion of fluids in the porous reservoir. Recently, however, it has been documented that fluid flow in porous media does not always follow strictly the normal diffusion process. Small deviations from normal diffusion, called anomalous diffusion, have been reported in some experimental studies. Such deviations can be caused by different factors such as the viscous state of the fluid, the fractal nature of the porous media and the pressure pulse in the system. In this work, we present explicit and implicit numerical solutions to the anomalous diffusion of single-phase fluids in heterogeneous reservoirs. An analytical solution is used to validate the numerical solution to the simple homogeneous case. The conventional wellbore flow model is modified to account for anomalous behavior. Example applications are used to show the behavior of wellbore and wellblock pressures during the single-phase anomalous flow of fluids in the reservoirs considered.

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

de Miguel, E.; Rull, L.F.; Gubbins, K.E.

Using molecular-dynamics computer simulation, we study the dynamical behavior of the isotropic and nematic phases of highly anisotropic molecular fluids. The interactions are modeled by means of the Gay-Berne potential with anisotropy parameters {kappa}=3 and {kappa}{prime}=5. The linear-velocity autocorrelation function shows no evidence of a negative region in the isotropic phase, even at the higher densities considered. The self-diffusion coefficient parallel to the molecular axis shows an anomalous increase with density as the system enters the nematic region. This enhancement in parallel diffusion is also observed in the isotropic side of the transition as a precursor effect. The molecular reorientationmore » is discussed in the light of different theoretical models. The Debye diffusion model appears to explain the reorientational mechanism in the nematic phase. None of the models gives a satisfactory account of the reorientation process in the isotropic phase.« less

Apparent Anomalous Diffusion in the Cytoplasm of Human Cells: The Effect of Probes' Polydispersity.

PubMed

Kalwarczyk, Tomasz; Kwapiszewska, Karina; Szczepanski, Krzysztof; Sozanski, Krzysztof; Szymanski, Jedrzej; Michalska, Bernadeta; Patalas-Krawczyk, Paulina; Duszynski, Jerzy; Holyst, Robert

2017-10-26

This work, based on in vivo and in vitro measurements, as well as in silico simulations, provides a consistent analysis of diffusion of polydisperse nanoparticles in the cytoplasm of living cells. Using the example of fluorescence correlation spectroscopy (FCS), we show the effect of polydispersity of probes on the experimental results. Although individual probes undergo normal diffusion, in the ensemble of probes, an effective broadening of the distribution of diffusion times occurs-similar to anomalous diffusion. We introduced fluorescently labeled dextrans into the cytoplasm of HeLa cells and found that cytoplasmic hydrodynamic drag, exponentially dependent on probe size, extraordinarily broadens the distribution of diffusion times across the focal volume. As a result, the in vivo FCS data were effectively fitted with the anomalous subdiffusion model while for a monodisperse probe the normal diffusion model was most suitable. Diffusion time obtained from the anomalous diffusion model corresponds to a probe whose size is determined by the weight-average molecular weight of the polymer. The apparent anomaly exponent decreases with increasing polydispersity of the probes. Our results and methodology can be applied in intracellular studies of the mobility of nanoparticles, polymers, or oligomerizing proteins.

Wanted: A Positive Control for Anomalous Subdiffusion

PubMed Central

Saxton, Michael J.

2012-01-01

Anomalous subdiffusion in cells and model systems is an active area of research. The main questions are whether diffusion is anomalous or normal, and if it is anomalous, its mechanism. The subject is controversial, especially the hypothesis that crowding causes anomalous subdiffusion. Anomalous subdiffusion measurements would be strengthened by an experimental standard, particularly one able to cross-calibrate the different types of measurements. Criteria for a calibration standard are proposed. First, diffusion must be anomalous over the length and timescales of the different measurements. The length-scale is fundamental; the time scale can be adjusted through the viscosity of the medium. Second, the standard must be theoretically well understood, with a known anomalous subdiffusion exponent, ideally readily tunable. Third, the standard must be simple, reproducible, and independently characterizable (by, for example, electron microscopy for nanostructures). Candidate experimental standards are evaluated, including obstructed lipid bilayers; aqueous systems obstructed by nanopillars; a continuum percolation system in which a prescribed fraction of randomly chosen obstacles in a regular array is ablated; single-file diffusion in pores; transient anomalous subdiffusion due to binding of particles in arrays such as transcription factors in randomized DNA arrays; and computer-generated physical trajectories. PMID:23260043

Analyzing signal attenuation in PFG anomalous diffusion via a non-Gaussian phase distribution approximation approach by fractional derivatives.

PubMed

Lin, Guoxing

2016-11-21

Anomalous diffusion exists widely in polymer and biological systems. Pulsed-field gradient (PFG) techniques have been increasingly used to study anomalous diffusion in nuclear magnetic resonance and magnetic resonance imaging. However, the interpretation of PFG anomalous diffusion is complicated. Moreover, the exact signal attenuation expression including the finite gradient pulse width effect has not been obtained based on fractional derivatives for PFG anomalous diffusion. In this paper, a new method, a Mainardi-Luchko-Pagnini (MLP) phase distribution approximation, is proposed to describe PFG fractional diffusion. MLP phase distribution is a non-Gaussian phase distribution. From the fractional derivative model, both the probability density function (PDF) of a spin in real space and the PDF of the spin's accumulating phase shift in virtual phase space are MLP distributions. The MLP phase distribution leads to a Mittag-Leffler function based PFG signal attenuation, which differs significantly from the exponential attenuation for normal diffusion and from the stretched exponential attenuation for fractional diffusion based on the fractal derivative model. A complete signal attenuation expression E α (-D f b α,β * ) including the finite gradient pulse width effect was obtained and it can handle all three types of PFG fractional diffusions. The result was also extended in a straightforward way to give a signal attenuation expression of fractional diffusion in PFG intramolecular multiple quantum coherence experiments, which has an n β dependence upon the order of coherence which is different from the familiar n 2 dependence in normal diffusion. The results obtained in this study are in agreement with the results from the literature. The results in this paper provide a set of new, convenient approximation formalisms to interpret complex PFG fractional diffusion experiments.

Facilitated Diffusion of Transcription Factor Proteins with Anomalous Bulk Diffusion.

PubMed

Liu, Lin; Cherstvy, Andrey G; Metzler, Ralf

2017-02-16

What are the physical laws of the diffusive search of proteins for their specific binding sites on DNA in the presence of the macromolecular crowding in cells? We performed extensive computer simulations to elucidate the protein target search on DNA. The novel feature is the viscoelastic non-Brownian protein bulk diffusion recently observed experimentally. We examine the influence of the protein-DNA binding affinity and the anomalous diffusion exponent on the target search time. In all cases an optimal search time is found. The relative contribution of intermittent three-dimensional bulk diffusion and one-dimensional sliding of proteins along the DNA is quantified. Our results are discussed in the light of recent single molecule tracking experiments, aiming at a better understanding of the influence of anomalous kinetics of proteins on the facilitated diffusion mechanism.

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.

Diffusion within the cytoplasm: a mesoscale model of interacting macromolecules.

PubMed

Trovato, Fabio; Tozzini, Valentina

2014-12-02

Recent experiments carried out in the dense cytoplasm of living cells have highlighted the importance of proteome composition and nonspecific intermolecular interactions in regulating macromolecule diffusion and organization. Despite this, the dependence of diffusion-interaction on physicochemical properties such as the degree of poly-dispersity and the balance between steric repulsion and nonspecific attraction among macromolecules was not systematically addressed. In this work, we study the problem of diffusion-interaction in the bacterial cytoplasm, combining theory and experimental data to build a minimal coarse-grained representation of the cytoplasm, which also includes, for the first time to our knowledge, the nucleoid. With stochastic molecular-dynamics simulations of a virtual cytoplasm we are able to track the single biomolecule motion, sizing from 3 to 80 nm, on submillisecond-long trajectories. We demonstrate that the size dependence of diffusion coefficients, anomalous exponents, and the effective viscosity experienced by biomolecules in the cytoplasm is fine-tuned by the intermolecular interactions. Accounting only for excluded volume in these potentials gives a weaker size-dependence than that expected from experimental data. On the contrary, adding nonspecific attraction in the range of 1-10 thermal energy units produces a stronger variation of the transport properties at growing biopolymer sizes. Normal and anomalous diffusive regimes emerge straightforwardly from the combination of high macromolecular concentration, poly-dispersity, stochasticity, and weak nonspecific interactions. As a result, small biopolymers experience a viscous cytoplasm, while the motion of big ones is jammed because the entanglements produced by the network of interactions and the entropic effects caused by poly-dispersity are stronger. Copyright © 2014 Biophysical Society. Published by Elsevier Inc. All rights reserved.

Anomalous thermoelectric phenomena in lattice models of multi-Weyl semimetals

NASA Astrophysics Data System (ADS)

Gorbar, E. V.; Miransky, V. A.; Shovkovy, I. A.; Sukhachov, P. O.

2017-10-01

The thermoelectric transport coefficients are calculated in a generic lattice model of multi-Weyl semimetals with a broken time-reversal symmetry by using the Kubo's linear response theory. The contributions connected with the Berry curvature-induced electromagnetic orbital and heat magnetizations are systematically taken into account. It is shown that the thermoelectric transport is profoundly affected by the nontrivial topology of multi-Weyl semimetals. In particular, the calculation reveals a number of thermal coefficients of the topological origin which describe the anomalous Nernst and thermal Hall effects in the absence of background magnetic fields. Similarly to the anomalous Hall effect, all anomalous thermoelectric coefficients are proportional to the integer topological charge of the Weyl nodes. The dependence of the thermoelectric coefficients on the chemical potential and temperature is also studied.

Anomalous Transport of Cosmic Rays in a Nonlinear Diffusion Model

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

Litvinenko, Yuri E.; Fichtner, Horst; Walter, Dominik

2017-05-20

We investigate analytically and numerically the transport of cosmic rays following their escape from a shock or another localized acceleration site. Observed cosmic-ray distributions in the vicinity of heliospheric and astrophysical shocks imply that anomalous, superdiffusive transport plays a role in the evolution of the energetic particles. Several authors have quantitatively described the anomalous diffusion scalings, implied by the data, by solutions of a formal transport equation with fractional derivatives. Yet the physical basis of the fractional diffusion model remains uncertain. We explore an alternative model of the cosmic-ray transport: a nonlinear diffusion equation that follows from a self-consistent treatmentmore » of the resonantly interacting cosmic-ray particles and their self-generated turbulence. The nonlinear model naturally leads to superdiffusive scalings. In the presence of convection, the model yields a power-law dependence of the particle density on the distance upstream of the shock. Although the results do not refute the use of a fractional advection–diffusion equation, they indicate a viable alternative to explain the anomalous diffusion scalings of cosmic-ray particles.« less

Anomalous current in diffusive ferromagnetic Josephson junctions

NASA Astrophysics Data System (ADS)

Silaev, M. A.; Tokatly, I. V.; Bergeret, F. S.

2017-05-01

We demonstrate that in diffusive superconductor/ferromagnet/superconductor (S/F/S) junctions a finite, anomalous Josephson current can flow even at zero phase difference between the S electrodes. The conditions for the observation of this effect are noncoplanar magnetization distribution and a broken magnetization inversion symmetry of the superconducting current. The latter symmetry is intrinsic for the widely used quasiclassical approximation and prevented previous works based on this approximation from obtaining the Josephson anomalous current. We show that this symmetry can be removed by introducing spin-dependent boundary conditions for the quasiclassical equations at the superconducting/ferromagnet interfaces in diffusive systems. Using this recipe, we consider generic multilayer magnetic systems and determine the ideal experimental conditions in order to maximize the anomalous current.

Parsing anomalous versus normal diffusive behavior of bedload sediment particles

USGS Publications Warehouse

Fathel, Siobhan; Furbish, David; Schmeeckle, Mark

2016-01-01

Bedload sediment transport is the basic physical ingredient of river evolution. Formulae exist for estimating transport rates, but the diffusive contribution to the sediment flux, and the associated spreading rate of tracer particles, are not clearly understood. The start-and-stop motions of sediment particles transported as bedload on a streambed mimic aspects of the Einstein–Smoluchowski description of the random-walk motions of Brownian particles. Using this touchstone description, recent work suggests the presence of anomalous diffusion, where the particle spreading rate differs from the linear dependence with time of Brownian behavior. We demonstrate that conventional measures of particle spreading reveal different attributes of bedload particle behavior depending on details of the calculation. When we view particle motions over start-and-stop timescales obtained from high-speed (250 Hz) imaging of coarse-sand particles, high-resolution measurements reveal ballistic-like behavior at the shortest (10−2 s) timescale, followed by apparent anomalous behavior due to correlated random walks in transition to normal diffusion (>10−1 s) – similar to Brownian particle behavior but involving distinctly different physics. However, when treated as a ‘virtual plume’ over this timescale range, particles exhibit inhomogeneous diffusive behavior because both the mean and the variance of particle travel distances increase nonlinearly with increasing travel times, a behavior that is unrelated to anomalous diffusion or to Brownian-like behavior. Our results indicate that care is needed in suggesting anomalous behavior when appealing to conventional measures of diffusion formulated for ideal particle systems.

Weakly anomalous diffusion with non-Gaussian propagators

NASA Astrophysics Data System (ADS)

Cressoni, J. C.; Viswanathan, G. M.; Ferreira, A. S.; da Silva, M. A. A.

2012-08-01

A poorly understood phenomenon seen in complex systems is diffusion characterized by Hurst exponent H≈1/2 but with non-Gaussian statistics. Motivated by such empirical findings, we report an exact analytical solution for a non-Markovian random walk model that gives rise to weakly anomalous diffusion with H=1/2 but with a non-Gaussian propagator.

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

Anomalous transport from holography. Part I

NASA Astrophysics Data System (ADS)

Bu, Yanyan; Lublinsky, Michael; Sharon, Amir

2016-11-01

We revisit the transport properties induced by the chiral anomaly in a charged plasma holographically dual to anomalous U(1) V ×U(1) A Maxwell theory in Schwarzschild-AdS5. Off-shell constitutive relations for vector and axial currents are derived using various approximations generalising most of known in the literature anomaly-induced phenomena and revealing some new ones. In a weak external field approximation, the constitutive relations have all-order derivatives resummed into six momenta-dependent transport co-efficient functions: the diffusion, the electric/magnetic conductivity, and three anomaly induced functions. The latter generalise the chiral magnetic and chiral separation effects. Nonlinear transport is studied assuming presence of constant background external fields. The chiral magnetic effect, including all order nonlinearity in magnetic field, is proven to be exact when the magnetic field is the only external field that is turned on. Non-linear corrections to the constitutive relations due to electric and axial external fields are computed.

Concentration-Encoded Subdiffusive Molecular Communication: Theory, Channel Characteristics, and Optimum Signal Detection.

PubMed

Mahfuz, Mohammad Upal; Makrakis, Dimitrios; Mouftah, Hussein T

2016-09-01

Unlike normal diffusion, in anomalous diffusion, the movement of a molecule is described by the correlated random walk model where the mean square displacement of a molecule depends on the power law of time. In molecular communication (MC), there are many scenarios when the propagation of molecules cannot be described by normal diffusion process, where anomalous diffusion is a better fit. In this paper, the effects of anomalous subdiffusion on concentration-encoded molecular communication (CEMC) are investigated. Although classical (i.e., normal) diffusion is a widely-used model of diffusion in molecular communication (MC) research, anomalous subdiffusion is quite common in biological media involving bio-nanomachines, yet inadequately addressed as a research issue so far. Using the fractional diffusion approach, the molecular propagation effects in the case of pure subdiffusion occurring in an unbounded three-dimensional propagation medium have been shown in detail in terms of temporal dispersion parameters of the impulse response of the subdiffusive channel. Correspondingly, the bit error rate (BER) performance of a CEMC system is investigated with sampling-based (SD) and strength (i.e., energy)-based (ED) signal detection methods. It is found that anomalous subdiffusion has distinctive time-dispersive properties that play a vital role in accurately designing a subdiffusive CEMC system. Unlike normal diffusion, to detect information symbols in subdiffusive CEMC, a receiver requires larger memory size to operate correctly and hence a more complex structure. An in-depth analysis has been made on the performances of SD and ED optimum receiver models under diffusion noise and intersymbol interference (ISI) scenarios when communication range, transmission data rate, and memory size vary. In subdiffusive CEMC, the SD method.

Anomalous Diffusion Measured by a Twice-Refocused Spin Echo Pulse Sequence: Analysis Using Fractional Order Calculus

PubMed Central

2011-01-01

Purpose To theoretically develop and experimentally validate a formulism based on a fractional order calculus (FC) diffusion model to characterize anomalous diffusion in brain tissues measured with a twice-refocused spin-echo (TRSE) pulse sequence. Materials and Methods The FC diffusion model is the fractional order generalization of the Bloch-Torrey equation. Using this model, an analytical expression was derived to describe the diffusion-induced signal attenuation in a TRSE pulse sequence. To experimentally validate this expression, a set of diffusion-weighted (DW) images was acquired at 3 Tesla from healthy human brains using a TRSE sequence with twelve b-values ranging from 0 to 2,600 s/mm2. For comparison, DW images were also acquired using a Stejskal-Tanner diffusion gradient in a single-shot spin-echo echo planar sequence. For both datasets, a Levenberg-Marquardt fitting algorithm was used to extract three parameters: diffusion coefficient D, fractional order derivative in space β, and a spatial parameter μ (in units of μm). Using adjusted R-squared values and standard deviations, D, β and μ values and the goodness-of-fit in three specific regions of interest (ROI) in white matter, gray matter, and cerebrospinal fluid were evaluated for each of the two datasets. In addition, spatially resolved parametric maps were assessed qualitatively. Results The analytical expression for the TRSE sequence, derived from the FC diffusion model, accurately characterized the diffusion-induced signal loss in brain tissues at high b-values. In the selected ROIs, the goodness-of-fit and standard deviations for the TRSE dataset were comparable with the results obtained from the Stejskal-Tanner dataset, demonstrating the robustness of the FC model across multiple data acquisition strategies. Qualitatively, the D, β, and μ maps from the TRSE dataset exhibited fewer artifacts, reflecting the improved immunity to eddy currents. Conclusion The diffusion-induced signal attenuation in a TRSE pulse sequence can be described by an FC diffusion model at high b-values. This model performs equally well for data acquired from the human brain tissues with a TRSE pulse sequence or a conventional Stejskal-Tanner sequence. PMID:21509877

Anomalous diffusion measured by a twice-refocused spin echo pulse sequence: analysis using fractional order calculus.

PubMed

Gao, Qing; Srinivasan, Girish; Magin, Richard L; Zhou, Xiaohong Joe

2011-05-01

To theoretically develop and experimentally validate a formulism based on a fractional order calculus (FC) diffusion model to characterize anomalous diffusion in brain tissues measured with a twice-refocused spin-echo (TRSE) pulse sequence. The FC diffusion model is the fractional order generalization of the Bloch-Torrey equation. Using this model, an analytical expression was derived to describe the diffusion-induced signal attenuation in a TRSE pulse sequence. To experimentally validate this expression, a set of diffusion-weighted (DW) images was acquired at 3 Tesla from healthy human brains using a TRSE sequence with twelve b-values ranging from 0 to 2600 s/mm(2). For comparison, DW images were also acquired using a Stejskal-Tanner diffusion gradient in a single-shot spin-echo echo planar sequence. For both datasets, a Levenberg-Marquardt fitting algorithm was used to extract three parameters: diffusion coefficient D, fractional order derivative in space β, and a spatial parameter μ (in units of μm). Using adjusted R-squared values and standard deviations, D, β, and μ values and the goodness-of-fit in three specific regions of interest (ROIs) in white matter, gray matter, and cerebrospinal fluid, respectively, were evaluated for each of the two datasets. In addition, spatially resolved parametric maps were assessed qualitatively. The analytical expression for the TRSE sequence, derived from the FC diffusion model, accurately characterized the diffusion-induced signal loss in brain tissues at high b-values. In the selected ROIs, the goodness-of-fit and standard deviations for the TRSE dataset were comparable with the results obtained from the Stejskal-Tanner dataset, demonstrating the robustness of the FC model across multiple data acquisition strategies. Qualitatively, the D, β, and μ maps from the TRSE dataset exhibited fewer artifacts, reflecting the improved immunity to eddy currents. The diffusion-induced signal attenuation in a TRSE pulse sequence can be described by an FC diffusion model at high b-values. This model performs equally well for data acquired from the human brain tissues with a TRSE pulse sequence or a conventional Stejskal-Tanner sequence. Copyright © 2011 Wiley-Liss, Inc.

Mechanisms underlying anomalous diffusion in the plasma membrane.

PubMed

Krapf, Diego

2015-01-01

The plasma membrane is a complex fluid where lipids and proteins undergo diffusive motion critical to biochemical reactions. Through quantitative imaging analyses such as single-particle tracking, it is observed that diffusion in the cell membrane is usually anomalous in the sense that the mean squared displacement is not linear with time. This chapter describes the different models that are employed to describe anomalous diffusion, paying special attention to the experimental evidence that supports these models in the plasma membrane. We review models based on anticorrelated displacements, such as fractional Brownian motion and obstructed diffusion, and nonstationary models such as continuous time random walks. We also emphasize evidence for the formation of distinct compartments that transiently form on the cell surface. Finally, we overview heterogeneous diffusion processes in the plasma membrane, which have recently attracted considerable interest. Copyright © 2015. Published by Elsevier Inc.

Fractional cable equation for general geometry: A model of axons with swellings and anomalous diffusion.

PubMed

López-Sánchez, Erick J; Romero, Juan M; Yépez-Martínez, Huitzilin

2017-09-01

Different experimental studies have reported anomalous diffusion in brain tissues and notably this anomalous diffusion is expressed through fractional derivatives. Axons are important to understand neurodegenerative diseases such as multiple sclerosis, Alzheimer's disease, and Parkinson's disease. Indeed, abnormal accumulation of proteins and organelles in axons is a hallmark of these diseases. The diffusion in the axons can become anomalous as a result of this abnormality. In this case the voltage propagation in axons is affected. Another hallmark of different neurodegenerative diseases is given by discrete swellings along the axon. In order to model the voltage propagation in axons with anomalous diffusion and swellings, in this paper we propose a fractional cable equation for a general geometry. This generalized equation depends on fractional parameters and geometric quantities such as the curvature and torsion of the cable. For a cable with a constant radius we show that the voltage decreases when the fractional effect increases. In cables with swellings we find that when the fractional effect or the swelling radius increases, the voltage decreases. Similar behavior is obtained when the number of swellings and the fractional effect increase. Moreover, we find that when the radius swelling (or the number of swellings) and the fractional effect increase at the same time, the voltage dramatically decreases.

Fractional cable equation for general geometry: A model of axons with swellings and anomalous diffusion

NASA Astrophysics Data System (ADS)

López-Sánchez, Erick J.; Romero, Juan M.; Yépez-Martínez, Huitzilin

2017-09-01

Different experimental studies have reported anomalous diffusion in brain tissues and notably this anomalous diffusion is expressed through fractional derivatives. Axons are important to understand neurodegenerative diseases such as multiple sclerosis, Alzheimer's disease, and Parkinson's disease. Indeed, abnormal accumulation of proteins and organelles in axons is a hallmark of these diseases. The diffusion in the axons can become anomalous as a result of this abnormality. In this case the voltage propagation in axons is affected. Another hallmark of different neurodegenerative diseases is given by discrete swellings along the axon. In order to model the voltage propagation in axons with anomalous diffusion and swellings, in this paper we propose a fractional cable equation for a general geometry. This generalized equation depends on fractional parameters and geometric quantities such as the curvature and torsion of the cable. For a cable with a constant radius we show that the voltage decreases when the fractional effect increases. In cables with swellings we find that when the fractional effect or the swelling radius increases, the voltage decreases. Similar behavior is obtained when the number of swellings and the fractional effect increase. Moreover, we find that when the radius swelling (or the number of swellings) and the fractional effect increase at the same time, the voltage dramatically decreases.

Diffusion of active chiral particles

NASA Astrophysics Data System (ADS)

Sevilla, Francisco J.

2016-12-01

The diffusion of chiral active Brownian particles in three-dimensional space is studied analytically, by consideration of the corresponding Fokker-Planck equation for the probability density of finding a particle at position x and moving along the direction v ̂ at time t , and numerically, by the use of Langevin dynamics simulations. The analysis is focused on the marginal probability density of finding a particle at a given location and at a given time (independently of its direction of motion), which is found from an infinite hierarchy of differential-recurrence relations for the coefficients that appear in the multipole expansion of the probability distribution, which contains the whole kinematic information. This approach allows the explicit calculation of the time dependence of the mean-squared displacement and the time dependence of the kurtosis of the marginal probability distribution, quantities from which the effective diffusion coefficient and the "shape" of the positions distribution are examined. Oscillations between two characteristic values were found in the time evolution of the kurtosis, namely, between the value that corresponds to a Gaussian and the one that corresponds to a distribution of spherical shell shape. In the case of an ensemble of particles, each one rotating around a uniformly distributed random axis, evidence is found of the so-called effect "anomalous, yet Brownian, diffusion," for which particles follow a non-Gaussian distribution for the positions yet the mean-squared displacement is a linear function of time.

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.

Fractionation of lithium isotopes in magmatic systems as a natural consequence of cooling

NASA Astrophysics Data System (ADS)

Gallagher, Kerry; Elliott, Tim

2009-02-01

High-temperature, diffusive fractionation has been invoked to account for striking Li isotopic variability recently observed within individual phenocrysts and xenolith minerals. It has been argued that chemical potential gradients required to drive such diffusion arise from changes in Li partitioning between coexisting phases during cooling. If so, Li isotopic zoning should be a common occurrence but the role of temperature-dependent partition coefficients in generating Li isotopic variability remains to be tested in a quantitative manner. Here we consider a basic scenario of a phenocryst in a cooling lava, using simple parameterisations of the temperature dependence of Li partitioning and diffusivity in clinopyroxene. Our model initially produces an asymmetric isotope profile across the crystal with a δ7Li minimum that remains close to the edge of a crystal. Such a distinctive shape mimics Li isotopic profiles documented in some olivine and clinopyroxene phenocrysts, which have isotopically normal cores but anomalously light rims. The temperature dependence of both the diffusivity and the partition coefficient of Li are key factors in generating this form of diffusion profile. Continued diffusion leads to an inversion in the sense of isotopic change between core and rim and results in the whole phenocryst attaining markedly light isotopic values. Our calculations show that significant Li isotopic zoning can occur as a natural consequence of cooling magmatic systems. Crystals that have experienced more complex thermal histories (e.g. re-entrained cumulates versus true phenocrysts) will therefore exhibit contrasting isotopic profiles and, as such, these data may be useful for tracing sub-volcanic processes.

Tissue microstructure features derived from anomalous diffusion measurements in magnetic resonance imaging.

PubMed

Yu, Qiang; Reutens, David; O'Brien, Kieran; Vegh, Viktor

2017-02-01

Tissue microstructure features, namely axon radius and volume fraction, provide important information on the function of white matter pathways. These parameters vary on the scale much smaller than imaging voxels (microscale) yet influence the magnetic resonance imaging diffusion signal at the image voxel scale (macroscale) in an anomalous manner. Researchers have already mapped anomalous diffusion parameters from magnetic resonance imaging data, but macroscopic variations have not been related to microscale influences. With the aid of a tissue model, we aimed to connect anomalous diffusion parameters to axon radius and volume fraction using diffusion-weighted magnetic resonance imaging measurements. An ex vivo human brain experiment was performed to directly validate axon radius and volume fraction measurements in the human brain. These findings were validated using electron microscopy. Additionally, we performed an in vivo study on nine healthy participants to map axon radius and volume fraction along different regions of the corpus callosum projecting into various cortical areas identified using tractography. We found a clear relationship between anomalous diffusion parameters and axon radius and volume fraction. We were also able to map accurately the trend in axon radius along the corpus callosum, and in vivo findings resembled the low-high-low-high behaviour in axon radius demonstrated previously. Axon radius and volume fraction measurements can potentially be used in brain connectivity studies and to understand the implications of white matter structure in brain diseases and disorders. Hum Brain Mapp 38:1068-1081, 2017. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.

Neoclassical diffusion at low L-shel

NASA Astrophysics Data System (ADS)

Cunningham, G.; Ripoll, J. F.; Loridan, V.; Schulz, M.

2017-12-01

At very low L-shell, the lifetime of MeV electrons is dominated by pitch-angle scattering due to Coulomb collisions with background neutrals and ions. Walt's evaluation of this lifetime explained Van Allen's observations of the decay of the radiation belts in the early 1960's, for L<1.25 but Imhof et al showed that the apparent lifetime of >500 keV electrons for L=[1.15,1.21] was much greater than predicted by Walt's model when the decay was observed over 3 years rather than just a few months. Imhof et al argued that inward radial diffusion from larger L would be a source of electrons at low L, thus increasing the apparent lifetimes that were observed, but did not speculate on the cause of such diffusion across L. Newkirk and Walt estimated the radial diffusion coefficient that would be needed to explain the apparent lifetimes observed by Imhof et al. The radial diffusion coefficients they inferred dropped sharply as L increased, contrasting with the radial diffusion coefficients that had been recently developed by Falthammar [1965], which increase as a power law in L. Newkirk and Walt noted Falthammar's speculation that pitch-angle diffusion caused by Coulomb scattering, when coupled to drift-shell splitting associated with non-dipolar terms in the near-Earth geomagnetic field, might be the physical basis for the radial diffusion, but they did not attempt to quantify this effect. Roederer et al demonstrated that Coulomb scattering plus drift-shell splitting could explain the Newkirk and Walt results but they did not perform an exhaustive study. In the field of magnetically confined fusion, the movement of charged particles to different drift-shells caused by the combination of collisions and drift-shell splitting is labeled `neoclassical' diffusion. By contrast, `anomalous' diffusion results from pitch-angle diffusion caused by wave turbulence combined with drift-shell splitting, an effect recently studied by O'Brien in the outer radiation belt. We have constructed a comprehensive model of neoclassical diffusion at low L as a function of pitch-angle, energy and L-shell, and find that we quantitatively reproduce the results in Newkirk and Walt and Imhof et al, conclusively demonstrating that neoclassical diffusion is an important effect for energetic electrons in the deep inner belt.

Anomalous fast diffusion in Cu-NiFe nanolaminates.

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

Jankowski, Alan F.

2017-09-01

For this work, the decomposition of the one-dimensional composition wave in Cu-NiFe nanolaminate structures is examined using x-ray diffraction to assess the kinetics of phase decomposition. The anomalously high diffusivity value found for long-term aging at room temperature is attributed to the inherent nanostructure that features paths for short-circuit diffusion in nanolaminates as attributed to interlayer grain boundaries.

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.

Molecular dynamics of liquid SiO2 under high pressure

NASA Technical Reports Server (NTRS)

Rustad, James R.; Yuen, David A.; Spera, Frank J.

1990-01-01

The molecular dynamics of pure SiO2 liquids was investigated up to pressures of 20 GPa at 4000 K using 252, 498, 864, and 1371 particles. The results obtained suggest that the pressure-induced maxima in the self-diffusion coefficients of both oxygen and silicon are dependent on the system size. In the case of larger systems, the maximum decreases and shifts to lower pressures. Changes in the velocity autocorrelation function with increasing pressure are described. The populations of anomalously coordinated silicon and oxygen are then discussed as a function of pressure and system size.

Anomalous diffusion in a dynamical optical lattice

NASA Astrophysics Data System (ADS)

Zheng, Wei; Cooper, Nigel R.

2018-02-01

Motivated by experimental progress in strongly coupled atom-photon systems in optical cavities, we study theoretically the quantum dynamics of atoms coupled to a one-dimensional dynamical optical lattice. The dynamical lattice is chosen to have a period that is incommensurate with that of an underlying static lattice, leading to a dynamical version of the Aubry-André model which can cause localization of single-particle wave functions. We show that atomic wave packets in this dynamical lattice generically spread via anomalous diffusion, which can be tuned between superdiffusive and subdiffusive regimes. This anomalous diffusion arises from an interplay between Anderson localization and quantum fluctuations of the cavity field.

Diffusive processes in a stochastic magnetic field

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

Wang, H.; Vlad, M.; Vanden Eijnden, E.

1995-05-01

The statistical representation of a fluctuating (stochastic) magnetic field configuration is studied in detail. The Eulerian correlation functions of the magnetic field are determined, taking into account all geometrical constraints: these objects form a nondiagonal matrix. The Lagrangian correlations, within the reasonable Corrsin approximation, are reduced to a single scalar function, determined by an integral equation. The mean square perpendicular deviation of a geometrical point moving along a perturbed field line is determined by a nonlinear second-order differential equation. The separation of neighboring field lines in a stochastic magnetic field is studied. We find exponentiation lengths of both signs describing,more » in particular, a decay (on the average) of any initial anisotropy. The vanishing sum of these exponentiation lengths ensures the existence of an invariant which was overlooked in previous works. Next, the separation of a particle`s trajectory from the magnetic field line to which it was initially attached is studied by a similar method. Here too an initial phase of exponential separation appears. Assuming the existence of a final diffusive phase, anomalous diffusion coefficients are found for both weakly and strongly collisional limits. The latter is identical to the well known Rechester-Rosenbluth coefficient, which is obtained here by a more quantitative (though not entirely deductive) treatment than in earlier works.« less

Diffusion of a particle in the spatially correlated exponential random energy landscape: Transition from normal to anomalous diffusion.

PubMed

Novikov, S V

2018-01-14

Diffusive transport of a particle in a spatially correlated random energy landscape having exponential density of states has been considered. We exactly calculate the diffusivity in the nondispersive quasi-equilibrium transport regime for the 1D transport model and found that for slow decaying correlation functions the diffusivity becomes singular at some particular temperature higher than the temperature of the transition to the true non-equilibrium dispersive transport regime. It means that the diffusion becomes anomalous and does not follow the usual ∝ t 1/2 law. In such situation, the fully developed non-equilibrium regime emerges in two stages: first, at some temperature there is the transition from the normal to anomalous diffusion, and then at lower temperature the average velocity for the infinite medium goes to zero, thus indicating the development of the true dispersive regime. Validity of the Einstein relation is discussed for the situation where the diffusivity does exist. We provide also some arguments in favor of conservation of the major features of the new transition scenario in higher dimensions.

Nonergodic property of the space-time coupled CTRW: Dependence on the long-tailed property and correlation

NASA Astrophysics Data System (ADS)

Liu, Jian; Li, Baohe; Chen, Xiaosong

2018-02-01

The space-time coupled continuous time random walk model is a stochastic framework of anomalous diffusion with many applications in physics, geology and biology. In this manuscript the time averaged mean squared displacement and nonergodic property of a space-time coupled continuous time random walk model is studied, which is a prototype of the coupled continuous time random walk presented and researched intensively with various methods. The results in the present manuscript show that the time averaged mean squared displacements increase linearly with lag time which means ergodicity breaking occurs, besides, we find that the diffusion coefficient is intrinsically random which shows both aging and enhancement, the analysis indicates that the either aging or enhancement phenomena are determined by the competition between the correlation exponent γ and the waiting time's long-tailed index α.

Diffuse reflectance of the ocean - The theory of its augmentation by chlorophyll a fluorescence at 685 nm

NASA Technical Reports Server (NTRS)

Gordon, H. R.

1979-01-01

The radiative transfer equation is modified to include the effect of fluorescent substances and solved in the quasi-single scattering approximation for a homogeneous ocean containing fluorescent particles with wavelength independent quantum efficiency and a Gaussian shaped emission line. The results are applied to the in vivo fluorescence of chlorophyll a (in phytoplankton) in the ocean to determine if the observed quantum efficiencies are large enough to explain the enhancement of the ocean's diffuse reflectance near 685 nm in chlorophyll rich waters without resorting to anomalous dispersion. The computations indicate that the required efficiencies are sufficiently low to account completely for the enhanced reflectance. The validity of the theory is further demonstrated by deriving values for the upwelling irradiance attenuation coefficient at 685 nm which are in close agreement with the observations.

Persistent random walk of cells involving anomalous effects and random death

NASA Astrophysics Data System (ADS)

Fedotov, Sergei; Tan, Abby; Zubarev, Andrey

2015-04-01

The purpose of this paper is to implement a random death process into a persistent random walk model which produces sub-ballistic superdiffusion (Lévy walk). We develop a stochastic two-velocity jump model of cell motility for which the switching rate depends upon the time which the cell has spent moving in one direction. It is assumed that the switching rate is a decreasing function of residence (running) time. This assumption leads to the power law for the velocity switching time distribution. This describes the anomalous persistence of cell motility: the longer the cell moves in one direction, the smaller the switching probability to another direction becomes. We derive master equations for the cell densities with the generalized switching terms involving the tempered fractional material derivatives. We show that the random death of cells has an important implication for the transport process through tempering of the superdiffusive process. In the long-time limit we write stationary master equations in terms of exponentially truncated fractional derivatives in which the rate of death plays the role of tempering of a Lévy jump distribution. We find the upper and lower bounds for the stationary profiles corresponding to the ballistic transport and diffusion with the death-rate-dependent diffusion coefficient. Monte Carlo simulations confirm these bounds.

Anomalous current diffusion and improved confinement in the HT-6M tohamak

NASA Astrophysics Data System (ADS)

Gao, X.; Li, J. G.; Wan, Y. X.; Huo, Y. P.; Guo, W. K.; Fan, S. P.; Yu, C. X.; Luo, J. R.; Yin, F. X.; Meng, Y. D.; Zheng, L.; Yin, F.; Lin, B. L.; Zhang, S. Y.; Wang, S. Y.; Lu, H. J.; Liu, S. X.; Tong, X. D.; Ding, L. C.; Wu, Z. Y.; Yin, X. J.; Guo, Q. L.; Gong, X. Z.; Wu, X. C.; Zhao, J. Y.; Xi, J. S.

1994-10-01

Current diffusion was studied during edge ohmic heating (EOH) experiments in the HT-6M tokamak. The EOH power system makes the plasma current linearly ramp up from an initial steady state ( Ip=55kA) to a second steady state ( Ip=60kA) at a fast ramp rate of 12 MA/s. A stable discharge of an improved confinement was observed experimentally in the HT-6M tokamak after the plasma current was ramped to rise rapidly to a second steady state. The plasma current is ramped up much faster than both the classical skin time and neoclassical skin time. Fast current ramp up increases the anomalous current diffusion. The measured values of {β P+l i}/{2} and the soft X-ray sawtooth inversion radius imply the anomalous current penetration. The mechanism of anomalous penetration and improved confinement is discussed.

Anomalous Diffusion Approximation of Risk Processes in Operational Risk of Non-Financial Corporations

NASA Astrophysics Data System (ADS)

Magdziarz, M.; Mista, P.; Weron, A.

2007-05-01

We introduce an approximation of the risk processes by anomalous diffusion. In the paper we consider the case, where the waiting times between successive occurrences of the claims belong to the domain of attraction of alpha -stable distribution. The relationship between the obtained approximation and the celebrated fractional diffusion equation is emphasised. We also establish upper bounds for the ruin probability in the considered model and give some numerical examples.

Fractional Dynamics of Single File Diffusion in Dusty Plasma Ring

NASA Astrophysics Data System (ADS)

Muniandy, S. V.; Chew, W. X.; Asgari, H.; Wong, C. S.; Lim, S. C.

2011-11-01

Single file diffusion (SFD) refers to the constrained motion of particles in quasi-one-dimensional channel such that the particles are unable to pass each other. Possible SFD of charged dust confined in biharmonic annular potential well with screened Coulomb interaction is investigated. Transition from normal diffusion to anomalous sub-diffusion behaviors is observed. Deviation from SFD's mean square displacement scaling behavior of 1/2-exponent may occur in strongly interacting systems. A phenomenological model based on fractional Langevin equation is proposed to account for the anomalous SFD behavior in dusty plasma ring.

Tunable anisotropic anomalous Nernst effect and orbital magnetization in Floquet Weyl semimetals

NASA Astrophysics Data System (ADS)

Niu, Zhi Ping; Wu, Xueshi

2018-03-01

Weyl semimetals and nodal line semimetals display a host of novel properties. Floquet Weyl semimetals with tunable Weyl points can be obtained from nodal line semimetals under the circularly polarized off-resonant light. Here we theoretically investigate the anomalous Nernst effect and orbital magnetization in Floquet Weyl semimetals. Due to the anisotropy of the band structure in Floquet Weyl semimetals, highly anisotropic Berry phase mediated anomalous Nernst effect and orbital magnetization in the absence of magnetic field are observed, indicating orientation-dependent applications in the design of nanodevices. The amplitude and sign of anomalous Nernst coefficient and orbital magnetization can be tuned by the light direction, amplitude and polarization. The effect of the chemical potential on anomalous Nernst coefficient and orbital magnetization is also discussed. The light-modulated anomalous Nernst effect and orbital magnetization make Floquet Weyl semimetals potential candidates for thermoelectric devices.

Continuous time anomalous diffusion in a composite medium.

PubMed

Stickler, B A; Schachinger, E

2011-08-01

The one-dimensional continuous time anomalous diffusion in composite media consisting of a finite number of layers in immediate contact is investigated. The diffusion process itself is described with the help of two probability density functions (PDFs), one of which is an arbitrary jump-length PDF, and the other is a long-tailed waiting-time PDF characterized by the waiting-time index β∈(0,1). The former is assumed to be a function of the space coordinate x and the time coordinate t while the latter is a function of x and the time interval. For such an environment a very general form of the diffusion equation is derived which describes the continuous time anomalous diffusion in a composite medium. This result is then specialized to two particular forms of the jump-length PDF, namely the continuous time Lévy flight PDF and the continuous time truncated Lévy flight PDF. In both cases the PDFs are characterized by the Lévy index α∈(0,2) which is regarded to be a function of x and t. It is possible to demonstrate that for particular choices of the indices α and β other equations for anomalous diffusion, well known from the literature, follow immediately. This demonstrates the very general applicability of the derivation and of the resulting fractional differential equation discussed here.

Liquid-liquid phase transition and anomalous diffusion in simulated liquid GeO 2

NASA Astrophysics Data System (ADS)

Hoang, Vo Van; Anh, Nguyen Huynh Tuan; Zung, Hoang

2007-03-01

We perform molecular dynamics (MD) simulation of diffusion in liquid GeO 2 at the temperatures ranged from 3000 to 5000 K and densities ranged from 3.65 to 7.90 g/cm 3. Simulations were done in a model containing 3000 particles with the new interatomic potentials for liquid and amorphous GeO 2, which have weak Coulomb interaction and Morse-type short-range interaction. We found a liquid-liquid phase transition in simulated liquid GeO 2 from a tetrahedral to an octahedral network structure upon compression. Moreover, such phase transition accompanied with an anomalous diffusion of particles in liquid GeO 2 that the diffusion constant of both Ge and O particles strongly increases with increasing density (e.g. with increasing pressure) and it shows a maximum at the density around 4.95 g/cm 3. The possible relation between anomalous diffusion of particles and structural phase transition in the system has been discussed.

Anomalous dimension in a two-species reaction-diffusion system

NASA Astrophysics Data System (ADS)

Vollmayr-Lee, Benjamin; Hanson, Jack; McIsaac, R. Scott; Hellerick, Joshua D.

2018-01-01

We study a two-species reaction-diffusion system with the reactions A+A\\to (0, A) and A+B\\to A , with general diffusion constants D A and D B . Previous studies showed that for dimensions d≤slant 2 the B particle density decays with a nontrivial, universal exponent that includes an anomalous dimension resulting from field renormalization. We demonstrate via renormalization group methods that the scaled B particle correlation function has a distinct anomalous dimension resulting in the asymptotic scaling \\tilde CBB(r, t) ˜ tφf(r/\\sqrt{t}) , where the exponent ϕ results from the renormalization of the square of the field associated with the B particles. We compute this exponent to first order in \

Meaningful interpretation of subdiffusive measurements in living cells (crowded environment) by fluorescence fluctuation microscopy.

PubMed

Baumann, Gerd; Place, Robert F; Földes-Papp, Zeno

2010-08-01

In living cell or its nucleus, the motions of molecules are complicated due to the large crowding and expected heterogeneity of the intracellular environment. Randomness in cellular systems can be either spatial (anomalous) or temporal (heterogeneous). In order to separate both processes, we introduce anomalous random walks on fractals that represented crowded environments. We report the use of numerical simulation and experimental data of single-molecule detection by fluorescence fluctuation microscopy for detecting resolution limits of different mobile fractions in crowded environment of living cells. We simulate the time scale behavior of diffusion times tau(D)(tau) for one component, e.g. the fast mobile fraction, and a second component, e.g. the slow mobile fraction. The less the anomalous exponent alpha the higher the geometric crowding of the underlying structure of motion that is quantified by the ratio of the Hausdorff dimension and the walk exponent d(f)/d(w) and specific for the type of crowding generator used. The simulated diffusion time decreases for smaller values of alpha # 1 but increases for a larger time scale tau at a given value of alpha # 1. The effect of translational anomalous motion is substantially greater if alpha differs much from 1. An alpha value close to 1 contributes little to the time dependence of subdiffusive motions. Thus, quantitative determination of molecular weights from measured diffusion times and apparent diffusion coefficients, respectively, in temporal auto- and crosscorrelation analyses and from time-dependent fluorescence imaging data are difficult to interpret and biased in crowded environments of living cells and their cellular compartments; anomalous dynamics on different time scales tau must be coupled with the quantitative analysis of how experimental parameters change with predictions from simulated subdiffusive dynamics of molecular motions and mechanistic models. We first demonstrate that the crowding exponent alpha also determines the resolution of differences in diffusion times between two components in addition to photophysical parameters well-known for normal motion in dilute solution. The resolution limit between two different kinds of single molecule species is also analyzed under translational anomalous motion with broken ergodicity. We apply our theoretical predictions of diffusion times and lower limits for the time resolution of two components to fluorescence images in human prostate cancer cells transfected with GFP-Ago2 and GFP-Ago1. In order to mimic heterogeneous behavior in crowded environments of living cells, we need to introduce so-called continuous time random walks (CTRW). CTRWs were originally performed on regular lattice. This purely stochastic molecule behavior leads to subdiffusive motion with broken ergodicity in our simulations. For the first time, we are able to quantitatively differentiate between anomalous motion without broken ergodicity and anomalous motion with broken ergodicity in time-dependent fluorescence microscopy data sets of living cells. Since the experimental conditions to measure a selfsame molecule over an extended period of time, at which biology is taken place, in living cells or even in dilute solution are very restrictive, we need to perform the time average over a subpopulation of different single molecules of the same kind. For time averages over subpopulations of single molecules, the temporal auto- and crosscorrelation functions are first found. Knowing the crowding parameter alpha for the cell type and cellular compartment type, respectively, the heterogeneous parameter gamma can be obtained from the measurements in the presence of the interacting reaction partner, e.g. ligand, with the same alpha value. The product alpha x gamma = gamma is not a simple fitting parameter in the temporal auto- and two-color crosscorrelation functions because it is related to the proper physical models of anomalous (spatial) and heterogeneous (temporal) randomness in cellular systems.We have already derived an analytical solution gamma for in the special case of gamma = 3/2. In the case of two-color crosscorrelation or/and two-color fluorescence imaging (co-localization experiments), the second component is also a two-color species gr, for example a different molecular complex with an additional ligand. Here, we first show that plausible biological mechanisms from FCS/ FCCS and fluorescence imaging in living cells are highly questionable without proper quantitative physical models of subdiffusive motion and temporal randomness. At best, such quantitative FCS/ FCCS and fluorescence imaging data are difficult to interpret under crowding and heterogeneous conditions. It is challenging to translate proper physical models of anomalous (spatial) and heterogeneous (temporal) randomness in living cells and their cellular compartments like the nucleus into biological models of the cell biological process under study testable by single-molecule approaches. Otherwise, quantitative FCS/FCCS and fluorescence imaging measurements in living cells are not well described and cannot be interpreted in a meaningful way.

The time-fractional radiative transport equation—Continuous-time random walk, diffusion approximation, and Legendre-polynomial expansion

NASA Astrophysics Data System (ADS)

Machida, Manabu

2017-01-01

We consider the radiative transport equation in which the time derivative is replaced by the Caputo derivative. Such fractional-order derivatives are related to anomalous transport and anomalous diffusion. In this paper we describe how the time-fractional radiative transport equation is obtained from continuous-time random walk and see how the equation is related to the time-fractional diffusion equation in the asymptotic limit. Then we solve the equation with Legendre-polynomial expansion.

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.

Interaction of ring current and radiation belt protons with ducted plasmaspheric hiss. 1: Diffusion coefficients and timescales

NASA Technical Reports Server (NTRS)

Kozyra, J. U.; Rasmussen, C. E.; Miller, R. H.; Lyons, L. R.

1994-01-01

Protons that are convected into the inner magnetosphere in response to enhanced magnetic activity can resonate with ducted plasmaspheric hiss in the outer plasmasphere via an anomalous Doppler-shifted cyclotron resonance. Plasmaspheric hiss is a right-hand-polarized electromagnetic emission that is observed to fill the plasmasphere on a routine basis. When plasmaspheric hiss is confined within field-aligned ducts or guided along density gradients, wave normal angles remain largely below 45 deg. This allows resonant interactions with ions at typical ring current and radiation belt energies to take place. Such field-aligned ducts have been observed both within the plasmasphere and in regions outside of the plasmasphere. Wave intensities are estimated using statistical information from studies of detached plasma regions. Diffusion coefficients are presented for a range of L shells and proton energies for a fixed wave distribution. Harmonic resonances in the range N = +/-100 are considered in order to include interactions between hiss at 100 Hz to 2 kHz frequencies, and protons in the energy range between approximately 10 keV and 1000 keV. Diffusion timescales are estimated to be of the order of tens of days and comparable to or shorter than lifetimes for Coulomb decay and charge exchange losses over most of the energy and spatial ranges of interest.

The Seebeck coefficient of superionic conductors

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

Mahan, G. D.

2015-01-28

We present a theory of the anomalous Seebeck coefficient found in the superionic conductor Cu{sub 2}Se. It has a phase transition at T = 400 K where the cations disorder but the anions do not. This disorder gives a temperature-dependent width to the electronic states in the conduction band. This width provides the anomalous Seebeck contribution.

Inferring Diffusion Dynamics from FCS in Heterogeneous Nuclear Environments

PubMed Central

Tsekouras, Konstantinos; Siegel, Amanda P.; Day, Richard N.; Pressé, Steve

2015-01-01

Fluorescence correlation spectroscopy (FCS) is a noninvasive technique that probes the diffusion dynamics of proteins down to single-molecule sensitivity in living cells. Critical mechanistic insight is often drawn from FCS experiments by fitting the resulting time-intensity correlation function, G(t), to known diffusion models. When simple models fail, the complex diffusion dynamics of proteins within heterogeneous cellular environments can be fit to anomalous diffusion models with adjustable anomalous exponents. Here, we take a different approach. We use the maximum entropy method to show—first using synthetic data—that a model for proteins diffusing while stochastically binding/unbinding to various affinity sites in living cells gives rise to a G(t) that could otherwise be equally well fit using anomalous diffusion models. We explain the mechanistic insight derived from our method. In particular, using real FCS data, we describe how the effects of cell crowding and binding to affinity sites manifest themselves in the behavior of G(t). Our focus is on the diffusive behavior of an engineered protein in 1) the heterochromatin region of the cell’s nucleus as well as 2) in the cell’s cytoplasm and 3) in solution. The protein consists of the basic region-leucine zipper (BZip) domain of the CCAAT/enhancer-binding protein (C/EBP) fused to fluorescent proteins. PMID:26153697

Feynman-Kac equations for reaction and diffusion processes

NASA Astrophysics Data System (ADS)

Hou, Ru; Deng, Weihua

2018-04-01

This paper provides a theoretical framework for deriving the forward and backward Feynman-Kac equations for the distribution of functionals of the path of a particle undergoing both diffusion and reaction processes. Once given the diffusion type and reaction rate, a specific forward or backward Feynman-Kac equation can be obtained. The results in this paper include those for normal/anomalous diffusions and reactions with linear/nonlinear rates. Using the derived equations, we apply our findings to compute some physical (experimentally measurable) statistics, including the occupation time in half-space, the first passage time, and the occupation time in half-interval with an absorbing or reflecting boundary, for the physical system with anomalous diffusion and spontaneous evanescence.

Anomalous diffusion of single metal atoms on a graphene oxide support

DOE PAGES

Furnival, Tom; Leary, Rowan K.; Tyo, Eric C.; ...

2017-04-21

Recent studies of single-atom catalysts open up the prospect of designing exceptionally active and environmentally efficient chemical processes. The stability and durability of such catalysts is governed by the strength with which the atoms are bound to their support and their diffusive behaviour. Here we use aberration-corrected STEM to image the diffusion of single copper adatoms on graphene oxide. As a result, we discover that individual atoms exhibit anomalous diffusion as a result of spatial and energetic disorder inherent in the support, and interpret the origins of this behaviour to develop a physical picture for the surface diffusion of singlemore » metal atoms.« less

Anomalous diffusion and long-range correlations in the score evolution of the game of cricket

NASA Astrophysics Data System (ADS)

Ribeiro, Haroldo V.; Mukherjee, Satyam; Zeng, Xiao Han T.

2012-08-01

We investigate the time evolution of the scores of the second most popular sport in the world: the game of cricket. By analyzing, event by event, the scores of more than 2000 matches, we point out that the score dynamics is an anomalous diffusive process. Our analysis reveals that the variance of the process is described by a power-law dependence with a superdiffusive exponent, that the scores are statistically self-similar following a universal Gaussian distribution, and that there are long-range correlations in the score evolution. We employ a generalized Langevin equation with a power-law correlated noise that describes all the empirical findings very well. These observations suggest that competition among agents may be a mechanism leading to anomalous diffusion and long-range correlation.

Fluorescence fluctuation analysis of BACE1-GFP fusion protein in cultured HEK293 cells

NASA Astrophysics Data System (ADS)

Gardeen, Spencer; Johnson, Joseph L.; Heikal, Ahmed A.

2016-10-01

Beta-site APP cleaving enzyme 1 (BACE1) is a type I transmembrane aspartyl protease. In the amyloidogenic pathway, BACE1 provides β-secretase activity that cleaves the amyloid precursor protein (APP) that leads to amyloid beta (Aβ) peptides. The aggregation of these Aβ will ultimately results in amyloid plaque formation, a hallmark of Alzheimer's disease (AD). Amyloid aggregation leads to progressive memory impairment and neural loss. Recent detergent protein extraction studies suggest that the untreated BACE1 protein forms a dimer that has significantly higher catalytic activity than its monomeric counterpart. Here, we examine the dimerization hypothesis of BACE1 in cultured HEK293 cells using fluorescence correlation spectroscopy (FCS). Cells were transfected with a BACE1-EGFP fusion protein construct and imaged using confocal and DIC microscopy to monitor labeled BACE1 localization and distribution within the cell. Our one-photon fluorescence fluctuation autocorrelation of BACE1- EGFP on the plasma membrane of HEK cells is modeled using two diffusing species on the plasma membrane with estimated diffusion coefficients of 1.39 x 10-7 cm2/sec and 2.8 x 10-8 cm2/sec under resting conditions and STA-200 inhibition, respectively. Anomalous diffusion model also provided adequate description of the observed autocorrelation function of BACE1- EGFP on the plasma membrane with an estimate exponent (α) of 0.8 and 0.5 for resting and STA-200 treated cells, respectively. The corresponding hydrodynamic radius of this transmembrane fusion protein was estimated using the measured diffusion coefficients assuming both Stokes-Einstein and Saffman-Delbruck models. Our results suggest a complex diffusion pattern of BACE1-EGFP on the plasma membrane of HEK cells with the possibility for dimer formation, especially under STA-200 inhibition.

X-ray-induced debromination of nucleic acids at the Br K absorption edge and implications for MAD phasing.

PubMed

Ennifar, E; Carpentier, P; Ferrer, J L; Walter, P; Dumas, P

2002-08-01

Multi-wavelength anomalous dispersion (MAD) using brominated derivatives is considered a common and convenient technique for solving chemically synthesized nucleic acid structures. Here, it is shown that a relatively moderate X-ray dose (of the order of 5 x 10(15) photons mm(-2)) can induce sufficient debromination to prevent structure determination. The decrease in bromine occupancy with radiation dose can be accounted for by a simple exponential, with an estimated rate constant at the absorption-peak wavelength, 7.4 (0.8) MGy, that is not significantly different from its value at the absorption-edge wavelength, 9.2 (2.6) MGy (the given e.s.d.s assess the relative closeness of the two values, not their absolute accuracy, which is probably worse). Chemically, these results (and others) are consistent with bromine cleavage resulting from direct photodissociation and/or from the action of free electrons, rather than from the action of hydroxyl radicals originating from water dissociation. The free bromine species (Br(-)) diffuse too quickly, even in amorphous ice around 100 K, to allow the determination of a diffusion coefficient. From a practical point of view, it is suggested that a single data collection with a crystal consisting of iodinated instead of brominated derivatives could provide both anomalous scattering and SIR phase information by the progressive cleavage of iodine.

Multiple Diffusion Mechanisms Due to Nanostructuring in Crowded Environments

PubMed Central

Sanabria, Hugo; Kubota, Yoshihisa; Waxham, M. Neal

2007-01-01

One of the key questions regarding intracellular diffusion is how the environment affects molecular mobility. Mostly, intracellular diffusion has been described as hindered, and the physical reasons for this behavior are: immobile barriers, molecular crowding, and binding interactions with immobile or mobile molecules. Using results from multi-photon fluorescence correlation spectroscopy, we describe how immobile barriers and crowding agents affect translational mobility. To study the hindrance produced by immobile barriers, we used sol-gels (silica nanostructures) that consist of a continuous solid phase and aqueous phase in which fluorescently tagged molecules diffuse. In the case of molecular crowding, translational mobility was assessed in increasing concentrations of 500 kDa dextran solutions. Diffusion of fluorescent tracers in both sol-gels and dextran solutions shows clear evidence of anomalous subdiffusion. In addition, data from the autocorrelation function were analyzed using the maximum entropy method as adapted to fluorescence correlation spectroscopy data and compared with the standard model that incorporates anomalous diffusion. The maximum entropy method revealed evidence of different diffusion mechanisms that had not been revealed using the anomalous diffusion model. These mechanisms likely correspond to nanostructuring in crowded environments and to the relative dimensions of the crowding agent with respect to the tracer molecule. Analysis with the maximum entropy method also revealed information about the degree of heterogeneity in the environment as reported by the behavior of diffusive molecules. PMID:17040979

Effects of soft interactions and bound mobility on diffusion in crowded environments: a model of sticky and slippery obstacles

NASA Astrophysics Data System (ADS)

Stefferson, Michael W.; Norris, Samantha L.; Vernerey, Franck J.; Betterton, Meredith D.; E Hough, Loren

2017-08-01

Crowded environments modify the diffusion of macromolecules, generally slowing their movement and inducing transient anomalous subdiffusion. The presence of obstacles also modifies the kinetics and equilibrium behavior of tracers. While previous theoretical studies of particle diffusion have typically assumed either impenetrable obstacles or binding interactions that immobilize the particle, in many cellular contexts bound particles remain mobile. Examples include membrane proteins or lipids with some entry and diffusion within lipid domains and proteins that can enter into membraneless organelles or compartments such as the nucleolus. Using a lattice model, we studied the diffusive movement of tracer particles which bind to soft obstacles, allowing tracers and obstacles to occupy the same lattice site. For sticky obstacles, bound tracer particles are immobile, while for slippery obstacles, bound tracers can hop without penalty to adjacent obstacles. In both models, binding significantly alters tracer motion. The type and degree of motion while bound is a key determinant of the tracer mobility: slippery obstacles can allow nearly unhindered diffusion, even at high obstacle filling fraction. To mimic compartmentalization in a cell, we examined how obstacle size and a range of bound diffusion coefficients affect tracer dynamics. The behavior of the model is similar in two and three spatial dimensions. Our work has implications for protein movement and interactions within cells.

Anomalous Diffusion in a Trading Model

NASA Astrophysics Data System (ADS)

Khidzir, Sidiq Mohamad; Wan Abdullah, Wan Ahmad Tajuddin

2009-07-01

The result of the trading model by Chakrabarti et al. [1] is the wealth distribution with a mixed exponential and power law distribution. Based on the motivation of studying the dynamics behind the flow of money similar to work done by Brockmann [2, 3] we track the flow of money in this trading model to observe anomalous diffusion in the form of long waiting times and Levy Flights.

Nonlinear ELM simulations based on a nonideal peeling–ballooning model using the BOUT++ code

DOE PAGES

Xu, X. Q.; Dudson, B. D.; Snyder, P. B.; ...

2011-09-23

A minimum set of equations based on the peeling–ballooning (P–B) model with nonideal physics effects (diamagnetic drift, E × B drift, resistivity and anomalous electron viscosity) is found to simulate pedestal collapse when using the BOUT++ simulation code, developed in part from the original fluid edge code BOUT. Linear simulations of P–B modes find good agreement in growth rate and mode structure with ELITE calculations. The influence of the E × B drift, diamagnetic drift, resistivity, anomalous electron viscosity, ion viscosity and parallel thermal diffusivity on P–B modes is being studied; we find that (1) the diamagnetic drift and Emore » × B drift stabilize the P–B mode in a manner consistent with theoretical expectations; (2) resistivity destabilizes the P–B mode, leading to resistive P–B mode; (3) anomalous electron and parallel ion viscosities destabilize the P–B mode, leading to a viscous P–B mode; (4) perpendicular ion viscosity and parallel thermal diffusivity stabilize the P–B mode. With addition of the anomalous electron viscosity under the assumption that the anomalous kinematic electron viscosity is comparable to the anomalous electron perpendicular thermal diffusivity, or the Prandtl number is close to unity, it is found from nonlinear simulations using a realistic high Lundquist number that the pedestal collapse is limited to the edge region and the ELM size is about 5–10% of the pedestal stored energy. Furthermore, this is consistent with many observations of large ELMs. The estimated island size is consistent with the size of fast pedestal pressure collapse. In the stable α-zones of ideal P–B modes, nonlinear simulations of viscous ballooning modes or current-diffusive ballooning mode (CDBM) for ITER H-mode scenarios are presented.« less

Solution of a modified fractional diffusion equation

NASA Astrophysics Data System (ADS)

Langlands, T. A. M.

2006-07-01

Recently, a modified fractional diffusion equation has been proposed [I. Sokolov, J. Klafter, From diffusion to anomalous diffusion: a century after Einstein's brownian motion, Chaos 15 (2005) 026103; A.V. Chechkin, R. Gorenflo, I.M. Sokolov, V.Yu. Gonchar, Distributed order time fractional diffusion equation, Frac. Calc. Appl. Anal. 6 (3) (2003) 259279; I.M. Sokolov, A.V. Checkin, J. Klafter, Distributed-order fractional kinetics, Acta. Phys. Pol. B 35 (2004) 1323.] for describing processes that become less anomalous as time progresses by the inclusion of a second fractional time derivative acting on the diffusion term. In this letter we give the solution of the modified equation on an infinite domain. In contrast to the solution of the traditional fractional diffusion equation, the solution of the modified equation requires an infinite series of Fox functions instead of a single Fox function.

Passive scalars: Mixing, diffusion, and intermittency in helical and nonhelical rotating turbulence

NASA Astrophysics Data System (ADS)

Imazio, P. Rodriguez; Mininni, P. D.

2017-03-01

We use direct numerical simulations to compute structure functions, scaling exponents, probability density functions, and effective transport coefficients of passive scalars in turbulent rotating helical and nonhelical flows. We show that helicity affects the inertial range scaling of the velocity and of the passive scalar when rotation is present, with a spectral law consistent with ˜k⊥-1.4 for the passive scalar variance spectrum. This scaling law is consistent with a phenomenological argument [P. Rodriguez Imazio and P. D. Mininni, Phys. Rev. E 83, 066309 (2011), 10.1103/PhysRevE.83.066309] for rotating nonhelical flows, which follows directly from Kolmogorov-Obukhov scaling and states that if energy follows a E (k ) ˜k-n law, then the passive scalar variance follows a law V (k ) ˜k-nθ with nθ=(5 -n ) /2 . With the second-order scaling exponent obtained from this law, and using the Kraichnan model, we obtain anomalous scaling exponents for the passive scalar that are in good agreement with the numerical results. Multifractal intermittency models are also considered. Intermittency of the passive scalar is stronger than in the nonhelical rotating case, a result that is also confirmed by stronger non-Gaussian tails in the probability density functions of field increments. Finally, Fick's law is used to compute the effective diffusion coefficients in the directions parallel and perpendicular to rotation. Calculations indicate that horizontal diffusion decreases in the presence of helicity in rotating flows, while vertical diffusion increases. A simple mean field argument explains this behavior in terms of the amplitude of velocity fluctuations.

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

Random walks exhibiting anomalous diffusion: elephants, urns and the limits of normality

NASA Astrophysics Data System (ADS)

Kearney, Michael J.; Martin, Richard J.

2018-01-01

A random walk model is presented which exhibits a transition from standard to anomalous diffusion as a parameter is varied. The model is a variant on the elephant random walk and differs in respect of the treatment of the initial state, which in the present work consists of a given number N of fixed steps. This also links the elephant random walk to other types of history dependent random walk. As well as being amenable to direct analysis, the model is shown to be asymptotically equivalent to a non-linear urn process. This provides fresh insights into the limiting form of the distribution of the walker’s position at large times. Although the distribution is intrinsically non-Gaussian in the anomalous diffusion regime, it gradually reverts to normal form when N is large under quite general conditions.

Communication: Probing anomalous diffusion in frequency space

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

Stachura, Sławomir; Synchrotron Soleil, L’Orme de Merisiers, 91192 Gif-sur-Yvette; Kneller, Gerald R., E-mail: gerald.kneller@cnrs-orleans.fr

Anomalous diffusion processes are usually detected by analyzing the time-dependent mean square displacement of the diffusing particles. The latter evolves asymptotically as W(t) ∼ 2D{sub α}t{sup α}, where D{sub α} is the fractional diffusion constant and 0 < α < 2. In this article we show that both D{sub α} and α can also be extracted from the low-frequency Fourier spectrum of the corresponding velocity autocorrelation function. This offers a simple method for the interpretation of quasielastic neutron scattering spectra from complex (bio)molecular systems, in which subdiffusive transport is frequently encountered. The approach is illustrated and validated by analyzing molecularmore » dynamics simulations of molecular diffusion in a lipid POPC bilayer.« less

Inferring diffusion dynamics from FCS in heterogeneous nuclear environments.

PubMed

Tsekouras, Konstantinos; Siegel, Amanda P; Day, Richard N; Pressé, Steve

2015-07-07

Fluorescence correlation spectroscopy (FCS) is a noninvasive technique that probes the diffusion dynamics of proteins down to single-molecule sensitivity in living cells. Critical mechanistic insight is often drawn from FCS experiments by fitting the resulting time-intensity correlation function, G(t), to known diffusion models. When simple models fail, the complex diffusion dynamics of proteins within heterogeneous cellular environments can be fit to anomalous diffusion models with adjustable anomalous exponents. Here, we take a different approach. We use the maximum entropy method to show-first using synthetic data-that a model for proteins diffusing while stochastically binding/unbinding to various affinity sites in living cells gives rise to a G(t) that could otherwise be equally well fit using anomalous diffusion models. We explain the mechanistic insight derived from our method. In particular, using real FCS data, we describe how the effects of cell crowding and binding to affinity sites manifest themselves in the behavior of G(t). Our focus is on the diffusive behavior of an engineered protein in 1) the heterochromatin region of the cell's nucleus as well as 2) in the cell's cytoplasm and 3) in solution. The protein consists of the basic region-leucine zipper (BZip) domain of the CCAAT/enhancer-binding protein (C/EBP) fused to fluorescent proteins. Copyright © 2015 Biophysical Society. Published by Elsevier Inc. All rights reserved.

Thermodynamics, Diffusion, and Structure of Liquid NaAlSi3O8 at Elevated Temperature and Pressure from Molecular Dynamics Simulations

NASA Astrophysics Data System (ADS)

Neilson, R.; Spera, F. J.; Ghiorso, M. S.

2014-12-01

Thermodynamic properties of silicate melts at high temperature (T) and pressure (P) are crucial to understanding Earth accretion, magma oceans, petrogenesis, and crustal growth. However, equations of state for silicate liquids at mantle conditions are scarce, due to experimental challenges. Molecular Dynamics (MD) simulations allow investigation of thermodynamic and transport properties of silicate melts at high P and T and enable the correlation of liquid structure with computed properties. Using classical MD, we studied liquid NaAlSi3O8 in the range 0-42 GPa and 3000-5137 K. Density ranged from 2.2 to 3.6 g/cm3, and all simulations were performed in the microcanonical (NEV) ensemble using the potential from Matsui (1998). An equation of state with internal energy E(V,T) was developed using the RT scaling-Vinet formulation (Ghiorso et al., 2009). From thermodynamic relationships, the Grüneisen parameter, isobaric expansivity, isothermal compressibility, heat capacity, and other functions are computed over the P-T range of the MD simulations. Diffusion coefficients (D) range from 1.5×10-9 to 5.9×10-8 m2/s and typically order Na>Al>O>Si at a given state point. Generally, D decreases with P and increases with T except for a low P anomalous region along the 3065 K isotherm. Anomalous diffusion for Al, Si, and O is congruent with laboratory experiments at P<10 GPa (e.g., Shimizu and Kushiro, 1984; Poe et al., 1997; Tinker and Lesher, 2001; Tinker et al., 2003). Activation energy for Na is on the order of -75.3 kJ/mol with activation volume -1.74 cm3/mol. The anomalous peak in diffusivity for Si and O occurs at ~3 GPa, which marks a subtle increase in the average coordination number (CN) for O around O from 9.35 to 10.31. The average CN for O around O generally increases with P, but it systematically drops at 8, 15, and 20 GPa for 3065, 3944, and 5137 K, respectively. The concentrations of AlO5 and SiO5 polyhedra maximize near 16 and 35 GPa, respectively.

Fractional cable equation models for anomalous electrodiffusion in nerve cells: infinite domain solutions.

PubMed

Langlands, T A M; Henry, B I; Wearne, S L

2009-12-01

We introduce fractional Nernst-Planck equations and derive fractional cable equations as macroscopic models for electrodiffusion of ions in nerve cells when molecular diffusion is anomalous subdiffusion due to binding, crowding or trapping. The anomalous subdiffusion is modelled by replacing diffusion constants with time dependent operators parameterized by fractional order exponents. Solutions are obtained as functions of the scaling parameters for infinite cables and semi-infinite cables with instantaneous current injections. Voltage attenuation along dendrites in response to alpha function synaptic inputs is computed. Action potential firing rates are also derived based on simple integrate and fire versions of the models. Our results show that electrotonic properties and firing rates of nerve cells are altered by anomalous subdiffusion in these models. We have suggested electrophysiological experiments to calibrate and validate the models.

A new fractional operator of variable order: Application in the description of anomalous diffusion

NASA Astrophysics Data System (ADS)

Yang, Xiao-Jun; Machado, J. A. Tenreiro

2017-09-01

In this paper, a new fractional operator of variable order with the use of the monotonic increasing function is proposed in sense of Caputo type. The properties in term of the Laplace and Fourier transforms are analyzed and the results for the anomalous diffusion equations of variable order are discussed. The new formulation is efficient in modeling a class of concentrations in the complex transport process.

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.

Anomalous Transport of High Energy Cosmic Rays in Galactic Superbubbles

NASA Technical Reports Server (NTRS)

Barghouty, Nasser F.

2014-01-01

High-energy cosmic rays may exhibit anomalous transport as they traverse and are accelerated by a collection of supernovae explosions in a galactic superbubble. Signatures of this anomalous transport can show up in the particles' evolution and their spectra. In a continuous-time-random- walk (CTRW) model assuming standard diffusive shock acceleration theory (DSA) for each shock encounter, and where the superbubble (an OB stars association) is idealized as a heterogeneous region of particle sources and sinks, acceleration and transport in the superbubble can be shown to be sub-diffusive. While the sub-diffusive transport can be attributed to the stochastic nature of the acceleration time according to DSA theory, the spectral break appears to be an artifact of transport in a finite medium. These CTRW simulations point to a new and intriguing phenomenon associated with the statistical nature of collective acceleration of high energy cosmic rays in galactic superbubbles.

Dual view FIDA measurements on MAST

NASA Astrophysics Data System (ADS)

Michael, C. A.; Conway, N.; Crowley, B.; Jones, O.; Heidbrink, W. W.; Pinches, S.; Braeken, E.; Akers, R.; Challis, C.; Turnyanskiy, M.; Patel, A.; Muir, D.; Gaffka, R.; Bailey, S.

2013-09-01

A fast-ion deuterium alpha (FIDA) spectrometer was installed on MAST to measure radially resolved information about the fast-ion density and its distribution in energy and pitch angle. Toroidally and vertically directed collection lenses are employed, to detect both passing and trapped particle dynamics, and reference views are installed to subtract the background. This background is found to contain a substantial amount of passive FIDA emission driven by edge neutrals, and to depend delicately on viewing geometry. Results are compared with theoretical expectations based on the codes NUBEAM (for fast-ion distributions) and FIDASIM. Calibrating via the measured beam emission peaks, the toroidal FIDA signal profile agrees with classical simulations in magnetohydrodynamic quiescent discharges where the neutron rate is also classical. Long-lived modes (LLMs) and chirping modes decrease the core FIDA signal significantly, and the profile can be matched closely to simulations using anomalous diffusive transport; a spatially uniform diffusion coefficient is sufficient for chirping modes, while a core localized diffusion is better for a LLM. Analysis of a discharge with chirping mode activity shows a dramatic drop in the core FIDA signal and rapid increase in the edge passive signal at the onset of the burst indicating a very rapid redistribution towards the edge. Vertical-viewing measurements show a discrepancy with simulations at higher Doppler shifts when the neutron rate is classical, which, combined with the fact that the toroidal signals agree, means that the difference must be occurring for pitch angles near the trapped-passing boundary, although uncertainties in the background subtraction, which are difficult to assess, may contribute to this. Further evidence of an anomalous transport mechanism for these particles is provided by the fact that an increase of beam power does not increase the higher energy vertical FIDA signals, while the toroidal signals do increase.

Conformable derivative approach to anomalous diffusion

NASA Astrophysics Data System (ADS)

Zhou, H. W.; Yang, S.; Zhang, S. Q.

2018-02-01

By using a new derivative with fractional order, referred to conformable derivative, an alternative representation of the diffusion equation is proposed to improve the modeling of anomalous diffusion. The analytical solutions of the conformable derivative model in terms of Gauss kernel and Error function are presented. The power law of the mean square displacement for the conformable diffusion model is studied invoking the time-dependent Gauss kernel. The parameters related to the conformable derivative model are determined by Levenberg-Marquardt method on the basis of the experimental data of chloride ions transportation in reinforced concrete. The data fitting results showed that the conformable derivative model agrees better with the experimental data than the normal diffusion equation. Furthermore, the potential application of the proposed conformable derivative model of water flow in low-permeability media is discussed.

Diffusive instabilities in a hyperbolic activator-inhibitor system with superdiffusion

NASA Astrophysics Data System (ADS)

Mvogo, Alain; Macías-Díaz, Jorge E.; Kofané, Timoléon Crépin

2018-03-01

We investigate analytically and numerically the conditions for wave instabilities in a hyperbolic activator-inhibitor system with species undergoing anomalous superdiffusion. In the present work, anomalous superdiffusion is modeled using the two-dimensional Weyl fractional operator, with derivative orders α ∈ [1,2]. We perform a linear stability analysis and derive the conditions for diffusion-driven wave instabilities. Emphasis is placed on the effect of the superdiffusion exponent α , the diffusion ratio d , and the inertial time τ . As the superdiffusive exponent increases, so does the wave number of the Turing instability. Opposite to the requirement for Turing instability, the activator needs to diffuse sufficiently faster than the inhibitor in order for the wave instability to occur. The critical wave number for wave instability decreases with the superdiffusive exponent and increases with the inertial time. The maximum value of the inertial time for a wave instability to occur in the system is τmax=3.6 . As one of the main results of this work, we conclude that both anomalous diffusion and inertial time influence strongly the conditions for wave instabilities in hyperbolic fractional reaction-diffusion systems. Some numerical simulations are conducted as evidence of the analytical predictions derived in this work.

Study of electron transport in a Hall thruster by axial–radial fully kinetic particle simulation

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

Cho, Shinatora, E-mail: choh.shinatora@jaxa.jp; Kubota, Kenichi; Funaki, Ikkoh

2015-10-15

Electron transport across a magnetic field in a magnetic-layer-type Hall thruster was numerically investigated for the future predictive modeling of Hall thrusters. The discharge of a 1-kW-class magnetic-layer-type Hall thruster designed for high-specific-impulse operation was modeled using an r-z two-dimensional fully kinetic particle code with and without artificial electron-diffusion models. The thruster performance results showed that both electron transport models captured the experimental result within discrepancies less than 20% in thrust and discharge current for all the simulated operation conditions. The electron cross-field transport mechanism of the so-called anomalous diffusion was self-consistently observed in the simulation without artificial diffusion models;more » the effective electron mobility was two orders of magnitude higher than the value obtained using the classical diffusion theory. To account for the self-consistently observed anomalous transport, the oscillation of plasma properties was speculated. It was suggested that the enhanced random-walk diffusion due to the velocity oscillation of low-frequency electron flow could explain the observed anomalous diffusion within an order of magnitude. The dominant oscillation mode of the electron flow velocity was found to be 20 kHz, which was coupled to electrostatic oscillation excited by global ionization instability.« less

Onset of anomalous diffusion from local motion rules

NASA Astrophysics Data System (ADS)

de Nigris, Sarah; Carletti, Timoteo; Lambiotte, Renaud

2017-02-01

Anomalous diffusion processes, in particular superdiffusive ones, are known to be efficient strategies for searching and navigation in animals and also in human mobility. One way to create such regimes are Lévy flights, where the walkers are allowed to perform jumps, the "flights," that can eventually be very long as their length distribution is asymptotically power-law distributed. In our work, we present a model in which walkers are allowed to perform, on a one-dimensional lattice, "cascades" of n unitary steps instead of one jump of a randomly generated length, as in the Lévy case, where n is drawn from a cascade distribution pn. We show that this local mechanism may give rise to superdiffusion or normal diffusion when pn is distributed as a power law. We also introduce waiting times that are power-law distributed as well and therefore the probability distribution scaling is steered by the two local distributions power-law exponents. As a perspective, our approach may engender a possible generalization of anomalous diffusion in context where distances are difficult to define, as in the case of complex networks, and also provide an interesting model for diffusion in temporal networks.

Development of advanced methods for analysis of experimental data in diffusion

NASA Astrophysics Data System (ADS)

Jaques, Alonso V.

There are numerous experimental configurations and data analysis techniques for the characterization of diffusion phenomena. However, the mathematical methods for estimating diffusivities traditionally do not take into account the effects of experimental errors in the data, and often require smooth, noiseless data sets to perform the necessary analysis steps. The current methods used for data smoothing require strong assumptions which can introduce numerical "artifacts" into the data, affecting confidence in the estimated parameters. The Boltzmann-Matano method is used extensively in the determination of concentration - dependent diffusivities, D(C), in alloys. In the course of analyzing experimental data, numerical integrations and differentiations of the concentration profile are performed. These methods require smoothing of the data prior to analysis. We present here an approach to the Boltzmann-Matano method that is based on a regularization method to estimate a differentiation operation on the data, i.e., estimate the concentration gradient term, which is important in the analysis process for determining the diffusivity. This approach, therefore, has the potential to be less subjective, and in numerical simulations shows an increased accuracy in the estimated diffusion coefficients. We present a regression approach to estimate linear multicomponent diffusion coefficients that eliminates the need pre-treat or pre-condition the concentration profile. This approach fits the data to a functional form of the mathematical expression for the concentration profile, and allows us to determine the diffusivity matrix directly from the fitted parameters. Reformulation of the equation for the analytical solution is done in order to reduce the size of the problem and accelerate the convergence. The objective function for the regression can incorporate point estimations for error in the concentration, improving the statistical confidence in the estimated diffusivity matrix. Case studies are presented to demonstrate the reliability and the stability of the method. To the best of our knowledge there is no published analysis of the effects of experimental errors on the reliability of the estimates for the diffusivities. For the case of linear multicomponent diffusion, we analyze the effects of the instrument analytical spot size, positioning uncertainty, and concentration uncertainty on the resulting values of the diffusivities. These effects are studied using Monte Carlo method on simulated experimental data. Several useful scaling relationships were identified which allow more rigorous and quantitative estimates of the errors in the measured data, and are valuable for experimental design. To further analyze anomalous diffusion processes, where traditional diffusional transport equations do not hold, we explore the use of fractional calculus in analytically representing these processes is proposed. We use the fractional calculus approach for anomalous diffusion processes occurring through a finite plane sheet with one face held at a fixed concentration, the other held at zero, and the initial concentration within the sheet equal to zero. This problem is related to cases in nature where diffusion is enhanced relative to the classical process, and the order of differentiation is not necessarily a second--order differential equation. That is, differentiation is of fractional order alpha, where 1 ≤ alpha < 2. For alpha = 2, the presented solutions reduce to the classical second-order diffusion solution for the conditions studied. The solution obtained allows the analysis of permeation experiments. Frequently, hydrogen diffusion is analyzed using electrochemical permeation methods using the traditional, Fickian-based theory. Experimental evidence shows the latter analytical approach is not always appropiate, because reported data shows qualitative (and quantitative) deviation from its theoretical scaling predictions. Preliminary analysis of data shows better agreement with fractional diffusion analysis when compared to traditional square-root scaling. Although there is a large amount of work in the estimation of the diffusivity from experimental data, reported studies typically present only the analytical description for the diffusivity, without scattering. However, because these studies do not consider effects produced by instrument analysis, their direct applicability is limited. We propose alternatives to address these, and to evaluate their influence on the final resulting diffusivity values.

Solar-wind/magnetospheric dynamos: MHD-scale collective entry of the solar wind energy, momentum and mass into the magnetosphere

NASA Technical Reports Server (NTRS)

Song, Yan; Lysak, Robert L.

1992-01-01

A quasi open MHD (Magnetohydrodynamic) scale anomalous transport controlled boundary layer model is proposed, where the MHD collective behavior of magnetofluids (direct dynamo effect, anomalous viscous interaction and anomalous diffusion of the mass and the magnetic field) plays the main role in the conversion of the Solar Wind (SW) kinetic and magnetic energy into electromagnetic energy in the Magnetosphere (MSp). The so called direct and indirect dynamo effects are based on inductive and purely dissipative energy conversion, respectively. The self organization ability of vector fields in turbulent magnetofluids implies an inductive response of the plasma, which leads to the direct dynamo effect. The direct dynamo effect describes the direct formation of localized field aligned currents and the transverse Alfven waves and provides a source for MHD scale anomalous diffusivity and viscosity. The SW/MSp coupling depends on the dynamo efficiency.

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.

On the role of adhesion in single-file dynamics

NASA Astrophysics Data System (ADS)

Fouad, Ahmed M.; Noel, John A.

2017-08-01

For a one-dimensional interacting system of Brownian particles with hard-core interactions (a single-file model), we study the effect of adhesion on both the collective diffusion (diffusion of the entire system with respect to its center of mass) and the tracer diffusion (diffusion of the individual tagged particles). For the case with no adhesion, all properties of these particle systems that are independent of particle labeling (symmetric in all particle coordinates and velocities) are identical to those of non-interacting particles (Lebowitz and Percus, 1967). We clarify this last fact twice. First, we derive our analytical predictions that show that the probability-density functions of single-file (ρsf) and ordinary (ρord) diffusion are identical, ρsf =ρord, predicting a nonanomalous (ordinary) behavior for the collective single-file diffusion, where the average second moment with respect to the center of mass, < x(t) 2 > , is calculated from ρ for both diffusion processes. Second, for single-file diffusion, we show, both analytically and through large-scale simulations, that < x(t) 2 > grows linearly with time, confirming the nonanomalous behavior. This nonanomalous collective behavior comes in contrast to the well-known anomalous sub-diffusion behavior of the individual tagged particles (Harris, 1965). We introduce adhesion to single-file dynamics as a second inter-particle interaction rule and, interestingly, we show that adding adhesion does reduce the magnitudes of both < x(t) 2 > and the mean square displacement per particle Δx2; but the diffusion behavior remains intact independent of adhesion in both cases. Moreover, we study the dependence of both the collective diffusion constant D and the tracer diffusion constant DT on the adhesion coefficient α.

Probing the type of anomalous diffusion with single-particle tracking.

PubMed

Ernst, Dominique; Köhler, Jürgen; Weiss, Matthias

2014-05-07

Many reactions in complex fluids, e.g. signaling cascades in the cytoplasm of living cells, are governed by a diffusion-driven encounter of reactants. Yet, diffusion in complex fluids often exhibits an anomalous characteristic ('subdiffusion'). Since different types of subdiffusion have distinct effects on timing and equilibria of chemical reactions, a thorough determination of the reactants' type of random walk is key to a quantitative understanding of reactions in complex fluids. Here we introduce a straightforward and simple approach for determining the type of subdiffusion from single-particle tracking data. Unlike previous approaches, our method also is sensitive to transient subdiffusion phenomena, e.g. obstructed diffusion below the percolation threshold. We validate our strategy with data from experiment and simulation.

Anomalous quantum diffusion and the topological metal

NASA Astrophysics Data System (ADS)

Tian, Chushun

2012-09-01

Electron wave scattering off disorders provides a key to many fascinating transport phenomena recently observed in topological insulators. Here, we present a nonperturbative diagrammatic theory of this subject. Surprisingly, quantum superdiffusion is found on the surface of three-dimensional strong topological insulators regardless of disorder strength (but not vanishing), where the diffusion coefficient grows in time logarithmically. Such a transport anomaly serves as a main characteristic of the novel quantum metal, the so-called “topological metal,” and indicates that it is a hybridization of Ohmic and perfect metals. It washes out the Anderson transition occurring in two-dimensional normal metals with disordered spin-orbit coupling, and leads to a logarithmic divergence of the conductance in the sample size instead. Therefore, the present work provides an analytical proof of the transport anomaly discovered numerically [Nomura, Koshino, and Ryu, Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.99.146806 99, 146806 (2007); Bardarson , Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.99.106801 99, 106801 (2007)].

Non-equilibrium forces drive the anomalous diffusion of telomeres in the nucleus of mammalian cells

NASA Astrophysics Data System (ADS)

Stadler, Lorenz; Weiss, Matthias

2017-11-01

Telomeres are vital nucleotide sequences at both ends of each chromosome, and their motion reports on the local dynamics of decondensed chromatin in the nucleus of interphase cells. Here, we show that the previously reported subdiffusive motion of telomeres is driven by non-equilibrium cytoskeletal forces. In particular, breaking down microtubules leads to a significantly reduced generalized diffusion coefficient of telomeres. This translates into a markedly reduced effective temperature in the stochastic forces that govern the telomeres’ random walk. Moreover, telomere motion in cells that lack microtubules is well described by the monomer dynamics of a Rouse polymer that is embeddded in a viscoelastic medium. In contrast, active cytoskeletal forces in untreated cells override the environment’s elastic contributions, resulting in the well-known scaling for conventional Rouse dynamics in viscous media. Our data highlight that even subdiffusive motion in cells in most cases may not be a simple thermal transport process but rather is driven by non-equilibrium events.

New fluorescence correlation spectroscopy enabling direct observation of spatiotemporal dependence of diffusion constants as an evidence of anomalous transport in extracellular matrices.

PubMed

Masuda, Akiko; Ushida, Kiminori; Okamoto, Takayuki

2005-05-01

The potential of fluorescence correlation spectroscopy (FCS) is extended to enable the direct observation of anomalous subdiffusion (ASD) in inhomogeneous media that are of great importance particularly in many biological systems, such as membranes, cytoplasm, and extracellular matrices (ECMs). Because ASD can be confirmed by monitoring the spatiotemporal dependence of observable diffusion coefficients (D(obs)), the size of the effective confocal volume (V(eff)) for FCS sampling (sampling volume) was continuously changed on a scale of 300-500 nm using a motorized variable beam expander through which an illuminating laser beam passes. This new method, namely, sampling-volume-controlled (SVC)-FCS, was applied to the analysis of hyaluronan (HA) aqueous solutions where the D(obs) of light-emitting solute (Alexa 488) markedly changed, corresponding to the change in V(eff) (220-340 nm in the half-axis), because the network structure of HA of 7-33 nm (nanostructure) interferes with the material transport within it. The results indicate that moderate ASD may occur even in the presence of a small amount ( approximately 0.1 wt %) of HA in ECM. Because the change in D(obs) along with the traveling distance (the mean-square displacement) can be identified even in systems with no deformation of the autocorrelation function, this technique has a great potential for general applications to many biological systems in which ASD shows complex time and space dependences.

Fractional motion model for characterization of anomalous diffusion from NMR signals.

PubMed

Fan, Yang; Gao, Jia-Hong

2015-07-01

Measuring molecular diffusion has been used to characterize the properties of living organisms and porous materials. NMR is able to detect the diffusion process in vivo and noninvasively. The fractional motion (FM) model is appropriate to describe anomalous diffusion phenomenon in crowded environments, such as living cells. However, no FM-based NMR theory has yet been established. Here, we present a general formulation of the FM-based NMR signal under the influence of arbitrary magnetic field gradient waveforms. An explicit analytic solution of the stretched exponential decay format for NMR signals with finite-width Stejskal-Tanner bipolar pulse magnetic field gradients is presented. Signals from a numerical simulation matched well with the theoretical prediction. In vivo diffusion-weighted brain images were acquired and analyzed using the proposed theory, and the resulting parametric maps exhibit remarkable contrasts between different brain tissues.

Fractional motion model for characterization of anomalous diffusion from NMR signals

NASA Astrophysics Data System (ADS)

Fan, Yang; Gao, Jia-Hong

2015-07-01

Measuring molecular diffusion has been used to characterize the properties of living organisms and porous materials. NMR is able to detect the diffusion process in vivo and noninvasively. The fractional motion (FM) model is appropriate to describe anomalous diffusion phenomenon in crowded environments, such as living cells. However, no FM-based NMR theory has yet been established. Here, we present a general formulation of the FM-based NMR signal under the influence of arbitrary magnetic field gradient waveforms. An explicit analytic solution of the stretched exponential decay format for NMR signals with finite-width Stejskal-Tanner bipolar pulse magnetic field gradients is presented. Signals from a numerical simulation matched well with the theoretical prediction. In vivo diffusion-weighted brain images were acquired and analyzed using the proposed theory, and the resulting parametric maps exhibit remarkable contrasts between different brain tissues.

Asymptotic neutron scattering laws for anomalously diffusing quantum particles

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

Kneller, Gerald R.; Université d’Orléans, Chateau de la Source-Ave. du Parc Floral, 45067 Orléans; Synchrotron-SOLEIL, L’Orme de Merisiers, 91192 Gif-sur-Yvette

2016-07-28

The paper deals with a model-free approach to the analysis of quasielastic neutron scattering intensities from anomalously diffusing quantum particles. All quantities are inferred from the asymptotic form of their time-dependent mean square displacements which grow ∝t{sup α}, with 0 ≤ α < 2. Confined diffusion (α = 0) is here explicitly included. We discuss in particular the intermediate scattering function for long times and the Fourier spectrum of the velocity autocorrelation function for small frequencies. Quantum effects enter in both cases through the general symmetry properties of quantum time correlation functions. It is shown that the fractional diffusion constantmore » can be expressed by a Green-Kubo type relation involving the real part of the velocity autocorrelation function. The theory is exact in the diffusive regime and at moderate momentum transfers.« less

Effect of concentration dependence of the diffusion coefficient on homogenization kinetics in multiphase binary alloy systems

NASA Technical Reports Server (NTRS)

Tenney, D. R.; Unnam, J.

1978-01-01

Diffusion calculations were performed to establish the conditions under which concentration dependence of the diffusion coefficient was important in single, two, and three phase binary alloy systems. Finite-difference solutions were obtained for each type of system using diffusion coefficient variations typical of those observed in real alloy systems. Solutions were also obtained using average diffusion coefficients determined by taking a logarithmic average of each diffusion coefficient variation considered. The constant diffusion coefficient solutions were used as reference in assessing diffusion coefficient variation effects. Calculations were performed for planar, cylindrical, and spherical geometries in order to compare the effect of diffusion coefficient variations with the effect of interface geometries. In most of the cases considered, the diffusion coefficient of the major-alloy phase was the key parameter that controlled the kinetics of interdiffusion.

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.

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.

Anomalous diffusion with linear reaction dynamics: from continuous time random walks to fractional reaction-diffusion equations.

PubMed

Henry, B I; Langlands, T A M; Wearne, S L

2006-09-01

We have revisited the problem of anomalously diffusing species, modeled at the mesoscopic level using continuous time random walks, to include linear reaction dynamics. If a constant proportion of walkers are added or removed instantaneously at the start of each step then the long time asymptotic limit yields a fractional reaction-diffusion equation with a fractional order temporal derivative operating on both the standard diffusion term and a linear reaction kinetics term. If the walkers are added or removed at a constant per capita rate during the waiting time between steps then the long time asymptotic limit has a standard linear reaction kinetics term but a fractional order temporal derivative operating on a nonstandard diffusion term. Results from the above two models are compared with a phenomenological model with standard linear reaction kinetics and a fractional order temporal derivative operating on a standard diffusion term. We have also developed further extensions of the CTRW model to include more general reaction dynamics.

Effective anomalous Hall coefficient in an ultrathin Co layer sandwiched by Pt layers

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

Zhang, Peng; Wu, Di; Jiang, Zhengsheng

2014-02-14

Anomalous Hall effect in Co/Pt multilayer is important to study the effect of interface with strong spin-orbit coupling. However, the shunting effect of the layers in such system and the circuit in the plane perpendicular to the injected current were overlooked in most works and thus, anomalous Hall coefficient in Co/Pt multilayer has not been determined accurately. Considering the shunting effect and the equivalent circuit, we show that the effective anomalous Hall coefficient of a 0.5 nm thick Co layer sandwiched by Pt layers R{sub S} is 0.29 ± 0.01 μΩ cm/T at the zero temperature limit and increases to about 0.73 μΩ cm/T at the temperaturemore » of 300 K. R{sub S} is one order larger than that in bulk Co film, indicating the large contribution of the Co/Pt interface. R{sub S} increases with the resistivity of Co as well as a resistivity independent contribution of −0.23 ± 0.01 μΩ cm/T. The equivalent anomalous Hall current in the Co layer has a maximum of 1.1% of the injected transverse current in the Co layer around the temperature of 80 K.« less

Divergent series and memory of the initial condition in the long-time solution of some anomalous diffusion problems.

PubMed

Yuste, S Bravo; Borrego, R; Abad, E

2010-02-01

We consider various anomalous d -dimensional diffusion problems in the presence of an absorbing boundary with radial symmetry. The motion of particles is described by a fractional diffusion equation. Their mean-square displacement is given by r(2) proportional, variant t(gamma)(00 , the emergence of such series in the long-time domain is a specific feature of subdiffusion problems. We present a method to regularize such series, and, in some cases, validate the procedure by using alternative techniques (Laplace transform method and numerical simulations). In the normal diffusion case, we find that the signature of the initial condition on the approach to the steady state rapidly fades away and the solution approaches a single (the main) decay mode in the long-time regime. In remarkable contrast, long-time memory of the initial condition is present in the subdiffusive case as the spatial part Psi1(r) describing the long-time decay of the solution to the steady state is determined by a weighted superposition of all spatial modes characteristic of the normal diffusion problem, the weight being dependent on the initial condition. Interestingly, Psi1(r) turns out to be independent of the anomalous diffusion exponent gamma .

Anomalous Diffusion Reports on the Interaction of Misfolded Proteins with the Quality Control Machinery in the Endoplasmic Reticulum

PubMed Central

Malchus, Nina; Weiss, Matthias

2010-01-01

A multitude of transmembrane proteins enters the endoplasmic reticulum (ER) as unfolded polypeptide chains. During their folding process, they interact repetitively with the ER's quality control machinery. Here, we have used fluorescence correlation spectroscopy to probe these interactions for a prototypical transmembrane protein, VSVG ts045, in vivo. While both folded and unfolded VSVG ts045 showed anomalous diffusion, the unfolded protein had a significantly stronger anomaly. This difference subsided when unfolded VSVG ts045 was in a complex with its chaperone calnexin, or when a mutant form of VSVG ts045 with only one glycan was used. Our experimental data and accompanying simulations suggest that the folding sensor of the quality control (UGT1) oligomerizes unfolded VSVG ts045, leading to a more anomalous/obstructed diffusion. In contrast, calnexin dissolves the oligomers, rendering unfolded VSVG ts045 more mobile, and hence prevents poisoning of the ER. PMID:20713018

Superstatistical generalised Langevin equation: non-Gaussian viscoelastic anomalous diffusion

NASA Astrophysics Data System (ADS)

Ślęzak, Jakub; Metzler, Ralf; Magdziarz, Marcin

2018-02-01

Recent advances in single particle tracking and supercomputing techniques demonstrate the emergence of normal or anomalous, viscoelastic diffusion in conjunction with non-Gaussian distributions in soft, biological, and active matter systems. We here formulate a stochastic model based on a generalised Langevin equation in which non-Gaussian shapes of the probability density function and normal or anomalous diffusion have a common origin, namely a random parametrisation of the stochastic force. We perform a detailed analysis demonstrating how various types of parameter distributions for the memory kernel result in exponential, power law, or power-log law tails of the memory functions. The studied system is also shown to exhibit a further unusual property: the velocity has a Gaussian one point probability density but non-Gaussian joint distributions. This behaviour is reflected in the relaxation from a Gaussian to a non-Gaussian distribution observed for the position variable. We show that our theoretical results are in excellent agreement with stochastic simulations.

Anomalous cation diffusion in salt-doped confined bilayer ice.

PubMed

Qiu, Hu; Xue, Minmin; Shen, Chun; Guo, Wanlin

2018-05-17

The diffusive dynamics of aqueous electrolyte solutions in nanoconfined spaces has attracted considerable attention due to their potential applications in desalination, biosensors and supercapacitors. Here we show by molecular dynamics simulations that lithium and sodium ions diffuse at a rate at least an order of magnitude higher than that of water molecules when the ions are trapped in an ice bilayer confined between two parallel plates. This novel picture is in sharp contrast to the prevailing view that the diffusion rate of ions is comparable to or even lower than that of water in both bulk and confined solutions. The predicted high ion mobility stems from frequent lateral hopping of ions along the coordination sites inside the hydrogen-bonding network connecting the two water layers of the ice bilayer. This anomalous diffusion should provide new insights into the physics of confined aqueous electrolytes.

Anomalous transport regimes and asymptotic concentration distributions in the presence of advection and diffusion on a comb structure

NASA Astrophysics Data System (ADS)

Dvoretskaya, Olga A.; Kondratenko, Peter S.

2009-04-01

We study the transport of impurity particles on a comb structure in the presence of advection. The main body concentration and asymptotic concentration distributions are obtained. Seven different transport regimes occur on the comb structure with finite teeth: classical diffusion, advection, quasidiffusion, subdiffusion, slow classical diffusion, and two kinds of slow advection. Quasidiffusion deserves special attention. It is characterized by a linear growth of the mean-square displacement. However, quasidiffusion is an anomalous transport regime. We established that a change in transport regimes in time leads to a change in regimes in space. Concentration tails have a cascade structure, namely, consisting of several parts.

Plasma Membrane is Compartmentalized by a Self-Similar Cortical Actin Meshwork

NASA Astrophysics Data System (ADS)

Sadegh, Sanaz; Higgins, Jenny L.; Mannion, Patrick C.; Tamkun, Michael M.; Krapf, Diego

2017-01-01

A broad range of membrane proteins display anomalous diffusion on the cell surface. Different methods provide evidence for obstructed subdiffusion and diffusion on a fractal space, but the underlying structure inducing anomalous diffusion has never been visualized because of experimental challenges. We addressed this problem by imaging the cortical actin at high resolution while simultaneously tracking individual membrane proteins in live mammalian cells. Our data confirm that actin introduces barriers leading to compartmentalization of the plasma membrane and that membrane proteins are transiently confined within actin fences. Furthermore, superresolution imaging shows that the cortical actin is organized into a self-similar meshwork. These results present a hierarchical nanoscale picture of the plasma membrane.

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.

Dynamics of comb-of-comb-network polymers in random layered flows

NASA Astrophysics Data System (ADS)

Katyal, Divya; Kant, Rama

2016-12-01

We analyze the dynamics of comb-of-comb-network polymers in the presence of external random flows. The dynamics of such structures is evaluated through relevant physical quantities, viz., average square displacement (ASD) and the velocity autocorrelation function (VACF). We focus on comparing the dynamics of the comb-of-comb network with the linear polymer. The present work displays an anomalous diffusive behavior of this flexible network in the random layered flows. The effect of the polymer topology on the dynamics is analyzed by varying the number of generations and branch lengths in these networks. In addition, we investigate the influence of external flow on the dynamics by varying flow parameters, like the flow exponent α and flow strength Wα. Our analysis highlights two anomalous power-law regimes, viz., subdiffusive (intermediate-time polymer stretching and flow-induced diffusion) and superdiffusive (long-time flow-induced diffusion). The anomalous long-time dynamics is governed by the temporal exponent ν of ASD, viz., ν =2 -α /2 . Compared to a linear polymer, the comb-of-comb network shows a shorter crossover time (from the subdiffusive to superdiffusive regime) but a reduced magnitude of ASD. Our theory displays an anomalous VACF in the random layered flows that scales as t-α /2. We show that the network with greater total mass moves faster.

Anomalous transport from holography: part II

NASA Astrophysics Data System (ADS)

Bu, Yanyan; Lublinsky, Michael; Sharon, Amir

2017-03-01

This is a second study of chiral anomaly-induced transport within a holographic model consisting of anomalous U(1)_V× U(1)_A Maxwell theory in Schwarzschild-AdS_5 spacetime. In the first part, chiral magnetic/separation effects (CME/CSE) are considered in the presence of a static spatially inhomogeneous external magnetic field. Gradient corrections to CME/CSE are analytically evaluated up to third order in the derivative expansion. Some of the third order gradient corrections lead to an anomaly-induced negative B^2-correction to the diffusion constant. We also find modifications to the chiral magnetic wave nonlinear in B. In the second part, we focus on the experimentally interesting case of the axial chemical potential being induced dynamically by a constant magnetic and time-dependent electric fields. Constitutive relations for the vector/axial currents are computed employing two different approximations: (a) derivative expansion (up to third order) but fully nonlinear in the external fields, and (b) weak electric field limit but resuming all orders in the derivative expansion. A non-vanishing nonlinear axial current (CSE) is found in the first case. The dependence on magnetic field and frequency of linear transport coefficient functions is explored in the second.

Transport properties of CO2-bearing MgSiO3 melt at mantle conditions

NASA Astrophysics Data System (ADS)

Ghosh, D. B.; Karki, B. B.

2017-12-01

Carbon dioxide, generally considered as the second most abundant volatile component in silicate magmas, is expected to significantly influence various melt properties. In particular, our knowledge about its dynamical effects is lacking over most of the Earth's mantle pressure regime. Here we report the first-principles molecular dynamics results on the transport properties of carbonated MgSiO3 liquid under the conditions of mantle relevance. They show that dissolved CO2 systematically enhances the diffusion rates of all elements and the associated electrical conductivity and lowers the melt viscosity on average by factors of 1.5 to 3 over the pressure range considered. They also predict anomalous dynamical behavior - increasing diffusivity and conductivity, and decreasing viscosity with compression in the low pressure regime. We attempt to link the predicted transport coefficients to the microsocopic structural changes that occur in response to pressure and temperature. This anomaly and the concomitant increase of pressure and temperature with depth together make these transport coefficients vary modestly over extended portions of the mantle regime. It is possible that the melt electrical conductivity at conditions corresponding to the 410 and 660 km seismic discontinuities is at a detectable level by electromagnetic sounding observation. Also, the low melt viscosity values 0.2-0.5 Pa s at these depths and near the core-mantle boundary may imply high mobility of possible melts in these regions.

Anomalous diffusion for bed load transport with a physically-based model

NASA Astrophysics Data System (ADS)

Fan, N.; Singh, A.; Foufoula-Georgiou, E.; Wu, B.

2013-12-01

Diffusion of bed load particles shows both normal and anomalous behavior for different spatial-temporal scales. Understanding and quantifying these different types of diffusion is important not only for the development of theoretical models of particle transport but also for practical purposes, e.g., river management. Here we extend a recently proposed physically-based model of particle transport by Fan et al. [2013] to further develop an Episodic Langevin equation (ELE) for individual particle motion which reproduces the episodic movement (start and stop) of sediment particles. Using the proposed ELE we simulate particle movements for a large number of uniform size particles, incorporating different probability distribution functions (PDFs) of particle waiting time. For exponential PDFs of waiting times, particles reveal ballistic motion in short time scales and turn to normal diffusion at long time scales. The PDF of simulated particle travel distances also shows a change in its shape from exponential to Gamma to Gaussian with a change in timescale implying different diffusion scaling regimes. For power-law PDF (with power - μ) of waiting times, the asymptotic behavior of particles at long time scales reveals both super-diffusion and sub-diffusion, however, only very heavy tailed waiting times (i.e. 1.0 < μ < 1.5) could result in sub-diffusion. We suggest that the contrast between our results and previous studies (for e.g., studies based on fractional advection-diffusion models of thin/heavy tailed particle hops and waiting times) results could be due the assumption in those studies that the hops are achieved instantaneously, but in reality, particles achieve their hops within finite times (as we simulate here) instead of instantaneously, even if the hop times are much shorter than waiting times. In summary, this study stresses on the need to rethink the alternative models to the previous models, such as, fractional advection-diffusion equations, for studying the anomalous diffusion of bed load particles. The implications of these results for modeling sediment transport are discussed.

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.

Is the acceleration of anomalous cosmic rays affected by the geometry of the termination shock?

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

Senanayake, U. K.; Florinski, V., E-mail: uks0001@uah.edu, E-mail: vaf0001@uah.edu

2013-12-01

Historically, anomalous cosmic rays (ACRs) were thought to be accelerated at the solar-wind termination shock (TS) by the diffusive shock acceleration process. When Voyager 1 crossed the TS in 2004, the measured ACR spectra did not match the theoretical prediction of a continuous power law, and the source of the high-energy ACRs was not observed. When the Voyager 2 crossed the TS in 2007, it produced similar results. Several possible explanations have since appeared in the literature, but we follow the suggestion that ACRs are still accelerated at the shock, only away from the Voyager crossing points. To investigate thismore » hypothesis closer, we study ACR acceleration using a three-dimensional, non-spherical model of the heliosphere that is axisymmetric with respect to the interstellar flow direction. We then compare the results with those obtained for a spherical TS. A semi-analytic model of the plasma and magnetic field backgrounds is developed to permit an investigation over a wide range of parameters under controlled conditions. The model is applied to helium ACRs, whose phase-space trajectories are stochastically integrated backward in time until a pre-specified, low-energy boundary, taken to be 0.5 MeV n{sup –1} (the so-called injection energy), is reached. Our results show that ACR acceleration is quite efficient on the heliotail-facing part of the TS. For small values of the perpendicular diffusion coefficient, our model yields a positive intensity gradient between the TS and about midway through the heliosheath, in agreement with the Voyager observations.« less

Ion distribution effects of turbulence on a kinetic auroral arc model

NASA Technical Reports Server (NTRS)

Cornwall, J. M.; Chiu, Y. T.

1982-01-01

An inverted-V auroral arc structure plasma-kinetic model is extended to phenomenologically include the effects of electrostatic turbulence, with k-parallel/k-perpendicular being much less than unity. It is shown that, unless plasma sheet ions are very much more energetic than the electrons, anomalous resistivity is not a large contributor to parallel electrostatic potential drops, since the support of the observed potential drop requires a greater dissipation of energy than can be provided by the plasma sheet. Wave turbulence can, however, be present, with the ion cyclotron turbulence levels suggested by the ion resonance broadening saturation mechanism of Dum and Dupree (1970) being comparable to those observed on auroral field lines. The diffusion coefficient and net growth rate are much smaller than estimates based solely on local plasma properties.

Poincaré recurrences of DNA sequences

NASA Astrophysics Data System (ADS)

Frahm, K. M.; Shepelyansky, D. L.

2012-01-01

We analyze the statistical properties of Poincaré recurrences of Homo sapiens, mammalian, and other DNA sequences taken from the Ensembl Genome data base with up to 15 billion base pairs. We show that the probability of Poincaré recurrences decays in an algebraic way with the Poincaré exponent β≈4 even if the oscillatory dependence is well pronounced. The correlations between recurrences decay with an exponent ν≈0.6 that leads to an anomalous superdiffusive walk. However, for Homo sapiens sequences, with the largest available statistics, the diffusion coefficient converges to a finite value on distances larger than one million base pairs. We argue that the approach based on Poncaré recurrences determines new proximity features between different species and sheds a new light on their evolution history.

Correlation of human papillomavirus status with apparent diffusion coefficient of diffusion-weighted MRI in head and neck squamous cell carcinomas.

PubMed

Driessen, Juliette P; van Bemmel, Alexander J M; van Kempen, Pauline M W; Janssen, Luuk M; Terhaard, Chris H J; Pameijer, Frank A; Willems, Stefan M; Stegeman, Inge; Grolman, Wilko; Philippens, Marielle E P

2016-04-01

Identification of prognostic patient characteristics in head and neck squamous cell carcinoma (HNSCC) is of great importance. Human papillomavirus (HPV)-positive HNSCCs have favorable response to (chemo)radiotherapy. Apparent diffusion coefficient, derived from diffusion-weighted MRI, has also shown to predict treatment response. The purpose of this study was to evaluate the correlation between HPV status and apparent diffusion coefficient. Seventy-three patients with histologically proven HNSCC were retrospectively analyzed. Mean pretreatment apparent diffusion coefficient was calculated by delineation of total tumor volume on diffusion-weighted MRI. HPV status was analyzed and correlated to apparent diffusion coefficient. Six HNSCCs were HPV-positive. HPV-positive HNSCC showed significantly lower apparent diffusion coefficient compared to HPV-negative. This correlation was independent of other patient characteristics. In HNSCC, positive HPV status correlates with low mean apparent diffusion coefficient. The favorable prognostic value of low pretreatment apparent diffusion coefficient might be partially attributed to patients with a positive HPV status. © 2015 Wiley Periodicals, Inc. Head Neck 38: E613-E618, 2016. © 2015 Wiley Periodicals, Inc.

The role of fractional time-derivative operators on anomalous diffusion

NASA Astrophysics Data System (ADS)

Tateishi, Angel A.; Ribeiro, Haroldo V.; Lenzi, Ervin K.

2017-10-01

The generalized diffusion equations with fractional order derivatives have shown be quite efficient to describe the diffusion in complex systems, with the advantage of producing exact expressions for the underlying diffusive properties. Recently, researchers have proposed different fractional-time operators (namely: the Caputo-Fabrizio and Atangana-Baleanu) which, differently from the well-known Riemann-Liouville operator, are defined by non-singular memory kernels. Here we proposed to use these new operators to generalize the usual diffusion equation. By analyzing the corresponding fractional diffusion equations within the continuous time random walk framework, we obtained waiting time distributions characterized by exponential, stretched exponential, and power-law functions, as well as a crossover between two behaviors. For the mean square displacement, we found crossovers between usual and confined diffusion, and between usual and sub-diffusion. We obtained the exact expressions for the probability distributions, where non-Gaussian and stationary distributions emerged. This former feature is remarkable because the fractional diffusion equation is solved without external forces and subjected to the free diffusion boundary conditions. We have further shown that these new fractional diffusion equations are related to diffusive processes with stochastic resetting, and to fractional diffusion equations with derivatives of distributed order. Thus, our results suggest that these new operators may be a simple and efficient way for incorporating different structural aspects into the system, opening new possibilities for modeling and investigating anomalous diffusive processes.

Anomalous dimensionality dependence of diffusion in a rugged energy landscape: How pathological is one dimension?

NASA Astrophysics Data System (ADS)

Seki, Kazuhiko; Bagchi, Kaushik; Bagchi, Biman

2016-05-01

Diffusion in one dimensional rugged energy landscape (REL) is predicted to be pathologically different (from any higher dimension) with a much larger chance of encountering broken ergodicity [D. L. Stein and C. M. Newman, AIP Conf. Proc. 1479, 620 (2012)]. However, no quantitative study of this difference has been reported, despite the prevalence of multidimensional physical models in the literature (like a high dimensional funnel guiding protein folding/unfolding). Paradoxically, some theoretical studies of these phenomena still employ a one dimensional diffusion description for analytical tractability. We explore the dimensionality dependent diffusion on REL by carrying out an effective medium approximation based analytical calculations and compare them with the available computer simulation results. We find that at an intermediate level of ruggedness (assumed to have a Gaussian distribution), where diffusion is well-defined, the value of the effective diffusion coefficient depends on dimensionality and changes (increases) by several factors (˜5-10) in going from 1d to 2d. In contrast, the changes in subsequent transitions (like 2d to 3d and 3d to 4d and so on) are far more modest, of the order of 10-20% only. When ruggedness is given by random traps with an exponential distribution of barrier heights, the mean square displacement (MSD) is sub-diffusive (a well-known result), but the growth of MSD is described by different exponents in one and higher dimensions. The reason for such strong ruggedness induced retardation in the case of one dimensional REL is discussed. We also discuss the special limiting case of infinite dimension (d = ∞) where the effective medium approximation becomes exact and where theoretical results become simple. We discuss, for the first time, the role of spatial correlation in the landscape on diffusion of a random walker.

Anomalous dimensionality dependence of diffusion in a rugged energy landscape: How pathological is one dimension?

PubMed

Seki, Kazuhiko; Bagchi, Kaushik; Bagchi, Biman

2016-05-21

Diffusion in one dimensional rugged energy landscape (REL) is predicted to be pathologically different (from any higher dimension) with a much larger chance of encountering broken ergodicity [D. L. Stein and C. M. Newman, AIP Conf. Proc. 1479, 620 (2012)]. However, no quantitative study of this difference has been reported, despite the prevalence of multidimensional physical models in the literature (like a high dimensional funnel guiding protein folding/unfolding). Paradoxically, some theoretical studies of these phenomena still employ a one dimensional diffusion description for analytical tractability. We explore the dimensionality dependent diffusion on REL by carrying out an effective medium approximation based analytical calculations and compare them with the available computer simulation results. We find that at an intermediate level of ruggedness (assumed to have a Gaussian distribution), where diffusion is well-defined, the value of the effective diffusion coefficient depends on dimensionality and changes (increases) by several factors (∼5-10) in going from 1d to 2d. In contrast, the changes in subsequent transitions (like 2d to 3d and 3d to 4d and so on) are far more modest, of the order of 10-20% only. When ruggedness is given by random traps with an exponential distribution of barrier heights, the mean square displacement (MSD) is sub-diffusive (a well-known result), but the growth of MSD is described by different exponents in one and higher dimensions. The reason for such strong ruggedness induced retardation in the case of one dimensional REL is discussed. We also discuss the special limiting case of infinite dimension (d = ∞) where the effective medium approximation becomes exact and where theoretical results become simple. We discuss, for the first time, the role of spatial correlation in the landscape on diffusion of a random walker.

Diffusion coefficients in organic-water solutions and comparison with Stokes-Einstein predictions

NASA Astrophysics Data System (ADS)

Evoy, E.; Kamal, S.; Bertram, A. K.

2017-12-01

Diffusion coefficients of organic species in particles containing secondary organic material (SOM) are necessary for predicting the growth and reactivity of these particles in the atmosphere. Previously, the Stokes-Einstein equation combined with viscosity measurements have been used to predict these diffusion coefficients. However, the accuracy of the Stokes-Einstein equation for predicting diffusion coefficients in SOM-water particles has not been quantified. To test the Stokes-Einstein equation, diffusion coefficients of fluorescent organic probe molecules were measured in citric acid-water and sorbitol-water solutions. These solutions were used as proxies for SOM-water particles found in the atmosphere. Measurements were performed as a function of water activity, ranging from 0.26-0.86, and as a function of viscosity ranging from 10-3 to 103 Pa s. Diffusion coefficients were measured using fluorescence recovery after photobleaching. The measured diffusion coefficients were compared with predictions made using the Stokes-Einstein equation combined with literature viscosity data. Within the uncertainties of the measurements, the measured diffusion coefficients agreed with the predicted diffusion coefficients, in all cases.

Ion Thermal Decoupling and Species Separation in Shock-Driven Implosions

DOE PAGES

Rinderknecht, Hans G.; Rosenberg, M. J.; Li, C. K.; ...

2015-01-14

Here, anomalous reduction of the fusion yields by 50% and anomalous scaling of the burn-averaged ion temperatures with the ion-species fraction has been observed for the first time in D 3He-filled shock-driven inertial confinement fusion implosions. Two ion kinetic mechanisms are used to explain the anomalous observations: thermal decoupling of the D and 3He populations and diffusive species separation. The observed insensitivity of ion temperature to a varying deuterium fraction is shown to be a signature of ion thermal decoupling in shock-heated plasmas. The burn-averaged deuterium fraction calculated from the experimental data demonstrates a reduction in the average core deuteriummore » density, as predicted by simulations that use a diffusion model. Accounting for each of these effects in simulations reproduces the observed yield trends.« less

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

Random-walk diffusion and drying of porous materials

NASA Astrophysics Data System (ADS)

Mehrafarin, M.; Faghihi, M.

2001-12-01

Based on random-walk diffusion, a microscopic model for drying is proposed to explain the characteristic features of the drying-rate curve of porous materials. The constant drying-rate period is considered as a normal diffusion process. The transition to the falling-rate regime is attributed to the fractal nature of porous materials which results in crossover to anomalous diffusion.

Anomalous dielectric relaxation with linear reaction dynamics in space-dependent force fields.

PubMed

Hong, Tao; Tang, Zhengming; Zhu, Huacheng

2016-12-28

The anomalous dielectric relaxation of disordered reaction with linear reaction dynamics is studied via the continuous time random walk model in the presence of space-dependent electric field. Two kinds of modified reaction-subdiffusion equations are derived for different linear reaction processes by the master equation, including the instantaneous annihilation reaction and the noninstantaneous annihilation reaction. If a constant proportion of walkers is added or removed instantaneously at the end of each step, there will be a modified reaction-subdiffusion equation with a fractional order temporal derivative operating on both the standard diffusion term and a linear reaction kinetics term. If the walkers are added or removed at a constant per capita rate during the waiting time between steps, there will be a standard linear reaction kinetics term but a fractional order temporal derivative operating on an anomalous diffusion term. The dielectric polarization is analyzed based on the Legendre polynomials and the dielectric properties of both reactions can be expressed by the effective rotational diffusion function and component concentration function, which is similar to the standard reaction-diffusion process. The results show that the effective permittivity can be used to describe the dielectric properties in these reactions if the chemical reaction time is much longer than the relaxation time.

Anomalous Diffusion of Single Particles in Cytoplasm

PubMed Central

Regner, Benjamin M.; Vučinić, Dejan; Domnisoru, Cristina; Bartol, Thomas M.; Hetzer, Martin W.; Tartakovsky, Daniel M.; Sejnowski, Terrence J.

2013-01-01

The crowded intracellular environment poses a formidable challenge to experimental and theoretical analyses of intracellular transport mechanisms. Our measurements of single-particle trajectories in cytoplasm and their random-walk interpretations elucidate two of these mechanisms: molecular diffusion in crowded environments and cytoskeletal transport along microtubules. We employed acousto-optic deflector microscopy to map out the three-dimensional trajectories of microspheres migrating in the cytosolic fraction of a cellular extract. Classical Brownian motion (BM), continuous time random walk, and fractional BM were alternatively used to represent these trajectories. The comparison of the experimental and numerical data demonstrates that cytoskeletal transport along microtubules and diffusion in the cytosolic fraction exhibit anomalous (nonFickian) behavior and posses statistically distinct signatures. Among the three random-walk models used, continuous time random walk provides the best representation of diffusion, whereas microtubular transport is accurately modeled with fractional BM. PMID:23601312

Dynamical transition for a particle in a squared Gaussian potential

NASA Astrophysics Data System (ADS)

Touya, C.; Dean, D. S.

2007-02-01

We study the problem of a Brownian particle diffusing in finite dimensions in a potential given by ψ = phi2/2 where phi is Gaussian random field. Exact results for the diffusion constant in the high temperature phase are given in one and two dimensions and it is shown to vanish in a power-law fashion at the dynamical transition temperature. Our results are confronted with numerical simulations where the Gaussian field is constructed, in a standard way, as a sum over random Fourier modes. We show that when the number of Fourier modes is finite the low temperature diffusion constant becomes non-zero and has an Arrhenius form. Thus we have a simple model with a fully understood finite size scaling theory for the dynamical transition. In addition we analyse the nature of the anomalous diffusion in the low temperature regime and show that the anomalous exponent agrees with that predicted by a trap model.

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

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.

Anomalous magnon Nernst effect of topological magnonic materials

NASA Astrophysics Data System (ADS)

Wang, X. S.; Wang, X. R.

2018-05-01

The magnon transport driven by a thermal gradient in a perpendicularly magnetized honeycomb lattice is studied. The system with the nearest-neighbor pseudodipolar interaction and the next-nearest-neighbor Dzyaloshinskii–Moriya interaction has various topologically nontrivial phases. When an in-plane thermal gradient is applied, a transverse in-plane magnon current is generated. This phenomenon is termed as the anomalous magnon Nernst effect that closely resembles the anomalous Nernst effect for an electronic system. The anomalous magnon Nernst coefficient and its sign are determined by the magnon Berry curvature distributions in the momentum space and magnon populations in the magnon bands. We predict a temperature-induced sign reversal in anomalous magnon Nernst effect under certain conditions.

High-frequency electrostatic waves in the magnetosphere.

NASA Technical Reports Server (NTRS)

Young, T. S. T.

1973-01-01

High-frequency electrostatic microinstabilities in magnetospheric plasmas are considered in detail. Rather special plasma parameters are found to be required to match the theoretical wave spectrum with satellite observations in the magnetosphere. In particular, it is necessary to have a cold and a warm species of electrons such that (1) the warm component has an anomalous velocity distribution function that is nonmonotonic in the perpendicular component of velocity and is the source of free energy driving the instabilities, (2) the density ratio of the cold component to the hot component is greater than about 0.01, and (3) the temperature ratio of the two components for cases of high particle density is no less than 0.1. These requirements and the corresponding instability criteria are satisfied only in the trapping region; this is also the region in which the waves are most frequently observed. The range of unstable wavelengths and an estimate of the diffusion coefficient are also obtained. The wave are found to induce strong diffusion in velocity space for low-energy electrons during periods of moderate wave amplitude.

Jigsaw puzzle metasurface for multiple functions: polarization conversion, anomalous reflection and diffusion.

PubMed

Zhao, Yi; Cao, Xiangyu; Gao, Jun; Liu, Xiao; Li, Sijia

2016-05-16

We demonstrate a simple reconfigurable metasurface with multiple functions. Anisotropic tiles are investigated and manufactured as fundamental elements. Then, the tiles are combined in a certain sequence to construct a metasurface. Each of the tiles can be adjusted independently which is like a jigsaw puzzle and the whole metasurface can achieve diverse functions by different layouts. For demonstration purposes, we realize polarization conversion, anomalous reflection and diffusion by a jigsaw puzzle metasurface with 6 × 6 pieces of anisotropic tile. Simulated and measured results prove that our method offers a simple and effective strategy for metasurface design.

Anomalous, non-Gaussian tracer diffusion in crowded two-dimensional environments

NASA Astrophysics Data System (ADS)

Ghosh, Surya K.; Cherstvy, Andrey G.; Grebenkov, Denis S.; Metzler, Ralf

2016-01-01

A topic of intense current investigation pursues the question of how the highly crowded environment of biological cells affects the dynamic properties of passively diffusing particles. Motivated by recent experiments we report results of extensive simulations of the motion of a finite sized tracer particle in a heterogeneously crowded environment made up of quenched distributions of monodisperse crowders of varying sizes in finite circular two-dimensional domains. For given spatial distributions of monodisperse crowders we demonstrate how anomalous diffusion with strongly non-Gaussian features arises in this model system. We investigate both biologically relevant situations of particles released either at the surface of an inner domain or at the outer boundary, exhibiting distinctly different features of the observed anomalous diffusion for heterogeneous distributions of crowders. Specifically we reveal an asymmetric spreading of tracers even at moderate crowding. In addition to the mean squared displacement (MSD) and local diffusion exponent we investigate the magnitude and the amplitude scatter of the time averaged MSD of individual tracer trajectories, the non-Gaussianity parameter, and the van Hove correlation function. We also quantify how the average tracer diffusivity varies with the position in the domain with a heterogeneous radial distribution of crowders and examine the behaviour of the survival probability and the dynamics of the tracer survival probability. Inter alia, the systems we investigate are related to the passive transport of lipid molecules and proteins in two-dimensional crowded membranes or the motion in colloidal solutions or emulsions in effectively two-dimensional geometries, as well as inside supercrowded, surface adhered cells.

Universal linear-temperature resistivity: possible quantum diffusion transport in strongly correlated superconductors.

PubMed

Hu, Tao; Liu, Yinshang; Xiao, Hong; Mu, Gang; Yang, Yi-Feng

2017-08-25

The strongly correlated electron fluids in high temperature cuprate superconductors demonstrate an anomalous linear temperature (T) dependent resistivity behavior, which persists to a wide temperature range without exhibiting saturation. As cooling down, those electron fluids lose the resistivity and condense into the superfluid. However, the origin of the linear-T resistivity behavior and its relationship to the strongly correlated superconductivity remain a mystery. Here we report a universal relation [Formula: see text], which bridges the slope of the linear-T-dependent resistivity (dρ/dT) to the London penetration depth λ L at zero temperature among cuprate superconductor Bi 2 Sr 2 CaCu 2 O 8+δ and heavy fermion superconductors CeCoIn 5 , where μ 0 is vacuum permeability, k B is the Boltzmann constant and ħ is the reduced Planck constant. We extend this scaling relation to different systems and found that it holds for other cuprate, pnictide and heavy fermion superconductors as well, regardless of the significant differences in the strength of electronic correlations, transport directions, and doping levels. Our analysis suggests that the scaling relation in strongly correlated superconductors could be described as a hydrodynamic diffusive transport, with the diffusion coefficient (D) approaching the quantum limit D ~ ħ/m*, where m* is the quasi-particle effective mass.

The role of intra-NAPL diffusion on mass transfer from MGP residuals

NASA Astrophysics Data System (ADS)

Shafieiyoun, Saeid; Thomson, Neil R.

2018-06-01

An experimental and computational study was performed to investigate the role of multi-component intra-NAPL diffusion on NAPL-water mass transfer. Molecular weight and the NAPL component concentrations were determined to be the most important parameters affecting intra-NAPL diffusion coefficients. Four NAPLs with different viscosities but the same quantified mass were simulated. For a spherical NAPL body, a combination of NAPL properties and interphase mass transfer rate can result in internal diffusion limitations. When the main intra-NAPL diffusion coefficients are in the range of self-diffusion coefficients (10-5 to 10-6 cm2/s), dissolution is not limited by internal diffusion except for high mass transfer rate coefficients (>180 cm/day). For a complex and relatively high viscous NAPL (>50 g/(cm s)), smaller intra-NAPL diffusion coefficients (<10-8) are expected and even low mass transfer rate coefficients ( 6 cm/day) can result in diffusion-limited dissolution.

The Plasma Membrane is Compartmentalized by a Self-Similar Cortical Actin Fractal

NASA Astrophysics Data System (ADS)

Sadegh, Sanaz; Higgin, Jenny; Mannion, Patrick; Tamkun, Michael; Krapf, Diego

A broad range of membrane proteins display anomalous diffusion on the cell surface. Different methods provide evidence for obstructed subdiffusion and diffusion on a fractal space, but the underlying structure inducing anomalous diffusion has never been visualized due to experimental challenges. We addressed this problem by imaging the cortical actin at high resolution while simultaneously tracking individual membrane proteins in live mammalian cells. Our data show that actin introduces barriers leading to compartmentalization of the plasma membrane and that membrane proteins are transiently confined within actin fences. Furthermore, superresolution imaging shows that the cortical actin is organized into a self-similar fractal. These results present a hierarchical nanoscale picture of the plasma membrane and demonstrate direct interactions between the actin cortex and the cell surface.

Some notes on hydrogen-related point defects and their role in the isotope exchange and electrical conductivity in olivine

NASA Astrophysics Data System (ADS)

Karato, Shun-ichiro

2015-11-01

Nominally anhydrous minerals such as olivine dissolve hydrogen in a variety of forms including free (or interstitial) proton (Hrad) and two protons trapped at the M-site ((2 H)M×). The strength of chemical bonding between protons and the surrounding atoms are different among different species, and consequently protons belonging to different species likely have different mobility (diffusion coefficients). I discuss the role of diffusion of protons in different species in the isotope exchange and hydrogen-assisted electrical conductivity adding a few notes to the previous work by Karato (2013) including a new way to test the model. I conclude that in the case of isotope exchange, the interaction among these species is strong because diffusion is heterogeneous, whereas there is no strong interaction among different species in electrical conduction where diffusion is homogeneous (in an infinite crystal). Consequently, the slowest diffusing species controls the rate of isotope exchange, whereas the fastest diffusing species controls electrical conductivity leading to a different temperature dependence of activation energy and anisotropy. This model explains the differences in the activation energy and anisotropy between isotope diffusion and electrical conductivity, and predicts that the mechanism of electrical conductivity changes with temperature providing an explanation for most of the discrepancies among different experimental observations at different temperatures except for those by Poe et al. (2010) who reported anomalously high water content dependence and highly anisotropic activation energy. When the results obtained at high temperatures are used, most of the geophysically observed high and highly anisotropic electrical conductivity in the asthenosphere can be explained without invoking partial melting.

Effective diffusion coefficient including the Marangoni effect

NASA Astrophysics Data System (ADS)

Kitahata, Hiroyuki; Yoshinaga, Natsuhiko

2018-04-01

Surface-active molecules supplied from a particle fixed at the water surface create a spatial gradient of the molecule concentration, resulting in Marangoni convection. Convective flow transports the molecules far from the particle, enhancing diffusion. We analytically derive the effective diffusion coefficient associated with the Marangoni convection rolls. The resulting estimated effective diffusion coefficient is consistent with our numerical results and the apparent diffusion coefficient measured in experiments.

Modeling and experiments for the time-dependent diffusion coefficient during methane desorption from coal

NASA Astrophysics Data System (ADS)

Cheng-Wu, Li; Hong-Lai, Xue; Cheng, Guan; Wen-biao, Liu

2018-04-01

Statistical analysis shows that in the coal matrix, the diffusion coefficient for methane is time-varying, and its integral satisfies the formula μt κ /(1 + β κ ). Therefore, a so-called dynamic diffusion coefficient model (DDC model) is developed. To verify the suitability and accuracy of the DDC model, a series of gas diffusion experiments were conducted using coal particles of different sizes. The results show that the experimental data can be accurately described by the DDC and bidisperse models, but the fit to the DDC model is slightly better. For all coal samples, as time increases, the effective diffusion coefficient first shows a sudden drop, followed by a gradual decrease before stabilizing at longer times. The effective diffusion coefficient has a negative relationship with the size of the coal particle. Finally, the relationship between the constants of the DDC model and the effective diffusion coefficient is discussed. The constant α (μ/R 2 ) denotes the effective coefficient at the initial time, and the constants κ and β control the attenuation characteristic of the effective diffusion coefficient.

Boundary value problems for multi-term fractional differential equations

NASA Astrophysics Data System (ADS)

Daftardar-Gejji, Varsha; Bhalekar, Sachin

2008-09-01

Multi-term fractional diffusion-wave equation along with the homogeneous/non-homogeneous boundary conditions has been solved using the method of separation of variables. It is observed that, unlike in the one term case, solution of multi-term fractional diffusion-wave equation is not necessarily non-negative, and hence does not represent anomalous diffusion of any kind.

Continuous Diffusion Model for Concentration Dependence of Nitroxide EPR Parameters in Normal and Supercooled Water.

PubMed

Merunka, Dalibor; Peric, Miroslav

2017-05-25

Electron paramagnetic resonance (EPR) spectra of radicals in solution depend on their relative motion, which modulates the Heisenberg spin exchange and dipole-dipole interactions between them. To gain information on radical diffusion from EPR spectra demands both reliable spectral fitting to find the concentration coefficients of EPR parameters and valid expressions between the concentration and diffusion coefficients. Here, we measured EPR spectra of the 14 N- and 15 N-labeled perdeuterated TEMPONE radicals in normal and supercooled water at various concentrations. By fitting the EPR spectra to the functions based on the modified Bloch equations, we obtained the concentration coefficients for the spin dephasing, coherence transfer, and hyperfine splitting parameters. Assuming the continuous diffusion model for radical motion, the diffusion coefficients of radicals were calculated from the concentration coefficients using the standard relations and the relations derived from the kinetic equations for the spin evolution of a radical pair. The latter relations give better agreement between the diffusion coefficients calculated from different concentration coefficients. The diffusion coefficients are similar for both radicals, which supports the presented method. They decrease with lowering temperature slower than is predicted by the Stokes-Einstein relation and slower than the rotational diffusion coefficients, which is similar to the diffusion of water molecules in supercooled water.

Anisotropic diffusion of fluorescently labeled ATP in rat cardiomyocytes determined by raster image correlation spectroscopy

PubMed Central

Vendelin, Marko; Birkedal, Rikke

2008-01-01

A series of experimental data points to the existence of profound diffusion restrictions of ADP/ATP in rat cardiomyocytes. This assumption is required to explain the measurements of kinetics of respiration, sarcoplasmic reticulum loading with calcium, and kinetics of ATP-sensitive potassium channels. To be able to analyze and estimate the role of intracellular diffusion restrictions on bioenergetics, the intracellular diffusion coefficients of metabolites have to be determined. The aim of this work was to develop a practical method for determining diffusion coefficients in anisotropic medium and to estimate the overall diffusion coefficients of fluorescently labeled ATP in rat cardiomyocytes. For that, we have extended raster image correlation spectroscopy (RICS) protocols to be able to discriminate the anisotropy in the diffusion coefficient tensor. Using this extended protocol, we estimated diffusion coefficients of ATP labeled with the fluorescent conjugate Alexa Fluor 647 (Alexa-ATP). In the analysis, we assumed that the diffusion tensor can be described by two values: diffusion coefficient along the myofibril and that across it. The average diffusion coefficients found for Alexa-ATP were as follows: 83 ± 14 μm2/s in the longitudinal and 52 ± 16 μm2/s in the transverse directions (n = 8, mean ± SD). Those values are ∼2 (longitudinal) and ∼3.5 (transverse) times smaller than the diffusion coefficient value estimated for the surrounding solution. Such uneven reduction of average diffusion coefficient leads to anisotropic diffusion in rat cardiomyocytes. Although the source for such anisotropy is uncertain, we speculate that it may be induced by the ordered pattern of intracellular structures in rat cardiomyocytes. PMID:18815224

Fluid self-diffusion in Scots pine sapwood tracheid cells.

PubMed

Johannessen, Espen H; Hansen, Eddy W; Rosenholm, Jarl B

2006-02-09

The self-diffusion coefficients of water and toluene in Scots pine sapwood was measured using low field pulsed field gradient nuclear magnetic resonance (PFG-NMR). Wood chips of 8 mm diameter were saturated with the respective liquids, and liquid self-diffusion was then traced in one dimension orthogonal to the tracheid cell walls in the wood's radial direction. The experimental echo attenuation curves were exponential, and characteristic self-diffusion coefficients were produced for diffusion times spanning from very short times to times on the order of magnitude of seconds. Observed self-diffusion coefficients were decaying asymptotically as a function of diffusion time, an effect which was ascribed to the cell walls' restriction on confined liquid diffusion. The observed self-diffusion behavior in Scots pine sapwood was compared to self-diffusion coefficients obtained from simulations of diffusion in a square. Principles of molecular displacements in confined geometries were used for elucidating the wood's cellular structure from the observed diffusion coefficients. The results were compared with a mathematical model for diffusion between parallel planes.

Molecular dynamics study on glycolic acid in the physiological salt solution

NASA Astrophysics Data System (ADS)

Matsunaga, S.

2018-05-01

Molecular dynamics (MD) study on glycolic acid in the physiological salt solution has been performed, which is a model of a biofuel cell. The structure and charge distribution of glycolic acid in aqueous solution used in MD is beforehand optimized by Gaussian09 utilizing the density functional theory. MD is performed in the NTV constant condition, i.e. the number of particles, temperature, and volume of MD cell are definite. The structure difference of the glycolic acid and oxalic acid is detected by the water distribution around the molecules using the pair distribution functions, gij(r), and the frequency dependent diffusion coefficients, Di(ν). The anomalous dielectric constant of the solution, i.e. about 12 times larger than that of water, has been obtained, which may be attributed to the ion pair formation in the solution.

Communication: Quantum molecular dynamics simulation of liquid para-hydrogen by nuclear and electron wave packet approach.

PubMed

Hyeon-Deuk, Kim; Ando, Koji

2014-05-07

Liquid para-hydrogen (p-H2) is a typical quantum liquid which exhibits strong nuclear quantum effects (NQEs) and thus anomalous static and dynamic properties. We propose a real-time simulation method of wave packet (WP) molecular dynamics (MD) based on non-empirical intra- and inter-molecular interactions of non-spherical hydrogen molecules, and apply it to condensed-phase p-H2. The NQEs, such as WP delocalization and zero-point energy, are taken into account without perturbative expansion of prepared model potential functions but with explicit interactions between nuclear and electron WPs. The developed MD simulation for 100 ps with 1200 hydrogen molecules is realized at feasible computational cost, by which basic experimental properties of p-H2 liquid such as radial distribution functions, self-diffusion coefficients, and shear viscosities are all well reproduced.

In Situ Effective Diffusion Coefficient Profiles in Live Biofilms Using Pulsed-Field Gradient Nuclear Magnetic Resonance

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

Renslow, Ryan S.; Majors, Paul D.; McLean, Jeffrey S.

2010-08-15

Diffusive mass transfer in biofilms is characterized by the effective diffusion coefficient. It is well-documented that the effective diffusion coefficient can vary by location in a biofilm. The current literature is dominated by effective diffusion coefficient measurements for distinct cell clusters and stratified biofilms showing this spatial variation. Regardless of whether distinct cell clusters or surface-averaging methods are used, position-dependent measurements of the effective diffusion coefficient are currently: 1) invasive to the biofilm, 2) performed under unnatural conditions, 3) lethal to cells, and/or 4) spatially restricted to only certain regions of the biofilm. Invasive measurements can lead to inaccurate resultsmore » and prohibit further (time dependent) measurements which are important for the mathematical modeling of biofilms. In this study our goals were to: 1) measure the effective diffusion coefficient for water in live biofilms, 2) monitor how the effective diffusion coefficient changes over time under growth conditions, and 3) correlate the effective diffusion coefficient with depth in the biofilm. We measured in situ two-dimensional effective diffusion coefficient maps within Shewanella oneidensis MR-1biofilms using pulsed-field gradient nuclear magnetic resonance methods, and used them to calculate surface-averaged relative effective diffusion coefficient (Drs) profiles. We found that 1) Drs decreased from the top of the biofilm to the bottom, 2) Drs profiles differed for biofilms of different ages, 3) Drs profiles changed over time and generally decreased with time, 4) all the biofilms showed very similar Drs profiles near the top of the biofilm, and 5) the Drs profile near the bottom of the biofilm was different for each biofilm. Practically, our results demonstrate that advanced biofilm models should use a variable effective diffusivity which changes with time and location in the biofilm.« less

Estimating the Diffusion Coefficients of Sugars Using Diffusion Experiments in Agar-Gel and Computer Simulations.

PubMed

Miyamoto, Shuichi; Atsuyama, Kenji; Ekino, Keisuke; Shin, Takashi

2018-01-01

The isolation of useful microbes is one of the traditional approaches for the lead generation in drug discovery. As an effective technique for microbe isolation, we recently developed a multidimensional diffusion-based gradient culture system of microbes. In order to enhance the utility of the system, it is favorable to have diffusion coefficients of nutrients such as sugars in the culture medium beforehand. We have, therefore, built a simple and convenient experimental system that uses agar-gel to observe diffusion. Next, we performed computer simulations-based on random-walk concepts-of the experimental diffusion system and derived correlation formulas that relate observable diffusion data to diffusion coefficients. Finally, we applied these correlation formulas to our experimentally-determined diffusion data to estimate the diffusion coefficients of sugars. Our values for these coefficients agree reasonably well with values published in the literature. The effectiveness of our simple technique, which has elucidated the diffusion coefficients of some molecules which are rarely reported (e.g., galactose, trehalose, and glycerol) is demonstrated by the strong correspondence between the literature values and those obtained in our experiments.

Study of diffusion coefficient of anhydrous trehalose glasses by using PFG-NMR spectroscopy

NASA Astrophysics Data System (ADS)

Kwon, Hyun-Joung; Takekawa, Reiji; Kawamura, Junichi; Tokuyama, Michio

2013-02-01

We investigated the temperature dependent long time self-diffusion coefficient of the anhydrous trehalose supercooled liquids by using pulsed field gradient nuclear magnetic resonance (PFG-NMR) spectroscopy. At the same temperature ranges, the diffusion coefficient convoluted from the α-relaxation time as Einstein-Smoluchowski relaxation, measured by using the dielectric loss spectroscopy are well overlapped with diffusion coefficients within experimental error. The temperature dependent diffusion coefficients obtained from different methods are normalized by fictive temperature and well satisfied the single master curve, proposed by Tokuyama.

Analytical study of fractional equations describing anomalous diffusion of energetic particles

NASA Astrophysics Data System (ADS)

Tawfik, A. M.; Fichtner, H.; Schlickeiser, R.; Elhanbaly, A.

2017-06-01

To present the main influence of anomalous diffusion on the energetic particle propagation, the fractional derivative model of transport is developed by deriving the fractional modified Telegraph and Rayleigh equations. Analytical solutions of the fractional modified Telegraph and the fractional Rayleigh equations, which are defined in terms of Caputo fractional derivatives, are obtained by using the Laplace transform and the Mittag-Leffler function method. The solutions of these fractional equations are given in terms of special functions like Fox’s H, Mittag-Leffler, Hermite and Hyper-geometric functions. The predicted travelling pulse solutions are discussed in each case for different values of fractional order.

Improved estimation of anomalous diffusion exponents in single-particle tracking experiments

NASA Astrophysics Data System (ADS)

Kepten, Eldad; Bronshtein, Irena; Garini, Yuval

2013-05-01

The mean square displacement is a central tool in the analysis of single-particle tracking experiments, shedding light on various biophysical phenomena. Frequently, parameters are extracted by performing time averages on single-particle trajectories followed by ensemble averaging. This procedure, however, suffers from two systematic errors when applied to particles that perform anomalous diffusion. The first is significant at short-time lags and is induced by measurement errors. The second arises from the natural heterogeneity in biophysical systems. We show how to estimate and correct these two errors and improve the estimation of the anomalous parameters for the whole particle distribution. As a consequence, we manage to characterize ensembles of heterogeneous particles even for rather short and noisy measurements where regular time-averaged mean square displacement analysis fails. We apply this method to both simulations and in vivo measurements of telomere diffusion in 3T3 mouse embryonic fibroblast cells. The motion of telomeres is found to be subdiffusive with an average exponent constant in time. Individual telomere exponents are normally distributed around the average exponent. The proposed methodology has the potential to improve experimental accuracy while maintaining lower experimental costs and complexity.

Anomalous increase of diffuse CO_{2} emission from Brava (Cape Verde): evidence of volcanic unrest or increase gas release from a stationary magma body?

NASA Astrophysics Data System (ADS)

García-Merino, Marta; García-Hernández, Rubén; Montrond, Eurico; Dionis, Samara; Fernandes, Paulo; Silva, Sonia V.; Alfama, Vera; Cabral, Jeremías; Pereira, Jose M.; Padrón, Eleazar; Pérez, Nemesio M.

2017-04-01

Brava (67 km2) is the southwestern most and the smallest inhabited island of the Cape Verde archipelago. It is located 18 km west of Fogo Island and rises 976 m from the sea level. Brava has not any documented historical eruptions, but its Holocene volcanism and relatively high seismic activity clearly indicate that it is an active volcanic island. Since there have been no historic eruptions in Brava, volcanic hazard awareness among the population and the authorities is very low; therefore, its volcano monitoring program is scarce. With the aim of helping to provide a multidisciplinary monitoring program for the volcanic surveillance of the island, diffuse CO2 emission surveys have been carried out since 2010; approximately every 2 years. Soil CO2 efflux measurements are periodically performed at ˜ 275 observation sites all over the island and after taking into consideration their accessibility and the island volcano-structural characteristics. At each sampling site, soil CO2 efflux measurement was performed by means of a portable NDIR sensor according to the accumulation chamber method. To quantify the total diffuse CO2 emission from Brava volcanic system, soil CO2 efflux maps were constructed using sequential Gaussian simulations (sGs). An increase trend of diffuse CO2 emission rate from 42 to 681 t d-1at Brava was observed; just one year prior the 2014-2015 Fogo eruption and almost three years before the anomalous seismic activity recorded on August 2016 with more than 1000 seismic events registered by the INMG on August 1st, 2016 (Bruno Faria, personal communication). Due to this anomalous seismic activity, a diffuse CO2 emission survey at Brava was performed from August 2 to 10, 2016, and the estimated degassing rate yield a value about 72 t d-1; typical background values. An additional survey was carried out from October 22 to November 6, 2016. For this last survey, the estimated diffuse CO2 emission from Brava showed the highest observed value with a degassing rate about 1.700 t d-1. These observed changes on diffuse CO2 emission are geochemical evidences which seem to support a volcanic unrest for the recent anomalous seismic activity registered at Brava.

Analytic expressions for ULF wave radiation belt radial diffusion coefficients

PubMed Central

Ozeke, Louis G; Mann, Ian R; Murphy, Kyle R; Jonathan Rae, I; Milling, David K

2014-01-01

We present analytic expressions for ULF wave-derived radiation belt radial diffusion coefficients, as a function of L and Kp, which can easily be incorporated into global radiation belt transport models. The diffusion coefficients are derived from statistical representations of ULF wave power, electric field power mapped from ground magnetometer data, and compressional magnetic field power from in situ measurements. We show that the overall electric and magnetic diffusion coefficients are to a good approximation both independent of energy. We present example 1-D radial diffusion results from simulations driven by CRRES-observed time-dependent energy spectra at the outer boundary, under the action of radial diffusion driven by the new ULF wave radial diffusion coefficients and with empirical chorus wave loss terms (as a function of energy, Kp and L). There is excellent agreement between the differential flux produced by the 1-D, Kp-driven, radial diffusion model and CRRES observations of differential electron flux at 0.976 MeV—even though the model does not include the effects of local internal acceleration sources. Our results highlight not only the importance of correct specification of radial diffusion coefficients for developing accurate models but also show significant promise for belt specification based on relatively simple models driven by solar wind parameters such as solar wind speed or geomagnetic indices such as Kp. Key Points Analytic expressions for the radial diffusion coefficients are presented The coefficients do not dependent on energy or wave m value The electric field diffusion coefficient dominates over the magnetic PMID:26167440

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.

Constrained diffusion or immobile fraction on cell surfaces: a new interpretation.

PubMed Central

Feder, T J; Brust-Mascher, I; Slattery, J P; Baird, B; Webb, W W

1996-01-01

Protein lateral mobility in cell membranes is generally measured using fluorescence photobleaching recovery (FPR). Since the development of this technique, the data have been interpreted by assuming free Brownian diffusion of cell surface receptors in two dimensions, an interpretation that requires that a subset of the diffusing species remains immobile. The origin of this so-called immobile fraction remains a mystery. In FPR, the motions of thousands of particles are inherently averaged, inevitably masking the details of individual motions. Recently, tracking of individual cell surface receptors has identified several distinct types of motion (Gross and Webb, 1988; Ghosh and Webb, 1988, 1990, 1994; Kusumi et al. 1993; Qian et al. 1991; Slattery, 1995), thereby calling into question the classical interpretation of FPR data as free Brownian motion of a limited mobile fraction. We have measured the motion of fluorescently labeled immunoglobulin E complexed to high affinity receptors (Fc epsilon RI) on rat basophilic leukemia cells using both single particle tracking and FPR. As in previous studies, our tracking results show that individual receptors may diffuse freely, or may exhibit restricted, time-dependent (anomalous) diffusion. Accordingly, we have analyzed FPR data by a new model to take this varied motion into account, and we show that the immobile fraction may be due to particles moving with the anomalous subdiffusion associated with restricted lateral mobility. Anomalous subdiffusion denotes random molecular motion in which the mean square displacements grow as a power law in time with a fractional positive exponent less than one. These findings call for a new model of cell membrane structure. PMID:8744314

Diffusion coefficient of the protein in various crystallization solutions: The key to growing high-quality crystals in space

NASA Astrophysics Data System (ADS)

Tanaka, Hiroaki; Takahashi, Sachiko; Yamanaka, Mari; Yoshizaki, Izumi; Sato, Masaru; Sano, Satoshi; Motohara, Moritoshi; Kobayashi, Tomoyuki; Yoshitomi, Susumu; Tanaka, Tetsuo; Fukuyama, Seijiro

2006-09-01

The diffusion coefficients of lysozyme and alpha-amylase were measured in the various polyethylene glycol (PEG) solutions. Obtained diffusion coefficients were studied with the viscosity coefficient of the solution. It was found that the diffusion process of the protein was suppressed with a factor of vγ, where ν is a relative viscosity coefficient of the PEG solution. The value of γ is -0.64 at PEG1500 for both proteins. The value increased to -0.48 at PEG8000 for lysozyme, while decreased to -0.72 for alpha-amylase. The equation of an approximate diffusion coefficient at certain PEG molecular weight and concentration was roughly obtained.

Extracting surface diffusion coefficients from batch adsorption measurement data: application of the classic Langmuir kinetics model.

PubMed

Chu, Khim Hoong

2017-11-09

Surface diffusion coefficients may be estimated by fitting solutions of a diffusion model to batch kinetic data. For non-linear systems, a numerical solution of the diffusion model's governing equations is generally required. We report here the application of the classic Langmuir kinetics model to extract surface diffusion coefficients from batch kinetic data. The use of the Langmuir kinetics model in lieu of the conventional surface diffusion model allows derivation of an analytical expression. The parameter estimation procedure requires determining the Langmuir rate coefficient from which the pertinent surface diffusion coefficient is calculated. Surface diffusion coefficients within the 10 -9 to 10 -6  cm 2 /s range obtained by fitting the Langmuir kinetics model to experimental kinetic data taken from the literature are found to be consistent with the corresponding values obtained from the traditional surface diffusion model. The virtue of this simplified parameter estimation method is that it reduces the computational complexity as the analytical expression involves only an algebraic equation in closed form which is easily evaluated by spreadsheet computation.

Anomalous temperature dependence of yield stress and work hardening coefficient of B2-stabilized NiTi alloys

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

Hosoda, Hideki; Mishima, Yoshinao; Suzuki, Tomoo

Yield stress and work hardening coefficient of B2-stabilized NiTi alloys are investigated using compression tests. Compositions of NiTi alloys are based on Ni-49mol.%Ti, to which Cr, Co and Al are chosen as ternary elements which reduce martensitic transformation temperatures of the B2 phase. Mechanical tests are carried out in liquid nitrogen at 77 K, air at room temperature (R.T.) and in an argon atmosphere between 473 K and 873 K. Only at 77 K, some alloys show characteristic stress-strain curves which indicate stress induced martensitic transformation (SIMT), but the others do not. Work hardening coefficient is found to be betweenmore » 2 and 11GPa in all the test temperature range. The values are extremely high compared with Young`s modulus of B2 NiTi. Yield stress and work hardening coefficient increase with test temperature between R.T. and about 650 K in most alloys. The anomalous temperature dependence of mechanical properties is not related to SIMT but to precipitation hardening and/or anomalous dislocation motion similar to B2-type CoTi. Solution hardening by adding ternary elements is evaluated to be small for Cr and Co additions, and large for Al addition, depending on difference in atomic size of the ternary element with respect to Ni or Ti.« less

No-Drag Frame for Anomalous Chiral Fluid

DOE PAGES

Stephanov, Mikhail A.; Yee, Ho-Ung

2016-03-24

For an anomalous fluid carrying dissipationless chiral magnetic and/or vortical currents we show that there is a frame in which a stationary obstacle experiences no drag, but energy and charge currents do not vanish, resembling superfluidity. Unlike ordinary superfluid flow, the anomalous chiral currents can transport entropy in this frame. Moreover, we show that the second law of thermodynamics completely determines the amounts of these anomalous nondissipative currents in the “no-drag frame” as polynomials in temperature and chemical potential with known anomaly coefficients. These general results are illustrated and confirmed by a calculation in the chiral kinetic theory and inmore » the quark-gluon plasma at high temperature.« less

Temperature effects on diffusion coefficient for 6-gingerol and 6-shogaol in subcritical water extraction

NASA Astrophysics Data System (ADS)

Ilia Anisa, Nor; Azian, Noor; Sharizan, Mohd; Iwai, Yoshio

2014-04-01

6-gingerol and 6-shogaol are the main constituents as anti-inflammatory or bioactive compounds from zingiber officinale Roscoe. These bioactive compounds have been proven for inflammatory disease, antioxidatives and anticancer. The effect of temperature on diffusion coefficient for 6-gingerol and 6-shogaol were studied in subcritical water extraction. The diffusion coefficient was determined by Fick's second law. By neglecting external mass transfer and solid particle in spherical form, a linear portion of Ln (1-(Ct/Co)) versus time was plotted in determining the diffusion coefficient. 6-gingerol obtained the higher yield at 130°C with diffusion coefficient of 8.582x10-11 m2/s whilst for 6-shogaol, the higher yield and diffusion coefficient at 170°C and 19.417 × 10-11 m2/s.

Derivation of diffusion coefficient of a Brownian particle in tilted periodic potential from the coordinate moments

NASA Astrophysics Data System (ADS)

Zhang, Yunxin

2009-07-01

In this research, diffusion of an overdamped Brownian particle in the tilted periodic potential is investigated. Using the one-dimensional hopping model, the formulations of the mean velocity V and effective diffusion coefficient D of the Brownian particle have been obtained [B. Derrida, J. Stat. Phys. 31 (1983) 433]. Based on the relation between the effective diffusion coefficient and the moments of the mean first passage time, the formulation of effective diffusion coefficient D of the Brownian particle also has been obtained [P. Reimann, et al., Phys. Rev. E 65 (2002) 031104]. In this research, we'll give another analytical expression of the effective diffusion coefficient D from the moments of the particle's coordinate.

Turbulence-induced anomalous electron diffusion in the plume of the VASIMR VX-200

NASA Astrophysics Data System (ADS)

Olsen, Christopher; Ballenger, Maxwell; Squire, Jared; Longmier, Benjamin; Carter, Mark; Glover, Tim

2012-10-01

The separation of electrons from magnetic nozzles is critical to the function of the VASIMR engine and is of general importance to the field of electric propulsion. Separation of electrons by means of anomalous cross field diffusion is considered. Plume measurements using spectral analysis of custom high frequency probes characterizes the nature of oscillating electric fields in the expanding magnetic nozzle. The oscillating electric field results in frequency dependent density variations that can lead to anomalously high transport in the absence of collisions mimicking collisional transport. The spatial structure of the fluctuating fields is consistent with turbulence caused by separation of energetic (> 100 eV) non-magnetized ions and low energy magnetized electrons via the modified two-stream instability (MTSI) and generalized lower hybrid drift instability (GLHDI). Electric fields as high as 300 V/m are observed at frequencies up to an order of magnitude above the lower hybrid frequency. The electric field fluctuations dissipate with increasing axial distance consistent with changes in ion flux streamlines as plasma detachment occurs.

Anomalous Dynamics of a Lipid Recognition Protein on a Membrane Surface

PubMed Central

Yamamoto, Eiji; Kalli, Antreas C.; Akimoto, Takuma; Yasuoka, Kenji; Sansom, Mark S. P.

2015-01-01

Pleckstrin homology (PH) domains are lipid-binding modules present in peripheral membrane proteins which interact with phosphatidyl-inositol phosphates (PIPs) in cell membranes. We use multiscale molecular dynamics simulations to characterize the localization and anomalous dynamics of the DAPP1 PH domain on the surface of a PIP-containing lipid bilayer. Both translational and rotational diffusion of the PH domain on the lipid membrane surface exhibit transient subdiffusion, with an exponent α ≈ 0.5 for times of less than 10 ns. In addition to a PIP3 molecule at the canonical binding site of the PH domain, we observe additional PIP molecules in contact with the protein. Fluctuations in the number of PIPs associated with the PH domain exhibit 1/f noise. We suggest that the anomalous diffusion and long-term correlated interaction of the PH domain with the membrane may contribute to an enhanced probability of encounter with target complexes on cell membrane surfaces. PMID:26657413

Tracking single Kv2.1 channels in live cells reveals anomalous subdiffusion and ergodicity breaking

NASA Astrophysics Data System (ADS)

Weigel, Aubrey; Simon, Blair; Tamkun, Michael; Krapf, Diego

2011-03-01

The dynamic organization of the plasma membrane is responsible for essential cellular processes, such as receptor trafficking and signaling. By studying the dynamics of transmembrane proteins a greater understanding of these processes as a whole can be achieved. It is broadly observed that the diffusion pattern of membrane protein displays anomalous subdiffusion. However, the mechanisms responsible for this behavior are not yet established. We explore the dynamics of the voltage gated potassium channel Kv2.1 by using single-particle tracking. We analyze Kv2.1 channel trajectories in terms of the time and ensemble distributions of square displacements. Our results reveal that all Kv2.1 channels experience anomalous subdiffusion and we observe that the Kv2.1 diffusion pattern is non-ergodic. We further investigated the role of the actin cytoskeleton in these channel dynamics by applying actin depolymerizing drugs. It is seen that with the breakdown of the actin cytoskeleton the Kv2.1 channel trajectories recover ergodicity.

Numerical Test of the Additivity Principle in Anomalous Transport

NASA Astrophysics Data System (ADS)

Tamaki, Shuji

2017-10-01

The additivity principle (AP) is one of the remarkable predictions that systematically generates all information on current fluctuations once the value of average current in the linear response regime is input. However, conditions to justify the AP are still ambiguous. We hence consider three tractable models, and discuss possible conditions. The models include the harmonic chain (HC), momentum exchange (ME) model, and momentum flip (MF) model, which respectively show ballistic, anomalous, and diffusive transport. We compare the heat current cumulants predicted by the AP with exact numerical data obtained for these models. The HC does not show the AP, whereas the MF model satisfies it, as expected, since the AP was originally proposed for diffusive systems. Surprisingly, the ME model also shows the AP. The ME model is known to show the anomalous transport similar to that shown in nonlinear systems such as the Fermi-Pasta-Ulam model. Our finding indicates that general nonlinear systems may satisfy the AP. Possible conditions for satisfying the AP are discussed.

Brownian Motion in a Speckle Light Field: Tunable Anomalous Diffusion and Selective Optical Manipulation

PubMed Central

Volpe, Giorgio; Volpe, Giovanni; Gigan, Sylvain

2014-01-01

The motion of particles in random potentials occurs in several natural phenomena ranging from the mobility of organelles within a biological cell to the diffusion of stars within a galaxy. A Brownian particle moving in the random optical potential associated to a speckle pattern, i.e., a complex interference pattern generated by the scattering of coherent light by a random medium, provides an ideal model system to study such phenomena. Here, we derive a theory for the motion of a Brownian particle in a speckle field and, in particular, we identify its universal characteristic timescale. Based on this theoretical insight, we show how speckle light fields can be used to control the anomalous diffusion of a Brownian particle and to perform some basic optical manipulation tasks such as guiding and sorting. Our results might broaden the perspectives of optical manipulation for real-life applications. PMID:24496461

Effective gaseous diffusion coefficients of select ultra-fine, super-fine and medium grain nuclear graphite

DOE PAGES

Kane, Joshua J.; Matthews, Austin C.; Orme, Christopher J.; ...

2018-05-05

Understanding “Where?” and “How much?” oxidation has occurred in a nuclear graphite component is critical to predicting any deleterious effects to physical, mechanical, and thermal properties. A key factor in answering these questions is characterizing the effective mass transport rates of gas species in nuclear graphites. Effective gas diffusion coefficients were determined for twenty-six graphite specimens spanning six modern grades of nuclear graphite. A correlation was established for the majority of grades examined allowing a reasonable estimate of the effective diffusion coefficient to be determined purely from an estimate of total porosity. The importance of Knudsen diffusion to the measuredmore » diffusion coefficients is also shown for modern grades. Furthermore, Knudsen diffusion has not historically been considered to contribute to measured diffusion coefficients of nuclear graphite.« less

Effective gaseous diffusion coefficients of select ultra-fine, super-fine and medium grain nuclear graphite

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

Kane, Joshua J.; Matthews, Austin C.; Orme, Christopher J.

Understanding “Where?” and “How much?” oxidation has occurred in a nuclear graphite component is critical to predicting any deleterious effects to physical, mechanical, and thermal properties. A key factor in answering these questions is characterizing the effective mass transport rates of gas species in nuclear graphites. Effective gas diffusion coefficients were determined for twenty-six graphite specimens spanning six modern grades of nuclear graphite. A correlation was established for the majority of grades examined allowing a reasonable estimate of the effective diffusion coefficient to be determined purely from an estimate of total porosity. The importance of Knudsen diffusion to the measuredmore » diffusion coefficients is also shown for modern grades. Furthermore, Knudsen diffusion has not historically been considered to contribute to measured diffusion coefficients of nuclear graphite.« less

Classification of nanoparticle diffusion processes in vital cells by a multifeature random forests approach: application to simulated data, darkfield, and confocal laser scanning microscopy

NASA Astrophysics Data System (ADS)

Wagner, Thorsten; Kroll, Alexandra; Wiemann, Martin; Lipinski, Hans-Gerd

2016-04-01

Darkfield and confocal laser scanning microscopy both allow for a simultaneous observation of live cells and single nanoparticles. Accordingly, a characterization of nanoparticle uptake and intracellular mobility appears possible within living cells. Single particle tracking makes it possible to characterize the particle and the surrounding cell. In case of free diffusion, the mean squared displacement for each trajectory of a nanoparticle can be measured which allows computing the corresponding diffusion coefficient and, if desired, converting it into the hydrodynamic diameter using the Stokes-Einstein equation and the viscosity of the fluid. However, within the more complex system of a cell's cytoplasm unrestrained diffusion is scarce and several other types of movements may occur. Thus, confined or anomalous diffusion (e.g. diffusion in porous media), active transport, and combinations thereof were described by several authors. To distinguish between these types of particle movement we developed an appropriate classification method, and simulated three types of particle motion in a 2D plane using a Monte Carlo approach: (1) normal diffusion, using random direction and step-length, (2) subdiffusion, using confinements like a reflective boundary with defined radius or reflective objects in the closer vicinity, and (3) superdiffusion, using a directed flow added to the normal diffusion. To simulate subdiffusion we devised a new method based on tracks of different length combined with equally probable obstacle interaction. Next we estimated the fractal dimension, elongation and the ratio of long-time / short-time diffusion coefficients. These features were used to train a random forests classification algorithm. The accuracy for simulated trajectories with 180 steps was 97% (95%-CI: 0.9481-0.9884). The balanced accuracy was 94%, 99% and 98% for normal-, sub- and superdiffusion, respectively. Nanoparticle tracking analysis was used with 100 nm polystyrene particles to get trajectories for normal diffusion. As a next step we identified diffusion types of nanoparticles in vital cells and incubated V79 fibroblasts with 50 nm gold nanoparticles, which appeared as intensely bright objects due to their surface plasmon resonance. The movement of particles in both the extracellular and intracellular space was observed by dark field and confocal laser scanning microscopy. After reducing background noise from the video it became possible to identify individual particle spots by a maximum detection algorithm and trace them using the robust single-particle tracking algorithm proposed by Jaqaman, which is able to handle motion heterogeneity and particle disappearance. The particle trajectories inside cells indicated active transport (superdiffusion) as well as subdiffusion. Eventually, the random forest classification algorithm, after being trained by the above simulations, successfully classified the trajectories observed in live cells.

Fractional phenomenology of cosmic ray anomalous diffusion

NASA Astrophysics Data System (ADS)

Uchaikin, V. V.

2013-11-01

We review the evolution of the cosmic ray diffusion concept from the ordinary (Einstein) model of Brownian motion to the fractional models that appeared in the last decade. The mathematical and physical foundations of these models are discussed, as are their consequences, related problems, and prospects for further development.

Determination of diffusion coefficients of biocides on their passage through organic resin-based renders.

PubMed

Styszko, Katarzyna; Kupiec, Krzysztof

2016-10-01

In this study the diffusion coefficients of isoproturon, diuron and cybutryn in acrylate and silicone resin-based renders were determined. The diffusion coefficients were determined using measuring concentrations of biocides in the liquid phase after being in contact with renders for specific time intervals. The mathematical solution of the transient diffusion equation for an infinite plate contacted on one side with a limited volume of water was used to calculate the diffusion coefficient. The diffusion coefficients through the acrylate render were 8.10·10(-9) m(2) s(-1) for isoproturon, 1.96·10(-9) m(2) s(-1) for diuron and 1.53·10(-9) m(2) s(-1) for cybutryn. The results for the silicone render were lower by one order of magnitude. The compounds with a high diffusion coefficient for one polymer had likewise high values for the other polymer. Copyright © 2016 Elsevier Ltd. All rights reserved.

Simultaneous Rapid Determination of the Solubility and Diffusion Coefficients of a Poorly Water-Soluble Drug Based on a Novel UV Imaging System.

PubMed

Lu, Yan; Li, Mingzhong

2016-01-01

The solubility and diffusion coefficient are two of the most important physicochemical properties of a drug compound. In practice, both have been measured separately, which is time consuming. This work utilizes a novel technique of UV imaging to determine the solubility and diffusion coefficients of poorly water-soluble drugs simultaneously. A 2-step optimal method is proposed to determine the solubility and diffusion coefficients of a poorly water-soluble pharmaceutical substance based on the Fick's second law of diffusion and UV imaging measurements. Experimental results demonstrate that the proposed method can be used to determine the solubility and diffusion coefficients of a drug with reasonable accuracy, indicating that UV imaging may provide a new opportunity to accurately measure the solubility and diffusion coefficients of a poorly water-soluble drug simultaneously and rapidly. Copyright © 2016 American Pharmacists Association®. Published by Elsevier Inc. All rights reserved.

NMR signals within the generalized Langevin model for fractional Brownian motion

NASA Astrophysics Data System (ADS)

Lisý, Vladimír; Tóthová, Jana

2018-03-01

The methods of Nuclear Magnetic Resonance belong to the best developed and often used tools for studying random motion of particles in different systems, including soft biological tissues. In the long-time limit the current mathematical description of the experiments allows proper interpretation of measurements of normal and anomalous diffusion. The shorter-time dynamics is however correctly considered only in a few works that do not go beyond the standard memoryless Langevin description of the Brownian motion (BM). In the present work, the attenuation function S (t) for an ensemble of spin-bearing particles in a magnetic-field gradient, expressed in a form applicable for any kind of stationary stochastic dynamics of spins with or without a memory, is calculated in the frame of the model of fractional BM. The solution of the model for particles trapped in a harmonic potential is obtained in an exceedingly simple way and used for the calculation of S (t). In the limit of free particles coupled to a fractal heat bath, the results compare favorably with experiments acquired in human neuronal tissues. The effect of the trap is demonstrated by introducing a simple model for the generalized diffusion coefficient of the particle.

Void formation in INCONEL MA-754 by high temperature oxidation

NASA Astrophysics Data System (ADS)

Rosenstein, Alan H.; Tien, John K.; Nix, William D.

1986-01-01

Subsurface void formation in oxide dispersion strengthened MA-754 caused by high temperature oxidation was investigated at temperatures of 1100, 1150, and 1200 °C for times of 1, 10, 50, and 100 hours. Material exposed at 1200 °C was examined using microprobe, SEM, and optical microscopy techniques. After exposure in air at 1200 °C for 100 hours, chromium depletion by as much as 10 wt pct was observed near the surface, and voids of various sizes up to 15 µm in diameter were found to depths of 300 µm. The fraction of voids increases with exposure time and, with the exception of anomalous values near the surface, decreases with depth. The maximum area fraction of voids observed was approximately 8 pct. Correlation of the void area fraction profile with the measured chromium depletion through a diffusion analysis shows that void formation is due to vacancy injection. Similar void formation in Ni-Cr alloys without oxide dispersions suggests that void formation is not dependent upon the presence of oxide dispersions. The diffusion coefficient for chromium in MA-754 at 1200 °C was computed from microprobe data to be 4 × 10-10 cm2 per second.

Communication: Quantum molecular dynamics simulation of liquid para-hydrogen by nuclear and electron wave packet approach

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

Hyeon-Deuk, Kim, E-mail: kim@kuchem.kyoto-u.ac.jp; Japan Science and Technology Agency, PRESTO, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012; Ando, Koji

2014-05-07

Liquid para-hydrogen (p-H{sub 2}) is a typical quantum liquid which exhibits strong nuclear quantum effects (NQEs) and thus anomalous static and dynamic properties. We propose a real-time simulation method of wave packet (WP) molecular dynamics (MD) based on non-empirical intra- and inter-molecular interactions of non-spherical hydrogen molecules, and apply it to condensed-phase p-H{sub 2}. The NQEs, such as WP delocalization and zero-point energy, are taken into account without perturbative expansion of prepared model potential functions but with explicit interactions between nuclear and electron WPs. The developed MD simulation for 100 ps with 1200 hydrogen molecules is realized at feasible computationalmore » cost, by which basic experimental properties of p-H{sub 2} liquid such as radial distribution functions, self-diffusion coefficients, and shear viscosities are all well reproduced.« less

Diffusion coefficients of organic molecules in sucrose-water solutions and comparison with Stokes-Einstein predictions

NASA Astrophysics Data System (ADS)

Chenyakin, Yuri; Ullmann, Dagny A.; Evoy, Erin; Renbaum-Wolff, Lindsay; Kamal, Saeid; Bertram, Allan K.

2017-02-01

The diffusion coefficients of organic species in secondary organic aerosol (SOA) particles are needed to predict the growth and reactivity of these particles in the atmosphere. Previously, viscosity measurements, along with the Stokes-Einstein relation, have been used to estimate the diffusion rates of organics within SOA particles or proxies of SOA particles. To test the Stokes-Einstein relation, we have measured the diffusion coefficients of three fluorescent organic dyes (fluorescein, rhodamine 6G and calcein) within sucrose-water solutions with varying water activity. Sucrose-water solutions were used as a proxy for SOA material found in the atmosphere. Diffusion coefficients were measured using fluorescence recovery after photobleaching. For the three dyes studied, the diffusion coefficients vary by 4-5 orders of magnitude as the water activity varied from 0.38 to 0.80, illustrating the sensitivity of the diffusion coefficients to the water content in the matrix. At the lowest water activity studied (0.38), the average diffusion coefficients were 1.9 × 10-13, 1.5 × 10-14 and 7.7 × 10-14 cm2 s-1 for fluorescein, rhodamine 6G and calcein, respectively. The measured diffusion coefficients were compared with predictions made using literature viscosities and the Stokes-Einstein relation. We found that at water activity ≥ 0.6 (which corresponds to a viscosity of ≤ 360 Pa s and Tg/T ≤ 0.81), predicted diffusion rates agreed with measured diffusion rates within the experimental uncertainty (Tg represents the glass transition temperature and T is the temperature of the measurements). When the water activity was 0.38 (which corresponds to a viscosity of 3.3 × 106 Pa s and a Tg/T of 0.94), the Stokes-Einstein relation underpredicted the diffusion coefficients of fluorescein, rhodamine 6G and calcein by a factor of 118 (minimum of 10 and maximum of 977), a factor of 17 (minimum of 3 and maximum of 104) and a factor of 70 (minimum of 8 and maximum of 494), respectively. This disagreement is significantly smaller than the disagreement observed when comparing measured and predicted diffusion coefficients of water in sucrose-water mixtures.

Mutual influence of molecular diffusion in gas and surface phases

NASA Astrophysics Data System (ADS)

Hori, Takuma; Kamino, Takafumi; Yoshimoto, Yuta; Takagi, Shu; Kinefuchi, Ikuya

2018-01-01

We develop molecular transport simulation methods that simultaneously deal with gas- and surface-phase diffusions to determine the effect of surface diffusion on the overall diffusion coefficients. The phenomenon of surface diffusion is incorporated into the test particle method and the mean square displacement method, which are typically employed only for gas-phase transport. It is found that for a simple cylindrical pore, the diffusion coefficients in the presence of surface diffusion calculated by these two methods show good agreement. We also confirm that both methods reproduce the analytical solution. Then, the diffusion coefficients for ink-bottle-shaped pores are calculated using the developed method. Our results show that surface diffusion assists molecular transport in the gas phase. Moreover, the surface tortuosity factor, which is known to be uniquely determined by physical structure, is influenced by the presence of gas-phase diffusion. This mutual influence of gas-phase diffusion and surface diffusion indicates that their simultaneous calculation is necessary for an accurate evaluation of the diffusion coefficients.

Molecular modeling of diffusion coefficient and ionic conductivity of CO2 in aqueous ionic solutions.

PubMed

Garcia-Ratés, Miquel; de Hemptinne, Jean-Charles; Bonet Avalos, Josep; Nieto-Draghi, Carlos

2012-03-08

Mass diffusion coefficients of CO(2)/brine mixtures under thermodynamic conditions of deep saline aquifers have been investigated by molecular simulation. The objective of this work is to provide estimates of the diffusion coefficient of CO(2) in salty water to compensate the lack of experimental data on this property. We analyzed the influence of temperature, CO(2) concentration,and salinity on the diffusion coefficient, the rotational diffusion, as well as the electrical conductivity. We observe an increase of the mass diffusion coefficient with the temperature, but no clear dependence is identified with the salinity or with the CO(2) mole fraction, if the system is overall dilute. In this case, we notice an important dispersion on the values of the diffusion coefficient which impairs any conclusive statement about the effect of the gas concentration on the mobility of CO(2) molecules. Rotational relaxation times for water and CO(2) increase by decreasing temperature or increasing the salt concentration. We propose a correlation for the self-diffusion coefficient of CO(2) in terms of the rotational relaxation time which can ultimately be used to estimate the mutual diffusion coefficient of CO(2) in brine. The electrical conductivity of the CO(2)-brine mixtures was also calculated under different thermodynamic conditions. Electrical conductivity tends to increase with the temperature and salt concentration. However, we do not observe any influence of this property with the CO(2) concentration at the studied regimes. Our results give a first evaluation of the variation of the CO(2)-brine mass diffusion coefficient, rotational relaxation times, and electrical conductivity under the thermodynamic conditions typically encountered in deep saline aquifers.

Role of Heterogeneous Macromolecular Crowding and Geometrical Irregularity at Central Excitatory Synapses in Shaping Synaptic Transmission

PubMed Central

Gupta, Rahul; Reneaux, Melissa; Karmeshu

2016-01-01

Besides the geometrical tortousity due to the extrasynaptic structures, macromolecular crowding and geometrical irregularities constituting the cleft composition at central excitatory synapses has a major and direct role in retarding the glutamate diffusion within the cleft space. However, the cleft composition may not only coarsely reduce the overall diffusivity of the glutamate but may also lead to substantial spatial variation in the diffusivity across the cleft space. Decrease in the overall diffusivity of the glutamate may have straightforward consequences to the glutamate transients in the cleft. However, how spatial variation in the diffusivity may further affect glutamate transients is an intriguing aspect. Therefore, to understand the role of cleft heterogeneity, the present study adopts a novel approach of glutamate diffusion which considers a gamma statistical distribution of the diffusion coefficient of glutamate (Dglut) across the cleft space, such that its moments discernibly capture the dual impacts of the cleft composition, and further applies the framework of superstatistics. The findings reveal a power law behavior in the glutamate transients, akin to the long-range anomalous subdiffusion, which leads to slower decay profile of cleft glutamate at higher intensity of cleft heterogeneity. Moreover, increase in the cleft heterogeneity is seen to eventually cause slower-rising excitatory postsynaptic currents with higher amplitudes, lesser noise, and prolonged duration of charge transfer across the postsynaptic membrane. Further, with regard to the conventional standard diffusion approach, the study suggests that the effective Dglut essentially derives from the median of the Dglut distribution and does not necessarily need to be the mean Dglut. Together, the findings indicate a strong implication of cleft heterogeneity to the metabolically cost-effective tuning of synaptic response during the phenomenon of plasticity at individual synapses and also provide an additional factor of variability in transmission across identical synapses. PMID:27907112

Spin Diffusion Coefficient of A1-PHASE of Superfluid 3He at Low Temperatures

NASA Astrophysics Data System (ADS)

Afzali, R.; Pashaee, F.

The spin diffusion coefficient tensor of the A1-phase of superfluid 3He at low temperatures and melting pressure is calculated using the Boltzmann equation approach and Pfitzner procedure. Then considering Bogoliubov-normal interaction, we show that the total spin diffusion is proportional to 1/T2, the spin diffusion coefficient of superfluid component D\\uparrowxzxz is proportional to T-2, and the spin diffusion coefficient of super-fluid component D\\uparrowxxxx (=D\\uarrowxyxy) is independent of temperature. Furthermore, it is seen that superfluid components play an important role in spin diffusion of the A1-phase.

Normal and anomalous diffusion in fluctuations of dust concentration nearby emission source

NASA Astrophysics Data System (ADS)

Szczurek, Andrzej; Maciejewska, Monika; Wyłomańska, Agnieszka; Sikora, Grzegorz; Balcerek, Michał; Teuerle, Marek

2018-02-01

Particulate matter (PM) is an important component of air. Nowadays, major attention is payed to fine dust. It has considerable environmental impact, including adverse effect on human health. One of important issues regarding PM is the temporal variation of its concentration. The variation contains information about factors influencing this quantity in time. The work focuses on the character of PM concentration dynamics indoors, in the vicinity of emission source. The objective was to recognize between the homogeneous or heterogeneous dynamics. The goal was achieved by detecting normal and anomalous diffusion in fluctuations of PM concentration. For this purpose we used anomalous diffusion exponent, β which was derived from Mean Square Displacement (MSD) analysis. The information about PM concentration dynamics may be used to design sampling strategy, which serves to attain representative information about PM behavior in time. The data analyzed in this work was collected from single-point PM concentration monitoring in the vicinity of seven emission sources in industrial environment. In majority of cases we observed heterogeneous character of PM concentration dynamics. It confirms the complexity of interactions between the emission sources and indoor environment. This result also votes against simplistic approach to PM concentration measurement indoors, namely their occasional character, short measurement periods and long term averaging.

Computational Study of Poloidal Angular Momentum Transport in DIII-D

NASA Astrophysics Data System (ADS)

Pankin, Alexei; Kruger, Scott; Kritz, Arnold; Rafiq, Tariq; Weiland, Jan

2013-10-01

The new Multi-Mode Model, MMM8.1, includes the capability to predict the anomalous poloidal momentum diffusivity [T. Rafiq et al., Phys. Plasmas 20, 032506 (2013)]. It is important to consider the effect of this diffusivity on the poloidal rotation of tokamak plasmas since some experimental observations suggest that neoclassical effects are not always sufficient to explain the observed poloidal rotation [B.A. Grierson et al., Phys. Plasmas 19, 056107 (2012)]. One of the objectives of this research is to determine if the anomalous contribution to the poloidal rotation can be significant in the regions of internal transport barriers (ITBs). In this study, the MMM8.1 model is used to compute the poloidal momentum diffusivity for a range of plasma parameters that correspond to the parameters that occur in DIII-D discharges. The parameters that are considered include the temperature and density gradients, and magnetic shear. The role of anomalous poloidal transport in the possible poloidal spin up in the ITB regions is discussed. Progress in the implementation of poloidal transport equations in the ASTRA transport code is reported and initial predictive simulation results for the poloidal rotation profiles are presented. This research is partially support by the DOE Grants DE-SC0006629 and DE-FG02-92ER54141.

Static and Dynamic Effects of Lateral Carrier Diffusion in Semiconductor Lasers

NASA Technical Reports Server (NTRS)

Li, Jian-Zhong; Cheung, Samson H.; Ning, C. Z.; Biegel, Bryan A. (Technical Monitor)

2002-01-01

Electron and hole diffusions in the plane of semiconductor quantum wells play an important part in the static and dynamic operations of semiconductor lasers. It is well known that the value of diffusion coefficients affects the threshold pumping current of a semiconductor laser. At the same time, the strength of carrier diffusion process is expected to affect the modulation bandwidth of an AC-modulated laser. It is important not only to investigate the combined DC and AC effects due to carrier diffusion, but also to separate the AC effects from that of the combined effects in order to provide design insights for high speed modulation. In this presentation, we apply a hydrodynamic model developed by the present authors recently from the semiconductor Bloch equations. The model allows microscopic calculation of the lateral carrier diffusion coefficient, which is a nonlinear function of the carrier density and plasma temperature. We first studied combined AC and DC effects of lateral carrier diffusion by studying the bandwidth dependence on diffusion coefficient at a given DC current under small signal modulation. The results show an increase of modulation bandwidth with decrease in the diffusion coefficient. We simultaneously studied the effects of nonlinearity in the diffusion coefficient. To clearly identify how much of the bandwidth increase is a result of decrease in the threshold pumping current for smaller diffusion coefficient, thus an effective increase of DC pumping, we study the bandwidth dependence on diffusion coefficient at a given relative pumping. A detailed comparison of the two cases will be presented.

Diffusion and mobility of atomic particles in a liquid

NASA Astrophysics Data System (ADS)

Smirnov, B. M.; Son, E. E.; Tereshonok, D. V.

2017-11-01

The diffusion coefficient of a test atom or molecule in a liquid is determined for the mechanism where the displacement of the test molecule results from the vibrations and motion of liquid molecules surrounding the test molecule and of the test particle itself. This leads to a random change in the coordinate of the test molecule, which eventually results in the diffusion motion of the test particle in space. Two models parameters of interaction of a particle and a liquid are used to find the activation energy of the diffusion process under consideration: the gas-kinetic cross section for scattering of test molecules in the parent gas and the Wigner-Seitz radius for test molecules. In the context of this approach, we have calculated the diffusion coefficient of atoms and molecules in water, where based on experimental data, we have constructed the dependence of the activation energy for the diffusion of test molecules in water on the interaction parameter and the temperature dependence for diffusion coefficient of atoms or molecules in water within the models considered. The statistically averaged difference of the activation energies for the diffusion coefficients of different test molecules in water that we have calculated based on each of the presented models does not exceed 10% of the diffusion coefficient itself. We have considered the diffusion of clusters in water and present the dependence of the diffusion coefficient on the cluster size. The accuracy of the presented formulas for the diffusion coefficient of atomic particles in water is estimated to be 50%.

Unsaturated soil moisture drying and wetting diffusion coefficient measurements in the laboratory.

DOT National Transportation Integrated Search

2009-09-01

ABSTRACTTransient moisture flow in an unsaturated soil in response to suction changes is controlled by the unsaturated moisture diffusion coefficient. The moisture diffusion coefficient can be determined by measuring suction profiles over time. The l...

A novel approach to interpretation of the time-dependent self-diffusion coefficient as a probe of porous media geometry.

PubMed

Loskutov, V V; Sevriugin, V A

2013-05-01

This article presents a new approximation describing fluid diffusion in porous media. Time dependence of the self-diffusion coefficient D(t) in the permeable porous medium is studied based on the assumption that diffusant molecules move randomly. An analytical expression for time dependence of the self-diffusion coefficient was obtained in the following form: D(t)=(D0-D∞)exp(-D0t/λ)+D∞, where D0 is the self-diffusion coefficient of bulk fluid, D∞ is the asymptotic value of the self-diffusion coefficient in the limit of long time values (t→∞), λ is the characteristic parameter of this porous medium with dimensionality of length. Applicability of the solution obtained to the analysis of experimental data is shown. The possibility of passing to short-time and long-time regimes is discussed. Copyright © 2013 Elsevier Inc. All rights reserved.

Single-image diffusion coefficient measurements of proteins in free solution.

PubMed

Zareh, Shannon Kian; DeSantis, Michael C; Kessler, Jonathan M; Li, Je-Luen; Wang, Y M

2012-04-04

Diffusion coefficient measurements are important for many biological and material investigations, such as studies of particle dynamics and kinetics, and size determinations. Among current measurement methods, single particle tracking (SPT) offers the unique ability to simultaneously obtain location and diffusion information about a molecule while using only femtomoles of sample. However, the temporal resolution of SPT is limited to seconds for single-color-labeled samples. By directly imaging three-dimensional diffusing fluorescent proteins and studying the widths of their intensity profiles, we were able to determine the proteins' diffusion coefficients using single protein images of submillisecond exposure times. This simple method improves the temporal resolution of diffusion coefficient measurements to submilliseconds, and can be readily applied to a range of particle sizes in SPT investigations and applications in which diffusion coefficient measurements are needed, such as reaction kinetics and particle size determinations. Copyright © 2012 Biophysical Society. Published by Elsevier Inc. All rights reserved.

Lévy/Anomalous Diffusion as a Mean-Field Theory for 3D Cloud Effects in Shortwave Radiative Transfer: Empirical Support, New Analytical Formulation, and Impact on Atmospheric Absorption

NASA Astrophysics Data System (ADS)

Buldyrev, S.; Davis, A.; Marshak, A.; Stanley, H. E.

2001-12-01

Two-stream radiation transport models, as used in all current GCM parameterization schemes, are mathematically equivalent to ``standard'' diffusion theory where the physical picture is a slow propagation of the diffuse radiation by Gaussian random walks. The space/time spread (technically, the Green function) of this diffusion process is described exactly by a Gaussian distribution; from the statistical physics viewpoint, this follows from the convergence of the sum of many (rescaled) steps between scattering events with a finite variance. This Gaussian picture follows directly from first principles (the radiative transfer equation) under the assumptions of horizontal uniformity and large optical depth, i.e., there is a homogeneous plane-parallel cloud somewhere in the column. The first-order effect of 3D variability of cloudiness, the main source of scattering, is to perturb the distribution of single steps between scatterings which, modulo the ``1-g'' rescaling, can be assumed effectively isotropic. The most natural generalization of the Gaussian distribution is the 1-parameter family of symmetric Lévy-stable distributions because the sum of many zero-mean random variables with infinite variance, but finite moments of order q < α (0 < α < 2), converge to them. It has been shown on heuristic grounds that for these Lévy-based random walks the typical number of scatterings is now (1-g)τ α for transmitted light. The appearance of a non-rational exponent is why this is referred to as ``anomalous'' diffusion. Note that standard/Gaussian diffusion is retrieved in the limit α = 2-. Lévy transport theory has been successfully used in the statistical physics literature to investigate a wide variety of systems with strongly nonlinear dynamics; these applications range from random advection in turbulent fluids to the erratic behavior of financial time-series and, most recently, self-regulating ecological systems. We will briefly survey the state-of-the-art observations that offer compelling empirical support for the Lévy/anomalous diffusion model in atmospheric radiation: (1) high-resolution spectroscopy of differential absorption in the O2 A-band from ground; (2) temporal transient records of lightning strokes transmitted through clouds to a sensitive detector in space; and (3) the Gamma-distributions of optical depths derived from Landsat cloud scenes at 30-m resolution. We will then introduce a rigorous analytical formulation of Lévy/anomalous transport through finite media based on fractional derivatives and Sonin calculus. A remarkable result from this new theoretical development is an extremal property of the α = 1+ case (divergent mean-free-path), as is observed in the cloudy atmosphere. Finally, we will discuss the implications of anomalous transport theory for bulk 3D effects on the current enhanced absorption problem as well as its role as the basis of a next-generation GCM radiation parameterization.

How molecular motors work in the crowded environment of living cells: coexistence and efficiency of normal and anomalous transport.

PubMed

Goychuk, Igor; Kharchenko, Vasyl O; Metzler, Ralf

2014-01-01

Recent experiments reveal both passive subdiffusion of various nanoparticles and anomalous active transport of such particles by molecular motors in the molecularly crowded environment of living biological cells. Passive and active microrheology reveals that the origin of this anomalous dynamics is due to the viscoelasticity of the intracellular fluid. How do molecular motors perform in such a highly viscous, dissipative environment? Can we explain the observed co-existence of the anomalous transport of relatively large particles of 100 to 500 nm in size by kinesin motors with the normal transport of smaller particles by the same molecular motors? What is the efficiency of molecular motors in the anomalous transport regime? Here we answer these seemingly conflicting questions and consistently explain experimental findings in a generalization of the well-known continuous diffusion model for molecular motors with two conformational states in which viscoelastic effects are included.

How Molecular Motors Work in the Crowded Environment of Living Cells: Coexistence and Efficiency of Normal and Anomalous Transport

PubMed Central

Goychuk, Igor; Kharchenko, Vasyl O.; Metzler, Ralf

2014-01-01

Recent experiments reveal both passive subdiffusion of various nanoparticles and anomalous active transport of such particles by molecular motors in the molecularly crowded environment of living biological cells. Passive and active microrheology reveals that the origin of this anomalous dynamics is due to the viscoelasticity of the intracellular fluid. How do molecular motors perform in such a highly viscous, dissipative environment? Can we explain the observed co-existence of the anomalous transport of relatively large particles of 100 to 500 nm in size by kinesin motors with the normal transport of smaller particles by the same molecular motors? What is the efficiency of molecular motors in the anomalous transport regime? Here we answer these seemingly conflicting questions and consistently explain experimental findings in a generalization of the well-known continuous diffusion model for molecular motors with two conformational states in which viscoelastic effects are included. PMID:24626511

Diffusion coefficients in systems with inclusion compounds. 1. alpha. -Cyclodextrin-L-phenylalanine-water at 25 degree C

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

Paduano, L.; Sartorio, R.; Vitagliano, V.

Diffusion coefficients in the ternary system {alpha}-cyclodextrin (at one concentration)-L-phenylalanine (at four concentrations)-water have been measured by using the Gouy interferometric technique. The effect of the inclusion equilibrium on the cross-term diffusion coefficients was observed. The measured diffusion coefficients in the ternary systems were used to calculate values of the binding constants. These values are in good agreement with the value obtained from calorimetric studies.

Banded Structures in Electron Pitch Angle Diffusion Coefficients from Resonant Wave Particle Interactions

NASA Technical Reports Server (NTRS)

Tripathi, A. K.; Singhal, R. P.; Khazanov, G. V.; Avanov, L. A.

2016-01-01

Electron pitch angle (D (alpha)) and momentum (D(pp)) diffusion coefficients have been calculated due to resonant interactions with electrostatic electron cyclotron harmonic (ECH) and whistler mode chorus waves. Calculations have been performed at two spatial locations L = 4.6 and 6.8 for electron energies 10 keV. Landau (n = 0) resonance and cyclotron harmonic resonances n = +/-1, +/-2,...+/-5 have been included in the calculations. It is found that diffusion coefficient versus pitch angle (alpha) profiles show large dips and oscillations or banded structures. The structures are more pronounced for ECH and lower band chorus (LBC) and particularly at location 4.6. Calculations of diffusion coefficients have also been performed for individual resonances. It is noticed that the main contribution of ECH waves in pitch angle diffusion coefficient is due to resonances n = +1 and n = +2. A major contribution to momentum diffusion coefficients appears from n = +2. However, the banded structures in D alpha and Dpp coefficients appear only in the profile of diffusion coefficients for n = +2. The contribution of other resonances to diffusion coefficients is found to be, in general, quite small or even negligible. For LBC and upper band chorus waves, the banded structures appear only in Landau resonance. The Dpp diffusion coefficient for ECH waves is one to two orders smaller than D alpha coefficients. For chorus waves, Dpp coefficients are about an order of magnitude smaller than D alpha coefficients for the case n does not = 0. In case of Landau resonance, the values of Dpp coefficient are generally larger than the values of D alpha coefficients particularly at lower energies. As an aid to the interpretation of results, we have also determined the resonant frequencies. For ECH waves, resonant frequencies have been estimated for wave normal angle 89 deg and harmonic resonances n = +1, +2, and +3, whereas for whistler mode waves, the frequencies have been calculated for angle 10 deg and Landau resonance. Further, in ECH waves, the banded structures appear for electron energies (is) greater than1 keV, and for whistler mode chorus waves, structures appear for energies greater than 2 keV at L = 4.6 and above 200 eV for L = 6.8. The results obtained in the present work will be helpful in the study of diffusion curves and will have important consequences for diffuse aurora and pancake distributions.

Banded Structures in Electron Pitch Angle Diffusion Coefficients from Resonant Wave-Particle Interactions

NASA Technical Reports Server (NTRS)

Tripathi, A. K.; Singhal, R. P.; Khazanov, G. V.; Avanov, L. A.

2016-01-01

Electron pitch angle (D(sub (alpha alpha))) and momentum (D(sub pp)) diffusion coefficients have been calculated due to resonant interactions with electrostatic electron cyclotron harmonic (ECH) and whistler mode chorus waves. Calculations have been performed at two spatial locations L=4.6 and 6.8 for electron energies less than or equal to 10 keV. Landau (n=0) resonance and cyclotron harmonic resonances n= +/- 1, +/-2, ... +/-5 have been included in the calculations. It is found that diffusion coefficient versus pitch angle (alpha) profiles show large dips and oscillations or banded structures. The structures are more pronounced for ECH and lower band chorus (LBC) and particularly at location 4.6. Calculations of diffusion coefficients have also been performed for individual resonances. It is noticed that the main contribution of ECH waves in pitch angle diffusion coefficient is due to resonances n=+1 and n=+2. A major contribution to momentum diffusion coefficients appears from n=+2. However, the banded structures in D(sub alpha alpha) and D(sub pp) coefficients appear only in the profile of diffusion coefficients for n=+2. The contribution of other resonances to diffusion coefficients is found to be, in general, quite small or even negligible. For LBC and upper band chorus waves, the banded structures appear only in Landau resonance. The D(sub pp) diffusion coefficient for ECH waves is one to two orders smaller than D(sub alpha alpha) coefficients. For chorus waves, D(sub pp) coefficients are about an order of magnitude smaller than D(sub alpha alpha) coefficients for the case n does not equal 0. In case of Landau resonance, the values of D(sub pp) coefficient are generally larger than the values of D(sub alpha alpha) coefficients particularly at lower energies. As an aid to the interpretation of results, we have also determined the resonant frequencies. For ECH waves, resonant frequencies have been estimated for wave normal angle 89 deg and harmonic resonances n= +1, +2, and +3, whereas for whistler mode waves, the frequencies have been calculated for angle 10 deg and Landau resonance. Further, in ECH waves, the banded structures appear for electron energies 1 greater than or equal to keV, and for whistler mode chorus waves, structures appear for energies greater than 2 keV at L=4.6 and above 200 eV for L=6.8. The results obtained in the present work will be helpful in the study of diffusion curves and will have important consequences for diffuse aurora and pancake distributions.

Bulk diffusion in a kinetically constrained lattice gas

NASA Astrophysics Data System (ADS)

Arita, Chikashi; Krapivsky, P. L.; Mallick, Kirone

2018-03-01

In the hydrodynamic regime, the evolution of a stochastic lattice gas with symmetric hopping rules is described by a diffusion equation with density-dependent diffusion coefficient encapsulating all microscopic details of the dynamics. This diffusion coefficient is, in principle, determined by a Green-Kubo formula. In practice, even when the equilibrium properties of a lattice gas are analytically known, the diffusion coefficient cannot be computed except when a lattice gas additionally satisfies the gradient condition. We develop a procedure to systematically obtain analytical approximations for the diffusion coefficient for non-gradient lattice gases with known equilibrium. The method relies on a variational formula found by Varadhan and Spohn which is a version of the Green-Kubo formula particularly suitable for diffusive lattice gases. Restricting the variational formula to finite-dimensional sub-spaces allows one to perform the minimization and gives upper bounds for the diffusion coefficient. We apply this approach to a kinetically constrained non-gradient lattice gas in two dimensions, viz. to the Kob-Andersen model on the square lattice.

Theory and simulation of time-fractional fluid diffusion in porous media

NASA Astrophysics Data System (ADS)

Carcione, José M.; Sanchez-Sesma, Francisco J.; Luzón, Francisco; Perez Gavilán, Juan J.

2013-08-01

We simulate a fluid flow in inhomogeneous anisotropic porous media using a time-fractional diffusion equation and the staggered Fourier pseudospectral method to compute the spatial derivatives. A fractional derivative of the order of 0 < ν < 2 replaces the first-order time derivative in the classical diffusion equation. It implies a time-dependent permeability tensor having a power-law time dependence, which describes memory effects and accounts for anomalous diffusion. We provide a complete analysis of the physics based on plane waves. The concepts of phase, group and energy velocities are analyzed to describe the location of the diffusion front, and the attenuation and quality factors are obtained to quantify the amplitude decay. We also obtain the frequency-domain Green function. The time derivative is computed with the Grünwald-Letnikov summation, which is a finite-difference generalization of the standard finite-difference operator to derivatives of fractional order. The results match the analytical solution obtained from the Green function. An example of the pressure field generated by a fluid injection in a heterogeneous sandstone illustrates the performance of the algorithm for different values of ν. The calculation requires storing the whole pressure field in the computer memory since anomalous diffusion ‘recalls the past’.

Measurement of effective air diffusion coefficients for trichloroethene in undisturbed soil cores.

PubMed

Bartelt-Hunt, Shannon L; Smith, James A

2002-06-01

In this study, we measure effective diffusion coefficients for trichloroethene in undisturbed soil samples taken from Picatinny Arsenal, New Jersey. The measured effective diffusion coefficients ranged from 0.0053 to 0.0609 cm2/s over a range of air-filled porosity of 0.23-0.49. The experimental data were compared to several previously published relations that predict diffusion coefficients as a function of air-filled porosity and porosity. A multiple linear regression analysis was developed to determine if a modification of the exponents in Millington's [Science 130 (1959) 100] relation would better fit the experimental data. The literature relations appeared to generally underpredict the effective diffusion coefficient for the soil cores studied in this work. Inclusion of a particle-size distribution parameter, d10, did not significantly improve the fit of the linear regression equation. The effective diffusion coefficient and porosity data were used to recalculate estimates of diffusive flux through the subsurface made in a previous study performed at the field site. It was determined that the method of calculation used in the previous study resulted in an underprediction of diffusive flux from the subsurface. We conclude that although Millington's [Science 130 (1959) 100] relation works well to predict effective diffusion coefficients in homogeneous soils with relatively uniform particle-size distributions, it may be inaccurate for many natural soils with heterogeneous structure and/or non-uniform particle-size distributions.

Determination of the diffusion coefficient of hydrogen ion in hydrogels.

PubMed

Schuszter, Gábor; Gehér-Herczegh, Tünde; Szűcs, Árpád; Tóth, Ágota; Horváth, Dezső

2017-05-17

The role of diffusion in chemical pattern formation has been widely studied due to the great diversity of patterns emerging in reaction-diffusion systems, particularly in H + -autocatalytic reactions where hydrogels are applied to avoid convection. A custom-made conductometric cell is designed to measure the effective diffusion coefficient of a pair of strong electrolytes containing sodium ions or hydrogen ions with a common anion. This together with the individual diffusion coefficient for sodium ions, obtained from PFGSE-NMR spectroscopy, allows the determination of the diffusion coefficient of hydrogen ions in hydrogels. Numerical calculations are also performed to study the behavior of a diffusion-migration model describing ionic diffusion in our system. The method we present for one particular case may be extended for various hydrogels and diffusing ions (such as hydroxide) which are relevant e.g. for the development of pH-regulated self-healing mechanisms and hydrogels used for drug delivery.

Extensive database of liquid phase diffusion coefficients of some frequently used test molecules in reversed-phase liquid chromatography and hydrophilic interaction liquid chromatography.

PubMed

Song, Huiying; Vanderheyden, Yoachim; Adams, Erwin; Desmet, Gert; Cabooter, Deirdre

2016-07-15

Diffusion plays an important role in all aspects of band broadening in chromatography. An accurate knowledge of molecular diffusion coefficients in different mobile phases is therefore crucial in fundamental column performance studies. Correlations available in literature, such as the Wilke-Chang equation, can provide good approximations of molecular diffusion under reversed-phase conditions. However, these correlations have been demonstrated to be less accurate for mobile phases containing a large percentage of acetonitrile, as is the case in hydrophilic interaction liquid chromatography. A database of experimentally measured molecular diffusion coefficients of some 45 polar and apolar compounds that are frequently used as test molecules under hydrophilic interaction liquid chromatography and reversed-phase conditions is therefore presented. Special attention is given to diffusion coefficients of polar compounds obtained in large percentages of acetonitrile (>90%). The effect of the buffer concentration (5-10mM ammonium acetate) on the obtained diffusion coefficients is investigated and is demonstrated to mainly influence the molecular diffusion of charged molecules. Diffusion coefficients are measured using the Taylor-Aris method and hence deduced from the peak broadening of a solute when flowing through a long open tube. The validity of the set-up employed for the measurement of the diffusion coefficients is demonstrated by ruling out the occurrence of longitudinal diffusion, secondary flow interactions and extra-column effects, while it is also shown that radial equilibration in the 15m long capillary is effective. Copyright © 2016 Elsevier B.V. All rights reserved.

Method of producing microporous joints in metal bodies

DOEpatents

Danko, Joseph C.

1982-01-01

Tungsten is placed in contact with either molybdenum, tantalum, niobium, vanadium, rhenium, or other metal of atoms having a different diffusion coefficient than tungsten. The metals are heated so that the atoms having the higher diffusion coefficient migrate to the metal having the lower diffusion rate, leaving voids in the higher diffusion coefficient metal. Heating is continued until the voids are interconnected.

First-principles multiple-barrier diffusion theory. The case study of interstitial diffusion in CdTe

DOE PAGES

Yang, Ji -Hui; Park, Ji -Sang; Kang, Joongoo; ...

2015-02-17

The diffusion of particles in solid-state materials generally involves several sequential thermal-activation processes. However, presently, diffusion coefficient theory only deals with a single barrier, i.e., it lacks an accurate description to deal with multiple-barrier diffusion. Here, we develop a general diffusion coefficient theory for multiple-barrier diffusion. Using our diffusion theory and first-principles calculated hopping rates for each barrier, we calculate the diffusion coefficients of Cd, Cu, Te, and Cl interstitials in CdTe for their full multiple-barrier diffusion pathways. As a result, we found that the calculated diffusivity agrees well with the experimental measurement, thus justifying our theory, which is generalmore » for many other systems.« less

Magnetotelluric investigation of the geothermal anomaly in Hailin, Mudanjiang, northeastern China

NASA Astrophysics Data System (ADS)

Zhang, Lili; Hao, Tianyao; Xiao, Qibin; Wang, Jie; Zhou, Liang; Qi, Min; Cui, Xiangpan; Cai, Ningxiao

2015-07-01

To study the occurrence conditions and locations of geothermal bodies in Hailin, Mudanjiang, northeastern China, we conducted a magnetotelluric investigation to delineate the electrical conductivity structure of the area on three parallel profiles. The area to the west of the Mudanjiang Fault lies in the Hailang sag of the Ning'an Basin. The data were processed using the mutual reference technique, static shift correction, and structural strike and dimensionality analysis based on tensor decomposition. Moreover, a modified anisotropic-diffusion-based method was used to suppress noise for the magnetotelluric time series data. This method retains the advantages of conventional anisotropic diffusion and is superior in its discrimination ability. The method is characteristic not only of the inherited features such as intra-region smoothing and edge preservation, but also of the adaptive selection of the diffusion coefficient. Data analysis revealed that the electrical resistivity structure can be approximated by a two-dimensional characterization. Two-dimensional inversion and rendering visualization show that a highly resistive granite basement is covered with conductive sedimentary layers and that a relatively low-resistivity anomalous structure with a resistivity of approximately 100-600 Ω·m is imbedded in the high-resistivity background. The anomalous structure has a narrow top and a wide bottom (the bottom depth is at least 3500 m). The shape and electrical features of the structure indicate favorable storage space for hot subsurface water. Fault activities and magma intrusion may result in the fractures of the basement, which are filled with hot water and thus produce the relatively low resistivity. Based on a comprehensive analysis, we infer that the structure is indicative of a geothermal reservoir. An exploratory well drilled near the structure confirms the occurrence of high temperatures. Several geological factors (cap rock, basement, and major faults) determine the favorable geothermal conditions of the reservoir. Large areas of granite form the major thermal source for the study area. The Mudanjiang and Hailang River Faults and their subsidiary faults provide another heat source and movement channels.

Gas-film coefficients for streams

USGS Publications Warehouse

Rathbun, R.E.; Tai, D.Y.

1983-01-01

Equations for predicting the gas-film coefficient for the volatilization of organic solutes from streams are developed. The film coefficient is a function of windspeed and water temperature. The dependence of the coefficient on windspeed is determined from published information on the evaporation of water from a canal. The dependence of the coefficient on temperature is determined from laboratory studies on the evaporation of water. Procedures for adjusting the coefficients for different organic solutes are based on the molecular diffusion coefficient and the molecular weight. The molecular weight procedure is easiest to use because of the availability of molecular weights. However, the theoretical basis of the procedure is questionable. The diffusion coefficient procedure is supported by considerable data. Questions, however, remain regarding the exact dependence of the film coefficint on the diffusion coefficient. It is suggested that the diffusion coefficient procedure with a 0.68-power dependence be used when precise estimate of the gas-film coefficient are needed and that the molecular weight procedure be used when only approximate estimates are needed.

Persistent mobility edges and anomalous quantum diffusion in order-disorder separated quantum films

NASA Astrophysics Data System (ADS)

Zhong, Jianxin; Stocks, G. Malcolm

2007-01-01

A concept of order-disorder separated quantum films is proposed for the design of ultrathin quantum films of a few atomic layers thick with unconventional transport properties. The concept is demonstrated through studying an atomic bilayer comprised of an ordered layer and a disordered layer. Without the disordered layer or the ordered layer, the system is a conducting two-dimensional (2D) crystal or an insulating disordered 2D electron system. Without the order-disorder phase separation, a disordered bilayer is insulating under large disorder. In an order-disorder separated atomic bilayer, however, we show that the system behaves remarkably different from conventional ordered or disordered electron systems, exhibiting metal-insulator transitions with persistent mobility edges and superdiffusive anomalous quantum diffusion.

An Ab Initio and Kinetic Monte Carlo Simulation Study of Lithium Ion Diffusion on Graphene

PubMed Central

Zhong, Kehua; Yang, Yanmin; Xu, Guigui; Zhang, Jian-Min; Huang, Zhigao

2017-01-01

The Li+ diffusion coefficients in Li+-adsorbed graphene systems were determined by combining first-principle calculations based on density functional theory with Kinetic Monte Carlo simulations. The calculated results indicate that the interactions between Li ions have a very important influence on lithium diffusion. Based on energy barriers directly obtained from first-principle calculations for single-Li+ and two-Li+ adsorbed systems, a new equation predicting energy barriers with more than two Li ions was deduced. Furthermore, it is found that the temperature dependence of Li+ diffusion coefficients fits well to the Arrhenius equation, rather than meeting the equation from electrochemical impedance spectroscopy applied to estimate experimental diffusion coefficients. Moreover, the calculated results also reveal that Li+ concentration dependence of diffusion coefficients roughly fits to the equation from electrochemical impedance spectroscopy in a low concentration region; however, it seriously deviates from the equation in a high concentration region. So, the equation from electrochemical impedance spectroscopy technique could not be simply used to estimate the Li+ diffusion coefficient for all Li+-adsorbed graphene systems with various Li+ concentrations. Our work suggests that interactions between Li ions, and among Li ion and host atoms will influence the Li+ diffusion, which determines that the Li+ intercalation dependence of Li+ diffusion coefficient should be changed and complex. PMID:28773122

On the Ageing of High Energy Lithium-Ion Batteries—Comprehensive Electrochemical Diffusivity Studies of Harvested Nickel Manganese Cobalt Electrodes

PubMed Central

Jaguemont, Joris; Van Den Bossche, Peter; Omar, Noshin; Van Mierlo, Joeri

2018-01-01

This paper examines the impact of the characterisation technique considered for the determination of the Li+ solid state diffusion coefficient in uncycled as in cycled Nickel Manganese Cobalt oxide (NMC) electrodes. As major characterisation techniques, Cyclic Voltammetry (CV), Galvanostatic Intermittent Titration Technique (GITT) and Electrochemical Impedance Spectroscopy (EIS) were systematically investigated. Li+ diffusion coefficients during the lithiation process of the uncycled and cycled electrodes determined by CV at 3.71 V are shown to be equal to 3.48×10−10 cm2·s−1 and 1.56×10−10 cm2·s−1 , respectively. The dependency of the Li+ diffusion with the lithium content in the electrodes is further studied in this paper with GITT and EIS. Diffusion coefficients calculated by GITT and EIS characterisations are shown to be in the range between 1.76×10−15 cm2·s−1 and 4.06×10−12 cm2·s−1, while demonstrating the same decreasing trend with the lithiation process of the electrodes. For both electrode types, diffusion coefficients calculated by CV show greater values compared to those determined by GITT and EIS. With ageing, CV and EIS techniques lead to diffusion coefficients in the electrodes at 3.71 V that are decreasing, in contrast to GITT for which results indicate increasing diffusion coefficient. After long-term cycling, ratios of the diffusion coefficients determined by GITT compared to CV become more significant with an increase about 1 order of magnitude, while no significant variation is seen between the diffusion coefficients calculated from EIS in comparison to CV. PMID:29360787

On the Ageing of High Energy Lithium-Ion Batteries-Comprehensive Electrochemical Diffusivity Studies of Harvested Nickel Manganese Cobalt Electrodes.

PubMed

Capron, Odile; Gopalakrishnan, Rahul; Jaguemont, Joris; Van Den Bossche, Peter; Omar, Noshin; Van Mierlo, Joeri

2018-01-23

This paper examines the impact of the characterisation technique considered for the determination of the L i + solid state diffusion coefficient in uncycled as in cycled Nickel Manganese Cobalt oxide (NMC) electrodes. As major characterisation techniques, Cyclic Voltammetry (CV), Galvanostatic Intermittent Titration Technique (GITT) and Electrochemical Impedance Spectroscopy (EIS) were systematically investigated. L i + diffusion coefficients during the lithiation process of the uncycled and cycled electrodes determined by CV at 3.71 V are shown to be equal to 3 . 48 × 10 - 10 cm 2 ·s - 1 and 1 . 56 × 10 - 10 cm 2 ·s - 1 , respectively. The dependency of the L i + diffusion with the lithium content in the electrodes is further studied in this paper with GITT and EIS. Diffusion coefficients calculated by GITT and EIS characterisations are shown to be in the range between 1 . 76 × 10 - 15 cm 2 ·s - 1 and 4 . 06 × 10 - 12 cm 2 ·s - 1 , while demonstrating the same decreasing trend with the lithiation process of the electrodes. For both electrode types, diffusion coefficients calculated by CV show greater values compared to those determined by GITT and EIS. With ageing, CV and EIS techniques lead to diffusion coefficients in the electrodes at 3.71 V that are decreasing, in contrast to GITT for which results indicate increasing diffusion coefficient. After long-term cycling, ratios of the diffusion coefficients determined by GITT compared to CV become more significant with an increase about 1 order of magnitude, while no significant variation is seen between the diffusion coefficients calculated from EIS in comparison to CV.

Diffusion and solubility coefficients determined by permeation and immersion experiments for organic solvents in HDPE geomembrane.

PubMed

Chao, Keh-Ping; Wang, Ping; Wang, Ya-Ting

2007-04-02

The chemical resistance of eight organic solvents in high density polyethylene (HDPE) geomembrane has been investigated using the ASTM F739 permeation method and the immersion test at different temperatures. The diffusion of the experimental organic solvents in HDPE geomembrane was non-Fickian kinetic, and the solubility coefficients can be consistent with the solubility parameter theory. The diffusion coefficients and solubility coefficients determined by the ASTM F739 method were significantly correlated to the immersion tests (p<0.001). The steady state permeation rates also showed a good agreement between ASTM F739 and immersion experiments (r(2)=0.973, p<0.001). Using a one-dimensional diffusion equation based on Fick's second law, the diffusion and solubility coefficients obtained by immersion test resulted in over estimates of the ASTM F739 permeation results. The modeling results indicated that the diffusion and solubility coefficients should be obtained using ASTM F739 method which closely simulates the practical application of HDPE as barriers in the field.

Radon diffusion coefficients in 360 waterproof materials of different chemical composition.

PubMed

Jiránek, M; Kotrbatá, M

2011-05-01

This paper summarises the results of radon diffusion coefficient measurements in 360 common waterproof materials available throughout Europe. The materials were grouped into 26 categories according to their chemical composition. It was found that the diffusion coefficients of materials used for protecting houses against radon vary within eight orders from 10(-15) to 10(-8) m(2) s(-1). The lowest values were obtained for bitumen membranes with an Al carrier film and for ethylene vinyl acetate membranes. The highest radon diffusion coefficient values were discovered for sodium bentonite membranes, rubber membranes made of ethylene propylene diene monomer and polymer cement coatings. The radon diffusion coefficients for waterproofings widely used for protecting houses, i.e. flexible polyvinyl chloride, high-, low-density polyethylene, polypropylene and bitumen membranes, vary in the range from 3 × 10(-12) to 3 × 10(-11) m(2) s(-1). Tests were performed which confirmed that the radon diffusion coefficient is also an effective tool for verifying the air-tightness of joints.

Electronic speckle pattern interferometry: a tool for determining diffusion and partition coefficients for proteins in gels.

PubMed

Karlsson, David; Zacchi, Guido; Axelsson, Anders

2002-01-01

The aim of this study was to demonstrate electronic speckle pattern interferometry (ESPI) as a powerful tool in determining diffusion coefficients and partition coefficients for proteins in gels. ESPI employs a CCD camera instead of a holographic plate as in conventional holographic interferometry. This gives the advantage of being able to choose the reference state freely. If a hologram at the reference state is taken and compared to a hologram during the diffusion process, an interferometric picture can be generated that describes the refraction index gradients and thus the concentration gradients in the gel as well as in the liquid. MATLAB is then used to fit Fick's law to the experimental data to obtain the diffusion coefficients in gel and liquid. The partition coefficient is obtained from the same experiment from the flux condition at the interface between gel and liquid. This makes the comparison between the different diffusants more reliable than when the measurements are performed in separate experiments. The diffusion and partitioning coefficients of lysozyme, BSA, and IgG in 4% agarose gel at pH 5.6 and in 0.1 M NaCl have been determined. In the gel the diffusion coefficients were 11.2 +/- 1.6, 4.8 +/- 0.6, and 3.0 +/- 0.3 m(2)/s for lysozyme, BSA, and IgG, respectively. The partition coefficients were determined to be 0.65 +/- 0.04, 0.44 +/- 0.06, and 0.51 +/- 0.04 for lysozyme, BSA, and IgG, respectively. The current study shows that ESPI is easy to use and gives diffusion coefficients and partition coefficients for proteins with sufficient accuracy from the same experiment.

Diffusion of rhodamine B and bovine serum albumin in fibrin gels seeded with primary endothelial cells.

PubMed

Shkilnyy, Andriy; Proulx, Pierre; Sharp, Jamie; Lepage, Martin; Vermette, Patrick

2012-05-01

Scaffolds with adequate mass transport properties are needed in many tissue engineering applications. Fibrin is considered a good biological material to fabricate such scaffolds. However, very little is known about mass transport in fibrin. Therefore, a method based on the analysis of fluorescence intensity for measuring the apparent diffusion coefficient of rhodamine B and fluorescein-labelled bovine serum albumin (FITC-BSA) is described. The experiments are performed in fibrin gels with and without human umbilical vein endothelial cells (HUVEC). The apparent diffusion coefficients of rhodamine B and FITC-BSA in fibrin (fibrinogen concentration of 4 mg/mL) with different cell densities are reported. A LIVE/DEAD(®) assay is performed to confirm the viability of HUVEC seeded at high densities. Diffusion coefficients for rhodamine B remain more or less constant up to 5×10(5) cells/mL and correlate well with literature values measured by other methods in water systems. This indicates that the presence of HUVEC in the fibrin gels (up to 5×10(5) cells/mL) has almost no effect on the diffusion coefficients. Higher cell densities (>5×10(5) cells/mL) result in a decrease of the diffusion coefficients. Diffusion coefficients of rhodamine B and FITC-BSA obtained by this method agree with diffusion coefficients in water predicted by the Stokes-Einstein equation. The experimental design used in this study can be applied to measure diffusion coefficients in different types of gels seeded or not with living cells. Copyright © 2012 Elsevier B.V. All rights reserved.

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.

Cosmic ray injection spectrum at the galactic sources

NASA Astrophysics Data System (ADS)

Lagutin, Anatoly; Tyumentsev, Alexander; Volkov, Nikolay

The spectra of cosmic rays measured at Earth are different from their source spectra. A key to understanding this difference, being crucial for solving the problem of cosmic-ray origin, is the determination of how cosmic-ray (CR) particles propagate through the turbulent interstellar medium (ISM). If the medium is a quasi-homogeneous the propagation process can be described by a normal diffusion model. However, during a last few decades many evidences, both from theory and observations, of the existence of multiscale structures in the Galaxy have been found. Filaments, shells, clouds are entities widely spread in the ISM. In such a highly non-homogeneous (fractal-like) ISM the normal diffusion model certainly is not kept valid. Generalization of this model leads to what is known as "anomalous diffusion". The main goal of the report is to retrieve the cosmic ray injection spectrum at the galactic sources in the framework of the anomalous diffusion (AD) model. The anomaly in this model results from large free paths ("Levy flights") of particles between galactic inhomogeneities. In order to evaluate the CR spectrum at the sources, we carried out new calculation of the CR spectra at Earth. AD equation in terms of fractional derivatives have been used to describe CR propagation from the nearby (r≤1 kpc) young (t≤ 1 Myr) and multiple old distant (r > 1 kpc) sources. The assessment of the key model parameters have been based on the results of the particles diffusion in the cosmic and laboratory plasma. We show that in the framework of the anomalous diffusion model the locally observed basic features of the cosmic rays (difference between spectral exponents of proton, He and other nuclei, "knee" problem, positron to electron ratio) can be explained if the injection spectrum at the main galactic sources of cosmic rays has spectral exponent p˜ 2.85. The authors acknowledge support from The Russian Foundation for Basic Research grant No. 14-02-31524.

Anomalous law of cooling

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

Lapas, Luciano C., E-mail: luciano.lapas@unila.edu.br; Ferreira, Rogelma M. S., E-mail: rogelma.maria@gmail.com; Rubí, J. Miguel, E-mail: mrubi@ub.edu

2015-03-14

We analyze the temperature relaxation phenomena of systems in contact with a thermal reservoir that undergoes a non-Markovian diffusion process. From a generalized Langevin equation, we show that the temperature is governed by a law of cooling of the Newton’s law type in which the relaxation time depends on the velocity autocorrelation and is then characterized by the memory function. The analysis of the temperature decay reveals the existence of an anomalous cooling in which the temperature may oscillate. Despite this anomalous behavior, we show that the variation of entropy remains always positive in accordance with the second law ofmore » thermodynamics.« less

Ion radial diffusion in an electrostatic impulse model for stormtime ring current formation

NASA Technical Reports Server (NTRS)

Chen, Margaret W.; Schulz, Michael; Lyons, Larry R.; Gorney, David J.

1992-01-01

Two refinements to the quasi-linear theory of ion radial diffusion are proposed and examined analytically with simulations of particle trajectories. The resonance-broadening correction by Dungey (1965) is applied to the quasi-linear diffusion theory by Faelthammar (1965) for an individual model storm. Quasi-linear theory is then applied to the mean diffusion coefficients resulting from simulations of particle trajectories in 20 model storms. The correction for drift-resonance broadening results in quasi-linear diffusion coefficients with discrepancies from the corresponding simulated values that are reduced by a factor of about 3. Further reductions in the discrepancies are noted following the averaging of the quasi-linear diffusion coefficients, the simulated coefficients, and the resonance-broadened coefficients for the 20 storms. Quasi-linear theory provides good descriptions of particle transport for a single storm but performs even better in conjunction with the present ensemble-averaging.

Perpendicular Diffusion Coefficient of Comic Rays: The Presence of Weak Adiabatic Focusing

NASA Astrophysics Data System (ADS)

Wang, J. F.; Qin, G.; Ma, Q. M.; Song, T.; Yuan, S. B.

2017-08-01

The influence of adiabatic focusing on particle diffusion is an important topic in astrophysics and plasma physics. In the past, several authors have explored the influence of along-field adiabatic focusing on the parallel diffusion of charged energetic particles. In this paper, using the unified nonlinear transport theory developed by Shalchi and the method of He and Schlickeiser, we derive a new nonlinear perpendicular diffusion coefficient for a non-uniform background magnetic field. This formula demonstrates that the particle perpendicular diffusion coefficient is modified by along-field adiabatic focusing. For isotropic pitch-angle scattering and the weak adiabatic focusing limit, the derived perpendicular diffusion coefficient is independent of the sign of adiabatic focusing characteristic length. For the two-component model, we simplify the perpendicular diffusion coefficient up to the second order of the power series of the adiabatic focusing characteristic quantity. We find that the first-order modifying factor is equal to zero and that the sign of the second order is determined by the energy of the particles.

Thermodynamic properties and diffusion of water + methane binary mixtures

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

Shvab, I.; Sadus, Richard J., E-mail: rsadus@swin.edu.au

2014-03-14

Thermodynamic and diffusion properties of water + methane mixtures in a single liquid phase are studied using NVT molecular dynamics. An extensive comparison is reported for the thermal pressure coefficient, compressibilities, expansion coefficients, heat capacities, Joule-Thomson coefficient, zero frequency speed of sound, and diffusion coefficient at methane concentrations up to 15% in the temperature range of 298–650 K. The simulations reveal a complex concentration dependence of the thermodynamic properties of water + methane mixtures. The compressibilities, heat capacities, and diffusion coefficients decrease with increasing methane concentration, whereas values of the thermal expansion coefficients and speed of sound increase. Increasing methanemore » concentration considerably retards the self-diffusion of both water and methane in the mixture. These effects are caused by changes in hydrogen bond network, solvation shell structure, and dynamics of water molecules induced by the solvation of methane at constant volume conditions.« less

Determination of Diffusion Coefficients in Cement-Based Materials: An Inverse Problem for the Nernst-Planck and Poisson Models

NASA Astrophysics Data System (ADS)

Szyszkiewicz-Warzecha, Krzysztof; Jasielec, Jerzy J.; Fausek, Janusz; Filipek, Robert

2016-08-01

Transport properties of ions have significant impact on the possibility of rebars corrosion thus the knowledge of a diffusion coefficient is important for reinforced concrete durability. Numerous tests for the determination of diffusion coefficients have been proposed but analysis of some of these tests show that they are too simplistic or even not valid. Hence, more rigorous models to calculate the coefficients should be employed. Here we propose the Nernst-Planck and Poisson equations, which take into account the concentration and electric potential field. Based on this model a special inverse method is presented for determination of a chloride diffusion coefficient. It requires the measurement of concentration profiles or flux on the boundary and solution of the NPP model to define the goal function. Finding the global minimum is equivalent to the determination of diffusion coefficients. Typical examples of the application of the presented method are given.

Kinetics of dodecanoic acid adsorption from caustic solution by activated carbon.

PubMed

Pendleton, Phillip; Wu, Sophie Hua

2003-10-15

This study examines the influences of adsorbent porosity and surface chemistry and of carbon dosage on dodecanoic acid adsorption kinetics from aqueous and 2 M NaOH solutions as batch adsorption processes. Both adsorbents are steam-activated carbons prepared from either coconut or coal precursors. Prior to use the adsorbents were washed in deionized water or 2 M NaOH. Mass transfer coefficients and effective overall diffusion coefficients indicate a minor contribution from adsorbent porosity. In contrast, high surface oxygen content impedes transport to and into the adsorbent structure. Carbon dosage shows a proportional increase in transport coefficients with increasing mass; these coefficients are constant when normalized per unit mass. Neither water nor NaOH treatment of the adsorbents has a significant influence on dodecanoic acid adsorption kinetics. Molecular and Knudsen diffusion coefficients are defined to demonstrate that the overall effective diffusion coefficient values and the diffusion process are controlled by surface diffusion.

A feasibility study for measuring stratospheric turbulence using metrac positioning system

NASA Technical Reports Server (NTRS)

Gage, K. S.; Jasperson, W. H.

1975-01-01

The feasibility of obtaining measurements of Lagrangian turbulence at stratospheric altitudes is demonstrated by using the METRAC System to track constant-level balloons. The basis for current estimates of diffusion coefficients are reviewed and it is pointed out that insufficient data is available upon which to base reliable estimates of vertical diffusion coefficients. It is concluded that diffusion coefficients could be directly obtained from Lagrangian turbulence measurements. The METRAC balloon tracking system is shown to possess the necessary precision in order to resolve the response of constant-level balloons to turbulence at stratospheric altitudes. A small sample of data recorded from a tropospheric tetroon flight tracked by the METRAC System is analyzed to obtain estimates of small-scale three-dimensional diffusion coefficients. It is recommended that this technique be employed to establish a climatology of diffusion coefficients and to ascertain the variation of these coefficients with altitude, season, and latitude.

Effective Stochastic Model for Reactive Transport

NASA Astrophysics Data System (ADS)

Tartakovsky, A. M.; Zheng, B.; Barajas-Solano, D. A.

2017-12-01

We propose an effective stochastic advection-diffusion-reaction (SADR) model. Unlike traditional advection-dispersion-reaction models, the SADR model describes mechanical and diffusive mixing as two separate processes. In the SADR model, the mechanical mixing is driven by random advective velocity with the variance given by the coefficient of mechanical dispersion. The diffusive mixing is modeled as a fickian diffusion with the effective diffusion coefficient. Both coefficients are given in terms of Peclet number (Pe) and the coefficient of molecular diffusion. We use the experimental results of to demonstrate that for transport and bimolecular reactions in porous media the SADR model is significantly more accurate than the traditional dispersion model, which overestimates the mass of the reaction product by as much as 25%.

Predicting Salt Permeability Coefficients in Highly Swollen, Highly Charged Ion Exchange Membranes.

PubMed

Kamcev, Jovan; Paul, Donald R; Manning, Gerald S; Freeman, Benny D

2017-02-01

This study presents a framework for predicting salt permeability coefficients in ion exchange membranes in contact with an aqueous salt solution. The model, based on the solution-diffusion mechanism, was tested using experimental salt permeability data for a series of commercial ion exchange membranes. Equilibrium salt partition coefficients were calculated using a thermodynamic framework (i.e., Donnan theory), incorporating Manning's counterion condensation theory to calculate ion activity coefficients in the membrane phase and the Pitzer model to calculate ion activity coefficients in the solution phase. The model predicted NaCl partition coefficients in a cation exchange membrane and two anion exchange membranes, as well as MgCl 2 partition coefficients in a cation exchange membrane, remarkably well at higher external salt concentrations (>0.1 M) and reasonably well at lower external salt concentrations (<0.1 M) with no adjustable parameters. Membrane ion diffusion coefficients were calculated using a combination of the Mackie and Meares model, which assumes ion diffusion in water-swollen polymers is affected by a tortuosity factor, and a model developed by Manning to account for electrostatic effects. Agreement between experimental and predicted salt diffusion coefficients was good with no adjustable parameters. Calculated salt partition and diffusion coefficients were combined within the framework of the solution-diffusion model to predict salt permeability coefficients. Agreement between model and experimental data was remarkably good. Additionally, a simplified version of the model was used to elucidate connections between membrane structure (e.g., fixed charge group concentration) and salt transport properties.

Protein diffusiophoresis and salt osmotic diffusion in aqueous solutions.

PubMed

Annunziata, Onofrio; Buzatu, Daniela; Albright, John G

2012-10-25

Diffusion of a solute can be induced by the concentration gradient of another solute in solution. This transport mechanism is known as cross-diffusion. We have investigated cross-diffusion in a ternary protein-salt-water system. Specifically, we measured the two cross-diffusion coefficients for the lysozyme-NaCl-water system at 25 °C and pH 4.5 as a function of protein and salt concentrations by Rayleigh interferometry. One cross-diffusion coefficient characterizes salt osmotic diffusion induced by a protein concentration gradient, and is related to protein-salt thermodynamic interactions as described by the theories of Donnan membrane equilibrium and protein preferential hydration. The other cross-diffusion coefficient characterizes protein diffusiophoresis induced by a salt concentration gradient, and is described as the difference between a preferential-interaction coefficient and a transport parameter. We first relate our experimental results to the protein net charge and the thermodynamic excess of water near the protein surface. We then extract the Stefan-Maxwell diffusion coefficient describing protein-salt interactions in water. We find that the value of this coefficient is negative, contrary to the friction interpretation of Stefan-Maxwell equations. This result is explained by considering protein hydration. Finally, protein diffusiophoresis is quantitatively examined by considering electrophoretic and hydration effects on protein migration and utilized to accurately estimate lysozyme electrophoretic mobility. To our knowledge, this is the first time that protein diffusiophoresis has been experimentally characterized and a protein-salt Stefan-Maxwell diffusion coefficient reported. This work represents a significant contribution for understanding and modeling the effect of concentration gradients in protein-salt aqueous systems relevant to diffusion-based mass-transfer technologies and transport in living systems.

Apparent diffusion coefficient evaluation for secondary changes in the cerebellum of rats after middle cerebral artery occlusion

PubMed Central

Yang, Yunjun; Gao, Lingyun; Fu, Jun; Zhang, Jun; Li, Yuxin; Yin, Bo; Chen, Weijian; Geng, Daoying

2013-01-01

Supratentorial cerebral infarction can cause functional inhibition of remote regions such as the cerebellum, which may be relevant to diaschisis. This phenomenon is often analyzed using positron emission tomography and single photon emission CT. However, these methods are expensive and radioactive. Thus, the present study quantified the changes of infarction core and remote regions after unilateral middle cerebral artery occlusion using apparent diffusion coefficient values. Diffusion-weighted imaging showed that the area of infarction core gradually increased to involve the cerebral cortex with increasing infarction time. Diffusion weighted imaging signals were initially increased and then stabilized by 24 hours. With increasing infarction time, the apparent diffusion coefficient value in the infarction core and remote bilateral cerebellum both gradually decreased, and then slightly increased 3–24 hours after infarction. Apparent diffusion coefficient values at remote regions (cerebellum) varied along with the change of supratentorial infarction core, suggesting that the phenomenon of diaschisis existed at the remote regions. Thus, apparent diffusion coefficient values and diffusion weighted imaging can be used to detect early diaschisis. PMID:25206615

A data-drive analysis for heavy quark diffusion coefficient

NASA Astrophysics Data System (ADS)

Xu, Yingru; Nahrgang, Marlene; Cao, Shanshan; Bernhard, Jonah E.; Bass, Steffen A.

2018-02-01

We apply a Bayesian model-to-data analysis on an improved Langevin framework to estimate the temperature and momentum dependence of the heavy quark diffusion coefficient in the quark-gluon plasma (QGP). The spatial diffusion coefficient is found to have a minimum around 1-3 near Tc in the zero momentum limit, and has a non-trivial momentum dependence. With the estimated diffusion coefficient, our improved Langevin model is able to simultaneously describe the D-meson RAA and v2 in three different systems at RHIC and the LHC.

Diffusion in the system K2O-SrO-SiO2. II - Cation self-diffusion coefficients.

NASA Technical Reports Server (NTRS)

Varshneya, A. K.; Cooper, A. R.

1972-01-01

The self-diffusion coefficients were measured by introducing a slab of glass previously irradiated in a reactor between two slabs of unirradiated glass. By heating the specimens, etching them sequentially and determining the radioactivity, self-diffusion coefficients for K and Sr were measured. It is pointed out that the results obtained in the investigations appear to support the proposal that the network of the base glass predominantly controls the activation energy for the diffusion of ions.

Estimation of Knudsen diffusion coefficients from tracer experiments conducted with a binary gas system and a porous medium.

PubMed

Hibi, Yoshihiko; Kashihara, Ayumi

2018-03-01

A previous study has reported that Knudsen diffusion coefficients obtained by tracer experiments conducted with a binary gas system and a porous medium are consistently smaller than those obtained by permeability experiments conducted with a single-gas system and a porous medium. To date, however, that study is the only one in which tracer experiments have been conducted with a binary gas system. Therefore, to confirm this difference in Knudsen diffusion coefficients, we used a method we had developed previously to conduct tracer experiments with a binary carbon dioxide-nitrogen gas system and five porous media with permeability coefficients ranging from 10 -13 to 10 -11  m 2 . The results showed that the Knudsen diffusion coefficient of N 2 (D N2 ) (cm 2 /s) was related to the effective permeability coefficient k e (m 2 ) as D N2  = 7.39 × 10 7 k e 0.767 . Thus, the Knudsen diffusion coefficients of N 2 obtained by our tracer experiments were consistently 1/27 of those obtained by permeability experiments conducted with many porous media and air by other researchers. By using an inversion simulation to fit the advection-diffusion equation to the distribution of concentrations at observation points calculated by mathematically solving the equation, we confirmed that the method used to obtain the Knudsen diffusion coefficient in this study yielded accurate values. Moreover, because the Knudsen diffusion coefficient did not differ when columns with two different lengths, 900 and 1500 mm, were used, this column property did not influence the flow of gas in the column. The equation of the dusty gas model already includes obstruction factors for Knudsen diffusion and molecular diffusion, which relate to medium heterogeneity and tortuosity and depend only on the structure of the porous medium. Furthermore, there is no need to take account of any additional correction factor for molecular diffusion except the obstruction factor because molecular diffusion is only treated in a multicomponent gas system. Thus, molecular diffusion considers only the obstruction factor related to tortuosity. Therefore, we introduced a correction factor for a multicomponent gas system into the DGM equation, multiplying the Knudsen diffusion coefficient, which includes the obstruction factor related to tortuosity, by this correction factor. From the present experimental results, the value of this correction factor was 1/27, and it depended only on the structure of the gas system in the porous medium. Copyright © 2018 Elsevier B.V. All rights reserved.

Estimation of Knudsen diffusion coefficients from tracer experiments conducted with a binary gas system and a porous medium

NASA Astrophysics Data System (ADS)

Hibi, Yoshihiko; Kashihara, Ayumi

2018-03-01

A previous study has reported that Knudsen diffusion coefficients obtained by tracer experiments conducted with a binary gas system and a porous medium are consistently smaller than those obtained by permeability experiments conducted with a single-gas system and a porous medium. To date, however, that study is the only one in which tracer experiments have been conducted with a binary gas system. Therefore, to confirm this difference in Knudsen diffusion coefficients, we used a method we had developed previously to conduct tracer experiments with a binary carbon dioxide-nitrogen gas system and five porous media with permeability coefficients ranging from 10-13 to 10-11 m2. The results showed that the Knudsen diffusion coefficient of N2 (DN2) (cm2/s) was related to the effective permeability coefficient ke (m2) as DN2 = 7.39 × 107ke0.767. Thus, the Knudsen diffusion coefficients of N2 obtained by our tracer experiments were consistently 1/27 of those obtained by permeability experiments conducted with many porous media and air by other researchers. By using an inversion simulation to fit the advection-diffusion equation to the distribution of concentrations at observation points calculated by mathematically solving the equation, we confirmed that the method used to obtain the Knudsen diffusion coefficient in this study yielded accurate values. Moreover, because the Knudsen diffusion coefficient did not differ when columns with two different lengths, 900 and 1500 mm, were used, this column property did not influence the flow of gas in the column. The equation of the dusty gas model already includes obstruction factors for Knudsen diffusion and molecular diffusion, which relate to medium heterogeneity and tortuosity and depend only on the structure of the porous medium. Furthermore, there is no need to take account of any additional correction factor for molecular diffusion except the obstruction factor because molecular diffusion is only treated in a multicomponent gas system. Thus, molecular diffusion considers only the obstruction factor related to tortuosity. Therefore, we introduced a correction factor for a multicomponent gas system into the DGM equation, multiplying the Knudsen diffusion coefficient, which includes the obstruction factor related to tortuosity, by this correction factor. From the present experimental results, the value of this correction factor was 1/27, and it depended only on the structure of the gas system in the porous medium.

Gene interference regulates aquaporin-4 expression in swollen tissue of rats with cerebral ischemic edema: Correlation with variation in apparent diffusion coefficient.

PubMed

Hu, Hui; Lu, Hong; He, Zhanping; Han, Xiangjun; Chen, Jing; Tu, Rong

2012-07-25

To investigate the effects of mRNA interference on aquaporin-4 expression in swollen tissue of rats with ischemic cerebral edema, and diagnose the significance of diffusion-weighted MRI, we injected 5 μL shRNA- aquaporin-4 (control group) or siRNA- aquaporin-4 solution (1:800) (RNA interference group) into the rat right basal ganglia immediately before occlusion of the middle cerebral artery. At 0.25 hours after occlusion of the middle cerebral artery, diffusion-weighted MRI displayed a high signal; within 2 hours, the relative apparent diffusion coefficient decreased markedly, aquaporin-4 expression increased rapidly, and intracellular edema was obviously aggravated; at 4 and 6 hours, the relative apparent diffusion coefficient slowly returned to control levels, aquaporin-4 expression slightly increased, and angioedema was observed. In the RNA interference group, during 0.25-6 hours after injection of siRNA- aquaporin-4 solution, the relative apparent diffusion coefficient slightly fluctuated and aquaporin-4 expression was upregulated; during 0.5-4 hours, the relative apparent diffusion coefficient was significantly higher, while aquaporin-4 expression was significantly lower when compared with the control group, and intracellular edema was markedly reduced; at 0.25 and 6 hours, the relative apparent diffusion coefficient and aquaporin-4 expression were similar when compared with the control group; obvious angioedema remained at 6 hours. Pearson's correlation test results showed that aquaporin-4 expression was negatively correlated with the apparent diffusion coefficient (r = -0.806, P < 0.01). These findings suggest that upregulated aquaporin-4 expression is likely to be the main molecular mechanism of intracellular edema and may be the molecular basis for decreased relative apparent diffusion coefficient. Aquaporin-4 gene interference can effectively inhibit the upregulation of aquaporin-4 expression during the stage of intracellular edema with time-effectiveness. Moreover, diffusion-weighted MRI can accurately detect intracellular edema.

A Huygens principle for diffusion and anomalous diffusion in spatially extended systems

PubMed Central

Gottwald, Georg A.; Melbourne, Ian

2013-01-01

We present a universal view on diffusive behavior in chaotic spatially extended systems for anisotropic and isotropic media. For anisotropic systems, strong chaos leads to diffusive behavior (Brownian motion with drift) and weak chaos leads to superdiffusive behavior (Lévy processes with drift). For isotropic systems, the drift term vanishes and strong chaos again leads to Brownian motion. We establish the existence of a nonlinear Huygens principle for weakly chaotic systems in isotropic media whereby the dynamics behaves diffusively in even space dimension and exhibits superdiffusive behavior in odd space dimensions. PMID:23653481

Combined inverse-forward artificial neural networks for fast and accurate estimation of the diffusion coefficients of cartilage based on multi-physics models.

PubMed

Arbabi, Vahid; Pouran, Behdad; Weinans, Harrie; Zadpoor, Amir A

2016-09-06

Analytical and numerical methods have been used to extract essential engineering parameters such as elastic modulus, Poisson׳s ratio, permeability and diffusion coefficient from experimental data in various types of biological tissues. The major limitation associated with analytical techniques is that they are often only applicable to problems with simplified assumptions. Numerical multi-physics methods, on the other hand, enable minimizing the simplified assumptions but require substantial computational expertise, which is not always available. In this paper, we propose a novel approach that combines inverse and forward artificial neural networks (ANNs) which enables fast and accurate estimation of the diffusion coefficient of cartilage without any need for computational modeling. In this approach, an inverse ANN is trained using our multi-zone biphasic-solute finite-bath computational model of diffusion in cartilage to estimate the diffusion coefficient of the various zones of cartilage given the concentration-time curves. Robust estimation of the diffusion coefficients, however, requires introducing certain levels of stochastic variations during the training process. Determining the required level of stochastic variation is performed by coupling the inverse ANN with a forward ANN that receives the diffusion coefficient as input and returns the concentration-time curve as output. Combined together, forward-inverse ANNs enable computationally inexperienced users to obtain accurate and fast estimation of the diffusion coefficients of cartilage zones. The diffusion coefficients estimated using the proposed approach are compared with those determined using direct scanning of the parameter space as the optimization approach. It has been shown that both approaches yield comparable results. Copyright © 2016 Elsevier Ltd. All rights reserved.

Effect of diffuser vane shape on the performance of a centrifugal compressor stage

NASA Astrophysics Data System (ADS)

Reddy, T. Ch Siva; Ramana Murty, G. V.; Prasad, M. V. S. S. S. M.

2014-04-01

The present paper reports the results of experimental investigations on the effect of diffuser vane shape on the performance of a centrifugal compressor stage. These studies were conducted on the chosen stage having a backward curved impeller of 500 mm tip diameter and 24.5 mm width and its design flow coefficient is ϕd=0.0535. Three different low solidity diffuser vane shapes namely uncambered aerofoil, constant thickness flat plate and circular arc cambered constant thickness plate were chosen as the variants for diffuser vane shape and all the three shapes have the same thickness to chord ratio (t/c=0.1). Flow coefficient, polytropic efficiency, total head coefficient, power coefficient and static pressure recovery coefficient were chosen as the parameters for evaluating the effect of diffuser vane shape on the stage performance. The results show that there is reasonable improvement in stage efficiency and total head coefficient with the use of the chosen diffuser vane shapes as compared to conventional vaneless diffuser. It is also noticed that the aero foil shaped LSD has shown better performance when compared to flat plate and circular arc profiles. The aerofoil vane shape of the diffuser blade is seen to be tolerant over a considerable range of incidence.

Application of the compensated Arrhenius formalism to self-diffusion: implications for ionic conductivity and dielectric relaxation.

PubMed

Petrowsky, Matt; Frech, Roger

2010-07-08

Self-diffusion coefficients are measured from -5 to 80 degrees C in a series of linear alcohols using pulsed field gradient NMR. The temperature dependence of these data is studied using a compensated Arrhenius formalism that assumes an Arrhenius-like expression for the diffusion coefficient; however, this expression includes a dielectric constant dependence in the exponential prefactor. Scaling temperature-dependent diffusion coefficients to isothermal diffusion coefficients so that the exponential prefactors cancel results in calculated energies of activation E(a). The exponential prefactor is determined by dividing the temperature-dependent diffusion coefficients by the Boltzmann term exp(-E(a)/RT). Plotting the prefactors versus the dielectric constant places the data on a single master curve. This procedure is identical to that previously used to study the temperature dependence of ionic conductivities and dielectric relaxation rate constants. The energies of activation determined from self-diffusion coefficients in the series of alcohols are strikingly similar to those calculated for the same series of alcohols from both dielectric relaxation rate constants and ionic conductivities of dilute electrolytes. The experimental results are described in terms of an activated transport mechanism that is mediated by relaxation of the solution molecules. This microscopic picture of transport is postulated to be common to diffusion, dielectric relaxation, and ionic transport.

Calculation method for steady-state pollutant concentration in mixing zones considering variable lateral diffusion coefficient.

PubMed

Wu, Wen; Wu, Zhouhu; Song, Zhiwen

2017-07-01

Prediction of the pollutant mixing zone (PMZ) near the discharge outfall in Huangshaxi shows large error when using the methods based on the constant lateral diffusion assumption. The discrepancy is due to the lack of consideration of the diffusion coefficient variation. The variable lateral diffusion coefficient is proposed to be a function of the longitudinal distance from the outfall. Analytical solution of the two-dimensional advection-diffusion equation of a pollutant is derived and discussed. Formulas to characterize the geometry of the PMZ are derived based on this solution, and a standard curve describing the boundary of the PMZ is obtained by proper choices of the normalization scales. The change of PMZ topology due to the variable diffusion coefficient is then discussed using these formulas. The criterion of assuming the lateral diffusion coefficient to be constant without large error in PMZ geometry is found. It is also demonstrated how to use these analytical formulas in the inverse problems including estimating the lateral diffusion coefficient in rivers by convenient measurements, and determining the maximum allowable discharge load based on the limitations of the geometrical scales of the PMZ. Finally, applications of the obtained formulas to onsite PMZ measurements in Huangshaxi present excellent agreement.

Quantized topological magnetoelectric effect of the zero-plateau quantum anomalous Hall state

DOE PAGES

Wang, Jing; Lian, Biao; Qi, Xiao-Liang; ...

2015-08-10

The topological magnetoelectric effect in a three-dimensional topological insulator is a novel phenomenon, where an electric field induces a magnetic field in the same direction, with a universal coefficient of proportionality quantized in units of $e²/2h$. Here in this paper, we propose that the topological magnetoelectric effect can be realized in the zero-plateau quantum anomalous Hall state of magnetic topological insulators or a ferromagnet-topological insulator heterostructure. The finite-size effect is also studied numerically, where the magnetoelectric coefficient is shown to converge to a quantized value when the thickness of the topological insulator film increases. We further propose a device setupmore » to eliminate nontopological contributions from the side surface.« less

Direct in situ observations of single Fe atom catalytic processes and anomalous diffusion at graphene edges

PubMed Central

Zhao, Jiong; Deng, Qingming; Avdoshenko, Stanislav M.; Fu, Lei; Eckert, Jürgen; Rümmeli, Mark H.

2014-01-01

Single-atom catalysts are of great interest because of their high efficiency. In the case of chemically deposited sp2 carbon, the implementation of a single transition metal atom for growth can provide crucial insight into the formation mechanisms of graphene and carbon nanotubes. This knowledge is particularly important if we are to overcome fabrication difficulties in these materials and fully take advantage of their distinct band structures and physical properties. In this work, we present atomically resolved transmission EM in situ investigations of single Fe atoms at graphene edges. Our in situ observations show individual iron atoms diffusing along an edge either removing or adding carbon atoms (viz., catalytic action). The experimental observations of the catalytic behavior of a single Fe atom are in excellent agreement with supporting theoretical studies. In addition, the kinetics of Fe atoms at graphene edges are shown to exhibit anomalous diffusion, which again, is in agreement with our theoretical investigations. PMID:25331874

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.

Prediction of the moments in advection-diffusion lattice Boltzmann method. II. Attenuation of the boundary layers via double-Λ bounce-back flux scheme.

PubMed

Ginzburg, Irina

2017-01-01

Impact of the unphysical tangential advective-diffusion constraint of the bounce-back (BB) reflection on the impermeable solid surface is examined for the first four moments of concentration. Despite the number of recent improvements for the Neumann condition in the lattice Boltzmann method-advection-diffusion equation, the BB rule remains the only known local mass-conserving no-flux condition suitable for staircase porous geometry. We examine the closure relation of the BB rule in straight channel and cylindrical capillary analytically, and show that it excites the Knudsen-type boundary layers in the nonequilibrium solution for full-weight equilibrium stencil. Although the d2Q5 and d3Q7 coordinate schemes are sufficient for the modeling of isotropic diffusion, the full-weight stencils are appealing for their advanced stability, isotropy, anisotropy and anti-numerical-diffusion ability. The boundary layers are not covered by the Chapman-Enskog expansion around the expected equilibrium, but they accommodate the Chapman-Enskog expansion in the bulk with the closure relation of the bounce-back rule. We show that the induced boundary layers introduce first-order errors in two primary transport properties, namely, mean velocity (first moment) and molecular diffusion coefficient (second moment). As a side effect, the Taylor-dispersion coefficient (second moment), skewness (third moment), and kurtosis (fourth moment) deviate from their physical values and predictions of the fourth-order Chapman-Enskog analysis, even though the kurtosis error in pure diffusion does not depend on grid resolution. In two- and three-dimensional grid-aligned channels and open-tubular conduits, the errors of velocity and diffusion are proportional to the diagonal weight values of the corresponding equilibrium terms. The d2Q5 and d3Q7 schemes do not suffer from this deficiency in grid-aligned geometries but they cannot avoid it if the boundaries are not parallel to the coordinate lines. In order to vanish or attenuate the disparity of the modeled transport coefficients with the equilibrium weights without any modification of the BB rule, we propose to use the two-relaxation-times collision operator with free-tunable product of two eigenfunctions Λ. Two different values Λ_{v} and Λ_{b} are assigned for bulk and boundary nodes, respectively. The rationale behind this is that Λ_{v} is adjustable for stability, accuracy, or other purposes, while the corresponding Λ_{b}(Λ_{v}) controls the primary accommodation effects. Two distinguished but similar functional relations Λ_{b}(Λ_{v}) are constructed analytically: they preserve advection velocity in parabolic profile, exactly in the two-dimensional channel and very accurately in a three-dimensional cylindrical capillary. For any velocity-weight stencil, the (local) double-Λ BB scheme produces quasi-identical solutions with the (nonlocal) specular-forward reflection for first four moments in a channel. In a capillary, this strategy allows for the accurate modeling of the Taylor-dispersion and non-Gaussian effects. As illustrative example, it is shown that in the flow around a circular obstacle, the double-Λ scheme may also vanish the dependency of mean velocity on the velocity weight; the required value for Λ_{b}(Λ_{v}) can be identified in a few bisection iterations in given geometry. A positive solution for Λ_{b}(Λ_{v}) may not exist in pure diffusion, but a sufficiently small value of Λ_{b} significantly reduces the disparity in diffusion coefficient with the mass weight in ducts and in the presence of rectangular obstacles. Although Λ_{b} also controls the effective position of straight or curved boundaries, the double-Λ scheme deals with the lower-order effects. Its idea and construction may help understanding and amelioration of the anomalous, zero- and first-order behavior of the macroscopic solution in the presence of the bulk and boundary or interface discontinuities, commonly found in multiphase flow and heterogeneous transport.

Prediction of the moments in advection-diffusion lattice Boltzmann method. II. Attenuation of the boundary layers via double-Λ bounce-back flux scheme

NASA Astrophysics Data System (ADS)

Ginzburg, Irina

2017-01-01

Impact of the unphysical tangential advective-diffusion constraint of the bounce-back (BB) reflection on the impermeable solid surface is examined for the first four moments of concentration. Despite the number of recent improvements for the Neumann condition in the lattice Boltzmann method-advection-diffusion equation, the BB rule remains the only known local mass-conserving no-flux condition suitable for staircase porous geometry. We examine the closure relation of the BB rule in straight channel and cylindrical capillary analytically, and show that it excites the Knudsen-type boundary layers in the nonequilibrium solution for full-weight equilibrium stencil. Although the d2Q5 and d3Q7 coordinate schemes are sufficient for the modeling of isotropic diffusion, the full-weight stencils are appealing for their advanced stability, isotropy, anisotropy and anti-numerical-diffusion ability. The boundary layers are not covered by the Chapman-Enskog expansion around the expected equilibrium, but they accommodate the Chapman-Enskog expansion in the bulk with the closure relation of the bounce-back rule. We show that the induced boundary layers introduce first-order errors in two primary transport properties, namely, mean velocity (first moment) and molecular diffusion coefficient (second moment). As a side effect, the Taylor-dispersion coefficient (second moment), skewness (third moment), and kurtosis (fourth moment) deviate from their physical values and predictions of the fourth-order Chapman-Enskog analysis, even though the kurtosis error in pure diffusion does not depend on grid resolution. In two- and three-dimensional grid-aligned channels and open-tubular conduits, the errors of velocity and diffusion are proportional to the diagonal weight values of the corresponding equilibrium terms. The d2Q5 and d3Q7 schemes do not suffer from this deficiency in grid-aligned geometries but they cannot avoid it if the boundaries are not parallel to the coordinate lines. In order to vanish or attenuate the disparity of the modeled transport coefficients with the equilibrium weights without any modification of the BB rule, we propose to use the two-relaxation-times collision operator with free-tunable product of two eigenfunctions Λ . Two different values Λv and Λb are assigned for bulk and boundary nodes, respectively. The rationale behind this is that Λv is adjustable for stability, accuracy, or other purposes, while the corresponding Λb(Λv) controls the primary accommodation effects. Two distinguished but similar functional relations Λb(Λv) are constructed analytically: they preserve advection velocity in parabolic profile, exactly in the two-dimensional channel and very accurately in a three-dimensional cylindrical capillary. For any velocity-weight stencil, the (local) double-Λ BB scheme produces quasi-identical solutions with the (nonlocal) specular-forward reflection for first four moments in a channel. In a capillary, this strategy allows for the accurate modeling of the Taylor-dispersion and non-Gaussian effects. As illustrative example, it is shown that in the flow around a circular obstacle, the double-Λ scheme may also vanish the dependency of mean velocity on the velocity weight; the required value for Λb(Λv) can be identified in a few bisection iterations in given geometry. A positive solution for Λb(Λv) may not exist in pure diffusion, but a sufficiently small value of Λb significantly reduces the disparity in diffusion coefficient with the mass weight in ducts and in the presence of rectangular obstacles. Although Λb also controls the effective position of straight or curved boundaries, the double-Λ scheme deals with the lower-order effects. Its idea and construction may help understanding and amelioration of the anomalous, zero- and first-order behavior of the macroscopic solution in the presence of the bulk and boundary or interface discontinuities, commonly found in multiphase flow and heterogeneous transport.

Diffusion in different models of active Brownian motion

NASA Astrophysics Data System (ADS)

Lindner, B.; Nicola, E. M.

2008-04-01

Active Brownian particles (ABP) have served as phenomenological models of self-propelled motion in biology. We study the effective diffusion coefficient of two one-dimensional ABP models (simplified depot model and Rayleigh-Helmholtz model) differing in their nonlinear friction functions. Depending on the choice of the friction function the diffusion coefficient does or does not attain a minimum as a function of noise intensity. We furthermore discuss the case of an additional bias breaking the left-right symmetry of the system. We show that this bias induces a drift and that it generally reduces the diffusion coefficient. For a finite range of values of the bias, both models can exhibit a maximum in the diffusion coefficient vs. noise intensity.

MEASUREMENT OF EFFECTIVE AIR DIFFUSION COEFFICIENTS FOR TRICHLOROETHENE IN UNDISTURBED SOIL CORES. (R826162)

EPA Science Inventory

Abstract

In this study, we measure effective diffusion coefficients for trichloroethene in undisturbed soil samples taken from Picatinny Arsenal, New Jersey. The measured effective diffusion coefficients ranged from 0.0053 to 0.0609 cm²/s over a range of air...

Thermodiffusion, molecular diffusion and Soret coefficient of binary and ternary mixtures of n-hexane, n-dodecane and toluene.

PubMed

Alonso de Mezquia, David; Wang, Zilin; Lapeira, Estela; Klein, Michael; Wiegand, Simone; Mounir Bou-Ali, M

2014-11-01

In this study, the thermodiffusion, molecular diffusion, and Soret coefficients of 12 binary mixtures composed of toluene, n-hexane and n-dodecane in the whole range of concentrations at atmospheric pressure and temperatures of 298.15 K and 308.15 K have been determined. The experimental measurements have been carried out using the Thermogravitational Column, the Sliding Symmetric Tubes and the Thermal Diffusion Forced Rayleigh Scattering techniques. The results obtained using the different techniques show a maximum deviation of 9% for the thermodiffusion coefficient, 8% for the molecular diffusion coefficient and 2% for the Soret coefficient. For the first time we report a decrease of the thermodiffusion coefficient with increasing ratio of the thermal expansion coefficient and viscosity for a binary mixture of an organic ring compound with a short n-alkane. This observation is discussed in terms of interactions between the different components. Additionally, the thermogravitational technique has been used to measure the thermodiffusion coefficients of four ternary mixtures consisting of toluene, n-hexane and n-dodecane at 298.15 K. In order to complete the study, the values obtained for the molecular diffusion coefficient in binary mixtures, and the thermodiffusion coefficient of binary and ternary mixtures have been compared with recently derived correlations.

Mass transport in polyelectrolyte solutions

NASA Astrophysics Data System (ADS)

Schipper, F. J. M.; Leyte, J. C.

1999-02-01

The self-diffusion coefficients of the three components of a salt-free heavy-water solution of polymethacrylic acid, completely neutralized with tetra-methylammonium hydroxide, were measured over a broad concentration range. Three concentration regions were observed for the self-diffusion of both the polyions and the counterions. At polyion concentrations below 0.01 mol monomer kg-1, the dilute concentration regime for the polymer, the polyion self-diffusion coefficient approaches the self-diffusion coefficient of a freely diffusing rod upon dilution. At polyelectrolyte concentrations above 0.1 mol monomer kg-1, the self-diffusion coefficients of the solvent, the counterions and the polymer decreased with concentration, suggesting that this decrease is due to a topological constraint on the motions of the components. In the intermediate-concentration region, the self-diffusion coefficients of the polyions and the counterions are independent of the concentration. The polyion dynamic behaviour is, in the intermediate- and high-concentration regions, reasonably well described by that of a hard sphere, with a radius of 3.7 nm. A correct prediction for the solvent dynamics is given by the obstruction effect of this hard sphere on the solvent. The relative counterion self-diffusion coefficient is predicted almost quantitatively over the entire concentration range with the Poisson-Boltzmann-Smoluchowski model for the spherical cell, provided that the sphere radius and the number of charges are chosen appropriately (approximately the number of charges in a persistence length). Using this model, the dependence of the counterion self-diffusion coefficient on the ionic strength, polyion concentration and counterion radius is calculated quantitatively over a large concentration range.

Influence of diffuse reflectance measurement accuracy on the scattering coefficient in determination of optical properties with integrating sphere optics (a secondary publication).

PubMed

Horibe, Takuro; Ishii, Katsunori; Fukutomi, Daichi; Awazu, Kunio

2015-12-30

An estimation error of the scattering coefficient of hemoglobin in the high absorption wavelength range has been observed in optical property calculations of blood-rich tissues. In this study, the relationship between the accuracy of diffuse reflectance measurement in the integrating sphere and calculated scattering coefficient was evaluated with a system to calculate optical properties combined with an integrating sphere setup and the inverse Monte Carlo simulation. Diffuse reflectance was measured with the integrating sphere using a small incident port diameter and optical properties were calculated. As a result, the estimation error of the scattering coefficient was improved by accurate measurement of diffuse reflectance. In the high absorption wavelength range, the accuracy of diffuse reflectance measurement has an effect on the calculated scattering coefficient.

Comparison of Experimental Methods for Estimating Matrix Diffusion Coefficients for Contaminant Transport Modeling

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

Telfeyan, Katherine Christina; Ware, Stuart Douglas; Reimus, Paul William

Diffusion cell and diffusion wafer experiments were conducted to compare methods for estimating matrix diffusion coefficients in rock core samples from Pahute Mesa at the Nevada Nuclear Security Site (NNSS). A diffusion wafer method, in which a solute diffuses out of a rock matrix that is pre-saturated with water containing the solute, is presented as a simpler alternative to the traditional through-diffusion (diffusion cell) method. Both methods yielded estimates of matrix diffusion coefficients that were within the range of values previously reported for NNSS volcanic rocks. The difference between the estimates of the two methods ranged from 14 to 30%,more » and there was no systematic high or low bias of one method relative to the other. From a transport modeling perspective, these differences are relatively minor when one considers that other variables (e.g., fracture apertures, fracture spacings) influence matrix diffusion to a greater degree and tend to have greater uncertainty than diffusion coefficients. For the same relative random errors in concentration measurements, the diffusion cell method yields diffusion coefficient estimates that have less uncertainty than the wafer method. However, the wafer method is easier and less costly to implement and yields estimates more quickly, thus allowing a greater number of samples to be analyzed for the same cost and time. Given the relatively good agreement between the methods, and the lack of any apparent bias between the methods, the diffusion wafer method appears to offer advantages over the diffusion cell method if better statistical representation of a given set of rock samples is desired.« less

Comparison of experimental methods for estimating matrix diffusion coefficients for contaminant transport modeling

NASA Astrophysics Data System (ADS)

Telfeyan, Katherine; Ware, S. Doug; Reimus, Paul W.; Birdsell, Kay H.

2018-02-01

Diffusion cell and diffusion wafer experiments were conducted to compare methods for estimating effective matrix diffusion coefficients in rock core samples from Pahute Mesa at the Nevada Nuclear Security Site (NNSS). A diffusion wafer method, in which a solute diffuses out of a rock matrix that is pre-saturated with water containing the solute, is presented as a simpler alternative to the traditional through-diffusion (diffusion cell) method. Both methods yielded estimates of effective matrix diffusion coefficients that were within the range of values previously reported for NNSS volcanic rocks. The difference between the estimates of the two methods ranged from 14 to 30%, and there was no systematic high or low bias of one method relative to the other. From a transport modeling perspective, these differences are relatively minor when one considers that other variables (e.g., fracture apertures, fracture spacings) influence matrix diffusion to a greater degree and tend to have greater uncertainty than effective matrix diffusion coefficients. For the same relative random errors in concentration measurements, the diffusion cell method yields effective matrix diffusion coefficient estimates that have less uncertainty than the wafer method. However, the wafer method is easier and less costly to implement and yields estimates more quickly, thus allowing a greater number of samples to be analyzed for the same cost and time. Given the relatively good agreement between the methods, and the lack of any apparent bias between the methods, the diffusion wafer method appears to offer advantages over the diffusion cell method if better statistical representation of a given set of rock samples is desired.

Determination of pollutant diffusion coefficients in naturally formed biofilms using a single tube extractive membrane bioreactor

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

Zhang, S.F.; Splendiani, A.; Freitas dos Santos, L.M.

A novel technique has been used to determine the effective diffusion coefficients for 1,1,2-trichloroethane (TCE), a nonreacting tracer, in biofilms growing on the external surface of a silicone rubber membrane tube during degradation of 1,2-dichloroethane (DCE) by Xanthobacter autotrophicus GJ10 and monochlorobenzene (MCB) by Pseudomonas JS150. Experiments were carried out in a single tube extractive membrane bioreactor (STEMB), whose configuration makes it possible to measure the transmembrane flux of substrates. A video imaging technique (VIT) was employed for in situ biofilm thickness measurement and recording. Diffusion coefficients of TCE in the biofilms and TCE mass transfer coefficients in the liquidmore » films adjacent to the biofilms were determined simultaneously using a resistances-in-series diffusion model. It was found that the flux and overall mass transfer coefficient of TCE decrease with increasing biofilm thickness, showing the importance of biofilm diffusion on the mass transfer process. Similar fluxes were observed for the nonreacting tracer (TCE) and the reactive substrates (MCB or DCE), suggesting that membrane-attached biofilm systems can be rate controlled primarily by substrate diffusion. The TCE diffusion coefficient in the JS150 biofilm appeared to be dependent on biofilm thickness, decreasing markedly for biofilm thicknesses of >1 mm. The values of the TCE diffusion coefficients in the JS150 biofilms <1-mm thick are approximately twice those in water and fall to around 30% of the water value for biofilms >1-mm thick.« less

Diffusion and plasticity at high temperature

NASA Astrophysics Data System (ADS)

Philibert, J.

1991-06-01

High temperature plastic deformation requires atomic migration whatever the mechanism of deformation. The constitutive equations contain a diffusion coefficient and the deformation rate follows an Arrhenius law. This paper will only discuss the case of viscous creep in order to elucidate the nature of the diffusion processes and the expression of the diffusion coefficient involved in alloys or compounds. La déformation plastique à haute température met en jeu des migrations atomiques, quel que soit le mécanisme de déformation. Les lois de comportement contiennent donc un coefficient de diffusion et la vitesse de déformation obéit à une loi d'Arrhenius. Dans cet article, qui ne conceme qu'un seul type de déformation, lefluage visqueux, on s'efforce de préciser la nature des processus de diffusion et du coefficient de diffusion mis en jeu dans le cas des alliages et des composés.

Theoretical and Experimental Investigation of the Translational Diffusion of Proteins in the Vicinity of Temperature-Induced Unfolding Transition.

PubMed

Molchanov, Stanislav; Faizullin, Dzhigangir A; Nesmelova, Irina V

2016-10-06

Translational diffusion is the most fundamental form of transport in chemical and biological systems. The diffusion coefficient is highly sensitive to changes in the size of the diffusing species; hence, it provides important information on the variety of macromolecular processes, such as self-assembly or folding-unfolding. Here, we investigate the behavior of the diffusion coefficient of a macromolecule in the vicinity of heat-induced transition from folded to unfolded state. We derive the equation that describes the diffusion coefficient of the macromolecule in the vicinity of the transition and use it to fit the experimental data from pulsed-field-gradient nuclear magnetic resonance (PFG NMR) experiments acquired for two globular proteins, lysozyme and RNase A, undergoing temperature-induced unfolding. A very good qualitative agreement between the theoretically derived diffusion coefficient and experimental data is observed.

Additivity Principle in High-Dimensional Deterministic Systems

NASA Astrophysics Data System (ADS)

Saito, Keiji; Dhar, Abhishek

2011-12-01

The additivity principle (AP), conjectured by Bodineau and Derrida [Phys. Rev. Lett. 92, 180601 (2004)PRLTAO0031-900710.1103/PhysRevLett.92.180601], is discussed for the case of heat conduction in three-dimensional disordered harmonic lattices to consider the effects of deterministic dynamics, higher dimensionality, and different transport regimes, i.e., ballistic, diffusive, and anomalous transport. The cumulant generating function (CGF) for heat transfer is accurately calculated and compared with the one given by the AP. In the diffusive regime, we find a clear agreement with the conjecture even if the system is high dimensional. Surprisingly, even in the anomalous regime the CGF is also well fitted by the AP. Lower-dimensional systems are also studied and the importance of three dimensionality for the validity is stressed.

Fractional Brownian motion with a reflecting wall

NASA Astrophysics Data System (ADS)

Wada, Alexander H. O.; Vojta, Thomas

2018-02-01

Fractional Brownian motion, a stochastic process with long-time correlations between its increments, is a prototypical model for anomalous diffusion. We analyze fractional Brownian motion in the presence of a reflecting wall by means of Monte Carlo simulations. Whereas the mean-square displacement of the particle shows the expected anomalous diffusion behavior ˜tα , the interplay between the geometric confinement and the long-time memory leads to a highly non-Gaussian probability density function with a power-law singularity at the barrier. In the superdiffusive case α >1 , the particles accumulate at the barrier leading to a divergence of the probability density. For subdiffusion α <1 , in contrast, the probability density is depleted close to the barrier. We discuss implications of these findings, in particular, for applications that are dominated by rare events.

Banded structures in electron pitch angle diffusion coefficients from resonant wave-particle interactions

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

Tripathi, A. K., E-mail: aktrip2001@yahoo.co.in; Singhal, R. P., E-mail: rpsiitbhu@yahoo.com; Khazanov, G. V., E-mail: George.V.Khazanov@nasa.gov

2016-04-15

Electron pitch angle (D{sub αα}) and momentum (D{sub pp}) diffusion coefficients have been calculated due to resonant interactions with electrostatic electron cyclotron harmonic (ECH) and whistler mode chorus waves. Calculations have been performed at two spatial locations L = 4.6 and 6.8 for electron energies ≤10 keV. Landau (n = 0) resonance and cyclotron harmonic resonances n = ±1, ±2, … ±5 have been included in the calculations. It is found that diffusion coefficient versus pitch angle (α) profiles show large dips and oscillations or banded structures. The structures are more pronounced for ECH and lower band chorus (LBC) and particularly at location 4.6. Calculations of diffusionmore » coefficients have also been performed for individual resonances. It is noticed that the main contribution of ECH waves in pitch angle diffusion coefficient is due to resonances n = +1 and n = +2. A major contribution to momentum diffusion coefficients appears from n = +2. However, the banded structures in D{sub αα} and D{sub pp} coefficients appear only in the profile of diffusion coefficients for n = +2. The contribution of other resonances to diffusion coefficients is found to be, in general, quite small or even negligible. For LBC and upper band chorus waves, the banded structures appear only in Landau resonance. The D{sub pp} diffusion coefficient for ECH waves is one to two orders smaller than D{sub αα} coefficients. For chorus waves, D{sub pp} coefficients are about an order of magnitude smaller than D{sub αα} coefficients for the case n ≠ 0. In case of Landau resonance, the values of D{sub pp} coefficient are generally larger than the values of D{sub αα} coefficients particularly at lower energies. As an aid to the interpretation of results, we have also determined the resonant frequencies. For ECH waves, resonant frequencies have been estimated for wave normal angle 89° and harmonic resonances n = +1, +2, and +3, whereas for whistler mode waves, the frequencies have been calculated for angle 10° and Landau resonance. Further, in ECH waves, the banded structures appear for electron energies ≥1 keV, and for whistler mode chorus waves, structures appear for energies >2 keV at L = 4.6 and above 200 eV for L = 6.8. The results obtained in the present work will be helpful in the study of diffusion curves and will have important consequences for diffuse aurora and pancake distributions.« less

Anomalous transmission of an ultrashort ionizing laser pulse through a thin foil.

PubMed

Ferrante, G; Zarcone, M; Uryupin, S A

2003-08-22

The formation of a highly anisotropic photoelectron velocity distribution as a result of the interaction of a powerful ultrashort laser pulse with a thin foil is found to yield a large skin-layer depth and an anomalous increase of the transmission coefficient. The physical reason for the effect is the influence of the incident wave magnetic field, through the Lorenz force, on the electron kinetics in the skin layer.

Three FORTRAN programs for finite-difference solutions to binary diffusion in one and two phases with composition-and time-dependent diffusion coefficients

USGS Publications Warehouse

Sanford, R.F.

1982-01-01

Geological examples of binary diffusion are numerous. They are potential indicators of the duration and rates of geological processes. Analytical solutions to the diffusion equations generally do not allow for variable diffusion coefficients, changing boundary conditions, and impingement of diffusion fields. The three programs presented here are based on Crank-Nicholson finite-difference approximations, which can take into account these complicating factors. Program 1 describes the diffusion of a component into an initially homogeneous phase that has a constant surface composition. Specifically it is written for Fe-Mg exchange in olivine at oxygen fugacities appropriate for the lunar crust, but other components, phases, or fugacities may be substituted by changing the values of the diffusion coefficient. Program 2 simulates the growth of exsolution lamellae. Program 3 describes the growth of reaction rims. These two programs are written for pseudobinary Ca-(Mg, Fe) exchange in pyroxenes. In all three programs, the diffusion coefficients and boundary conditions can be varied systematically with time. To enable users to employ widely different numerical values for diffusion coefficients and diffusion distance, the grid spacing in the space dimension and the increment by which the grid spacing in the time dimension is increased at each time step are input constants that can be varied each time the programs are run to yield a solution of the desired accuracy. ?? 1982.

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

Determination of malignancy and characterization of hepatic tumor type with diffusion-weighted magnetic resonance imaging: comparison of apparent diffusion coefficient and intravoxel incoherent motion-derived measurements.

PubMed

Doblas, Sabrina; Wagner, Mathilde; Leitao, Helena S; Daire, Jean-Luc; Sinkus, Ralph; Vilgrain, Valérie; Van Beers, Bernard E

2013-10-01

The objective of this study was to compare the value of the apparent diffusion coefficient (ADC) determined with 3 b values and the intravoxel incoherent motion (IVIM)-derived parameters in the determination of malignancy and characterization of hepatic tumor type. Seventy-six patients with 86 solid hepatic lesions, including 8 hemangiomas, 20 lesions of focal nodular hyperplasia, 9 adenomas, 30 hepatocellular carcinomas, 13 metastases, and 6 cholangiocarcinomas, were assessed in this prospective study. Diffusion-weighted images were acquired with 11 b values to measure the ADCs (with b = 0, 150, and 500 s/mm) and the IVIM-derived parameters, namely, the pure diffusion coefficient and the perfusion-related diffusion fraction and coefficient. The diffusion parameters were compared between benign and malignant tumors and between tumor types, and their diagnostic value in identifying tumor malignancy was assessed. The apparent and pure diffusion coefficients were significantly higher in benign than in malignant tumors (benign: 2.32 [0.87] × 10 mm/s and 1.42 [0.37] × 10 mm/s vs malignant: 1.64 [0.51] × 10 mm/s and 1.14 [0.28] × 10 mm/s, respectively; P < 0.0001 and P = 0.0005), whereas the perfusion-related diffusion parameters did not differ significantly between the 2 groups. The apparent and pure diffusion coefficients provided similar accuracy in assessing tumor malignancy (areas under the receiver operating characteristic curve of 0.770 and 0.723, respectively). In the multigroup analysis, the ADC was found to be significantly higher in hemangiomas than in hepatocellular carcinomas, metastases, and cholangiocarcinomas. In the same manner, it was higher in lesions of focal nodular hyperplasia than in metastases and cholangiocarcinomas. However, the pure diffusion coefficient was significantly higher only in hemangiomas versus hepatocellular and cholangiocellular carcinomas. Compared with the ADC, the diffusion parameters derived from the IVIM model did not improve the determination of malignancy and characterization of hepatic tumor type.

Maxwell-Stefan diffusion coefficient estimation for ternary systems: an ideal ternary alcohol system.

PubMed

Allie-Ebrahim, Tariq; Zhu, Qingyu; Bräuer, Pierre; Moggridge, Geoff D; D'Agostino, Carmine

2017-06-21

The Maxwell-Stefan model is a popular diffusion model originally developed to model diffusion of gases, which can be considered thermodynamically ideal mixtures, although its application has been extended to model diffusion in non-ideal liquid mixtures as well. A drawback of the model is that it requires the Maxwell-Stefan diffusion coefficients, which are not based on measurable quantities but they have to be estimated. As a result, numerous estimation methods, such as the Darken model, have been proposed to estimate these diffusion coefficients. However, the Darken model was derived, and is only well defined, for binary systems. This model has been extended to ternary systems according to two proposed forms, one by R. Krishna and J. M. van Baten, Ind. Eng. Chem. Res., 2005, 44, 6939-6947 and the other by X. Liu, T. J. H. Vlugt and A. Bardow, Ind. Eng. Chem. Res., 2011, 50, 10350-10358. In this paper, the two forms have been analysed against the ideal ternary system of methanol/butan-1-ol/propan-1-ol and using experimental values of self-diffusion coefficients. In particular, using pulsed gradient stimulated echo nuclear magnetic resonance (PGSTE-NMR) we have measured the self-diffusion coefficients in various methanol/butan-1-ol/propan-1-ol mixtures. The experimental values of self-diffusion coefficients were then used as the input data required for the Darken model. The predictions of the two proposed multicomponent forms of this model were then compared to experimental values of mutual diffusion coefficients for the ideal alcohol ternary system. This experimental-based approach showed that the Liu's model gives better predictions compared to that of Krishna and van Baten, although it was only accurate to within 26%. Nonetheless, the multicomponent Darken model in conjunction with self-diffusion measurements from PGSTE-NMR represents an attractive method for a rapid estimation of mutual diffusion in multicomponent systems, especially when compared to exhaustive MD simulations.

Experimental study of mass diffusion coefficients of hydrogen in dimethyl phosphate and n-heptane

NASA Astrophysics Data System (ADS)

Guo, Y.; Zhu, L. K.; Zhang, Y. P.; Liu, J.; Guo, J. S.

2017-11-01

In this study, a laser holographic interferometer experimental system was developed for studying the gas-liquid mass diffusion coefficient. Then the experimental system’s uncertainty was analyzed to be at most ±0.2% therefore, this system was reliable. The mass diffusion coefficient of hydrogen in dimethyl phosphate and n-heptane was measured at atmospheric pressure in the temperature range of 273.15-338.15 K. Then, the experimental data were used to fit the correlations of the mass diffusion coefficient of hydrogen in dimethyl phosphate and n-heptane with temperature.

Chromatographic determination of the diffusion coefficients of light hydrocarbons in polymers

NASA Astrophysics Data System (ADS)

Yakubenko, E. E.; Korolev, A. A.; Chapala, P. P.; Bermeshev, M. V.; Kanat'eva, A. Yu.; Kurganov, A. A.

2017-01-01

Gas-chromatographic determination of the diffusion coefficients that allows for the compressibility of the mobile phase has been suggested. The diffusion coefficients were determined for light hydrocarbons C1-C4 in four polymers with a high free volume, which are candidates for use as gas-separating membranes. The diffusion coefficients calculated from chromatographic data were shown to be one or two orders of magnitude smaller than the values obtained by the membrane method. This may be due to the presence of an additional flow through the membrane caused by the pressure gradient across the membrane in membrane methods.

TEMPEST simulations of the plasma transport in a single-null tokamak geometry

NASA Astrophysics Data System (ADS)

Xu, X. Q.; Bodi, K.; Cohen, R. H.; Krasheninnikov, S.; Rognlien, T. D.

2010-06-01

We present edge kinetic ion transport simulations of tokamak plasmas in magnetic divertor geometry using the fully nonlinear (full-f) continuum code TEMPEST. Besides neoclassical transport, a term for divergence of anomalous kinetic radial flux is added to mock up the effect of turbulent transport. To study the relative roles of neoclassical and anomalous transport, TEMPEST simulations were carried out for plasma transport and flow dynamics in a single-null tokamak geometry, including the pedestal region that extends across the separatrix into the scrape-off layer and private flux region. A series of TEMPEST simulations were conducted to investigate the transition of midplane pedestal heat flux and flow from the neoclassical to the turbulent limit and the transition of divertor heat flux and flow from the kinetic to the fluid regime via an anomalous transport scan and a density scan. The TEMPEST simulation results demonstrate that turbulent transport (as modelled by large diffusion) plays a similar role to collisional decorrelation of particle orbits and that the large turbulent transport (large diffusion) leads to an apparent Maxwellianization of the particle distribution. We also show the transition of parallel heat flux and flow at the entrance to the divertor plates from the fluid to the kinetic regime. For an absorbing divertor plate boundary condition, a non-half-Maxwellian is found due to the balance between upstream radial anomalous transport and energetic ion endloss.

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.

Molecular dynamics simulation of real-fluid mutual diffusion coefficients with the Lennard-Jones potential model

NASA Astrophysics Data System (ADS)

Stoker, J. M.; Rowley, R. L.

1989-09-01

Mutual diffusion coefficients for selected alkanes in carbon tetrachloride were calculated using molecular dynamics and Lennard-Jones (LJ) potentials. Use of effective spherical LJ parameters is desirable when possible for two reasons: (i) computer time is saved due to the simplicity of the model and (ii) the number of parameters in the model is kept to a minimum. Results of this study indicate that mutual diffusivity is particularly sensitive to the molecular size cross parameter, σ12, and that the commonly used Lorentz-Berthelot rules are inadequate for mixtures in which the component structures differ significantly. Good agreement between simulated and experimental mutual diffusivities is obtained with a combining rule for σ12 which better represents these asymmetric mixtures using pure component LJ parameters obtained from self-diffusion coefficient data. The effect of alkane chain length on the mutual diffusion coefficient is correctly predicted. While the effects of alkane branching upon the diffusion coefficient are comparable in size to the uncertainty of these calculations, the qualitative trend due to branching is also correctly predicted by the MD results.

Time of Flight Electrochemistry: Diffusion Coefficient Measurements Using Interdigitated Array (IDA) Electrodes

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

Liu, Fei; Kolesov, Grigory; Parkinson, Bruce A.

2014-09-26

A simple and straightforward method for measuring diffusion coefficients using interdigitated array (IDA) electrodes is reported. The method does not require that the exact electrode area be known but depends only the size of the gap between the IDA electrode pairs. Electroactive molecules produced at the generator electrode of the IDA by a voltage step or scan can diffuse to the collector electrode and the time delay before the current for the reverse electrochemical reaction is detected at the collector is used to calculate the diffusion coefficient. The measurement of the diffusion rate of Ru(NH3)6+2 in aqueous solution has beenmore » used as an example measuring diffusion coefficients using this method. Additionally, a digital simulation of the electrochemical response of the IDA electrodes was used to simulate the entire current/voltage/time behavior of the system and verify the experimentally measured diffusion coefficients. This work was supported as part of the Center for Molecular Electrocatalysis, an Energy Frontier Research Center funded by the Department of Energy, Office of Science, Office of Basic Energy Sciences.« less

Serial diffusion-weighted imaging in subacute sclerosing panencephalitis.

PubMed

Kanemura, Hideaki; Aihara, Masao

2008-06-01

Subacute sclerosing panencephalitis may be associated with clinical features of frontal lobe dysfunction. We previously reported that frontal lobe volume falls significantly as clinical stage progresses, using three-dimensional magnetic resonance imaging-based brain volumetry. The hypothesis that frontal volume increases correlate with clinical improvement, however, was not tested in our previous study. Therefore, we reevaluated our patient with subacute sclerosing panencephalitis, to determine whether apparent diffusion coefficient maps can characterize the clinical course of subacute sclerosing panencephalitis. We studied an 8-year-old boy with subacute sclerosing panencephalitis, using serial diffusion-weighted imaging magnetic resonance imaging, and measured the regional apparent diffusion coefficient. The regional apparent diffusion coefficient of the frontal lobe decreased significantly with clinical progression, whereas it increased to within normal range during clinical improvements. The apparent diffusion coefficient of the other regions did not change. These results suggest that the clinical signs of patients with subacute sclerosing panencephalitis are attributable to frontal lobe dysfunction, and that apparent diffusion coefficient measurements may be useful in predicting the clinical course of subacute sclerosing panencephalitis.

Quantitative differentiation of breast lesions at 3T diffusion-weighted imaging (DWI) using the ratio of distributed diffusion coefficient (DDC).

PubMed

Ertas, Gokhan; Onaygil, Can; Akin, Yasin; Kaya, Handan; Aribal, Erkin

2016-12-01

To investigate the accuracy of diffusion coefficients and diffusion coefficient ratios of breast lesions and of glandular breast tissue from mono- and stretched-exponential models for quantitative diagnosis in diffusion-weighted magnetic resonance imaging (MRI). We analyzed pathologically confirmed 170 lesions (85 benign and 85 malignant) imaged using a 3.0T MR scanner. Small regions of interest (ROIs) focusing on the highest signal intensity for lesions and also for glandular tissue of contralateral breast were obtained. Apparent diffusion coefficient (ADC) and distributed diffusion coefficient (DDC) were estimated by performing nonlinear fittings using mono- and stretched-exponential models, respectively. Coefficient ratios were calculated by dividing the lesion coefficient by the glandular tissue coefficient. A stretched exponential model provides significantly better fits then the monoexponential model (P < 0.001): 65% of the better fits for glandular tissue and 71% of the better fits for lesion. High correlation was found in diffusion coefficients (0.99-0.81 and coefficient ratios (0.94) between the models. The highest diagnostic accuracy was found by the DDC ratio (area under the curve [AUC] = 0.93) when compared with lesion DDC, ADC ratio, and lesion ADC (AUC = 0.91, 0.90, 0.90) but with no statistically significant difference (P > 0.05). At optimal thresholds, the DDC ratio achieves 93% sensitivity, 80% specificity, and 87% overall diagnostic accuracy, while ADC ratio leads to 89% sensitivity, 78% specificity, and 83% overall diagnostic accuracy. The stretched exponential model fits better with signal intensity measurements from both lesion and glandular tissue ROIs. Although the DDC ratio estimated by using the model shows a higher diagnostic accuracy than the ADC ratio, lesion DDC, and ADC, it is not statistically significant. J. Magn. Reson. Imaging 2016;44:1633-1641. © 2016 International Society for Magnetic Resonance in Medicine.

Diffusion coefficients of nitric oxide in water: A molecular dynamics study

NASA Astrophysics Data System (ADS)

Pokharel, Sunil; Pantha, Nurapati; Adhikari, N. P.

2016-09-01

Self-diffusion coefficients along with the mutual diffusion coefficients of nitric oxide (NO) and SPC/E water (H2O) as solute and solvent of the mixture, have been studied within the framework of classical molecular dynamics level of calculations using GROMACS package. The radial distribution function (RDF) of the constituent compounds are calculated to study solute-solute, solute-solvent and solvent-solvent molecular interactions as a function of temperature. A dilute solution of five NO molecules (mole fraction 0.018) and 280 H2O molecules (mole fraction 0.982) has been taken as the sample. The self-diffusion coefficient of the solvent is calculated by using mean square displacement (MSD) where as that for solute (NO) is calculated by using MSD and velocity auto-correlation function (VACF). The results are then compared with the available experimental values. The results from the present work for water come in good agreement, very precise at low temperatures, with the experimental values. The diffusion coefficients of NO, on the other hands, agree well with the available theoretical studies, and also with experiment at low temperatures (up to 310 K). The results at the higher temperatures (up to 333 K), however, deviate significantly with the experimental observations. Also, the mutual diffusion coefficients of NO in water have been calculated by using Darken’s relation. The temperature dependence of the calculated diffusion coefficients follow the Arrhenius behavior.

The Gini coefficient: a methodological pilot study to assess fetal brain development employing postmortem diffusion MRI.

PubMed

Viehweger, Adrian; Riffert, Till; Dhital, Bibek; Knösche, Thomas R; Anwander, Alfred; Stepan, Holger; Sorge, Ina; Hirsch, Wolfgang

2014-10-01

Diffusion-weighted imaging (DWI) is important in the assessment of fetal brain development. However, it is clinically challenging and time-consuming to prepare neuromorphological examinations to assess real brain age and to detect abnormalities. To demonstrate that the Gini coefficient can be a simple, intuitive parameter for modelling fetal brain development. Postmortem fetal specimens(n = 28) were evaluated by diffusion-weighted imaging (DWI) on a 3-T MRI scanner using 60 directions, 0.7-mm isotropic voxels and b-values of 0, 150, 1,600 s/mm(2). Constrained spherical deconvolution (CSD) was used as the local diffusion model. Fractional anisotropy (FA), apparent diffusion coefficient (ADC) and complexity (CX) maps were generated. CX was defined as a novel diffusion metric. On the basis of those three parameters, the Gini coefficient was calculated. Study of fetal brain development in postmortem specimens was feasible using DWI. The Gini coefficient could be calculated for the combination of the three diffusion parameters. This multidimensional Gini coefficient correlated well with age (Adjusted R(2) = 0.59) between the ages of 17 and 26 gestational weeks. We propose a new method that uses an economics concept, the Gini coefficient, to describe the whole brain with one simple and intuitive measure, which can be used to assess the brain's developmental state.

Anomalous fluxes in the plateau regime for a weakly turbulent, magnetically confined plasma

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

Balescu, R.

1990-09-01

The anomalous particle and heat fluxes, together with the parallel electric current, are determined for a confined plasma in the plateau regime in the presence of weak electrostatic drift-wave turbulence. Proper account is taken of nonstationarity and of the finite ion Larmor radius (FLR). The quasineutrality of the drift-wave fluctuations imposes a consistency condition, by which the evaluation of the anomalous fluxes is closely related to the drift-wave dispersion equation. On the other hand, these fluxes are related to the thermodynamic forces via the poloidal fluxes. For the weak turbulence approximation considered here, a unified formulation of the anomalous transportmore » problem has been obtained, including all aspects of neoclassical theory. The complete set of transport coefficients is calculated and various relations between them are exhibited. It clearly appears, for instance, that the anomalous ion heat flux is a pure FLR effect that vanishes as the Larmor radius goes to zero. The Onsager symmetry is broken for anomalous transport. The Appendix is devoted to a general discussion of the concept of heat flux in turbulent plasmas.« less

Effective diffusion coefficients of DNAPL waste components in saturated low permeability soil materials

NASA Astrophysics Data System (ADS)

Ayral-Cinar, Derya; Demond, Avery H.

2017-12-01

Diffusion is regarded as the dominant transport mechanism into and out of low permeable subsurface lenses and layers in the subsurface. But, some reports of mass storage in such zones are higher than what might be attributable to diffusion, based on estimated diffusion coefficients. Despite the importance of diffusion to efforts to estimate the quantity of residual contamination in the subsurface, relatively few studies present measured diffusion coefficients of organic solutes in saturated low permeability soils. This study reports the diffusion coefficients of a trichloroethylene (TCE), and an anionic surfactant, Aerosol OT (AOT), in water-saturated silt and a silt-montmorillonite (25:75) mixture, obtained using steady-state experiments. The relative diffusivity ranged from 0.11 to 0.17 for all three compounds for the silt and the silt-clay mixture that was allowed to expand. In the case in which the swelling was constrained, the relative diffusivity was about 0.07. In addition, the relative diffusivity of 13C-labeled TCE through a water saturated silt-clay mixture that had contacted a field dense non-aqueous phase liquid (DNAPL) for 18 months was measured and equaled 0.001. These experimental results were compared with the estimates generated using common correlations, and it was found that, in all cases, the measured diffusion coefficients were significantly lower than the estimated. Thus, the discrepancy between mass accumulations observed in the field and the mass storage that can attributable to diffusion may be greater than previously believed.

The tracer diffusion coefficient of soft nanoparticles in a linear polymer matrix

DOE PAGES

Imel, Adam E.; Rostom, Sahar; Holley, Wade; ...

2017-03-09

The diffusion properties of nanoparticles in polymer nanocomposites are largely unknown and are often difficult to determine experimentally. To address this shortcoming, we have developed a novel method to determine the tracer diffusion coefficient of soft polystyrene nanoparticles in a linear polystyrene matrix. Monitoring the interdiffusion of soft nanoparticles into a linear polystyrene matrix provides the mutual diffusion coefficient of this system, from which the tracer diffusion coefficient of the soft nanoparticle can be determined using the slow mode theory. Utilizing this protocol, the role of nanoparticle molecular weight and rigidity on its tracer diffusion coefficient is provided. These resultsmore » demonstrate that the diffusive behavior of these soft nanoparticles differ from that of star polymers, which is surprising since our recent studies suggest that the nanoparticle interacts with a linear polymer similarly to that of a star polymer. It appears that these deformable nanoparticles mostly closely mimic the diffusive behavior of fractal macromolecular architectures or microgels, where the transport of the nanoparticle relies on the cooperative motion of neighboring linear chains. Finally, the less cross-linked, and thus more deformable, nanoparticles diffuse faster than the more highly crosslinked nanoparticles, presumably because the increased deformability allows the nanoparticle to distort and fit into available space.« less

An anomalous subdiffusion model for calcium spark in cardiac myocytes

NASA Astrophysics Data System (ADS)

Tan, Wenchang; Fu, Chaoqi; Fu, Ceji; Xie, Wenjun; Cheng, Heping

2007-10-01

The elementary events of excitation-contraction coupling in heart muscle are Ca2+ sparks, which arise from ryanodine receptors in the sarcoplasmic reticulum (SR). Here, an anomalous subdiffusion model is developed to explore Ca2+ spark formation in cardiac myocytes. Numerical simulations reproduce the brightness, the time course, and spatial size of a typical cardiac Ca2+ spark. It is suggested that the diffusion of Ca2+ spark in the cytoplasm may no longer obey Fickian second law, but the anomalous space subdiffusion. The physical reason is perhaps due to the effects of the electric field of the calcium ions and the viscoelasticity of the cytoplasm and its complex structures.

Monitoring quiescent volcanoes by diffuse He degassing: case study Teide volcano

NASA Astrophysics Data System (ADS)

Pérez, Nemesio M.; Melián, Gladys; Asensio-Ramos, María; Padrón, Eleazar; Hernández, Pedro A.; Barrancos, José; Padilla, Germán; Rodríguez, Fátima; Calvo, David; Alonso, Mar

2016-04-01

Tenerife (2,034 km2), the largest of the Canary Islands, is the only island that has developed a central volcanic complex (Teide-Pico Viejo stratovolcanoes), characterized by the eruption of differentiated magmas. This central volcanic complex has been built in the intersection of the three major volcanic rift-zones of Tenerife, where most of the historical volcanic activity has taken place. The existence of a volcanic-hydrothermal system beneath Teide volcano is suggested by the occurrence of a weak fumarolic system, steamy ground and high rates of diffuse CO2 degassing all around the summit cone of Teide (Pérez et al., 2013). Diffuse emission studies of non-reactive and/or highly mobile gases such as helium have recently provided promising results to detect changes in the magmatic gas component at surface related to volcanic unrest episodes (Padrón et al., 2013). The geochemical properties of He minimize the interaction of this noble gas on its movement toward the earth's surface, and its isotopic composition is not affected by subsequent chemical reactions. It is highly mobile, chemically inert, physically stable, non-biogenic, sparingly soluble in water under ambient conditions, almost non-adsorbable, and highly diffusive with a diffusion coefficient ˜10 times that of CO2. As part of the geochemical monitoring program for the volcanic surveillance of Teide volcano, yearly surveys of diffuse He emission through the surface of the summit cone of Teide volcano have been performed since 2006. Soil He emission rate was measured yearly at ˜130 sampling sites selected in the surface environment of the summit cone of Teide volcano (Tenerife, Canary Islands), covering an area of ˜0.5 km2, assuming that He emission is governed by convection and diffusion. The distribution of the sampling sites was carefully chosen to homogeneously cover the target area, allowing the computation of the total He emission by sequential Gaussian simulation (sGs). Nine surveys have been carried out since 2006, showing an average emission rate of 8.0 kg/d. This value showed an anomalous increase up to 29 kg/d in the summer of 2010. The number of seismic events registered in and around Tenerife Island by the National Geographic Institute (IGN) reached also the highest value (1,176) in 2010. This excellent agreement between both times series suggest that the anomalous seismicity registered in 2010 was likely due to strain/stress changes caused by input of magmatic fluids beneath the central volcanic system of the island. These results suggest that monitoring of He degassing rates in oceanic volcanic islands is an excellent early warning geochemical precursory signal for volcanic unrest. References Padrón et al., 2013. Geology, DOI: 10.1130/G34027.1. Pérez et al., 2013. J. Geol. Soc., DOI: 10.1144/jgs2012-125.

Fractional and fractal dynamics approach to anomalous diffusion in porous media: application to landslide behavior

NASA Astrophysics Data System (ADS)

Martelloni, Gianluca; Bagnoli, Franco

2016-04-01

In the past three decades, fractional and fractal calculus (that is, calculus of derivatives and integral of any arbitrary real or complex order) appeared to be an important tool for its applications in many fields of science and engineering. This theory allows to face, analytically and/or numerically, fractional differential equations and fractional partial differential equations. In particular, one of the several applications deals with anomalous diffusion processes. The latter phenomena can be clearly described from the statistical viewpoint. Indeed, in various complex systems, the diffusion processes usually no longer follow Gaussian statistics, and thus Fick's second law fails to describe the related transport behavior. In particular, one observes deviations from the linear time dependence of the mean squared displacement ⟨x2(t)⟩ ∝ t, (1) which is characteristic of Brownian motion, i.e., a direct consequence of the central limit theorem and the Markovian nature of the underlying stochastic process [1-17]. Instead, anomalous diffusion is found in a wide diversity of systems and its feature is the non-linear growth of the mean squared displacement over time. Especially the power-law pattern, with exponent γ different from 1 ⟨ ⟩ x2(t) ∝ tγ, (2) characterizes many systems [18, 19], but a variety of other rules, such as a logarithmic time dependence, exist [20]. The anomalous diffusion, as expressed in Eq. (2) is connected with the breakdown of the central limit theorem, caused by either broad distributions or long-range correlations, e.g., the extreme statistics and the power law distributions, typical of the self-organized criticality [42, 43]. Instead, anomalous diffusion rests on the validity of the Levy-Gnedenko generalized central limit theorem [21-23]. Particularly, broad spatial jumps or waiting time distributions lead to non-Gaussian distribution and non-Markovian time evolution of the system. Anomalous diffusion has been known since Richardson's treatise on turbulent diffusion in 1926 [24] and today, the list of system displaying anomalous dynamical behavior is quite extensive. We only report some examples: charge carrier transport in amorphous semiconductors [25], porous systems [26], reptation dynamics in polymeric systems [27, 28], transport on fractal geometries [29], the long-time dynamics of DNA sequences [30]. In this scenario, the fractional calculus is used to generalized the Fokker-Planck linear equation -∂P (x,t)=D ∇2P (x,t), ∂t (3) where P (x,t) is the density of probability in the space x=[x1, x2, x3] and time t, while D >0 is the diffusion coefficient. Such processes are characterized by Eq. (1). An example of Eq. (3) generalization is ∂∂tP (x,t)=D∇ αP β(x,t) - ∞ < α ≤ 2 β > - 1 , (4) where the fractional based-derivatives Laplacian Σ(∂α/∂xα)i, (i = 1, 2, 3), of non-linear term Pβ(x,t) is taken into account [31]. Another generalized form is represented by equation ∂∂tδδP(x,t)=D ∇ αP(x,t) δ > 0 α ≤ 2 , (5) that considers also the fractional time-derivative [32]. These fractional-described processes exhibit a power law patters as expressed by Eq. (2). This general introduction introduces the presented work, whose aim is to develop a theoretical model in order to forecast the triggering and propagation of landslides, using the techniques of fractional calculus. The latter is suitable for modeling the water infiltration (i.e., the pore water pressure diffusion in the soil) and the dynamical processes in the fractal media [33]. Alternatively the fractal representation of temporal and spatial derivative (the fractal order only appears in the denominator of the derivative) is considered and the results are compared to the fractional one. The prediction of landslides and the discovering of the triggering mechanism, is one of the challenging problems in earth science. Landslides can be triggered by different factors but in most cases the trigger is an intense or long rain that percolates into the soil causing an increasing of the pore water pressure. In literature two type of models exist for attempting to forecast the landslides triggering: statistical or empirical modeling based on rainfall thresholds derived from the analysis of temporal series of daily rain [34] and geotechnical modeling, i.e., slope stability models that take into account water infiltration by rainfall considering classical Richardson equations [35-39]. Regarding the propagation of landslides, the models follow Eulerian (e.g., finite element methods, [40]) or Lagrangian approach (e.g., particle or molecular dynamics methods [41-46]). In a preliminary work [44], the possibility of the integration between fractional-based infiltration modeling and molecular dynamics approach, to model both the triggering and propagation, has been investigated in order to characterize the granular material varying the order of fractional derivative taking into account the equation -∂δ ∂2θ(z,t) ∂tδθ(z,t)=D ∂z2 , (6) where θ(z,t) represents the water content depending on time t and soil depth z [47], while the parameter δ, with 0.5 ≤ δ < 1, represents the fractional derivative order to consider anomalous sub-diffusion [48]; when δ = 1 we have classical derivative, i.e., normal diffusion, and when δ > 1 super-diffusion [32]. To sum up, in [44], a three-dimensional model is developed, the water content is expressed in term of pore pressure (interpreted as a scalar field acting on the particles), whose increasing induces the shear strength reduction. The latter is taking into account by means of Mohr-Coulomb criterion that represents a failure criterion based on limit equilibrium theory [49, 50]. Moreover, the fluctuations depending on positions, in term of pore pressure, are also considered. Concerning the interaction between particles, a Lennard-Jones potential is taking into account and other active forces as gravity, dynamic friction and viscosity are also considered. For the updating of positions, the Verlet algorithm is used [51]. The outcome of simulations are quite satisfactory and, although the model proposed in [44] is still quite schematic, the results encourage the investigations in this direction as this types of modeling can represent a new method to simulate landslides triggered by rainfall. Particularly, the results are consistent with the behavior of real landslides, e.g., it is possible to apply the method of the inverse surface displacement velocity for predicting the failure time (Fukuzono method [52]). An interesting behavior emerges from the dynamic and statistical points of view. In the simulations emerging phenomena such as detachments, fractures and arching are observed. Finally, in the simulated system, a transition of the mean energy increment distribution from Gaussian to power law, varying the value of some parameters (i.e., viscosity coefficient) is observed or, fixed all parameters, the same behavior can be observed in the time, during single simulation, due to the stick and slip phases. As mentioned, considering that our understanding of the triggering mechanisms is limited and alternative approaches based on interconnected elements are meaningful to reproduce transition from slowly moving mass to catastrophic mass release, we are motivated to investigate mathematical methods, as fractional calculus, for the comprehension of non-linearity of the infiltration phenomena and particle-based approach to achieve a realistic description of the behavior of granular materials. References [1] A. Einstein, in: R. Furth (Ed.), Investigations on the theory of the Brownian movement, Dover, New York, 1956. [2] N. Wax (Ed.), Selected Papers on Noise and Stochastic Processes, Dover, New York, 1954. [3] H.S. Carslaw, J.C. Jaegher, Conduction of Heat in Solids, Clarendon Press, Oxford, 1959. [4] E. Nelson, Dynamical Theories of Brownian Motion, Princeton University Press, Princeton, 1967. [5] P. Levy, Processus stochastiques et mouvement Brownien, Gauthier-Villars, Paris, 1965. [6] R. Becker, Theorie der Warme, Heidelberger Taschenbucher, Vol. 10, Springer, Berlin, 1966; Theory of Heat, Springer, Berlin, 1967. [7] S.R. de Groot, P. Mazur, Non-equilibrium Thermodynamics, North-Holland, Amsterdam, 1969. [8] J.L. Doob, Stochastic Processes, Wiley, New York, 1953. [9] J. Crank, The Mathematics of Diffusion, Clarendon Press, Oxford, 1970. [10] D.R. Cox, H.D. Miller, The Theory of Stochastic Processes, Methuen, London, 1965. [11] R. Aris, The Mathematical Theory of Diffusion and Reaction in Permeable Catalysis, Vols. I and II, Clarendon Press, Oxford, 1975. [12] L.D. Landau, E.M. Lifschitz, Statistische Physik, Akademie, Leipzig, 1989; Statistical Physics, Pergamon, Oxford, 1980. [13] N.G. van Kampen, Stochastic Processes in Physics and Chemistry, North-Holland, Amsterdam, 1981. [14] H. Risken, The Fokker-Planck Equation, Springer, Berlin, 1989. [15] W.T. Coffey, Yu.P. Kalmykov, J.T. Waldron, The Langevin Equation, World Scientific, Singapore, 1996. [16] B.D. Hughes, Random Walks and Random Environments, Vol. 1: Random Walks, Oxford University Press, Oxford, 1995. [17] G.H. Weiss, R.J. Rubin, Adv. Chem. Phys. 52 (1983) 363. [18] A. Blumen, J. Klafter, G. Zumofen, in: I. Zschokke (Ed.), Optical Spectroscopy of Glasses, Reidel, Dordrecht, 1986. [19] G.M. Zaslavsky, S. Benkadda, Chaos, Kinetics and Nonlinear Dynamics in Fluids and Plasmas, Springer, Berlin, 1998. [20] R. Metzler, J. Klafter, The random walk's guide to anomalous diffusion: a fractional dynamics approach, Physics Reports 339 (2000) 1-77. [21] P. Levy, Calcul des Probabilites, Gauthier-Villars, Paris, 1925. [22] P. Levy, Theorie de l'addition des variables Aleatoires, Gauthier-Villars, Paris, 1954. [23] B.V. Gnedenko, A.N. Kolmogorov, Limit Distributions for Sums of Random Variables, Addison-Wesley, Reading, MA, 1954. [24] L.F. Richardson, Atmospheric diffusion shown on a distance-neighbour graph, Proc. R. Soc.Lond. A 110, 709-737, 1926. [25] H. Scher, E.W. Montroll, Phys. Rev. B 12 (1975) 2455. [26] J. P. Bouchaud, A. Georges, Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applications, Physics reports, 195(4-5), 127293, 1990. [27] P.-G. de Gennes, Scaling Concepts in Polymer Physics, Cornell University Press, Ithaca, 1979. [28] M. Doi, S.F. Edwards, The Theory of Polymer Dynamics, Clarendon Press, Oxford, 1986. [29] M. Porto, A. Bunde, S. Havlin, H.E. Roman, Phys. Rev. E 56 (2), 1997. [30] P. Allegrini, M. Buiatti, P. Grigolini, B. J. West, Non-Gaussian statistics of anomalous diffusion: The DNA sequences of prokaryotes, Physical Review E 58(3), 1998. [31] M. Bologna, C. Tsallis, P. Grigolini, Anomalous diffusion associated with nonlinear fractional derivative Fokker-Planck-like equation: Exact time-dependent solutions, Physical Review E, 62(2), 2000. [32] W. Chen, H. Sun, X. Zhang, D. Korosak, Anomalous diffusion modeling by fractal and fractional derivatives, Computers and Mathematics with Applications, 59, 1754-1758, 2010. [33] V.E. Tarasov, Fractional Hydrodynamic Equations for Fractal Media, Annals of Physics, 318(2), 286-307, 2005. [34] G. Martelloni, S. Segoni, R. Fanti, F. Catani, Rainfall thresholds for the forecasting of landslide occurrence at regional scale. Landslides Journal, 9(4), 485-495, 2012. [35] M.G. Anderson, S. Howes, Development and application of a combined soil water-slope stability model, Q. J. Eng. Geol. London, 18: 225-236, 1985. [36] R.M. Iverson, Landslide triggering by rain infiltration, Water Resources Research 36(7): 1897-1910, 2000. [37] N. Lu, J. Godt, Infinite slope stability under steady unsaturated seepage conditions, Water Resources Research, Vol. 44, W11404, doi:10.1029/2008WR006976, 2008. [38] W. Wu, R.C. Sidle, A Distributed Slope Stability Model for Steep Forested Basins, Water Resour. Res., 31(8), 2097-2110, doi:10.1029/95WR01136, 1995. [39] G.B. Crosta, P. Frattini, Distributed modelling of shallow landslides triggered by intense rainfall, Natural Hazards and System Sciences 3: 81-93, 2003. [40] A. Patra, A. Bauer, C. Nichita, E. Pitman, M. Sheridan, M. Bursik, et al., Parallel adaptive numerical simulation of dry avalanches over natural terrain, J Volcanol Geotherm Res, 1-21, 2005. [41] E. Massaro, G. Martelloni, F. Bagnoli, Particle based method for shallow landslides: modeling sliding surface lubrification by rainfall, CMSIM International Journal of Nonlinear Scienze ISSN 2241-0503, 147-158, 2011. [42] G. Martelloni, E. Massaro, F. Bagnoli, A computational toy model for shallow landslides: Molecular Dynamics approach, Communications in Nonlinear Science and Numerical Simulation, 18(9), 2479-2492, 2013. [43] G. Martelloni, E. Massaro, F. Bagnoli, Computational modelling for landslide: molecular dynamic 2D application to shallow and deep landslides, In: EGU General Assembly 2012, Vienna (AT), Vol. 14, EGU2012-12219. [44] G. Martelloni, F. Bagnoli, Particle-based models for hydrologically triggered deep seated landslides, In: EGU General Assembly 2013, Vienna (AT), Vol. 15, EGU2013-10599-1. [45] P.A. Cundall, O.D.L. Strack, A discrete numerical model for granular assemblies, Geotechnique 29 819, 47-65, 1979. [46] G. Martelloni, F. Bagnoli, Infiltration effects on a two-dimensional molecular dynamics model of landslides. In NHAZ (Natural Hazards)), special issue in "Modeling in landslide research: advanced methods", 2014. [47] Y. Pachepsky, D. Timlin, W. Rawls, Generalized Richards' equation to simulate water transport in unsaturated soils, Journal of Hidrology 272: 3-13, 2003. [48] G. Drazer, D.H. Zanette, Experimental evidence of power-law trapping-time distributions in porous media, Physical Review E, 60(5), 1999. [49] C.A. Coulomb, Essai sur une application des regles des maximis et minimis a quelques problemes de statique relatifs, a la architecture. Mem. Acad. Roy. Div. Sav., 7: 343-387, 1776. [50] K. Terzaghi, Theoretical soil mechanics. New York: Wiley, 1943. [51] L. Verlet, Computer "Experiments" on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules. Physycal Review, 159: 98, 1967. [52] T. Fukuzono, A new method for predicting the failure time of a slope. Proc. 4th Int. Conf. Field Workshop Landslides, 145-150. Tokyo: Jpn. Landslide Soc., 1985.

Simultaneous characterization of lateral lipid and prothrombin diffusion coefficients by z-scan fluorescence correlation spectroscopy.

PubMed

Stefl, Martin; Kułakowska, Anna; Hof, Martin

2009-08-05

A new (to our knowledge) robust approach for the determination of lateral diffusion coefficients of weakly bound proteins is applied for the phosphatidylserine specific membrane interaction of bovine prothrombin. It is shown that z-scan fluorescence correlation spectroscopy in combination with pulsed interleaved dual excitation allows simultaneous monitoring of the lateral diffusion of labeled protein and phospholipids. Moreover, from the dependencies of the particle numbers on the axial sample positions at different protein concentrations phosphatidylserine-dependent equilibrium dissociation constants are derived confirming literature values. Increasing the amount of membrane-bound prothrombin retards the lateral protein and lipid diffusion, indicating coupling of both processes. The lateral diffusion coefficients of labeled lipids are considerably larger than the simultaneously determined lateral diffusion coefficients of prothrombin, which contradicts findings reported for the isolated N-terminus of prothrombin.

Transport of neutral solute across articular cartilage: the role of zonal diffusivities.

PubMed

Arbabi, V; Pouran, B; Weinans, H; Zadpoor, A A

2015-07-01

Transport of solutes through diffusion is an important metabolic mechanism for the avascular cartilage tissue. Three types of interconnected physical phenomena, namely mechanical, electrical, and chemical, are all involved in the physics of transport in cartilage. In this study, we use a carefully designed experimental-computational setup to separate the effects of mechanical and chemical factors from those of electrical charges. Axial diffusion of a neutral solute Iodixanol into cartilage was monitored using calibrated microcomputed tomography micro-CT images for up to 48 hr. A biphasic-solute computational model was fitted to the experimental data to determine the diffusion coefficients of cartilage. Cartilage was modeled either using one single diffusion coefficient (single-zone model) or using three diffusion coefficients corresponding to superficial, middle, and deep cartilage zones (multizone model). It was observed that the single-zone model cannot capture the entire concentration-time curve and under-predicts the near-equilibrium concentration values, whereas the multizone model could very well match the experimental data. The diffusion coefficient of the superficial zone was found to be at least one order of magnitude larger than that of the middle zone. Since neutral solutes were used, glycosaminoglycan (GAG) content cannot be the primary reason behind such large differences between the diffusion coefficients of the different cartilage zones. It is therefore concluded that other features of the different cartilage zones such as water content and the organization (orientation) of collagen fibers may be enough to cause large differences in diffusion coefficients through the cartilage thickness.

Unifying diffusion and seepage for nonlinear gas transport in multiscale porous media

NASA Astrophysics Data System (ADS)

Song, Hongqing; Wang, Yuhe; Wang, Jiulong; Li, Zhengyi

2016-09-01

We unify the diffusion and seepage process for nonlinear gas transport in multiscale porous media via a proposed new general transport equation. A coherent theoretical derivation indicates the wall-molecule and molecule-molecule collisions drive the Knudsen and collective diffusive fluxes, and constitute the system pressure across the porous media. A new terminology, nominal diffusion coefficient can summarize Knudsen and collective diffusion coefficients. Physical and numerical experiments show the support of the new formulation and provide approaches to obtain the diffusion coefficient and permeability simultaneously. This work has important implication for natural gas extraction and greenhouse gases sequestration in geological formations.

Numerical study of centrifugal compressor stage vaneless diffusers

NASA Astrophysics Data System (ADS)

Galerkin, Y.; Soldatova, K.; Solovieva, O.

2015-08-01

The authors analyzed CFD calculations of flow in vaneless diffusers with relative width in range from 0.014 to 0.100 at inlet flow angles in range from 100 to 450 with different inlet velocity coefficients, Reynolds numbers and surface roughness. The aim is to simulate calculated performances by simple algebraic equations. The friction coefficient that represents head losses as friction losses is proposed for simulation. The friction coefficient and loss coefficient are directly connected by simple equation. The advantage is that friction coefficient changes comparatively little in range of studied parameters. Simple equations for this coefficient are proposed by the authors. The simulation accuracy is sufficient for practical calculations. To create the complete algebraic model of the vaneless diffuser the authors plan to widen this method of modeling to diffusers with different relative length and for wider range of Reynolds numbers.

Determination of partition and diffusion coefficients of formaldehyde in selected building materials and impact of relative humidity.

PubMed

Xu, Jing; Zhang, Jianshun S; Liu, Xiaoyu; Gao, Zhi

2012-06-01

The partition and effective diffusion coefficients of formaldehyde were measured for three materials (conventional gypsum wallboard, "green" gypsum wallboard, and "green" carpet) under three relative humidity (RH) conditions (20%, 50%, and 70% RH). The "green" materials contained recycled materials and were friendly to environment. A dynamic dual-chamber test method was used. Results showed that a higher relative humidity led to a larger effective diffusion coefficient for two kinds of wallboards and carpet. The carpet was also found to be very permeable resulting in an effective diffusion coefficient at the same order of magnitude with the formaldehyde diffusion coefficient in air. The partition coefficient (K(ma)) of formaldehyde in conventional wallboard was 1.52 times larger at 50% RH than at 20% RH, whereas it decreased slightly from 50% to 70% RH, presumably due to the combined effects of water solubility of formaldehyde and micro-pore blocking by condensed moisture at the high RH level. The partition coefficient of formaldehyde increased slightly with the increase of relative humidity in "green" wallboard and "green" carpet. At the same relative humidity level, the "green" wallboard had larger partition coefficient and effective diffusion coefficient than the conventional wallboard, presumably due to the micro-pore structure differences between the two materials. The data generated could be used to assess the sorption effects of formaldehyde on building materials and to evaluate its impact on the formaldehyde concentration in buildings.

Determination of diffusion coefficients of various livestock antibiotics in water at infinite dilution

NASA Astrophysics Data System (ADS)

Soriano, Allan N.; Adamos, Kristoni G.; Bonifacio, Pauline B.; Adornado, Adonis P.; Bungay, Vergel C.; Vairavan, Rajendaran

2017-11-01

The fate of antibiotics entering the environment raised concerns on the possible effect of antimicrobial resistance bacteria. Prediction of the fate and transport of these particles are needed to be determined, significantly the diffusion coefficient of antibiotic in water at infinite dilution. A systematic determination of diffusion coefficient of antibiotic in water at infinite dilution of five different kinds of livestock antibiotics namely: Amtyl, Ciprotyl, Doxylak Forte, Trisullak, and Vetracin Gold in the 293.15 to 313.15 K temperature range are reported through the use of the method involving the electrolytic conductivity measurements. A continuous stirred tank reactor is utilized to measure the electrolytic conductivities of the considered systems. These conductivities are correlated by using the Nernst-Haskell equation to determine the infinite dilution diffusion coefficient. Determined diffusion coefficients are based on the assumption that in dilute solution, these antibiotics behave as strong electrolyte from which H+ cation dissociate from the antibiotic's anion.

Determination of molecular diffusion coefficient in n-alkane binary mixtures: empirical correlations.

PubMed

De Mezquia, D Alonso; Bou-Ali, M Mounir; Larrañaga, M; Madariaga, J A; Santamaría, C

2012-03-08

In this work we have measured the molecular diffusion coefficient of the n-alkane binary series nC(i)-nC(6), nC(i)-nC(10), and nC(i)-nC(12) at 298 K and 1 atm and a mass fraction of 0.5 by using the so-called sliding symmetric tubes technique. The results show that the diffusion coefficient at this concentration is proportional to the inverse viscosity of the mixture. In addition, we have also measured the diffusion coefficient of the systems nC(12)-nC(6), nC(12)-nC(7), and nC(12)-nC(8) as a function of concentration. From the data obtained, it is shown that the diffusion coefficient of the n-alkane binary mixtures at any concentration can be calculated from the molecular weight of the components and the dynamic viscosity of the corresponding mixture at 50% mass fraction.

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.

Measurement of the ferric diffusion coefficient in agarose and gelatine gels by utilization of the evolution of a radiation induced edge as reflected in relaxation rate images.

PubMed

Pedersen, T V; Olsen, D R; Skretting, A

1997-08-01

A method has been developed to determine the diffusion coefficients of ferric ions in ferrous sulphate doped gels. A radiation induced edge was created in the gel, and two spin-echo sequences were used to acquire a pair of images of the gel at different points of time. For each of these image pairs, a longitudinal relaxation rate image was derived. From profiles through these images, the standard deviations of the Gaussian functions that characterize diffusion were determined. These data provided the basis for the determination of the ferric diffusion coefficients by two different methods. Simulations indicate that the use of single spin-echo images in this procedure may in some cases lead to a significant underestimation of the diffusion coefficient. The technique was applied to different agarose and gelatine gels that were prepared, irradiated and imaged simultaneously. The results indicate that the diffusion coefficient is lower in a gelatine gel than in an agarose gel. Addition of xylenol orange to a gelatine gel lowers the diffusion coefficient from 1.45 to 0.81 mm2 h-1, at the cost of significantly lower Rl sensitivity. The addition of benzoic acid to the latter gel did not increase the Rl sensitivity.

Ion acceleration in a plasma focus

NASA Technical Reports Server (NTRS)

Gary, S. P.

1974-01-01

The electric and magnetic fields associated with anomalous diffusion to the axis of a linear plasma discharge are used to compute representative ion trajectories. Substantial axial acceleration of the ions is demonstrated.

Translational Diffusion of Macromolecule-sized Solutes in Cytoplasm and Nucleus

PubMed Central

Seksek, Olivier; Biwersi, Joachim; Verkman, A.S.

1997-01-01

Fluorescence recovery after photobleaching (FRAP) was used to quantify the translational diffusion of microinjected FITC-dextrans and Ficolls in the cytoplasm and nucleus of MDCK epithelial cells and Swiss 3T3 fibroblasts. Absolute diffusion coefficients (D) were measured using a microsecond-resolution FRAP apparatus and solution standards. In aqueous media (viscosity 1 cP), D for the FITC-dextrans decreased from 75 to 8.4 × 10−7 cm2/s with increasing dextran size (4–2,000 kD). D in cytoplasm relative to that in water (D/Do) was 0.26 ± 0.01 (MDCK) and 0.27 ± 0.01 (fibroblasts), and independent of FITC-dextran and Ficoll size (gyration radii [RG] 40–300 Å). The fraction of mobile FITC-dextran molecules (fmob), determined by the extent of fluorescence recovery after spot photobleaching, was >0.75 for RG < 200 Å, but decreased to <0.5 for RG > 300 Å. The independence of D/Do on FITC-dextran and Ficoll size does not support the concept of solute “sieving” (size-dependent diffusion) in cytoplasm. Photobleaching measurements using different spot diameters (1.5–4 μm) gave similar D/Do, indicating that microcompartments, if present, are of submicron size. Measurements of D/Do and fmob in concentrated dextran solutions, as well as in swollen and shrunken cells, suggested that the low fmob for very large macromolecules might be related to restrictions imposed by immobile obstacles (such as microcompartments) or to anomalous diffusion (such as percolation). In nucleus, D/Do was 0.25 ± 0.02 (MDCK) and 0.27 ± 0.03 (fibroblasts), and independent of solute size (RG 40–300 Å). Our results indicate relatively free and rapid diffusion of macromolecule-sized solutes up to approximately 500 kD in cytoplasm and nucleus. PMID:9214387

Effects of different cooling treatments on water diffusion, microcirculation, and water content within exercised muscles: evaluation by magnetic resonance T2-weighted and diffusion-weighted imaging.

PubMed

Yanagisawa, Osamu; Takahashi, Hideyuki; Fukubayashi, Toru

2010-09-01

In this study, we determined the effects of different cooling treatments on exercised muscles. Seven adults underwent four post-exercise treatments (20-min ice-bag application, 60-min gel-pack application at 10 degrees C and 17 degrees C, and non-cooling treatment) with at least 1 week between treatments. Magnetic resonance diffusion- and T2-weighted images were obtained to calculate the apparent diffusion coefficients (apparent diffusion coefficient 1, which reflects intramuscular water diffusion and microcirculation, and apparent diffusion coefficient 2, which is approximately equal to the true diffusion coefficient that excludes as much of the effect of intramuscular microcirculation as possible) and the T2 values (intramuscular water content level) of the ankle dorsiflexors, respectively, before and after ankle dorsiflexion exercise and after post-exercise treatment. The T2 values increased significantly after exercise and returned to pre-exercise values after each treatment; no significant differences were observed among the four post-exercise treatments. Both apparent diffusion coefficients also increased significantly after exercise and decreased significantly after the three cooling treatments; no significant difference was detected among the three cooling treatments. Local cooling suppresses both water diffusion and microcirculation within exercised muscles. Moreover, although the treatment time was longer, adequate cooling effects could be achieved using the gel-pack applications at relatively mild cooling temperatures.

CO2 diffusion in champagne wines: a molecular dynamics study.

PubMed

Perret, Alexandre; Bonhommeau, David A; Liger-Belair, Gérard; Cours, Thibaud; Alijah, Alexander

2014-02-20

Although diffusion is considered as the main physical process responsible for the nucleation and growth of carbon dioxide bubbles in sparkling beverages, the role of each type of molecule in the diffusion process remains unclear. In the present study, we have used the TIP5P and SPC/E water models to perform force field molecular dynamics simulations of CO2 molecules in water and in a water/ethanol mixture respecting Champagne wine proportions. CO2 diffusion coefficients were computed by applying the generalized Fick's law for the determination of multicomponent diffusion coefficients, a law that simplifies to the standard Fick's law in the case of champagnes. The CO2 diffusion coefficients obtained in pure water and water/ethanol mixtures composed of TIP5P water molecules were always found to exceed the coefficients obtained in mixtures composed of SPC/E water molecules, a trend that was attributed to a larger propensity of SPC/E water molecules to form hydrogen bonds. Despite the fact that the SPC/E model is more accurate than the TIP5P model to compute water self-diffusion and CO2 diffusion in pure water, the diffusion coefficients of CO2 molecules in the water/ethanol mixture are in much better agreement with the experimental values of 1.4 - 1.5 × 10(-9) m(2)/s obtained for Champagne wines when the TIP5P model is employed. This difference was deemed to rely on the larger propensity of SPC/E water molecules to maintain the hydrogen-bonded network between water molecules and form new hydrogen bonds with ethanol, although statistical issues cannot be completely excluded. The remarkable agreement between the theoretical CO2 diffusion coefficients obtained within the TIP5P water/ethanol mixture and the experimental data specific to Champagne wines makes us infer that the diffusion coefficient in these emblematic hydroalcoholic sparkling beverages is expected to remain roughly constant whathever their proportions in sugars, glycerol, or peptides.

General solution of a fractional Parker diffusion-convection equation describing the superdiffusive transport of energetic particles

NASA Astrophysics Data System (ADS)

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

2018-06-01

Anomalous diffusion models of energetic particles in space plasmas are developed by introducing the fractional Parker diffusion-convection equation. Analytical solution of the space-time fractional equation is obtained by use of the Caputo and Riesz-Feller fractional derivatives with the Laplace-Fourier transforms. The solution is given in terms of the Fox H-function. Profiles of particle densities are illustrated for different values of the space fractional order and the so-called skewness parameter.

Comparison of experimental methods for estimating matrix diffusion coefficients for contaminant transport modeling

DOE PAGES

Telfeyan, Katherine Christina; Ware, Stuart Doug; Reimus, Paul William; ...

2018-01-31

Here, diffusion cell and diffusion wafer experiments were conducted to compare methods for estimating effective matrix diffusion coefficients in rock core samples from Pahute Mesa at the Nevada Nuclear Security Site (NNSS). A diffusion wafer method, in which a solute diffuses out of a rock matrix that is pre-saturated with water containing the solute, is presented as a simpler alternative to the traditional through-diffusion (diffusion cell) method. Both methods yielded estimates of effective matrix diffusion coefficients that were within the range of values previously reported for NNSS volcanic rocks. The difference between the estimates of the two methods ranged frommore » 14 to 30%, and there was no systematic high or low bias of one method relative to the other. From a transport modeling perspective, these differences are relatively minor when one considers that other variables (e.g., fracture apertures, fracture spacings) influence matrix diffusion to a greater degree and tend to have greater uncertainty than effective matrix diffusion coefficients. For the same relative random errors in concentration measurements, the diffusion cell method yields effective matrix diffusion coefficient estimates that have less uncertainty than the wafer method. However, the wafer method is easier and less costly to implement and yields estimates more quickly, thus allowing a greater number of samples to be analyzed for the same cost and time. Given the relatively good agreement between the methods, and the lack of any apparent bias between the methods, the diffusion wafer method appears to offer advantages over the diffusion cell method if better statistical representation of a given set of rock samples is desired.« less

Comparison of experimental methods for estimating matrix diffusion coefficients for contaminant transport modeling

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

Telfeyan, Katherine Christina; Ware, Stuart Doug; Reimus, Paul William

Here, diffusion cell and diffusion wafer experiments were conducted to compare methods for estimating effective matrix diffusion coefficients in rock core samples from Pahute Mesa at the Nevada Nuclear Security Site (NNSS). A diffusion wafer method, in which a solute diffuses out of a rock matrix that is pre-saturated with water containing the solute, is presented as a simpler alternative to the traditional through-diffusion (diffusion cell) method. Both methods yielded estimates of effective matrix diffusion coefficients that were within the range of values previously reported for NNSS volcanic rocks. The difference between the estimates of the two methods ranged frommore » 14 to 30%, and there was no systematic high or low bias of one method relative to the other. From a transport modeling perspective, these differences are relatively minor when one considers that other variables (e.g., fracture apertures, fracture spacings) influence matrix diffusion to a greater degree and tend to have greater uncertainty than effective matrix diffusion coefficients. For the same relative random errors in concentration measurements, the diffusion cell method yields effective matrix diffusion coefficient estimates that have less uncertainty than the wafer method. However, the wafer method is easier and less costly to implement and yields estimates more quickly, thus allowing a greater number of samples to be analyzed for the same cost and time. Given the relatively good agreement between the methods, and the lack of any apparent bias between the methods, the diffusion wafer method appears to offer advantages over the diffusion cell method if better statistical representation of a given set of rock samples is desired.« less

Multispecies diffusion models: A study of uranyl species diffusion

NASA Astrophysics Data System (ADS)

Liu, Chongxuan; Shang, Jianying; Zachara, John M.

2011-12-01

Rigorous numerical description of multispecies diffusion requires coupling of species, charge, and aqueous and surface complexation reactions that collectively affect diffusive fluxes. The applicability of a fully coupled diffusion model is, however, often constrained by the availability of species self-diffusion coefficients, as well as by computational complication in imposing charge conservation. In this study, several diffusion models with variable complexity in charge and species coupling were formulated and compared to describe reactive multispecies diffusion in groundwater. Diffusion of uranyl [U(VI)] species was used as an example in demonstrating the effectiveness of the models in describing multispecies diffusion. Numerical simulations found that a diffusion model with a single, common diffusion coefficient for all species was sufficient to describe multispecies U(VI) diffusion under a steady state condition of major chemical composition, but not under transient chemical conditions. Simulations revealed that for multispecies U(VI) diffusion under transient chemical conditions, a fully coupled diffusion model could be well approximated by a component-based diffusion model when the diffusion coefficient for each chemical component was properly selected. The component-based diffusion model considers the difference in diffusion coefficients between chemical components, but not between the species within each chemical component. This treatment significantly enhanced computational efficiency at the expense of minor charge conservation. The charge balance in the component-based diffusion model can be enforced, if necessary, by adding a secondary migration term resulting from model simplification. The effect of ion activity coefficient gradients on multispecies diffusion is also discussed. The diffusion models were applied to describe U(VI) diffusive mass transfer in intragranular domains in two sediments collected from U.S. Department of Energy's Hanford 300A, where intragranular diffusion is a rate-limiting process controlling U(VI) adsorption and desorption. The grain-scale reactive diffusion model was able to describe U(VI) adsorption/desorption kinetics that had been previously described using a semiempirical, multirate model. Compared with the multirate model, the diffusion models have the advantage to provide spatiotemporal speciation evolution within the diffusion domains.

Estimation of diffusion coefficients from voltammetric signals by support vector and gaussian process regression

PubMed Central

2014-01-01

Background Support vector regression (SVR) and Gaussian process regression (GPR) were used for the analysis of electroanalytical experimental data to estimate diffusion coefficients. Results For simulated cyclic voltammograms based on the EC, Eqr, and EqrC mechanisms these regression algorithms in combination with nonlinear kernel/covariance functions yielded diffusion coefficients with higher accuracy as compared to the standard approach of calculating diffusion coefficients relying on the Nicholson-Shain equation. The level of accuracy achieved by SVR and GPR is virtually independent of the rate constants governing the respective reaction steps. Further, the reduction of high-dimensional voltammetric signals by manual selection of typical voltammetric peak features decreased the performance of both regression algorithms compared to a reduction by downsampling or principal component analysis. After training on simulated data sets, diffusion coefficients were estimated by the regression algorithms for experimental data comprising voltammetric signals for three organometallic complexes. Conclusions Estimated diffusion coefficients closely matched the values determined by the parameter fitting method, but reduced the required computational time considerably for one of the reaction mechanisms. The automated processing of voltammograms according to the regression algorithms yields better results than the conventional analysis of peak-related data. PMID:24987463

The influence of screening of the polyion electrostatic potential on the counterion dynamics in polyelectrolyte solutions

NASA Astrophysics Data System (ADS)

Schipper, F. J. M.; Hollander, J. G.; Leyte, J. C.

1998-10-01

The self-diffusion coefficient of tetra-methylammonium counterion in solutions of polymethacrylic acid in 0953-8984/10/41/004/img1 has been measured over a broad polyion concentration range at a constant degree of neutralization and at different ratios of added monovalent or bivalent salt to polyions. A maximum counterion self-diffusion coefficient was observed as a function of polyion concentration. The value of the self-diffusion coefficient at the maximum did not depend on the valency of the added salt. The maximum was found at lower polymer concentrations and with a higher value, when the ratio of added salt to polyions was increased, as predicted by the Poisson-Boltzmann-Smoluchowski equation in the cylindrical cell model for polyelectrolytes. At higher polyion concentrations a maximum counterion self-diffusion coefficient against the ratio of added salt and polyions was observed, which has not been reported before. Upon increasing this ratio the electrostatic potential of the polyelectrolyte gets screened, leading to an increase of the counterion self-diffusion coefficient. Concentration effects of the added salt on the other hand ultimately lead to a decrease of the counterion self-diffusion coefficient, which explains the occurrence of a maximum.

Topological Weyl superconductor to diffusive thermal Hall metal crossover in the B phase of UPt3

NASA Astrophysics Data System (ADS)

Goswami, Pallab; Nevidomskyy, Andriy H.

2015-12-01

The recent phase-sensitive measurements in the superconducting B phase of UPt3 provide strong evidence for the triplet, chiral kz(kx±i ky) 2 pairing symmetries, which endow the Cooper pairs with orbital angular momentum projections Lz=±2 along the c axis. In the absence of disorder such pairing can support both line and point nodes, and both types of nodal quasiparticles exhibit nontrivial topology in the momentum space. The point nodes, located at the intersections of the closed Fermi surfaces with the c axis, act as the double monopoles and the antimonopoles of the Berry curvature, and generalize the notion of Weyl quasiparticles. Consequently, the B phase should support an anomalous thermal Hall effect, the polar Kerr effect, in addition to the protected Fermi arcs on the (1 ,0 ,0 ) and the (0 ,1 ,0 ) surfaces. The line node at the Fermi surface equator acts as a vortex loop in the momentum space and gives rise to the zero-energy, dispersionless Andreev bound states on the (0 ,0 ,1 ) surface. At the transition from the B phase to the A phase, the time-reversal symmetry is restored, and only the line node survives inside the A phase. As both line and double-Weyl point nodes possess linearly vanishing density of states, we show that weak disorder acts as a marginally relevant perturbation. Consequently, an infinitesimal amount of disorder destroys the ballistic quasiparticle pole, while giving rise to a diffusive phase with a finite density of states at the zero energy. The resulting diffusive phase exhibits T -linear specific heat, and an anomalous thermal Hall effect. We predict that the low-temperature thermodynamic and transport properties display a crossover between a ballistic thermal Hall semimetal and a diffusive thermal Hall metal. By contrast, the diffusive phase obtained from a time-reversal-invariant pairing exhibits only the T -linear specific heat without any anomalous thermal Hall effect.

Multilevel Preconditioners for Reaction-Diffusion Problems with Discontinuous Coefficients

DOE PAGES

Kolev, Tzanio V.; Xu, Jinchao; Zhu, Yunrong

2015-08-23

In this study, we extend some of the multilevel convergence results obtained by Xu and Zhu, to the case of second order linear reaction-diffusion equations. Specifically, we consider the multilevel preconditioners for solving the linear systems arising from the linear finite element approximation of the problem, where both diffusion and reaction coefficients are piecewise-constant functions. We discuss in detail the influence of both the discontinuous reaction and diffusion coefficients to the performance of the classical BPX and multigrid V-cycle preconditioner.

Note: On the relation between Lifson-Jackson and Derrida formulas for effective diffusion coefficient

NASA Astrophysics Data System (ADS)

Kalnin, Juris R.; Berezhkovskii, Alexander M.

2013-11-01

The Lifson-Jackson formula provides the effective free diffusion coefficient for a particle diffusing in an arbitrary one-dimensional periodic potential. Its counterpart, when the underlying dynamics is described in terms of an unbiased nearest-neighbor Markovian random walk on a one-dimensional periodic lattice is given by the formula obtained by Derrida. It is shown that the latter formula can be considered as a discretized version of the Lifson-Jackson formula with correctly chosen position-dependent diffusion coefficient.

Consequences of using nonlinear particle trajectories to compute spatial diffusion coefficients. [for cosmic ray propagation in interstellar and interplanetary space

NASA Technical Reports Server (NTRS)

Goldstein, M. L.

1977-01-01

In a study of cosmic ray propagation in interstellar and interplanetary space, a perturbed orbit resonant scattering theory for pitch angle diffusion in a slab model of magnetostatic turbulence is slightly generalized and used to compute the diffusion coefficient for spatial propagation parallel to the mean magnetic field. This diffusion coefficient has been useful for describing the solar modulation of the galactic cosmic rays, and for explaining the diffusive phase in solar flares in which the initial anisotropy of the particle distribution decays to isotropy.

Translational diffusion coefficients of volatile compounds in various aqueous solutions at low and subzero temperatures.

PubMed

Covarrubias-Cervantes, Marco; Champion, Dominique; Debeaufort, Frédéric; Voilley, Andrée

2005-08-24

Translational diffusion coefficients (D(12)) of volatile compounds were measured in model media with the profile concentration method. The influence of sample temperature (from 25 to -10 degrees C) was studied on translational diffusion in sucrose or maltodextrin solutions at various concentrations. Results show that diffusivity of volatile compounds in sucrose solutions is controlled by temperature, molecule size, and the viscosity of the liquid phase as expected with the Stokes-Einstein equation; moreover, physicochemical interactions between volatile compounds and the medium are determinant for diffusion estimation. At negative temperature, the winding path induced by an ice crystal content of >70% lowered volatile compound diffusion. On the contrary, no influence on translational diffusion coefficients was observed for lower ice content.

Experimental Method Development for Estimating Solid-phase Diffusion Coefficients and Material/Air Partition Coefficients of SVOCs

EPA Science Inventory

The solid-phase diffusion coefficient (Dm) and material-air partition coefficient (Kma) are key parameters for characterizing the sources and transport of semivolatile organic compounds (SVOCs) in the indoor environment. In this work, a new experimental method was developed to es...

Diffusion of cations in chromia layers grown on iron-base alloys

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

Lobnig, R.E.; Hennesen, K.; Grabke, H.J.

Diffusion of the cations Cr, Fe, Mn, and Ni in Cr{sub 2}O{sub 3} has been investigated at 1,173 K. The diffusion measurements were performed on chromia layers grown on the model alloys Fe-20Cr and Fe-20Cr-12Ni in order to consider effects of small amounts of dissolved alien cations in Cr{sub 2}O{sub 3}. The samples were diffusion annealed in H{sub 2}-H{sub 2}O at an oxygen partial pressure close to the Cr{sub 2}O{sub 3}/Cr equilibrium. For all tracers the lattice-diffusion coefficients are 3-5 orders of magnitude smaller than the grain-boundary diffusion coefficients. The lattice diffusivity of Mn is about two orders of magnitudemore » greater than the other lattice-diffusion coefficients, especially in Cr{sub 2}O{sub 3} grown on Fe-20Cr-12Ni. The values of the diffusion coefficients for Cr, Fe, and Ni are in the same range. Diffusion of the tracers in Cr{sub 2}O{sub 3} grown on different alloys did not show significant differences with the exception of Mn.« less

1D momentum-conserving systems: the conundrum of anomalous versus normal heat transport

NASA Astrophysics Data System (ADS)

Li, Yunyun; Liu, Sha; Li, Nianbei; Hänggi, Peter; Li, Baowen

2015-04-01

Transport and the spread of heat in Hamiltonian one dimensional momentum conserving nonlinear systems is commonly thought to proceed anomalously. Notable exceptions, however, do exist of which the coupled rotator model is a prominent case. Therefore, the quest arises to identify the origin of manifest anomalous energy and momentum transport in those low dimensional systems. We develop the theory for both, the statistical densities for momentum- and energy-spread and particularly its momentum-/heat-diffusion behavior, as well as its corresponding momentum/heat transport features. We demonstrate that the second temporal derivative of the mean squared deviation of the momentum spread is proportional to the equilibrium correlation of the total momentum flux. Subtracting the part which corresponds to a ballistic momentum spread relates (via this integrated, subleading momentum flux correlation) to an effective viscosity, or equivalently, to the underlying momentum diffusivity. We next put forward the intriguing hypothesis: normal spread of this so adjusted excess momentum density causes normal energy spread and alike normal heat transport (Fourier Law). Its corollary being that an anomalous, superdiffusive broadening of this adjusted excess momentum density in turn implies an anomalous energy spread and correspondingly anomalous, superdiffusive heat transport. This hypothesis is successfully corroborated within extensive molecular dynamics simulations over large extended time scales. Our numerical validation of the hypothesis involves four distinct archetype classes of nonlinear pair-interaction potentials: (i) a globally bounded pair interaction (the noted coupled rotator model), (ii) unbounded interactions acting at large distances (the coupled rotator model amended with harmonic pair interactions), (iii) the case of a hard point gas with unbounded square-well interactions and (iv) a pair interaction potential being unbounded at short distances while displaying an asymptotic free part (Lennard-Jones model). We compare our findings with recent predictions obtained from nonlinear fluctuating hydrodynamics theory.

Many-body Effects in a Laterally Inhomogeneous Semiconductor Quantum Well

NASA Technical Reports Server (NTRS)

Ning, Cun-Zheng; Li, Jian-Zhong; Biegel, Bryan A. (Technical Monitor)

2002-01-01

Many body effects on conduction and diffusion of electrons and holes in a semiconductor quantum well are studied using a microscopic theory. The roles played by the screened Hartree-Fock (SHE) terms and the scattering terms are examined. It is found that the electron and hole conductivities depend only on the scattering terms, while the two-component electron-hole diffusion coefficients depend on both the SHE part and the scattering part. We show that, in the limit of the ambipolax diffusion approximation, however, the diffusion coefficients for carrier density and temperature are independent of electron-hole scattering. In particular, we found that the SHE terms lead to a reduction of density-diffusion coefficients and an increase in temperature-diffusion coefficients. Such a reduction or increase is explained in terms of a density-and temperature dependent energy landscape created by the bandgap renormalization.

Determination of the zincate diffusion coefficient and its application to alkaline battery problems

NASA Technical Reports Server (NTRS)

May, C. E.; Kautz, Harold E.

1978-01-01

The diffusion coefficient for the zincate ion at 24 C was found to be 9.9 X 10 to the minus 7th power squared cm per sec + or - 30 percent in 45 percent potassium hydroxide and 1.4 x 10 to the minus 7 squared cm per sec + or - 25 percent in 40 percent sodium hydroxide. Comparison of these values with literature values at different potassium hydroxide concentrations show that the Stokes-Einstein equation is obeyed. The diffusion coefficient is characteristic of the zincate ion (not the cation) and independent of its concentration. Calculations with the measured value of the diffusion coefficient show that the zinc concentration in an alkaline zincate half cell becomes uniform throughout in tens of hours by diffusion alone. Diffusion equations are derived which are applicable to finite size chambers. Details and discussion of the experimental method are also given.

Coiled to diffuse: Brownian motion of a helical bacterium.

PubMed

Butenko, Alexander V; Mogilko, Emma; Amitai, Lee; Pokroy, Boaz; Sloutskin, Eli

2012-09-11

We employ real-time three-dimensional confocal microscopy to follow the Brownian motion of a fixed helically shaped Leptospira interrogans (LI) bacterium. We extract from our measurements the translational and the rotational diffusion coefficients of this bacterium. A simple theoretical model is suggested, perfectly reproducing the experimental diffusion coefficients, with no tunable parameters. An older theoretical model, where edge effects are neglected, dramatically underestimates the observed rates of translation. Interestingly, the coiling of LI increases its rotational diffusion coefficient by a factor of 5, compared to a (hypothetical) rectified bacterium of the same contour length. Moreover, the translational diffusion coefficients would have decreased by a factor of ~1.5, if LI were rectified. This suggests that the spiral shape of the spirochaete bacteria, in addition to being employed for their active twisting motion, may also increase the ability of these bacteria to explore the surrounding fluid by passive Brownian diffusion.

Determination of the zincate diffusion coefficient and its application to alkaline battery problems

NASA Technical Reports Server (NTRS)

May, C. E.; Kautz, H. E.

1978-01-01

The diffusion coefficient for the zincate ion at 24 C was found to be 9.9 x 10 to the -7th power sq cm/sec + or - 30% in 45% potassium hydroxide and 1.4 x 10 to the -7th power sq cm/sec + or - 25% in 40% sodium hydroxide. Comparison of these values with literature values at different potassium hydroxide concentrations show that the Stokes-Einstein equation is obeyed. The diffusion coefficient is characteristic of the zincate ion (not the cation) and independent of its concentration. Calculations with the measured value of the diffusion coefficient show that the zinc concentration in an alkaline zincate half-cell becomes uniform throughout in tens of hours by diffusion alone. Diffusion equations are derived which are applicable to finite-size chambers. Details and discussion of the experimental method are also given.

The effect of recombination and attachment on meteor radar diffusion coefficient profiles

NASA Astrophysics Data System (ADS)

Lee, C. S.; Younger, J. P.; Reid, I. M.; Kim, Y. H.; Kim, J.-H.

2013-04-01

Estimates of the ambipolar diffusion coefficient producedusing meteor radar echo decay times display an increasing trend below 80-85 km, which is inconsistent with a diffusion-only theory of the evolution of meteor trails. Data from the 33 MHz meteor radar at King Sejong Station, Antarctica, have been compared with observations from the Aura Earth Observing System Microwave Limb Sounder satellite instrument. It has been found that the height at which the diffusion coefficient gradient reverses follows the height of a constant neutral atmospheric density surface. Numerical simulations of meteor trail diffusion including dissociative recombination with atmospheric ions and three-body attachment of free electrons to neutral molecules indicate that three-body attachment is responsible for the distortion of meteor radar diffusion coefficient profiles at heights below 90 km, including the gradient reversal below 80-85 km. Further investigation has revealed that meteor trails with low initial electron line density produce decay times more consistent with a diffusion-only model of meteor trail evolution.

Negative Correlation between the Diffusion Coefficient and Transcriptional Activity of the Glucocorticoid Receptor.

PubMed

Mikuni, Shintaro; Yamamoto, Johtaro; Horio, Takashi; Kinjo, Masataka

2017-08-25

The glucocorticoid receptor (GR) is a transcription factor, which interacts with DNA and other cofactors to regulate gene transcription. Binding to other partners in the cell nucleus alters the diffusion properties of GR. Raster image correlation spectroscopy (RICS) was applied to quantitatively characterize the diffusion properties of EGFP labeled human GR (EGFP-hGR) and its mutants in the cell nucleus. RICS is an image correlation technique that evaluates the spatial distribution of the diffusion coefficient as a diffusion map. Interestingly, we observed that the averaged diffusion coefficient of EGFP-hGR strongly and negatively correlated with its transcriptional activities in comparison to that of EGFP-hGR wild type and mutants with various transcriptional activities. This result suggests that the decreasing of the diffusion coefficient of hGR was reflected in the high-affinity binding to DNA. Moreover, the hyper-phosphorylation of hGR can enhance the transcriptional activity by reduction of the interaction between the hGR and the nuclear corepressors.

Rumor Diffusion in an Interests-Based Dynamic Social Network

PubMed Central

Mao, Xinjun; Guessoum, Zahia; Zhou, Huiping

2013-01-01

To research rumor diffusion in social friend network, based on interests, a dynamic friend network is proposed, which has the characteristics of clustering and community, and a diffusion model is also proposed. With this friend network and rumor diffusion model, based on the zombie-city model, some simulation experiments to analyze the characteristics of rumor diffusion in social friend networks have been conducted. The results show some interesting observations: (1) positive information may evolve to become a rumor through the diffusion process that people may modify the information by word of mouth; (2) with the same average degree, a random social network has a smaller clustering coefficient and is more beneficial for rumor diffusion than the dynamic friend network; (3) a rumor is spread more widely in a social network with a smaller global clustering coefficient than in a social network with a larger global clustering coefficient; and (4) a network with a smaller clustering coefficient has a larger efficiency. PMID:24453911

Rumor diffusion in an interests-based dynamic social network.

PubMed

Tang, Mingsheng; Mao, Xinjun; Guessoum, Zahia; Zhou, Huiping

2013-01-01

To research rumor diffusion in social friend network, based on interests, a dynamic friend network is proposed, which has the characteristics of clustering and community, and a diffusion model is also proposed. With this friend network and rumor diffusion model, based on the zombie-city model, some simulation experiments to analyze the characteristics of rumor diffusion in social friend networks have been conducted. The results show some interesting observations: (1) positive information may evolve to become a rumor through the diffusion process that people may modify the information by word of mouth; (2) with the same average degree, a random social network has a smaller clustering coefficient and is more beneficial for rumor diffusion than the dynamic friend network; (3) a rumor is spread more widely in a social network with a smaller global clustering coefficient than in a social network with a larger global clustering coefficient; and (4) a network with a smaller clustering coefficient has a larger efficiency.

Venus' superrotation, mixing length theory and eddy diffusion - A parametric study

NASA Technical Reports Server (NTRS)

Mayr, H. G.; Harris, I.; Schatten, K. H.; Stevens-Rayburn, D. R.; Chan, K. L.

1988-01-01

The concept of the Hadley mechanism is adopted to describe the axisymmetric circulation of the Venus atmosphere. It is shown that, for the atmosphere of a slowly rotating planet such as Venus, a form of the nonliner 'closure' (self-consistent solution) of the fluid dynamics system which constrains the magnitude of the eddy diffusion coefficients can be postulated. A nonlinear one-layer spectral model of the zonally symmetric circulation was then used to establish the relationship between the heat source, the meridional circulation, and the eddy diffusion coefficients, yielding large zonal velocities. Computer experiments indicated that proportional changes in the heat source and eddy diffusion coefficients do not significantly change the zonal velocities. It was also found that, for large eddy diffusion coefficients, the meridional velocity is virtually constant; below a threshold in the diffusion rate, the meridional velocity decreases; and, for large eddy diffusion and small heating rates, the zonal velocities decrease with decreasing planetary rotation rates.

Arbitrary-order corrections for finite-time drift and diffusion coefficients

NASA Astrophysics Data System (ADS)

Anteneodo, C.; Riera, R.

2009-09-01

We address a standard class of diffusion processes with linear drift and quadratic diffusion coefficients. These contributions to dynamic equations can be directly drawn from data time series. However, real data are constrained to finite sampling rates and therefore it is crucial to establish a suitable mathematical description of the required finite-time corrections. Based on Itô-Taylor expansions, we present the exact corrections to the finite-time drift and diffusion coefficients. These results allow to reconstruct the real hidden coefficients from the empirical estimates. We also derive higher-order finite-time expressions for the third and fourth conditional moments that furnish extra theoretical checks for this class of diffusion models. The analytical predictions are compared with the numerical outcomes of representative artificial time series.

Diffusion coefficient and shear viscosity of rigid water models.

PubMed

Tazi, Sami; Boţan, Alexandru; Salanne, Mathieu; Marry, Virginie; Turq, Pierre; Rotenberg, Benjamin

2012-07-18

We report the diffusion coefficient and viscosity of popular rigid water models: two non-polarizable ones (SPC/E with three sites, and TIP4P/2005 with four sites) and a polarizable one (Dang-Chang, four sites). We exploit the dependence of the diffusion coefficient on the system size (Yeh and Hummer 2004 J. Phys. Chem. B 108 15873) to obtain the size-independent value. This also provides an estimate of the viscosity of all water models, which we compare to the Green-Kubo result. In all cases, a good agreement is found. The TIP4P/2005 model is in better agreement with the experimental data for both diffusion and viscosity. The SPC/E and Dang-Chang models overestimate the diffusion coefficient and underestimate the viscosity.

Effective diffusion coefficients of DNAPL waste components in saturated low permeability soil materials.

PubMed

Ayral-Cinar, Derya; Demond, Avery H

2017-12-01

Diffusion is regarded as the dominant transport mechanism into and out of low permeable subsurface lenses and layers in the subsurface. But, some reports of mass storage in such zones are higher than what might be attributable to diffusion, based on estimated diffusion coefficients. Despite the importance of diffusion to efforts to estimate the quantity of residual contamination in the subsurface, relatively few studies present measured diffusion coefficients of organic solutes in saturated low permeability soils. This study reports the diffusion coefficients of a trichloroethylene (TCE), and an anionic surfactant, Aerosol OT (AOT), in water-saturated silt and a silt-montmorillonite (25:75) mixture, obtained using steady-state experiments. The relative diffusivity ranged from 0.11 to 0.17 for all three compounds for the silt and the silt-clay mixture that was allowed to expand. In the case in which the swelling was constrained, the relative diffusivity was about 0.07. In addition, the relative diffusivity of 13 C-labeled TCE through a water saturated silt-clay mixture that had contacted a field dense non-aqueous phase liquid (DNAPL) for 18months was measured and equaled 0.001. These experimental results were compared with the estimates generated using common correlations, and it was found that, in all cases, the measured diffusion coefficients were significantly lower than the estimated. Thus, the discrepancy between mass accumulations observed in the field and the mass storage that can attributable to diffusion may be greater than previously believed. Copyright © 2017. Published by Elsevier B.V.

Measurement of gas diffusion coefficient in liquid-saturated porous media using magnetic resonance imaging

NASA Astrophysics Data System (ADS)

Song, Yongchen; Hao, Min; Zhao, Yuechao; Zhang, Liang

2014-12-01

In this study, the dual-chamber pressure decay method and magnetic resonance imaging (MRI) were used to dynamically visualize the gas diffusion process in liquid-saturated porous media, and the relationship of concentration-distance for gas diffusing into liquid-saturated porous media at different times were obtained by MR images quantitative analysis. A non-iterative finite volume method was successfully applied to calculate the local gas diffusion coefficient in liquid-saturated porous media. The results agreed very well with the conventional pressure decay method, thus it demonstrates that the method was feasible of determining the local diffusion coefficient of gas in liquid-saturated porous media at different times during diffusion process.

Spectral Properties of Limit-Periodic Schrödinger Operators (PhD Thesis)

NASA Astrophysics Data System (ADS)

Gideonse, Hendrik David, XIX

The Acoustic Ramp is a wedge-shaped, number-theoretical quadratic-residue-type acoustic diffuser. Since the late 1970's, several methodologies for the testing and analysis of diffusers have been developed including, the ISO Scattering Coefficient and the AES Diffusion Coefficient. These coefficients are the source of some controversy today and this paper makes the attempt to investigate the benefits and weaknesses of these tools by using them to research and test the Acoustic Ramp. Several issues are exposed in using the coefficients, the most important of which being the validity of the comparison of the diffuser's behavior to that of a like sized flat panel. Further issues comprise of an intuitive disconnect between the perceived merits of polar plots and the numerical value of coefficients derived from the plots.

Distributional behavior of diffusion coefficients obtained by single trajectories in annealed transit time model

NASA Astrophysics Data System (ADS)

Akimoto, Takuma; Yamamoto, Eiji

2016-12-01

Local diffusion coefficients in disordered systems such as spin glass systems and living cells are highly heterogeneous and may change over time. Such a time-dependent and spatially heterogeneous environment results in irreproducibility of single-particle-tracking measurements. Irreproducibility of time-averaged observables has been theoretically studied in the context of weak ergodicity breaking in stochastic processes. Here, we provide rigorous descriptions of equilibrium and non-equilibrium diffusion processes for the annealed transit time model, which is a heterogeneous diffusion model in living cells. We give analytical solutions for the mean square displacement (MSD) and the relative standard deviation of the time-averaged MSD for equilibrium and non-equilibrium situations. We find that the time-averaged MSD grows linearly with time and that the time-averaged diffusion coefficients are intrinsically random (irreproducible) even in the long-time measurements in non-equilibrium situations. Furthermore, the distribution of the time-averaged diffusion coefficients converges to a universal distribution in the sense that it does not depend on initial conditions. Our findings pave the way for a theoretical understanding of distributional behavior of the time-averaged diffusion coefficients in disordered systems.

Measurement of diffusion coefficients important in modeling the absorption rate of carbon dioxide into aqueous N-methyldiethanolamine

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

Rowley, R.L.; Adams, M.E.; Marshall, T.L.

1997-03-01

Natural gas processors use amine treating processes to remove the acid gases H{sub 2}S and CO{sub 2} from gas streams. Absorption rates of gaseous CO{sub 2} into aqueous N-methyldiethanolamine (MDEA) solutions were measured in a quiescent, inverted-tube diffusiometer by monitoring the rate of pressure drop. The absorption rate was found to be insensitive to the diffusion coefficient of CO{sub 2} in solution but very sensitive to the diffusion rate of bicarbonate and protonated MDEA ions. Evidence also suggested that chemical reaction equilibrium is rapid relative to diffusion. A numerical model was developed on the basis of these observations. The modelmore » was used to regress diffusion coefficients of bicarbonate and protonated amine, which must be equivalent by electroneutrality arguments, from measured absorption rates. Complete modeling of the absorption process also required data for the diffusion coefficient of MDEA in water. These were measured using a Taylor dispersion apparatus. CO{sub 2} absorption rates and diffusion coefficients of bicarbonate and protonated MDEA were obtained at 298.2 K and 318.2 K in solutions containing 20, 35, and 50 mass % MDEA in water.« less

Fractional Brownian motion with a reflecting wall.

PubMed

Wada, Alexander H O; Vojta, Thomas

2018-02-01

Fractional Brownian motion, a stochastic process with long-time correlations between its increments, is a prototypical model for anomalous diffusion. We analyze fractional Brownian motion in the presence of a reflecting wall by means of Monte Carlo simulations. Whereas the mean-square displacement of the particle shows the expected anomalous diffusion behavior 〈x^{2}〉∼t^{α}, the interplay between the geometric confinement and the long-time memory leads to a highly non-Gaussian probability density function with a power-law singularity at the barrier. In the superdiffusive case α>1, the particles accumulate at the barrier leading to a divergence of the probability density. For subdiffusion α<1, in contrast, the probability density is depleted close to the barrier. We discuss implications of these findings, in particular, for applications that are dominated by rare events.

Nonequilibrium transport of charge carriers and transient electroluminescence in organic light-emitting diodes

NASA Astrophysics Data System (ADS)

Nikitenko, V. R.; von Seggern, H.

2007-11-01

An analytic theory of nonequilibrium hopping charge transport in disordered organic materials includes quasiequilibrium (normal) and extremely nonequilibrium (dispersive) regimes as limiting cases at long and short times, respectively. In the intermediate interval of time quasiequilibrium value of mobility is nearly established while the coefficient of field-assisted diffusion continues to increase (quasidispersive regime). Therefore, normalized time dependencies of transient current in time-of-flight (TOF) conditions are practically independent of field strength and sample thickness, in good agreement both with data of TOF experiments for molecularly doped polymers and results of numerical simulations of Gaussian disorder model. An analytic model of transient electroluminescence (TEL) is developed on the base of the mentioned theory. Strong asymmetry of mobilities is presumed. In analogy with TOF transients, dispersion parameter of normalized TEL intensity is anomalously large and almost field independent in the quasidispersive regime of transport. The method for determination of mobility from TEL data is proposed.

Formulation, in vitro evaluation and kinetic analysis of chitosan-gelatin bilayer muco-adhesive buccal patches of insulin nanoparticles.

PubMed

Mahdizadeh Barzoki, Zahra; Emam-Djomeh, Zahra; Mortazavian, Elaheh; Akbar Moosavi-Movahedi, Ali; Rafiee Tehrani, M

2016-11-01

The present study was performed to optimise the formulation of a muco-adhesive buccal patch for insulin nanoparticles (NPs) delivery. Insulin NPs were synthesised by an ionic gelation technique using N-di methyl ethyl chitosan cysteine (DMEC-Cys) as permeation enhancer biopolymer, tripolyphosphate (TPP) and insulin. Buccal patches were developed by solvent-casting technique using chitosan and gelatine as muco-adhesive polymers. Optimised patches were embedded with 3 mg of insulin-loaded NPs with a homogeneous distribution of NPs in the muco-adhesive matrix, which displayed adequate physico-mechanical properties. The drug release characteristics, release mechanism and kinetics were investigated. Data fitting to Peppas equation with a correlation coefficient indicated that the mechanism of drug release followed an anomalous transport that means drug release was afforded through drug diffusion along with polymer erosion. In vitro drug release, release kinetics, physical and mechanical studies for all patch formulations reflected the ideal characteristics of this buccal patch for the delivery of insulin NPs.

Preparation and physical characterization of pure beta-carotene.

PubMed

Laughlin, Robert G; Bunke, Gregory M; Eads, Charles D; Laidig, William D; Shelley, John C

2002-05-01

Pure all-trans beta-carotene has been prepared on the 10's of grams scale by isothermal Fractional Dissolution (FD) of commercial laboratory samples in tetrahydrofuran (THF). beta-Carotene purified in this way is black, with a faint brownish tinge. The electronic spectra of black samples extend into the near infrared, with end-absorption past 750 nm. Black samples react directly with dioxygen under mild conditions to yield the familiar orange or red powders. Pure beta-carotene rigorously obeys Beer's Law in octane over the entire UV-Vis spectral range, while commercial laboratory samples and recrystallized samples do not. NMR self-diffusion coefficient data demonstrate that beta-carotene exists as simple molecular solutions in octane and toluene. The anomalously high crystallinity of beta-carotene can be attributed (from analysis using molecular mechanics) to the facts that: (1) the number of theoretically possible conformers of beta-carotene is extremely small, and (2) only a small fraction of these (ca. 12%, or 127) may actually exist in fluid phases.

Interdiffusion, Intrinsic Diffusion, Atomic Mobility, and Vacancy Wind Effect in γ(bcc) Uranium-Molybdenum Alloy

NASA Astrophysics Data System (ADS)

Huang, Ke; Keiser, Dennis D.; Sohn, Yongho

2013-02-01

U-Mo alloys are being developed as low enrichment uranium fuels under the Reduced Enrichment for Research and Test Reactor (RERTR) Program. In order to understand the fundamental diffusion behavior of this system, solid-to-solid pure U vs Mo diffusion couples were assembled and annealed at 923 K, 973 K, 1073 K, 1173 K, and 1273 K (650 °C, 700 °C, 800 °C, 900 °C, and 1000 °C) for various times. The interdiffusion microstructures and concentration profiles were examined via scanning electron microscopy and electron probe microanalysis, respectively. As the Mo concentration increased from 2 to 26 at. pct, the interdiffusion coefficient decreased, while the activation energy increased. A Kirkendall marker plane was clearly identified in each diffusion couple and utilized to determine intrinsic diffusion coefficients. Uranium intrinsically diffused 5-10 times faster than Mo. Molar excess Gibbs free energy of U-Mo alloy was applied to calculate the thermodynamic factor using ideal, regular, and subregular solution models. Based on the intrinsic diffusion coefficients and thermodynamic factors, Manning's formalism was used to calculate the tracer diffusion coefficients, atomic mobilities, and vacancy wind parameters of U and Mo at the marker composition. The tracer diffusion coefficients and atomic mobilities of U were about five times larger than those of Mo, and the vacancy wind effect increased the intrinsic flux of U by approximately 30 pct.

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.

Gene interference regulates aquaporin-4 expression in swollen tissue of rats with cerebral ischemic edema

PubMed Central

Hu, Hui; Lu, Hong; He, Zhanping; Han, Xiangjun; Chen, Jing; Tu, Rong

2012-01-01

To investigate the effects of mRNA interference on aquaporin-4 expression in swollen tissue of rats with ischemic cerebral edema, and diagnose the significance of diffusion-weighted MRI, we injected 5 μL shRNA- aquaporin-4 (control group) or siRNA- aquaporin-4 solution (1:800) (RNA interference group) into the rat right basal ganglia immediately before occlusion of the middle cerebral artery. At 0.25 hours after occlusion of the middle cerebral artery, diffusion-weighted MRI displayed a high signal; within 2 hours, the relative apparent diffusion coefficient decreased markedly, aquaporin-4 expression increased rapidly, and intracellular edema was obviously aggravated; at 4 and 6 hours, the relative apparent diffusion coefficient slowly returned to control levels, aquaporin-4 expression slightly increased, and angioedema was observed. In the RNA interference group, during 0.25–6 hours after injection of siRNA- aquaporin-4 solution, the relative apparent diffusion coefficient slightly fluctuated and aquaporin-4 expression was upregulated; during 0.5–4 hours, the relative apparent diffusion coefficient was significantly higher, while aquaporin-4 expression was significantly lower when compared with the control group, and intracellular edema was markedly reduced; at 0.25 and 6 hours, the relative apparent diffusion coefficient and aquaporin-4 expression were similar when compared with the control group; obvious angioedema remained at 6 hours. Pearson's correlation test results showed that aquaporin-4 expression was negatively correlated with the apparent diffusion coefficient (r = −0.806, P < 0.01). These findings suggest that upregulated aquaporin-4 expression is likely to be the main molecular mechanism of intracellular edema and may be the molecular basis for decreased relative apparent diffusion coefficient. Aquaporin-4 gene interference can effectively inhibit the upregulation of aquaporin-4 expression during the stage of intracellular edema with time-effectiveness. Moreover, diffusion-weighted MRI can accurately detect intracellular edema. PMID:25657707

Perpendicular Diffusion Coefficient of Comic Rays: The Presence of Weak Adiabatic Focusing

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

Wang, J. F.; Ma, Q. M.; Song, T.

The influence of adiabatic focusing on particle diffusion is an important topic in astrophysics and plasma physics. In the past, several authors have explored the influence of along-field adiabatic focusing on the parallel diffusion of charged energetic particles. In this paper, using the unified nonlinear transport theory developed by Shalchi and the method of He and Schlickeiser, we derive a new nonlinear perpendicular diffusion coefficient for a non-uniform background magnetic field. This formula demonstrates that the particle perpendicular diffusion coefficient is modified by along-field adiabatic focusing. For isotropic pitch-angle scattering and the weak adiabatic focusing limit, the derived perpendicular diffusionmore » coefficient is independent of the sign of adiabatic focusing characteristic length. For the two-component model, we simplify the perpendicular diffusion coefficient up to the second order of the power series of the adiabatic focusing characteristic quantity. We find that the first-order modifying factor is equal to zero and that the sign of the second order is determined by the energy of the particles.« less

Studies of multi-ion-fluid yield anomaly in shock-driven implosions

NASA Astrophysics Data System (ADS)

Rinderknecht, H. G.; Rosenberg, M. J.; Li, C. K.; Zylstra, A. B.; Sio, H.; Gatu Johnson, M.; Frenje, J. A.; Séguin, F. H.; Petrasso, R. D.; Amendt, P. A.; Bellei, C.; Wilks, S. C.; Zimmerman, G.; Hoffman, N. M.; Kagan, G.; Molvig, K.; Glebov, V. Yu.; Stoeckl, C.; Marshall, F. J.; Seka, W.; Delettrez, J. A.; Sangster, T. C.; Betti, R.; Goncharov, V. N.; Meyerhofer, D. D.

2014-10-01

A. NIKROO, GA - Anomalously reduced yields relative to hydrodynamically calculated values have been observed for mixtures of D:3He compared to pure D2 gas-filled implosions in a series of shock-driven implosions at OMEGA. An extensive suite of measurements including temporal and spatial measurements of both the DD- and D3He-fusion reactions were obtained to identify the origin and physics behind this anomalous yield reduction. Measured spectral linewidths of fusion products suggest that the D ions are not thermalized to 3He during the burn, contributing to the reduced yield. The hypothesis that ion-species separation due to diffusive processes contributes to the observed yield reduction is explored using hydrodynamic simulations incorporating ion diffusion. Recent observations by Rosenberg et al. of a yield reduction with increased ion-ion mean free path do not explain the observed anomalous yield trend. Future work that will directly probe species separation with high-precision relative fusion reaction rate measurements between DD-neutrons and D3He-protons using the DualPTD instrument is discussed. This work was supported in part by the U.S. DOE, NLUF, LLE, and LLNL.

Diffusion of water and sodium counter-ions in nanopores of a β-lactoglobulin crystal: a molecular dynamics study

NASA Astrophysics Data System (ADS)

Malek, Kourosh; Odijk, Theo; Coppens, Marc-Olivier

2005-07-01

The dynamics of water and sodium counter-ions (Na+) in a C2221 orthorhombic β-lactoglobulin crystal is investigated by means of 5 ns molecular dynamics simulations. The effect of the fluctuation of the protein atoms on the motion of water and sodium ions is studied by comparing simulations in a rigid and in a flexible lattice. The electrostatic interactions of sodium ions with the positively charged LYS residues inside the crystal channels significantly influence the ionic motion. According to our results, water molecules close to the protein surface undergo an anomalous diffusive motion. On the other hand, the motion of water molecules further away from the protein surface is normal diffusive. Protein fluctuations affect the diffusion constant of water, which increases from 0.646 ± 0.108 to 0.887 ± 0.41 nm2 ns-1, when protein fluctuations are taken into account. The pore size (0.63-1.05 nm) and the water diffusivities are in good agreement with previous experimental results. The dynamics of sodium ions is disordered. LYS residues inside the pore are the main obstacles to the motion of sodium ions. However, the simulation time is still too short for providing a precise description of anomalous diffusion of sodium ions. The results are not only of interest for studying ion and water transport through biological nanopores, but may also elucidate water-protein and ion-protein interactions in protein crystals.

Determination of the diffusion coefficient and phase-transfer rate parameter in LaNi{sub 5} and MmNi{sub 3.6}Co{sub 0.8}Mn{sub 0.4}Al{sub 0.3} using microelectrodes

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

Lundqvist, A.; Lindbergh, G.

1998-11-01

A potential-step method for determining the diffusion coefficient and phase-transfer parameter in metal hydrides by using microelectrodes was investigated. It was shown that a large potential step is not enough to ensure a completely diffusion-limited mass transfer if a surface-phase transfer reaction takes place at a finite rate. It was shown, using a kinetic expression for the surface phase-transfer reaction, that the slope of the logarithm of the current vs. time curve will be constant both in the case of the mass-transfer limited by diffusion or by diffusion and a surface-phase transfer. The diffusion coefficient and phase-transfer rate parameter weremore » accurately determined for MmNi{sub 3.6}Co{sub 0.8}Mn{sub 0.4}Al{sub 0.3} using a fit to the whole transient. The diffusion coefficient was found to be (1.3 {+-} 0.3) {times} 10{sup {minus}13} m{sup 2}/s. The fit was good and showed that a pure diffusion model was not enough to explain the observed transient. The diffusion coefficient and phase-transfer rate parameter were also estimated for pure LaNi{sub 5}. A fit of the whole curve showed that neither a pure diffusion model nor a model including phase transfer could explain the whole transient.« less

Determination of diffusion coefficients of carbon dioxide in water between 268 and 473 K in a high-pressure capillary optical cell with in situ Raman spectroscopic measurements

USGS Publications Warehouse

Lu, Wanjun; Guo, Huirong; Chou, I.-Ming; Burruss, R.C.; Li, Lanlan

2013-01-01

Accurate values of diffusion coefficients for carbon dioxide in water and brine at reservoir conditions are essential to our understanding of transport behavior of carbon dioxide in subsurface pore space. However, the experimental data are limited to conditions at low temperatures and pressures. In this study, diffusive transfer of carbon dioxide in water at pressures up to 45 MPa and temperatures from 268 to 473 K was observed within an optical capillary cell via time-dependent Raman spectroscopy. Diffusion coefficients were estimated by the least-squares method for the measured variations in carbon dioxide concentration in the cell at various sample positions and time. At the constant pressure of 20 MPa, the measured diffusion coefficients of carbon dioxide in water increase with increasing temperature from 268 to 473 K. The relationship between diffusion coefficient of carbon dioxide in water [D(CO2) in m2/s] and temperature (T in K) was derived with Speedy–Angell power-law approach as: D(CO2)=D0[T/Ts-1]m where D0 = 13.942 × 10−9 m2/s, Ts = 227.0 K, and m = 1.7094. At constant temperature, diffusion coefficients of carbon dioxide in water decrease with pressure increase. However, this pressure effect is rather small (within a few percent).

Entropy-scaling laws for diffusion coefficients in liquid metals under high pressures

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

Cao, Qi-Long, E-mail: qlcao@mail.ustc.edu.cn; Shao, Ju-Xiang; Wang, Fan-Hou, E-mail: eatonch@gmail.com

2015-04-07

Molecular dynamic simulations on the liquid copper and tungsten are used to investigate the empirical entropy-scaling laws D{sup *}=A exp(BS{sub ex}), proposed independently by Rosenfeld and Dzugutov for diffusion coefficient, under high pressure conditions. We show that the scaling laws hold rather well for them under high pressure conditions. Furthermore, both the original diffusion coefficients and the reduced diffusion coefficients exhibit an Arrhenius relationship D{sub M}=D{sub M}{sup 0} exp(−E{sub M}/K{sub B}T), (M=un,R,D) and the activation energy E{sub M} increases with increasing pressure, the diffusion pre-exponential factors (D{sub R}{sup 0} and D{sub D}{sup 0}) are nearly independent of the pressure and element. Themore » pair correlation entropy, S{sub 2}, depends linearly on the reciprocal temperature S{sub 2}=−E{sub S}/T, and the activation energy, E{sub S}, increases with increasing pressure. In particular, the ratios of the activation energies (E{sub un}, E{sub R}, and E{sub D}) obtained from diffusion coefficients to the activation energy, E{sub S}, obtained from the entropy keep constants in the whole pressure range. Therefore, the entropy-scaling laws for the diffusion coefficients and the Arrhenius law are linked via the temperature dependence of entropy.« less

Anomalous Nernst effect in a microfabricated thermoelectric element made of chiral antiferromagnet Mn3Sn

NASA Astrophysics Data System (ADS)

Narita, Hideki; Ikhlas, Muhammad; Kimata, Motoi; Nugroho, Agustinus Agung; Nakatsuji, Satoru; Otani, YoshiChika

2017-11-01

Toward realizing a thermopile made of the chiral anti-ferromagnet Mn3Sn, focused ion beam (FIB) lithography was employed to microfabricate a thermoelectric element consisting of a Ta/Al2O3/Mn3Sn layered structure. In this device, the Ta layer acts as a heater producing Joule heat diffusing across the Al2O3 insulating layer into the thin Mn3Sn layer. The measured Nernst signal exhibits a clear hysteresis in an applied temperature gradient and magnetic field at 300 K, and its magnitude is proportional to the square of the electrical current applied to the Ta heater. The spontaneous, zero field voltage signal in the device is of the order of a few μV, which is almost the same order of magnitude as observed in the bulk single-crystal Mn3Sn under a temperature gradient. The anomalous Nernst coefficient SANE of the microfabricated element was determined using a temperature gradient simulated by finite-element modeling. The obtained value of SANE is 0.27 μV/K, which is in good agreement with that of the reported experimental value of SANE (0.3 μV/K) for bulk single-crystal Mn3Sn. This result indicates that FIB microfabrication does not significantly alter the thermoelectric properties of bulk Mn3Sn. As the chiral antiferromagnet produces almost no stray field, our study opens the avenue for the fabrication of an efficient thermopile by densely packing the microfabricated antiferromagnetic elements.

Solute diffusion in liquid metals

NASA Technical Reports Server (NTRS)

Bhat, B. N.

1973-01-01

A gas model of diffusion in liquid metals is presented. In this model, ions of liquid metals are assumed to behave like the molecules in a dense gas. Diffusion coefficient of solute is discussed with reference to its mass, ionic size, and pair potential. The model is applied to the case of solute diffusion in liquid silver. An attempt was made to predict diffusion coefficients of solutes with reasonable accuracy.

Matrix diffusion coefficients in volcanic rocks at the Nevada test site: influence of matrix porosity, matrix permeability, and fracture coating minerals.

PubMed

Reimus, Paul W; Callahan, Timothy J; Ware, S Doug; Haga, Marc J; Counce, Dale A

2007-08-15

Diffusion cell experiments were conducted to measure nonsorbing solute matrix diffusion coefficients in forty-seven different volcanic rock matrix samples from eight different locations (with multiple depth intervals represented at several locations) at the Nevada Test Site. The solutes used in the experiments included bromide, iodide, pentafluorobenzoate (PFBA), and tritiated water ((3)HHO). The porosity and saturated permeability of most of the diffusion cell samples were measured to evaluate the correlation of these two variables with tracer matrix diffusion coefficients divided by the free-water diffusion coefficient (D(m)/D*). To investigate the influence of fracture coating minerals on matrix diffusion, ten of the diffusion cells represented paired samples from the same depth interval in which one sample contained a fracture surface with mineral coatings and the other sample consisted of only pure matrix. The log of (D(m)/D*) was found to be positively correlated with both the matrix porosity and the log of matrix permeability. A multiple linear regression analysis indicated that both parameters contributed significantly to the regression at the 95% confidence level. However, the log of the matrix diffusion coefficient was more highly-correlated with the log of matrix permeability than with matrix porosity, which suggests that matrix diffusion coefficients, like matrix permeabilities, have a greater dependence on the interconnectedness of matrix porosity than on the matrix porosity itself. The regression equation for the volcanic rocks was found to provide satisfactory predictions of log(D(m)/D*) for other types of rocks with similar ranges of matrix porosity and permeability as the volcanic rocks, but it did a poorer job predicting log(D(m)/D*) for rocks with lower porosities and/or permeabilities. The presence of mineral coatings on fracture walls did not appear to have a significant effect on matrix diffusion in the ten paired diffusion cell experiments.

Matrix diffusion coefficients in volcanic rocks at the Nevada test site: Influence of matrix porosity, matrix permeability, and fracture coating minerals

NASA Astrophysics Data System (ADS)

Reimus, Paul W.; Callahan, Timothy J.; Ware, S. Doug; Haga, Marc J.; Counce, Dale A.

2007-08-01

Diffusion cell experiments were conducted to measure nonsorbing solute matrix diffusion coefficients in forty-seven different volcanic rock matrix samples from eight different locations (with multiple depth intervals represented at several locations) at the Nevada Test Site. The solutes used in the experiments included bromide, iodide, pentafluorobenzoate (PFBA), and tritiated water ( 3HHO). The porosity and saturated permeability of most of the diffusion cell samples were measured to evaluate the correlation of these two variables with tracer matrix diffusion coefficients divided by the free-water diffusion coefficient ( Dm/ D*). To investigate the influence of fracture coating minerals on matrix diffusion, ten of the diffusion cells represented paired samples from the same depth interval in which one sample contained a fracture surface with mineral coatings and the other sample consisted of only pure matrix. The log of ( Dm/ D*) was found to be positively correlated with both the matrix porosity and the log of matrix permeability. A multiple linear regression analysis indicated that both parameters contributed significantly to the regression at the 95% confidence level. However, the log of the matrix diffusion coefficient was more highly-correlated with the log of matrix permeability than with matrix porosity, which suggests that matrix diffusion coefficients, like matrix permeabilities, have a greater dependence on the interconnectedness of matrix porosity than on the matrix porosity itself. The regression equation for the volcanic rocks was found to provide satisfactory predictions of log( Dm/ D*) for other types of rocks with similar ranges of matrix porosity and permeability as the volcanic rocks, but it did a poorer job predicting log( Dm/ D*) for rocks with lower porosities and/or permeabilities. The presence of mineral coatings on fracture walls did not appear to have a significant effect on matrix diffusion in the ten paired diffusion cell experiments.

Lévy/Anomalous Diffusion as a Mean-Field Theory for 3D Cloud Effects in SW-RT: Empirical Support, New Analytical Formulation, and Impact on Atmospheric Absorption

NASA Astrophysics Data System (ADS)

Pfeilsticker, K.; Davis, A.; Marshak, A.; Suszcynsky, D. M.; Buldryrev, S.; Barker, H.

2001-12-01

2-stream RT models, as used in all current GCMs, are mathematically equivalent to standard diffusion theory where the physical picture is a slow propagation of the diffuse radiation by Gaussian random walks. In other words, after the conventional van de Hulst rescaling by 1/(1-g) in R3 and also by (1-g) in t, solar photons follow convoluted fractal trajectories in the atmosphere. For instance, we know that transmitted light is typically scattered about (1-g)τ 2 times while reflected light is scattered on average about τ times, where τ is the optical depth of the column. The space/time spread of this diffusion process is described exactly by a Gaussian distribution; from the statistical physics viewpoint, this follows from the convergence of the sum of many (rescaled) steps between scattering events with a finite variance. This Gaussian picture follows from directly from first principles (the RT equation) under the assumptions of horizontal uniformity and large optical depth, i.e., there is a homogeneous plane-parallel cloud somewhere in the column. The first-order effect of 3D variability of cloudiness, the main source of scattering, is to perturb the distribution of single steps between scatterings which, modulo the '1-g' rescaling, can be assumed effectively isotropic. The most natural generalization of the Gaussian distribution is the 1-parameter family of symmetric Lévy-stable distributions because the sum of many zero-mean random variables with infinite variance, but finite moments of order q < α (0 < α < 2), converge to them. It has been shown on heuristic grounds that for these Lévy-based random walks the typical number of scatterings is now (1-g)τ α for transmitted light. The appearance of a non-rational exponent is why this is referred to as anomalous diffusion. Note that standard/Gaussian diffusion is retrieved in the limit α = 2-. Lévy transport theory has been successfully used in the statistical physics to investigate a wide variety of systems with strongly nonlinear dynamics; these applications range from random advection in turbulent fluids to the erratic behavior of financial time-series and, most recently, self-regulating ecological systems. We will briefly survey the state-of-the-art observations that offer compelling empirical support for the Lévy/anomalous diffusion model in atmospheric radiation: (1) high-resolution spectroscopy of differential absorption in the O2 A-band from ground; (2) temporal transient records of lightning strokes transmitted through clouds to a sensitive detector in space; and (3) the Gamma-distributions of optical depths derived from Landsat cloud scenes at 30-m resolution. We will then introduce a rigorous analytical formulation of anomalous transport through finite media based on fractional derivatives and Sonin calculus. A remarkable result from this new theoretical development is an extremal property of the α = 1+ case (divergent mean-free-path), as is observed in the cloudy atmosphere. Finally, we will discuss the implications of anomalous transport theory for bulk 3D effects on the current enhanced absorption problem as well as its role as the basis of a next-generation GCM RT parameterization.

Investigation on dispersion in the active optical waveguide resonator

NASA Astrophysics Data System (ADS)

Qiu, Zihan; Gao, Yining; Xie, Wei

2018-03-01

Introducing active gain in the optical waveguide resonator not only compensates the loss, but also can change the dispersion relationship in the ring resonator. It is demonstrated that the group delay time is negative when the resonator is in the undercoupled condition, which also means the resonator exhibits the fast light effect. Theoretical analysis indicates that fast light effect due to anomalous dispersion, would be manipulated by the gain coefficient controlled by the input pump light power and that fast light would enhance scale factor of the optical resonant gyroscope. Resonance optical gyroscope (ROG)'s scale factor for measuring rotation rate is enhanced by anomalous dispersion with superluminal light propagation. The sensitivity of ROG could be enhanced by anomalous dispersion by coupled resonators even considering the effect of anomalous dispersion and propagation gain on broadened linewidth, and this could result in at least two orders of magnitude enhancement in sensitivity.

Anisotropy of the innermost inner core from body wave and normal mode observations

NASA Astrophysics Data System (ADS)

Deuss, A. F.; Smink, M.; Bouwman, D.; Ploegstra, J.; van Tent, R.

2016-12-01

It has been known for a long time that the Earth's inner core is cylindrically anisotropic, with waves that travel in the direction of the Earth's rotation axis arriving several seconds before waves travelling in the equatorial direction. Recently, several studies have suggested that the Earth's rotation axis may not be the fast anisotropy direction in the innermost inner core. Beghein and Trampert (2003) found that the Earth's rotation axis is slow, with the equatorial plane being fast. Wang et al (2015) found instead that the fast symmetry axis is in the equatorial plane. Here, we use both body wave and normal mode observations to test these two different hypotheses. Similar to Wang, we correct body wave PKIKP data for anisotropy in the upper inner core, and investigate if there is any anisotropy remaining in the innermost inner core. We find that the results strongly depend on the very limited number of polar direction waves with angle less than 25 degrees. With the limited data it is difficult to distinguish between the two different hypotheses, and if any tilted anisotropy is required at all. Normal modes see inner core anisotropy with north-south symmetry axis as anomalous zonal coefficients. We will show theoretically that if the anisotropy symmetry axis is tilted, non-zonal coefficients will also become anomalous. We search consistent anomalous non-zonal coefficients for modes sensitive to the innermost inner core. If the symmetry axis is still north south, but this is now the slow direction and the equatorial plane fast, then we predict negative zonal coefficients. This is observed for some normal modes, explaining why Beghein and Trampert (2003) found this type of anisotropy in the innermost inner core.

Photon diffusion coefficient in scattering and absorbing media.

PubMed

Pierrat, Romain; Greffet, Jean-Jacques; Carminati, Rémi

2006-05-01

We present a unified derivation of the photon diffusion coefficient for both steady-state and time-dependent transport in disordered absorbing media. The derivation is based on a modal analysis of the time-dependent radiative transfer equation. This approach confirms that the dynamic diffusion coefficient is given by the random-walk result D = cl(*)/3, where l(*) is the transport mean free path and c is the energy velocity, independent of the level of absorption. It also shows that the diffusion coefficient for steady-state transport, often used in biomedical optics, depends on absorption, in agreement with recent theoretical and experimental works. These two results resolve a recurrent controversy in light propagation and imaging in scattering media.

Molecular dynamics simulation of solute diffusion in Lennard-Jones fluids

NASA Astrophysics Data System (ADS)

Yamaguchi, T.; Kimura, Y.; Hirota, N.

We performed a molecular dynamics (MD) simulation for a system of 5 solute molecules in 495 solvent molecules interacting through the Lennard-Jones (LJ) 12-6 potential, in order to study solvent density effects on the diffusion coefficients in supercritical fluids. The effects of the size of the solute and the strength of the solute-solvent attractive interaction on the diffusion coefficient of the solute were examined. The diffusion coefficients of the solute molecules were calculated at T = 1.5 (in the LJ reduced unit), slightly above the critical temperature, from rho = 0.1 to rho = 0.95, where rho is the number density in the LJ reduced unit. The memory function in the generalized Langevin equation was calculated, in order to know the molecular origin of the friction on a solute. The memory function is separated into fast and slow components. The former arises from the solute-solvent repulsive interaction, and is interpreted as collisional Enskog-like friction. The interaction strength dependence of the collisional friction is larger in the low- and medium-density regions, which is consistent with the 'clustering' picture, i.e., the local density enhancement due to the solute-solvent attractive interaction. However, the slow component of the memory function suppresses the effect of the local density on the diffusion coefficients, and as a result the effect of the attractive interaction is smaller on the diffusion coefficients than on the local density. Nonetheless, the solvent density dependence of the effect of the attraction on the diffusion coefficient varies with the local density, and it is concluded that the local density is the principal factor that determines the interaction strength dependence of the diffusion coefficient in the low- and medium-density regions (p < 0.6).

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

Sarman, Sten, E-mail: sarman@ownit.nu; Wang, Yong-Lei; Laaksonen, Aatto

The self-diffusion coefficients of nematic phases of various model systems consisting of regular convex calamitic and discotic ellipsoids and non-convex bodies such as bent-core molecules and soft ellipsoid strings have been obtained as functions of the shear rate in a shear flow. Then the self-diffusion coefficient is a second rank tensor with three different diagonal components and two off-diagonal components. These coefficients were found to be determined by a combination of two mechanisms, which previously have been found to govern the self-diffusion of shearing isotropic liquids, namely, (i) shear alignment enhancing the diffusion in the direction parallel to the streamlinesmore » and hindering the diffusion in the perpendicular directions and (ii) the distortion of the shell structure in the liquid whereby a molecule more readily can escape from a surrounding shell of nearest neighbors, so that the mobility increases in every direction. Thus, the diffusion parallel to the streamlines always increases with the shear rate since these mechanisms cooperate in this direction. In the perpendicular directions, these mechanisms counteract each other so that the behaviour becomes less regular. In the case of the nematic phases of the calamitic and discotic ellipsoids and of the bent core molecules, mechanism (ii) prevails so that the diffusion coefficients increase. However, the diffusion coefficients of the soft ellipsoid strings decrease in the direction of the velocity gradient because the broadsides of these molecules are oriented perpendicularly to this direction due the shear alignment (i). The cross coupling coefficient relating a gradient of tracer particles in the direction of the velocity gradient and their flow in the direction of the streamlines is negative and rather large, whereas the other coupling coefficient relating a gradient in the direction of the streamlines and a flow in the direction of the velocity gradient is very small.« less

[Lateral diffusion of saturated phosphatidylcholines in cholesterol-containing bilayers].

PubMed

Filippov, A V; Rudakova, M A; Oradd, G; Lindblom, J

2007-01-01

Lateral diffusion in oriented bilayers of saturated cholesterol-containing phosphatidylcholines, dipalmitoylphosphatidylcholine and dimyrilstoylphosphatidylcholine upon their limiting hydration has been studied by NMR with impulse gradient of magnetic field. For both systems, similar dependences of the coefficient of lateral diffusion on temperature and cholesterol concentration were observed, which agree with the phase diagram showing the presence of regions of ordered and unordered liquid-crystalline phases and a two-phase region. Under similar conditions, the coefficient of lateral diffusion for dipalmytoylphosphatidylcholine has lower values, which is in qualitative agreement with its greater molecular mass. A comparison of data for dipalmytoylphosphatidylcholine with the results obtained earlier for dipalmytoylsphyngomyelin/cholesterol under the same conditions shows, despite a similarity in phase diagrams, greater (two- to threefold) differences in the values of the coefficient of lateral diffusion and a different mode of dependence of the coefficient on cholesterol concentration. A comparison of data for dimyrilstoylphosphatidylcholine with the results obtained previously shows that the values of the coefficient of lateral diffusion and the mode of its dependence on cholesterol concentration coincide in the region of higher concentrations (more than 15 mole %) and differ in the region of lower concentrations (below 15 mole %). The discrepancies may be explained by different contents of water in the systems during the measurements. At a limiting hydration (more than 35%) of water, the coefficient of lateral diffusion decreases with increasing cholesterol concentration. If the content of water is about 25% (as a result of equilibrium hydration from vapors), the coefficient of lateral diffusion of phosphatidylcholine is probably independent of cholesterol concentration. This results from a denser packing of molecules in the bilayer at a lower water concentration, an effect that competes with the ordering effect of cholesterol.

Interfacial Stresses and the Anomalous Character of Thermoelastic-Deformation Curves of a Cu-Al-Ni Shape-Memory Alloy

NASA Astrophysics Data System (ADS)

Malygin, G. A.; Nikolaev, V. I.; Pulnev, S. A.; Chikiryaka, A. V.

2017-12-01

Thermoelastic-deformation curves of a single-crystalline Cu-13.5 wt % Al-4.0 wt % Ni shapememory (SM) alloy have been studied. Cyclic temperature variation in a 300-450 K interval revealed an anomalous character of thermoelastic hysteresis loops with regions of accelerated straining at both heating and cooling stages. The observed phenomenon can be used for increasing the response speed of SM-alloy based drive and sensor devices. Analysis of this phenomenon in the framework of the theory of diffuse martensitic transformations showed that the anomalous character of thermoelastic hysteresis loops may be related to the influence of interfacial stresses on the dynamics of martensitic transformations in these SM alloys.

A novel multiple headspace extraction gas chromatographic method for measuring the diffusion coefficient of methanol in water and in olive oil.

PubMed

Zhang, Chun-Yun; Chai, Xin-Sheng

2015-03-13

A novel method for the determination of the diffusion coefficient (D) of methanol in water and olive oil has been developed. Based on multiple headspace extraction gas chromatography (MHE-GC), the methanol released from the liquid sample of interest in a closed sample vial was determined in a stepwise fashion. A theoretical model was derived to establish the relationship between the diffusion coefficient and the GC signals from MHE-GC measurements. The results showed that the present method has an excellent precision (RSD<1%) in the linear fitting procedure and good accuracy for the diffusion coefficients of methanol in both water and olive oil, when compared with data reported in the literature. The present method is simple and practical and can be a valuable tool for the determination of the diffusion coefficient of volatile analyte(s) into food simulants from food and beverage packaging material, both in research studies and in actual applications. Copyright © 2015 Elsevier B.V. All rights reserved.

Prediction of stream volatilization coefficients

USGS Publications Warehouse

Rathbun, Ronald E.

1990-01-01

Equations are developed for predicting the liquid-film and gas-film reference-substance parameters for quantifying volatilization of organic solutes from streams. Molecular weight and molecular-diffusion coefficients of the solute are used as correlating parameters. Equations for predicting molecular-diffusion coefficients of organic solutes in water and air are developed, with molecular weight and molal volume as parameters. Mean absolute errors of prediction for diffusion coefficients in water are 9.97% for the molecular-weight equation, 6.45% for the molal-volume equation. The mean absolute error for the diffusion coefficient in air is 5.79% for the molal-volume equation. Molecular weight is not a satisfactory correlating parameter for diffusion in air because two equations are necessary to describe the values in the data set. The best predictive equation for the liquid-film reference-substance parameter has a mean absolute error of 5.74%, with molal volume as the correlating parameter. The best equation for the gas-film parameter has a mean absolute error of 7.80%, with molecular weight as the correlating parameter.

Anomalous diffusion of water molecules at grain boundaries in ice Ih.

PubMed

Moreira, Pedro Augusto Franco Pinheiro; Veiga, Roberto Gomes de Aguiar; Ribeiro, Ingrid de Almeida; Freitas, Rodrigo; Helfferich, Julian; de Koning, Maurice

2018-05-23

Using ab initio and classical molecular dynamics simulations, we study pre-melting phenomena in pristine coincident-site-lattice grain boundaries (GBs) in proton-disordered hexagonal ice Ih at temperatures just below the melting point Tm. Concerning pre-melt-layer thicknesses, the results are consistent with the available experimental estimates for low-disorder impurity-free GBs. With regard to molecular mobility, the simulations provide a key new insight: the translational motion of the water molecules is found to be subdiffusive for time scales from ∼10 ns up to at least 0.1 μs. Moreover, the fact that the anomalous diffusion occurs even at temperatures just below Tm where the bulk supercooled liquid still diffuses normally suggests that it is related to the confinement of the GB pre-melt layers by the surrounding crystalline environment. Furthermore, we show that this behavior can be characterized by continuous-time random walk models in which the waiting-time distributions decay according to power-laws that are very similar to those describing dynamics in glass-forming systems.

TEMPEST Simulations of the Plasma Transport in a Single-Null Tokamak Geometry

DOE PAGES

X. Q. Xu; Bodi, K.; Cohen, R. H.; ...

2010-05-28

We present edge kinetic ion transport simulations of tokamak plasmas in magnetic divertor geometry using the fully nonlinear (full-f) continuum code TEMPEST. Besides neoclassical transport, a term for divergence of anomalous kinetic radial flux is added to mock up the effect of turbulent transport. In order to study the relative roles of neoclassical and anomalous transport, TEMPEST simulations were carried out for plasma transport and flow dynamics in a single-null tokamak geometry, including the pedestal region that extends across the separatrix into the scrape-off layer and private flux region. In a series of TEMPEST simulations were conducted to investigate themore » transition of midplane pedestal heat flux and flow from the neoclassical to the turbulent limit and the transition of divertor heat flux and flow from the kinetic to the fluid regime via an anomalous transport scan and a density scan. The TEMPEST simulation results demonstrate that turbulent transport (as modelled by large diffusion) plays a similar role to collisional decorrelation of particle orbits and that the large turbulent transport (large diffusion) leads to an apparent Maxwellianization of the particle distribution. Moreover, we show the transition of parallel heat flux and flow at the entrance to the divertor plates from the fluid to the kinetic regime. For an absorbing divertor plate boundary condition, a non-half-Maxwellian is found due to the balance between upstream radial anomalous transport and energetic ion endloss.« less

TEMPEST Simulations of the Plasma Transport in a Single-Null Tokamak Geometry

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

X. Q. Xu; Bodi, K.; Cohen, R. H.

We present edge kinetic ion transport simulations of tokamak plasmas in magnetic divertor geometry using the fully nonlinear (full-f) continuum code TEMPEST. Besides neoclassical transport, a term for divergence of anomalous kinetic radial flux is added to mock up the effect of turbulent transport. In order to study the relative roles of neoclassical and anomalous transport, TEMPEST simulations were carried out for plasma transport and flow dynamics in a single-null tokamak geometry, including the pedestal region that extends across the separatrix into the scrape-off layer and private flux region. In a series of TEMPEST simulations were conducted to investigate themore » transition of midplane pedestal heat flux and flow from the neoclassical to the turbulent limit and the transition of divertor heat flux and flow from the kinetic to the fluid regime via an anomalous transport scan and a density scan. The TEMPEST simulation results demonstrate that turbulent transport (as modelled by large diffusion) plays a similar role to collisional decorrelation of particle orbits and that the large turbulent transport (large diffusion) leads to an apparent Maxwellianization of the particle distribution. Moreover, we show the transition of parallel heat flux and flow at the entrance to the divertor plates from the fluid to the kinetic regime. For an absorbing divertor plate boundary condition, a non-half-Maxwellian is found due to the balance between upstream radial anomalous transport and energetic ion endloss.« less

Stochastic tools hidden behind the empirical dielectric relaxation laws

NASA Astrophysics Data System (ADS)

Stanislavsky, Aleksander; Weron, Karina

2017-03-01

The paper is devoted to recent advances in stochastic modeling of anomalous kinetic processes observed in dielectric materials which are prominent examples of disordered (complex) systems. Theoretical studies of dynamical properties of ‘structures with variations’ (Goldenfield and Kadanoff 1999 Science 284 87-9) require application of such mathematical tools—by means of which their random nature can be analyzed and, independently of the details distinguishing various systems (dipolar materials, glasses, semiconductors, liquid crystals, polymers, etc), the empirical universal kinetic patterns can be derived. We begin with a brief survey of the historical background of the dielectric relaxation study. After a short outline of the theoretical ideas providing the random tools applicable to modeling of relaxation phenomena, we present probabilistic implications for the study of the relaxation-rate distribution models. In the framework of the probability distribution of relaxation rates we consider description of complex systems, in which relaxing entities form random clusters interacting with each other and single entities. Then we focus on stochastic mechanisms of the relaxation phenomenon. We discuss the diffusion approach and its usefulness for understanding of anomalous dynamics of relaxing systems. We also discuss extensions of the diffusive approach to systems under tempered random processes. Useful relationships among different stochastic approaches to the anomalous dynamics of complex systems allow us to get a fresh look at this subject. The paper closes with a final discussion on achievements of stochastic tools describing the anomalous time evolution of complex systems.

The γ parameter of the stretched-exponential model is influenced by internal gradients: validation in phantoms.

PubMed

Palombo, Marco; Gabrielli, Andrea; De Santis, Silvia; Capuani, Silvia

2012-03-01

In this paper, we investigate the image contrast that characterizes anomalous and non-gaussian diffusion images obtained using the stretched exponential model. This model is based on the introduction of the γ stretched parameter, which quantifies deviation from the mono-exponential decay of diffusion signal as a function of the b-value. To date, the biophysical substrate underpinning the contrast observed in γ maps, in other words, the biophysical interpretation of the γ parameter (or the fractional order derivative in space, β parameter) is still not fully understood, although it has already been applied to investigate both animal models and human brain. Due to the ability of γ maps to reflect additional microstructural information which cannot be obtained using diffusion procedures based on gaussian diffusion, some authors propose this parameter as a measure of diffusion heterogeneity or water compartmentalization in biological tissues. Based on our recent work we suggest here that the coupling between internal and diffusion gradients provide pseudo-superdiffusion effects which are quantified by the stretching exponential parameter γ. This means that the image contrast of Mγ maps reflects local magnetic susceptibility differences (Δχ(m)), thus highlighting better than T(2)(∗) contrast the interface between compartments characterized by Δχ(m). Thanks to this characteristic, Mγ imaging may represent an interesting tool to develop contrast-enhanced MRI for molecular imaging. The spectroscopic and imaging experiments (performed in controlled micro-beads dispersion) that are reported here, strongly suggest internal gradients, and as a consequence Δχ(m), to be an important factor in fully understanding the source of contrast in anomalous diffusion methods that are based on a stretched exponential model analysis of diffusion data obtained at varying gradient strengths g. Copyright © 2012 Elsevier Inc. All rights reserved.

Dissipative particle dynamics study of velocity autocorrelation function and self-diffusion coefficient in terms of interaction potential strength

NASA Astrophysics Data System (ADS)

Zohravi, Elnaz; Shirani, Ebrahim; Pishevar, Ahmadreza; Karimpour, Hossein

2018-07-01

This research focuses on numerically investigating the self-diffusion coefficient and velocity autocorrelation function (VACF) of a dissipative particle dynamics (DPD) fluid as a function of the conservative interaction strength. Analytic solutions to VACF and self-diffusion coefficients in DPD were obtained by many researchers in some restricted cases including ideal gases, without the account of conservative force. As departure from the ideal gas conditions are accentuated with increasing the relative proportion of conservative force, it is anticipated that the VACF should gradually deviate from its normally expected exponentially decay. This trend is confirmed through numerical simulations and an expression in terms of the conservative force parameter, density and temperature is proposed for the self-diffusion coefficient. As it concerned the VACF, the equivalent Langevin equation describing Brownian motion of particles with a harmonic potential is adapted to the problem and reveals an exponentially decaying oscillatory pattern influenced by the conservative force parameter, dissipative parameter and temperature. Although the proposed model for obtaining the self-diffusion coefficient with consideration of the conservative force could not be verified due to computational complexities, nonetheless the Arrhenius dependency of the self-diffusion coefficient to temperature and pressure permits to certify our model over a definite range of DPD parameters.

Interdiffusion and stress development in single-crystalline Pd/Ag bilayers

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

Noah, Martin A., E-mail: m.noah@is.mpg.de; Flötotto, David; Wang, Zumin

Interdiffusion and stress evolution in single-crystalline Pd/single-crystalline Ag thin films were investigated by Auger electron spectroscopy sputter-depth profiling and in-situ X-ray diffraction, respectively. The concentration-dependent chemical diffusion coefficient, as well as the impurity diffusion coefficient of Ag in Pd could be determined in the low temperature range of 356 °C–455 °C. As a consequence of the similarity of the strong concentration-dependences of the intrinsic diffusion coefficients, the chemical diffusion coefficient varies only over three orders of magnitude over the whole composition range, despite the large difference of six orders of magnitude of the self-diffusion coefficients of Ag in Ag and Pd inmore » Pd. It is shown that the Darken-Manning treatment should be adopted for interpretation of the experimental data; the Nernst-Planck treatment yielded physically unreasonable results. Apart from the development of compressive thermal stress, the development of stress in both sublayers separately could be ascribed to compositional stress (tensile in the Ag sublayer and compressive in the Pd sublayer) and dominant relaxation processes, especially in the Ag sublayer. The effect of these internal stresses on the values determined for the diffusion coefficients is shown to be negligible.« less

Diffusion heterogeneity tensor MRI (?-Dti): mathematics and initial applications in spinal cord regeneration after trauma - biomed 2009.

PubMed

Ellington, Benjamin M; Schmit, Brian D; Gourab, Krishnaj; Sieber-Blum, Maya; Hu, Yao F; Schmainda, Kathleen M

2009-01-01

Diffusion weighted magnetic resonance imaging (DWI) is a powerful tool for evaluation of microstructural anomalies in numerous central nervous system pathologies. Diffusion tensor imaging (DTI) allows for the magnitude and direction of water self diffusion to be estimated by sampling the apparent diffusion coefficient (ADC) in various directions. Clinical DWI and DTI performed at a single level of diffusion weighting, however, does not allow for multiple diffusion compartments to be elicited. Furthermore, assumptions made regarding the precise number of diffusion compartments intrinsic to the tissue of interest have resulted in a lack of consensus between investigations. To overcome these challenges, a stretched-exponential model of diffusion was applied to examine the diffusion coefficient and "heterogeneity index" within highly compartmentalized brain tumors. The purpose of the current study is to expand on the stretched-exponential model of diffusion to include directionality of both diffusion heterogeneity and apparent diffusion coefficient. This study develops the mathematics of this new technique along with an initial application in quantifying spinal cord regeneration following acute injection of epidermal neural crest stem cell (EPI-NCSC) grafts.

Determination of diffusion coefficients and diffusion characteristics for chlorferon and diethylthiophosphate in Ca-alginate gel beads.

PubMed

Ha, Jiyeon; Engler, Cady R; Lee, Seung Jae

2008-07-01

Diffusion characteristics of chlorferon and diethylthiophosphate (DETP) in Ca-alginate gel beads were studied to assist in designing and operating bioreactor systems. Diffusion coefficients for chlorferon and DETP in Ca-alginate gel beads determined at conditions suitable for biodegradation studies were 2.70 x 10(-11) m(2)/s and 4.28 x 10(-11) m(2)/s, respectively. Diffusivities of chlorferon and DETP were influenced by several factors, including viscosity of the bulk solution, agitation speed, and the concentrations of diffusing substrate and immobilized cells. Diffusion coefficients increased with increasing agitation speed, probably due to poor mixing at low speed and some attrition of beads at high speeds. Diffusion coefficients also increased with decreasing substrate concentration. Increased cell concentration in the gel beads caused lower diffusivity. Theoretical models to predict diffusivities as a function of cell weight fraction overestimated the effective diffusivities for both chlorferon and DETP, but linear relations between effective diffusivity and cell weight fraction were derived from experimental data. Calcium-alginate gel beads with radii of 1.65-1.70 mm used in this study were not subject to diffusional limitations: external mass transfer resistances were negligible based on Biot number calculations and effectiveness factors indicated that internal mass transfer resistance was negligible. Therefore, the degradation rates of chlorferon and DETP inside Ca-alginate gel beads were reaction-limited. (c) 2007 Wiley Periodicals, Inc.

Diffusion coefficients of water in biobased hydrogel polymer matrices by nuclear magnetic resonance imaging

USDA-ARS?s Scientific Manuscript database

The diffusion coefficient of water in biobased hydrogels were measured utilizing a simple NMR method. This method tracks the migration of deuterium oxide through imaging data that is fit to a diffusion equation. The results show that a 5 wt% soybean oil based hydrogel gives aqueous diffusion of 1.37...

Portable vapor diffusion coefficient meter

DOEpatents

Ho, Clifford K [Albuquerque, NM

2007-06-12

An apparatus for measuring the effective vapor diffusion coefficient of a test vapor diffusing through a sample of porous media contained within a test chamber. A chemical sensor measures the time-varying concentration of vapor that has diffused a known distance through the porous media. A data processor contained within the apparatus compares the measured sensor data with analytical predictions of the response curve based on the transient diffusion equation using Fick's Law, iterating on the choice of an effective vapor diffusion coefficient until the difference between the predicted and measured curves is minimized. Optionally, a purge fluid can forced through the porous media, permitting the apparatus to also measure a gas-phase permeability. The apparatus can be made lightweight, self-powered, and portable for use in the field.

Communication: Coordinate-dependent diffusivity from single molecule trajectories

NASA Astrophysics Data System (ADS)

Berezhkovskii, Alexander M.; Makarov, Dmitrii E.

2017-11-01

Single-molecule observations of biomolecular folding are commonly interpreted using the model of one-dimensional diffusion along a reaction coordinate, with a coordinate-independent diffusion coefficient. Recent analysis, however, suggests that more general models are required to account for single-molecule measurements performed with high temporal resolution. Here, we consider one such generalization: a model where the diffusion coefficient can be an arbitrary function of the reaction coordinate. Assuming Brownian dynamics along this coordinate, we derive an exact expression for the coordinate-dependent diffusivity in terms of the splitting probability within an arbitrarily chosen interval and the mean transition path time between the interval boundaries. This formula can be used to estimate the effective diffusion coefficient along a reaction coordinate directly from single-molecule trajectories.

Normal versus anomalous self-diffusion in two-dimensional fluids: memory function approach and generalized asymptotic Einstein relation.

PubMed

Shin, Hyun Kyung; Choi, Bongsik; Talkner, Peter; Lee, Eok Kyun

2014-12-07

Based on the generalized Langevin equation for the momentum of a Brownian particle a generalized asymptotic Einstein relation is derived. It agrees with the well-known Einstein relation in the case of normal diffusion but continues to hold for sub- and super-diffusive spreading of the Brownian particle's mean square displacement. The generalized asymptotic Einstein relation is used to analyze data obtained from molecular dynamics simulations of a two-dimensional soft disk fluid. We mainly concentrated on medium densities for which we found super-diffusive behavior of a tagged fluid particle. At higher densities a range of normal diffusion can be identified. The motion presumably changes to sub-diffusion for even higher densities.

Normal versus anomalous self-diffusion in two-dimensional fluids: Memory function approach and generalized asymptotic Einstein relation

NASA Astrophysics Data System (ADS)

Shin, Hyun Kyung; Choi, Bongsik; Talkner, Peter; Lee, Eok Kyun

2014-12-01

Based on the generalized Langevin equation for the momentum of a Brownian particle a generalized asymptotic Einstein relation is derived. It agrees with the well-known Einstein relation in the case of normal diffusion but continues to hold for sub- and super-diffusive spreading of the Brownian particle's mean square displacement. The generalized asymptotic Einstein relation is used to analyze data obtained from molecular dynamics simulations of a two-dimensional soft disk fluid. We mainly concentrated on medium densities for which we found super-diffusive behavior of a tagged fluid particle. At higher densities a range of normal diffusion can be identified. The motion presumably changes to sub-diffusion for even higher densities.

Diffusion of organic pollutants within a biofilm in porous media

NASA Astrophysics Data System (ADS)

Fan, Chihhao; Kao, Chen-Fei; Liu, You-Hsi

2017-04-01

The occurrence of aquatic pollution is an inevitable environmental impact resulting from human civilization and societal advancement. Either from the natural or anthropogenic sources, the aqueous contaminants enter the natural environment and aggravate its quality. To assure the aquatic environment quality, the attached-growth biological degradation is often applied to removing organic contaminants by introducing contaminated water into a porous media which is covered by microorganism. Additionally, many natural aquatic systems also form such similar mechanism to increase their self-purification capability. To better understand this transport phenomenon and degradation mechanism in the biofilm for future application, the mathematic characterization of organic contaminant diffusion within the biofilm requires further exploration. The present study aimed to formulate a mathematic representation to quantify the diffusion of the organic contaminant in the biofilm. The BOD was selected as the target contaminant. A series of experiments were conducted to quantify the BOD diffusion in the biofilm under the conditions of influent BOD variation from 50 to 300 mg/L, COD:N:P ratios of 100:5:1 and 100:15:3, with or without auxiliary aeration. For diffusion coefficient calculation, the boundary condition of zero diffusion at the interface between microbial phase and contact media was assumed. With the principle of conservation of mass, the removed contaminants equal those that diffuse into the biofilm, and eq 1 results, and the diffusion coefficient (i.e., eq 2) can be solved through calculus with equations from table of integral. ∂2Sf- Df ∂z2 = Rf (1) --(QSin--QSout)2Y--- Df = 2μmaxxf(Sb + Ks ln-Ks-) Sb+Ks (2) Using the obtained experimental data, the diffusion coefficient was calculated to be 2.02*10-6 m2/d with influent COD of 50 mg/L at COD:N:P ratio of 100:5:1 with aeration, and this coefficient increased to 6.02*10-6 m2/d as the influent concentration increased to 300 mg/L. Meanwhile, the diffusion coefficient decreased to 2.61*10-7 m2/d as the retention time increased to 3 hours. Generally, the variation in diffusion coefficients between different COD:N:P ratios exhibits similar pattern with a slight decrease for the ratio of 100:15:3. The difference in diffusion coefficients between 1 and 2 hours was apparently greater than that between 2 and 3 hours, implying the diffusion was a critical factor for contaminant removal for the treatment condition with retention time of 1 hour or less, because higher retention time leads to better microbial degradation due to sufficient contact time for biological reactions. For 1 hour retention time, the increase in diffusion coefficient becomes limited as the influent COD concentration was equal to or above 150 mg/L. These obtained diffusion coefficients were applied to estimating the treatment efficiency for real domestic sewage. The result was found that the estimated effluent BOD concentrations were quite comparable to that obtained through experimental measurements.

NMR investigation of water diffusion in different biofilm structures.

PubMed

Herrling, Maria P; Weisbrodt, Jessica; Kirkland, Catherine M; Williamson, Nathan H; Lackner, Susanne; Codd, Sarah L; Seymour, Joseph D; Guthausen, Gisela; Horn, Harald

2017-12-01

Mass transfer in biofilms is determined by diffusion. Different mostly invasive approaches have been used to measure diffusion coefficients in biofilms, however, data on heterogeneous biomass under realistic conditions is still missing. To non-invasively elucidate fluid-structure interactions in complex multispecies biofilms pulsed field gradient-nuclear magnetic resonance (PFG-NMR) was applied to measure the water diffusion in five different types of biomass aggregates: one type of sludge flocs, two types of biofilm, and two types of granules. Data analysis is an important issue when measuring heterogeneous systems and is shown to significantly influence the interpretation and understanding of water diffusion. With respect to numerical reproducibility and physico-chemical interpretation, different data processing methods were explored: (bi)-exponential data analysis and the Γ distribution model. Furthermore, the diffusion coefficient distribution in relation to relaxation was studied by D-T 2 maps obtained by 2D inverse Laplace transform (2D ILT). The results show that the effective diffusion coefficients for all biofilm samples ranged from 0.36 to 0.96 relative to that of water. NMR diffusion was linked to biofilm structure (e.g., biomass density, organic and inorganic matter) as observed by magnetic resonance imaging and to traditional biofilm parameters: diffusion was most restricted in granules with compact structures, and fast diffusion was found in heterotrophic biofilms with fluffy structures. The effective diffusion coefficients in the biomass were found to be broadly distributed because of internal biomass heterogeneities, such as gas bubbles, precipitates, and locally changing biofilm densities. Thus, estimations based on biofilm bulk properties in multispecies systems can be overestimated and mean diffusion coefficients might not be sufficiently informative to describe mass transport in biofilms and the near bulk. © 2017 Wiley Periodicals, Inc.

Diffusion of neutral and ionic species in charged membranes: boric acid, arsenite, and water.

PubMed

Goli, Esmaiel; Hiemstra, Tjisse; Van Riemsdijk, Willem H; Rahnemaie, Rasoul; Malakouti, Mohammad Jafar

2010-10-15

Dynamic ion speciation using DMT (Donnan membrane technique) requires insight into the physicochemical characteristics of diffusion in charged membranes (tortuosity, local diffusion coefficients) as well as ion accumulation. The latter can be precluded by studying the diffusion of neutral species, such as boric acid, B(OH)₃⁰(aq), arsenite, As(OH)₃⁰(aq), or water. In this study, the diffusion rate of B(OH)₃⁰ has been evaluated as a function of the concentration, pH, and ionic strength. The rate is linearly dependent on the concentration of solely the neutral species, without a significant contribution of negatively charged species such as B(OH)₄⁻, present at high pH. A striking finding is the very strong effect (factor of ~10) of the type of cation (K(+), Na(+), Ca(2+), Mg(2+), Al(3+), and H(+)) on the diffusion coefficient of B(OH)₃⁰ and also As(OH)₃⁰. The decrease of the diffusion coefficient can be rationalized as an enhancement of the mean viscosity of the confined solution in the membrane. The diffusion coefficients can be described by a semiempirical relationship, linking the mean viscosity of the confined solute of the membrane to the viscosity of the free solution. In proton-saturated membranes, as used in fuel cells, viscosity is relatively more enhanced; i.e., a stronger water network is formed. Extraordinarily, our B(OH)₃-calibrated model (in HNO₃) correctly predicts the reported diffusion coefficient of water (D(H₂O)), measured with ¹H NMR and quasi-elastic neutron scattering in H(+)-Nafion membranes. Upon drying these membranes, the local hydronium, H(H₂O)(n)(+), concentration and corresponding viscosity increase, resulting in a severe reduction of the diffusion coefficient (D(H₂O) ≈ 5-50 times), in agreement with the model. The present study has a second goal, i.e., development of the methodology for measuring the free concentration of neutral species in solution. Our data suggest that the free concentration can be measured with DMT in natural systems if one accounts for the variation in the cation composition of the membrane and corresponding viscosity/diffusion coefficient.

Anomalous Change of Hall Coefficient in Overdoped La2-xSrxCu1-yZnyO4 around x = 0.2

NASA Astrophysics Data System (ADS)

Tonishi, Jun; Suzuki, Takao; Goto, Takayuki

2006-09-01

The Hall coefficient (RH) has been measured in 0.5% Zn-doped La2-xSrxCu0.995Zn0.005O4 under high magnetic fields up to 12 T. With decreasing temperature, RH increases and begins to decrease below a temperature TRH. This characteristic temperature TRH has the local maximum around x = 0.195, and this Sr-concentration coincides with that the superconducting transition temperature is slightly suppressed. This behavior is quite similar to the phenomena observed in the stripe phase in x ˜ 0.12. These results suggest that the anomalous decrease of RH around x = 0.195 observed in this study is responsible for the "1/4"-anomaly [as reported by Kakinuma et al., Phys. Rev. B 59, 1491 (1999).].

Kinetic modeling of ultrasound-assisted extraction of phenolic compounds from grape marc: influence of acoustic energy density and temperature.

PubMed

Tao, Yang; Zhang, Zhihang; Sun, Da-Wen

2014-07-01

The effects of acoustic energy density (6.8-47.4 W/L) and temperature (20-50 °C) on the extraction yields of total phenolics and tartaric esters during ultrasound-assisted extraction from grape marc were investigated in this study. The ultrasound treatment was performed in a 25-kHz ultrasound bath system and the 50% aqueous ethanol was used as the solvent. The initial extraction rate and final extraction yield increased with the increase of acoustic energy density and temperature. The two site kinetic model was used to simulate the kinetics of extraction process and the diffusion model based on the Fick's second law was employed to determine the effective diffusion coefficient of phenolics in grape marc. Both models gave satisfactory quality of data fit. The diffusion process was divided into one fast stage and one slow stage and the diffusion coefficients in both stages were calculated. Within the current experimental range, the diffusion coefficients of total phenolics and tartaric esters for both diffusion stages increased with acoustic energy density. Meanwhile, the rise of temperature also resulted in the increase of diffusion coefficients of phenolics except the diffusion coefficient of total phenolics in the fast stage, the value of which being the highest at 40 °C. Moreover, an empirical equation was suggested to correlate the effective diffusion coefficient of phenolics in grape marc with acoustic energy density and temperature. In addition, the performance comparison of ultrasound-assisted extraction and convention methods demonstrates that ultrasound is an effective and promising technology to extract bioactive substances from grape marc. Copyright © 2014 Elsevier B.V. All rights reserved.

Breast Cancer: Diffusion Kurtosis MR Imaging-Diagnostic Accuracy and Correlation with Clinical-Pathologic Factors.

PubMed

Sun, Kun; Chen, Xiaosong; Chai, Weimin; Fei, Xiaochun; Fu, Caixia; Yan, Xu; Zhan, Ying; Chen, Kemin; Shen, Kunwei; Yan, Fuhua

2015-10-01

To assess diagnostic accuracy with diffusion kurtosis imaging (DKI) in patients with breast lesions and to evaluate the potential association between DKI-derived parameters and breast cancer clinical-pathologic factors. Institutional review board approval and written informed consent were obtained. Data from 97 patients (mean age ± standard deviation, 45.7 years ± 13.1; range, 19-70 years) with 98 lesions (57 malignant and 41 benign) who were treated between January 2014 and April 2014 were retrospectively analyzed. DKI (with b values of 0-2800 sec/mm(2)) and conventional diffusion-weighted imaging data were acquired. Kurtosis and diffusion coefficients from DKI and apparent diffusion coefficients from diffusion-weighted imaging were measured by two radiologists. Student t test, Wilcoxon signed-rank test, Jonckheere-Terpstra test, receiver operating characteristic curves, and Spearman correlation were used for statistical analysis. Kurtosis coefficients were significantly higher in the malignant lesions than in the benign lesions (1.05 ± 0.22 vs 0.65 ± 0.11, respectively; P < .0001). Diffusivity and apparent diffusion coefficients in the malignant lesions were significantly lower than those in the benign lesions (1.13 ± 0.27 vs 1.97 ± 0.33 and 1.02 ± 0.18 vs 1.48 ± 0.33, respectively; P < .0001). Significantly higher specificity for differentiation of malignant from benign lesions was shown with the use of kurtosis and diffusivity coefficients than with the use of apparent diffusion coefficients (83% [34 of 41] and 83% [34 of 41] vs 76% [31 of 41], respectively; P < .0001) with equal sensitivity (95% [54 of 57]). In patients with invasive breast cancer, kurtosis was positively correlated with tumor histologic grade (r = 0.75) and expression of the Ki-67 protein (r = 0.55). Diffusivity was negatively correlated with tumor histologic grades (r = -0.44) and Ki-67 expression (r = -0.46). DKI showed higher specificity than did conventional diffusion-weighted imaging for assessment of benign and malignant breast lesions. Patients with grade 3 breast cancer or tumors with high expression of Ki-67 were associated with higher kurtosis and lower diffusivity coefficients; however, this association must be confirmed in prospective studies. (©) RSNA, 2015 Online supplemental material is available for this article.

Research and Development of Methods for Estimating Physicochemical Properties of Organic Compounds of Environmental Concern

DTIC Science & Technology

1979-02-01

coefficient (at equilibrium) when hysteresis is apparent. 6. Coefficient n in Freundlich equation for 1/n soil or sediment adsorption isotherms ýX - KC . 7...Biodegradation Chemical structures cal clasaes (e.g., Diffusion Correlations phenols). General Diffusion coefficients Equations terms for organic...OF THE FATE AND TRANSPORT OF ORGANIC CHEMICALS Adsorption coefficients: K, n* from Freundlich equation + Desorption coefficients: K’*, n’* from

Self-diffusion in the non-Newtonian regime of shearing liquid crystal model systems based on the Gay-Berne potential

NASA Astrophysics Data System (ADS)

Sarman, Sten; Wang, Yong-Lei; Laaksonen, Aatto

2016-02-01

The self-diffusion coefficients of nematic phases of various model systems consisting of regular convex calamitic and discotic ellipsoids and non-convex bodies such as bent-core molecules and soft ellipsoid strings have been obtained as functions of the shear rate in a shear flow. Then the self-diffusion coefficient is a second rank tensor with three different diagonal components and two off-diagonal components. These coefficients were found to be determined by a combination of two mechanisms, which previously have been found to govern the self-diffusion of shearing isotropic liquids, namely, (i) shear alignment enhancing the diffusion in the direction parallel to the streamlines and hindering the diffusion in the perpendicular directions and (ii) the distortion of the shell structure in the liquid whereby a molecule more readily can escape from a surrounding shell of nearest neighbors, so that the mobility increases in every direction. Thus, the diffusion parallel to the streamlines always increases with the shear rate since these mechanisms cooperate in this direction. In the perpendicular directions, these mechanisms counteract each other so that the behaviour becomes less regular. In the case of the nematic phases of the calamitic and discotic ellipsoids and of the bent core molecules, mechanism (ii) prevails so that the diffusion coefficients increase. However, the diffusion coefficients of the soft ellipsoid strings decrease in the direction of the velocity gradient because the broadsides of these molecules are oriented perpendicularly to this direction due the shear alignment (i). The cross coupling coefficient relating a gradient of tracer particles in the direction of the velocity gradient and their flow in the direction of the streamlines is negative and rather large, whereas the other coupling coefficient relating a gradient in the direction of the streamlines and a flow in the direction of the velocity gradient is very small.

Polarizabilities and van der Waals C{sub 6} coefficients of fullerenes from an atomistic electrodynamics model: Anomalous scaling with number of carbon atoms

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

Saidi, Wissam A., E-mail: alsaidi@pitt.edu; Norman, Patrick

2016-07-14

The van der Waals C{sub 6} coefficients of fullerenes are shown to exhibit an anomalous dependence on the number of carbon atoms N such that C{sub 6} ∝ N{sup 2.2} as predicted using state-of-the-art quantum mechanical calculations based on fullerenes with small sizes, and N{sup 2.75} as predicted using a classical-metallic spherical-shell approximation of the fullerenes. We use an atomistic electrodynamics model where each carbon atom is described by a polarizable object to extend the quantum mechanical calculations to larger fullerenes. The parameters of this model are optimized to describe accurately the static and complex polarizabilities of the fullerenes bymore » fitting against accurate ab initio calculations. This model shows that C{sub 6} ∝ N{sup 2.8}, which is supportive of the classical-metallic spherical-shell approximation. Additionally, we show that the anomalous dependence of the polarizability on N is attributed to the electric charge term, while the dipole–dipole term scales almost linearly with the number of carbon atoms.« less

Correlation properties of interstellar dust: Diffuse interstellar bands

NASA Technical Reports Server (NTRS)

Somerville, W. B.

1989-01-01

Results are presented from a research program in which an attempt was made to establish the physical nature of the interstellar grains, and the carriers of the diffuse interstellar bands, by comparing relations between different observed properties; the properties used include the extinction in the optical and ultraviolet (including wavelength 2200 and the far-UV rise), cloud density, atomic depletions, and strengths of the diffuse bands. Observations and also data from literature were used, selecting particularly sight-lines where some observed property was found to have anomalous behavior.

Lack of anomalous diffusion in linear translationally-invariant systems determined by only one initial condition

NASA Astrophysics Data System (ADS)

Khorrami, Mohammad; Shariati, Ahmad; Aghamohammadi, Amir; Fatollahi, Amir H.

2012-01-01

It is shown that as far as the linear diffusion equation meets both time- and space-translational invariance, the time dependence of a moment of degree α is a polynomial of degree at most equal to α, while all connected moments are at most linear functions of time. As a special case, the variance is an at most linear function of time.

Experimental Determination of Impurity and Interdiffusion Coefficients in Seven Ti and Zr Binary Systems Using Diffusion Multiples

NASA Astrophysics Data System (ADS)

Chen, Zhangqi; Liu, Zi-Kui; Zhao, Ji-Cheng

2018-05-01

Diffusion coefficients of seven binary systems (Ti-Mo, Ti-Nb, Ti-Ta, Ti-Zr, Zr-Mo, Zr-Nb, and Zr-Ta) at 1200 °C, 1000 °C, and 800 °C were experimentally determined using three Ti-Mo-Nb-Ta-Zr diffusion multiples. Electron probe microanalysis (EPMA) was performed to collect concentration profiles at the binary diffusion regions. Forward simulation analysis (FSA) was then applied to extract both impurity and interdiffusion coefficients in Ti-rich and Zr-rich part of the bcc phase. Excellent agreements between our results and most of the literature data validate the high-throughput approach combining FSA with diffusion multiples to obtain a large amount of systematic diffusion data, which will help establish the diffusion (mobility) databases for the design and development of biomedical and structural Ti alloys.

Diffusion modulation of DNA by toehold exchange

NASA Astrophysics Data System (ADS)

Rodjanapanyakul, Thanapop; Takabatake, Fumi; Abe, Keita; Kawamata, Ibuki; Nomura, Shinichiro M.; Murata, Satoshi

2018-05-01

We propose a method to control the diffusion speed of DNA molecules with a target sequence in a polymer solution. The interaction between solute DNA and diffusion-suppressing DNA that has been anchored to a polymer matrix is modulated by the concentration of the third DNA molecule called the competitor by a mechanism called toehold exchange. Experimental results show that the sequence-specific modulation of the diffusion coefficient is successfully achieved. The diffusion coefficient can be modulated up to sixfold by changing the concentration of the competitor. The specificity of the modulation is also verified under the coexistence of a set of DNA with noninteracting base sequences. With this mechanism, we are able to control the diffusion coefficient of individual DNA species by the concentration of another DNA species. This methodology introduces a programmability to a DNA-based reaction-diffusion system.

Experimental Determination of Impurity and Interdiffusion Coefficients in Seven Ti and Zr Binary Systems Using Diffusion Multiples

NASA Astrophysics Data System (ADS)

Chen, Zhangqi; Liu, Zi-Kui; Zhao, Ji-Cheng

2018-07-01

Diffusion coefficients of seven binary systems (Ti-Mo, Ti-Nb, Ti-Ta, Ti-Zr, Zr-Mo, Zr-Nb, and Zr-Ta) at 1200 °C, 1000 °C, and 800 °C were experimentally determined using three Ti-Mo-Nb-Ta-Zr diffusion multiples. Electron probe microanalysis (EPMA) was performed to collect concentration profiles at the binary diffusion regions. Forward simulation analysis (FSA) was then applied to extract both impurity and interdiffusion coefficients in Ti-rich and Zr-rich part of the bcc phase. Excellent agreements between our results and most of the literature data validate the high-throughput approach combining FSA with diffusion multiples to obtain a large amount of systematic diffusion data, which will help establish the diffusion (mobility) databases for the design and development of biomedical and structural Ti alloys.

Stefan-Maxwell Relations and Heat Flux with Anisotropic Transport Coefficients for Ionized Gases in a Magnetic Field with Application to the Problem of Ambipolar Diffusion

NASA Astrophysics Data System (ADS)

Kolesnichenko, A. V.; Marov, M. Ya.

2018-01-01

The defining relations for the thermodynamic diffusion and heat fluxes in a multicomponent, partially ionized gas mixture in an external electromagnetic field have been obtained by the methods of the kinetic theory. Generalized Stefan-Maxwell relations and algebraic equations for anisotropic transport coefficients (the multicomponent diffusion, thermal diffusion, electric and thermoelectric conductivity coefficients as well as the thermal diffusion ratios) associated with diffusion-thermal processes have been derived. The defining second-order equations are derived by the Chapman-Enskog procedure using Sonine polynomial expansions. The modified Stefan-Maxwell relations are used for the description of ambipolar diffusion in the Earth's ionospheric plasma (in the F region) composed of electrons, ions of many species, and neutral particles in a strong electromagnetic field.

Determination of diffusion coefficients of hydrogen and deuterium in Zr-2.5%Nb pressure tube material using hot vacuum extraction-quadrupole mass spectrometry

NASA Astrophysics Data System (ADS)

Shrivastava, Komal Chandra; Kulkarni, A. S.; Ramanjaneyulu, P. S.; Sunil, Saurav; Saxena, M. K.; Singh, R. N.; Tomar, B. S.; Ramakumar, K. L.

2015-06-01

The diffusion coefficients of hydrogen and deuterium in Zr-2.5%Nb alloy were measured in the temperature range 523 to 673 K, employing hot vacuum extraction-quadrupole mass spectrometry (HVE-QMS). One end of the Zr-2.5%Nb alloy specimens was charged electrolytically with the desired hydrogen isotope. After annealing at different temperatures for a predetermined time, the specimens were cut into thin slices, which were analyzed for their H2/D2 content using the HVE-QMS technique. The depth profile data were fitted into the equation representing the solution of Fick's second law of diffusion. The activation energy of hydrogen/deuterium diffusion was obtained from the Arrhenius relation between the diffusion coefficient and temperature. The temperature dependent diffusion coefficient can be represented as DH = 1.41 × 10-7 exp(-36,000/RT) and DD = 6.16 × 10-8 exp(-35,262/RT) for hydrogen and deuterium, respectively.

Dynamics of the DNA repair proteins WRN and BLM in the nucleoplasm and nucleoli.

PubMed

Bendtsen, Kristian Moss; Jensen, Martin Borch; May, Alfred; Rasmussen, Lene Juel; Trusina, Ala; Bohr, Vilhelm A; Jensen, Mogens H

2014-11-01

We have investigated the mobility of two EGFP-tagged DNA repair proteins, WRN and BLM. In particular, we focused on the dynamics in two locations, the nucleoli and the nucleoplasm. We found that both WRN and BLM use a "DNA-scanning" mechanism, with rapid binding-unbinding to DNA resulting in effective diffusion. In the nucleoplasm WRN and BLM have effective diffusion coefficients of 1.62 and 1.34 μm(2)/s, respectively. Likewise, the dynamics in the nucleoli are also best described by effective diffusion, but with diffusion coefficients a factor of ten lower than in the nucleoplasm. From this large reduction in diffusion coefficient we were able to classify WRN and BLM as DNA damage scanners. In addition to WRN and BLM we also classified other DNA damage proteins and found they all fall into one of two categories. Either they are scanners, similar to WRN and BLM, with very low diffusion coefficients, suggesting a scanning mechanism, or they are almost freely diffusing, suggesting that they interact with DNA only after initiation of a DNA damage response.

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.

New method and installation for rapid determination of radon diffusion coefficient in various materials.

PubMed

Tsapalov, Andrey; Gulabyants, Loren; Livshits, Mihail; Kovler, Konstantin

2014-04-01

The mathematical apparatus and the experimental installation for the rapid determination of radon diffusion coefficient in various materials are developed. The single test lasts not longer than 18 h and allows testing numerous materials, such as gaseous and liquid media, as well as soil, concrete and radon-proof membranes, in which diffusion coefficient of radon may vary in an extremely wide range, from 1·10(-12) to 5·10(-5) m(2)/s. The uncertainty of radon diffusion coefficient estimation depends on the permeability of the sample and varies from about 5% (for the most permeable materials) to 40% (for less permeable materials, such as radon-proof membranes). Copyright © 2014. Published by Elsevier Ltd.

Prediction and validation of diffusion coefficients in a model drug delivery system using microsecond atomistic molecular dynamics simulation and vapour sorption analysis.

PubMed

Forrey, Christopher; Saylor, David M; Silverstein, Joshua S; Douglas, Jack F; Davis, Eric M; Elabd, Yossef A

2014-10-14

Diffusion of small to medium sized molecules in polymeric medical device materials underlies a broad range of public health concerns related to unintended leaching from or uptake into implantable medical devices. However, obtaining accurate diffusion coefficients for such systems at physiological temperature represents a formidable challenge, both experimentally and computationally. While molecular dynamics simulation has been used to accurately predict the diffusion coefficients, D, of a handful of gases in various polymers, this success has not been extended to molecules larger than gases, e.g., condensable vapours, liquids, and drugs. We present atomistic molecular dynamics simulation predictions of diffusion in a model drug eluting system that represent a dramatic improvement in accuracy compared to previous simulation predictions for comparable systems. We find that, for simulations of insufficient duration, sub-diffusive dynamics can lead to dramatic over-prediction of D. We present useful metrics for monitoring the extent of sub-diffusive dynamics and explore how these metrics correlate to error in D. We also identify a relationship between diffusion and fast dynamics in our system, which may serve as a means to more rapidly predict diffusion in slowly diffusing systems. Our work provides important precedent and essential insights for utilizing atomistic molecular dynamics simulations to predict diffusion coefficients of small to medium sized molecules in condensed soft matter systems.

Measurement of the Diffusion Coefficient of Water in RP-3 and RP-5 Jet Fuels Using Digital Holography Interferometry

NASA Astrophysics Data System (ADS)

Li, Chaoyue; Feng, Shiyu; Shao, Lei; Pan, Jun; Liu, Weihua

2018-04-01

The diffusion coefficient of water in jet fuel was measured employing double-exposure digital holographic interferometry to clarify the diffusion process and make the aircraft fuel system safe. The experimental method and apparatus are introduced in detail, and the digital image processing program is coded in MATLAB according to the theory of the Fourier transform. At temperatures ranging from 278.15 K to 333.15 K in intervals of 5 K, the diffusion coefficient of water in RP-3 and RP-5 jet fuels ranges from 2.6967 × 10 -10 m2·s-1 to 8.7332 × 10 -10 m2·s-1 and from 2.3517 × 10 -10 m2·s-1 to 8.0099 × 10-10 m2·s-1, respectively. The relationship between the measured diffusion coefficient and temperature can be well fitted by the Arrhenius law. The diffusion coefficient of water in RP-3 jet fuel is higher than that of water in RP-5 jet fuel at the same temperature. Furthermore, the viscosities of the two jet fuels were measured and found to be expressible in the form of the Arrhenius equation. The relationship among the diffusion coefficient, viscosity and temperature is analyzed according to the classic prediction model, namely the Stokes-Einstein correlation, and this correlation is further revised via experimental data to obtain a more accurate predication result.

Effect of the computational domain size and shape on the self-diffusion coefficient in a Lennard-Jones liquid.

PubMed

Kikugawa, Gota; Ando, Shotaro; Suzuki, Jo; Naruke, Yoichi; Nakano, Takeo; Ohara, Taku

2015-01-14

In the present study, molecular dynamics (MD) simulations on the monatomic Lennard-Jones liquid in a periodic boundary system were performed in order to elucidate the effect of the computational domain size and shape on the self-diffusion coefficient measured by the system. So far, the system size dependence in cubic computational domains has been intensively investigated and these studies showed that the diffusion coefficient depends linearly on the inverse of the system size, which is theoretically predicted based on the hydrodynamic interaction. We examined the system size effect not only in the cubic cell systems but also in rectangular cell systems which were created by changing one side length of the cubic cell with the system density kept constant. As a result, the diffusion coefficient in the direction perpendicular to the long side of the rectangular cell significantly increases more or less linearly with the side length. On the other hand, the diffusion coefficient in the direction along the long side is almost constant or slightly decreases. Consequently, anisotropy of the diffusion coefficient emerges in a rectangular cell with periodic boundary conditions even in a bulk liquid simulation. This unexpected result is of critical importance because rectangular fluid systems confined in nanospace, which are present in realistic nanoscale technologies, have been widely studied in recent MD simulations. In order to elucidate the underlying mechanism for this serious system shape effect on the diffusion property, the correlation structures of particle velocities were examined.

Molecular-dynamics simulation of mutual diffusion in nonideal liquid mixtures

NASA Astrophysics Data System (ADS)

Rowley, R. L.; Stoker, J. M.; Giles, N. F.

1991-05-01

The mutual-diffusion coefficients, D 12, of n-hexane, n-heptane, and n-octane in chloroform were modeled using equilibrium molecular-dynamics (MD) simulations of simple Lennard-Jones (LJ) fluids. Pure-component LJ parameters were obtained by comparison of simulations to experimental self-diffusion coefficients. While values of “effective” LJ parameters are not expected to simulate accurately diverse thermophysical properties over a wide range of conditions, it was recently shown that effective parameters obtained from pure self-diffusion coefficients can accurately model mutual diffusion in ideal, liquid mixtures. In this work, similar simulations are used to model diffusion in nonideal mixtures. The same combining rules used in the previous study for the cross-interaction parameters were found to be adequate to represent the composition dependence of D 12. The effect of alkane chain length on D 12 is also correctly predicted by the simulations. A commonly used assumption in empirical correlations of D 12, that its kinetic portion is a simple, compositional average of the intradiffusion coefficients, is inconsistent with the simulation results. In fact, the value of the kinetic portion of D 12 was often outside the range of values bracketed by the two intradiffusion coefficients for the nonideal system modeled here.

Communication: A method to compute the transport coefficient of pure fluids diffusing through planar interfaces from equilibrium molecular dynamics simulations.

PubMed

Vermorel, Romain; Oulebsir, Fouad; Galliero, Guillaume

2017-09-14

The computation of diffusion coefficients in molecular systems ranks among the most useful applications of equilibrium molecular dynamics simulations. However, when dealing with the problem of fluid diffusion through vanishingly thin interfaces, classical techniques are not applicable. This is because the volume of space in which molecules diffuse is ill-defined. In such conditions, non-equilibrium techniques allow for the computation of transport coefficients per unit interface width, but their weak point lies in their inability to isolate the contribution of the different physical mechanisms prone to impact the flux of permeating molecules. In this work, we propose a simple and accurate method to compute the diffusional transport coefficient of a pure fluid through a planar interface from equilibrium molecular dynamics simulations, in the form of a diffusion coefficient per unit interface width. In order to demonstrate its validity and accuracy, we apply our method to the case study of a dilute gas diffusing through a smoothly repulsive single-layer porous solid. We believe this complementary technique can benefit to the interpretation of the results obtained on single-layer membranes by means of complex non-equilibrium methods.

Fluorescence correlation spectroscopy experiments to quantify free diffusion coefficients in reaction-diffusion systems: The case of Ca2 + and its dyes

NASA Astrophysics Data System (ADS)

Sigaut, Lorena; Villarruel, Cecilia; Ponce, María Laura; Ponce Dawson, Silvina

2017-06-01

Many cell signaling pathways involve the diffusion of messengers that bind and unbind to and from intracellular components. Quantifying their net transport rate under different conditions then requires having separate estimates of their free diffusion coefficient and binding or unbinding rates. In this paper, we show how performing sets of fluorescence correlation spectroscopy (FCS) experiments under different conditions, it is possible to quantify free diffusion coefficients and on and off rates of reaction-diffusion systems. We develop the theory and present a practical implementation for the case of the universal second messenger, calcium (Ca2 +) and single-wavelength dyes that increase their fluorescence upon Ca2 + binding. We validate the approach with experiments performed in aqueous solutions containing Ca2 + and Fluo4 dextran (both in its high and low affinity versions). Performing FCS experiments with tetramethylrhodamine-dextran in Xenopus laevis oocytes, we infer the corresponding free diffusion coefficients in the cytosol of these cells. Our approach can be extended to other physiologically relevant reaction-diffusion systems to quantify biophysical parameters that determine the dynamics of various variables of interest.

Weak ergodicity breaking, irreproducibility, and ageing in anomalous diffusion processes

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

Metzler, Ralf

2014-01-14

Single particle traces are standardly evaluated in terms of time averages of the second moment of the position time series r(t). For ergodic processes, one can interpret such results in terms of the known theories for the corresponding ensemble averaged quantities. In anomalous diffusion processes, that are widely observed in nature over many orders of magnitude, the equivalence between (long) time and ensemble averages may be broken (weak ergodicity breaking), and these time averages may no longer be interpreted in terms of ensemble theories. Here we detail some recent results on weakly non-ergodic systems with respect to the time averagedmore » mean squared displacement, the inherent irreproducibility of individual measurements, and methods to determine the exact underlying stochastic process. We also address the phenomenon of ageing, the dependence of physical observables on the time span between initial preparation of the system and the start of the measurement.« less

Transport diffusion in deformed carbon nanotubes

NASA Astrophysics Data System (ADS)

Feng, Jiamei; Chen, Peirong; Zheng, Dongqin; Zhong, Weirong

2018-03-01

Using non-equilibrium molecular dynamics and Monte Carlo methods, we have studied the transport diffusion of gas in deformed carbon nanotubes. Perfect carbon nanotube and various deformed carbon nanotubes are modeled as transport channels. It is found that the transport diffusion coefficient of gas does not change in twisted carbon nanotubes, but changes in XY-distortion, Z-distortion and local defect carbon nanotubes comparing with that of the perfect carbon nanotube. Furthermore, the change of transport diffusion coefficient is found to be associated with the deformation factor. The relationship between transport diffusion coefficient and temperature is also discussed in this paper. Our results may contribute to understanding the mechanism of molecular transport in nano-channel.

The surface diffusion coefficient for an arbitrarily curved fluid-fluid interface. (I). General expression

NASA Astrophysics Data System (ADS)

M. C. Sagis, Leonard

2001-03-01

In this paper, we develop a theory for the calculation of the surface diffusion coefficient for an arbitrarily curved fluid-fluid interface. The theory is valid for systems in hydrodynamic equilibrium, with zero mass-averaged velocities in the bulk and interfacial regions. We restrict our attention to systems with isotropic bulk phases, and an interfacial region that is isotropic in the plane parallel to the dividing surface. The dividing surface is assumed to be a simple interface, without memory effects or yield stresses. We derive an expression for the surface diffusion coefficient in terms of two parameters of the interfacial region: the coefficient for plane-parallel diffusion D (AB)aa(ξ) , and the driving force d(B)I||(ξ) . This driving force is the parallel component of the driving force for diffusion in the interfacial region. We derive an expression for this driving force using the entropy balance.

Correlation Between the Field Line and Particle Diffusion Coefficients in the Stochastic Fields of a Tokamak

NASA Astrophysics Data System (ADS)

Calvin, Mark; Punjabi, Alkesh

1996-11-01

We use the method of quasi-magnetic surfaces to calculate the correlation between the field line and particle diffusion coefficients. The magnetic topology of a tokamak is perturbed by a spectrum of neighboring resonant resistive modes. The Hamiltonian equations of motion for the field line are integrated numerically. Poincare plots of the quasi-magnetic surfaces are generated initially and after the field line has traversed a considerable distance. From the areas of the quasi-magnetic surfaces and the field line distance, we estimate the field line diffusion coefficient. We start plasma particles on the initial quasi-surface, and calculate the particle diffusion coefficient from our Monte Carlo method (Punjabi A., Boozer A., Lam M., Kim H. and Burke K., J. Plasma Phys.), 44, 405 (1990). We then estimate the correlation between the particle and field diffusion as the strength of the resistive modes is varied.

Anomalous transport in the H-mode pedestal of Alcator C-Mod discharges

NASA Astrophysics Data System (ADS)

Pankin, A. Y.; Hughes, J. W.; Greenwald, M. J.; Kritz, A. H.; Rafiq, T.

2017-02-01

Anomalous transport in the H-mode pedestal region of five Alcator C-Mod discharges, representing a collisionality scan is analyzed. The understanding of anomalous transport in the pedestal region is important for the development of a comprehensive model for the H-mode pedestal slope. In this research, a possible role of the drift resistive inertial ballooning modes (Rafiq et al 2010 Phys. Plasmas 17 082511) in the edge of Alcator C-Mod discharges is analyzed. The stability analysis, carried out using the TRANSP code, indicates that the DRIBM modes are strongly unstable in Alcator C-Mod discharges with large electron collisionality. An improved interpretive analysis of H-mode pedestal experimental data is carried out utilizing the additive flux minimization technique (Pankin et al 2013 Phys. Plasmas 20 102501) together with the guiding-center neoclassical kinetic XGC0 code. The neoclassical and neutral physics are simulated in the XGC0 code and the anomalous fluxes are computed using the additive flux minimization technique. The anomalous fluxes are reconstructed and compared with each other for the collisionality scan Alcator C-Mod discharges. It is found that the electron thermal anomalous diffusivities at the pedestal top increase with the electron collisionality. This dependence can also point to the drift resistive inertial ballooning modes as the modes that drive the anomalous transport in the plasma edge of highly collisional discharges.

Computation of thermodynamic and transport properties to predict thermophoretic effects in an argon-krypton mixture

NASA Astrophysics Data System (ADS)

Miller, Nicholas A. T.; Daivis, Peter J.; Snook, Ian K.; Todd, B. D.

2013-10-01

Thermophoresis is the movement of molecules caused by a temperature gradient. Here we report the results of a study of thermophoresis using non-equilibrium molecular dynamics simulations of a confined argon-krypton fluid subject to two different temperatures at thermostated walls. The resulting temperature profile between the walls is used along with the Soret coefficient to predict the concentration profile that develops across the channel. We obtain the Soret coefficient by calculating the mutual diffusion and thermal diffusion coefficients. We report an appropriate method for calculating the transport coefficients for binary systems, using the Green-Kubo integrals and radial distribution functions obtained from equilibrium molecular dynamics simulations of the bulk fluid. Our method has the unique advantage of separating the mutual diffusion and thermal diffusion coefficients, and calculating the sign and magnitude of their individual contributions to thermophoresis in binary mixtures.

Fractional Brownian motors and stochastic resonance

NASA Astrophysics Data System (ADS)

Goychuk, Igor; Kharchenko, Vasyl

2012-05-01

We study fluctuating tilt Brownian ratchets based on fractional subdiffusion in sticky viscoelastic media characterized by a power law memory kernel. Unlike the normal diffusion case, the rectification effect vanishes in the adiabatically slow modulation limit and optimizes in a driving frequency range. It is shown also that the anomalous rectification effect is maximal (stochastic resonance effect) at optimal temperature and can be of surprisingly good quality. Moreover, subdiffusive current can flow in the counterintuitive direction upon a change of temperature or driving frequency. The dependence of anomalous transport on load exhibits a remarkably simple universality.

Molecular Diffusion Coefficients: Experimental Determination and Demonstration.

ERIC Educational Resources Information Center

Fate, Gwendolyn; Lynn, David G.

1990-01-01

Presented are laboratory methods which allow the demonstration and determination of the diffusion coefficients of compounds ranging in size from water to small proteins. Included are the procedures involving the use of a spectrometer, UV cell, triterated agar, and oxygen diffusion. Results including quantification are described. (CW)

pH responsive cross-linked polymeric matrices based on natural polymers: effect of process variables on swelling characterization and drug delivery properties.

PubMed

Naeem, Fahad; Khan, Samiullah; Jalil, Aamir; Ranjha, Nazar Muhammad; Riaz, Amina; Haider, Malik Salman; Sarwar, Shoaib; Saher, Fareha; Afzal, Samrin

2017-01-01

Introduction: The current work was aimed to design and synthesize novel crosslinked pH-sensitive gelatin/pectin (Ge/Pec) hydrogels using different polymeric ratios and to explore the effect of polymers and degree of crosslinking on dynamic, equilibrium swelling and in vitro release behavior of the model drug (Mannitol). Methods: The Ge/Pec based hydrogels were prepared using glutaraldehyde as the crosslinker. Various structural parameters that affect their release behavior were determined, including swelling study, porosity, sol-gel analysis, average molecular weight between crosslinks (Mc), volume fraction of polymer (V2,s), solvent interaction parameter (χ) and diffusion coefficient. The synthesized hydrogels were subjected to various characterization tools like Fourier transform infrared spectroscopy (FTIR), X-ray diffraction (XRD) and DSC differential scanning calorimetry (DSC) and scanning electron microscopy (SEM). Results: The hydrogels show highest water uptake and release at lower pH values. The FTIR spectra showed an interaction between Ge and Pec, and the drug-loaded samples also showed the drug-related peaks, indicating proper loading of the drug. DSC and TGA studies confirmed the thermal stability of hydrogel samples, while SEM showed the porous nature of hydrogels. The drug release followed non-Fickian diffusion or anomalous mechanism. Conclusion: Aforementioned characterizations reveal the successful formation of copolymer hydrogels. The pH-sensitive swelling ability and drug release behavior suggest that the rate of polymer chain relaxation and drug diffusion from these hydrogels are comparable which also predicts their possible use for site-specific drug delivery.

pH responsive cross-linked polymeric matrices based on natural polymers: effect of process variables on swelling characterization and drug delivery properties

PubMed Central

Naeem, Fahad; Khan, Samiullah; Jalil, Aamir; Ranjha, Nazar Muhammad; Riaz, Amina; Haider, Malik Salman; Sarwar, Shoaib; Saher, Fareha; Afzal, Samrin

2017-01-01

Introduction: The current work was aimed to design and synthesize novel crosslinked pH-sensitive gelatin/pectin (Ge/Pec) hydrogels using different polymeric ratios and to explore the effect of polymers and degree of crosslinking on dynamic, equilibrium swelling and in vitro release behavior of the model drug (Mannitol). Methods: The Ge/Pec based hydrogels were prepared using glutaraldehyde as the crosslinker. Various structural parameters that affect their release behavior were determined, including swelling study, porosity, sol-gel analysis, average molecular weight between crosslinks (Mc), volume fraction of polymer (V2,s), solvent interaction parameter (χ) and diffusion coefficient. The synthesized hydrogels were subjected to various characterization tools like Fourier transform infrared spectroscopy (FTIR), X-ray diffraction (XRD) and DSC differential scanning calorimetry (DSC) and scanning electron microscopy (SEM). Results:The hydrogels show highest water uptake and release at lower pH values. The FTIR spectra showed an interaction between Ge and Pec, and the drug-loaded samples also showed the drug-related peaks, indicating proper loading of the drug. DSC and TGA studies confirmed the thermal stability of hydrogel samples, while SEM showed the porous nature of hydrogels. The drug release followed non-Fickian diffusion or anomalous mechanism. Conclusion: Aforementioned characterizations reveal the successful formation of copolymer hydrogels. The pH-sensitive swelling ability and drug release behavior suggest that the rate of polymer chain relaxation and drug diffusion from these hydrogels are comparable which also predicts their possible use for site-specific drug delivery. PMID:29159145

Nucleation-controlled microstructures and anomalous eutectic formation in undercooled Co-Sn and Ni-Si eutectic melts

NASA Astrophysics Data System (ADS)

Li, Mingjun; Kuribayashi, Kazuhiko

2003-12-01

Co-20.5 at. pct Sn and Ni-21.4 at. pct Si eutectic alloys have been levitated and undercooled in an electromagnetic levitator (EML) and then solidified spontaneously at different undercoolings. The original surface and cross-sectional morphologies of these solidified samples consist of separate eutectic colonies regardless of melt undercooling, indicating that microstructures in the free solidification of the eutectic systems are nucleation controlled. Regular lamellae always grow from the periphery of an independent anomalous eutectic grain in each eutectic colony. This typical morphology shows that the basic unit should be a single eutectic colony, when discussing the solidification behavior. Special emphasis is focused on the anomalous eutectic formation after a significant difference in linear kinetic coefficients is recognized for terminal eutectic phases, in particular when a eutectic reaction contains a nonfaceted disordered solid solution and a faceted ordered intermetallic compound as the terminal eutectic phases. It is this remarkable difference in the linear kinetic coefficients that leads to a pronounced difference in kinetic undercoolings. The sluggish kinetics in the interface atomic attachment of the intermetallic compound originates the occurrence of the decoupled growth of two eutectic phases. Hence, the current eutectic models are modified to incorporate kinetic undercooling, in order to account for the competitive growth behavior of eutectic phases in a single eutectic colony. The critical condition for generating the decoupled growth of eutectic phases is proposed. Further analysis reveals that a dimensionless critical undercooling may be appropriate to show the tendency for the anomalous eutectic-forming ability when considering the difference in linear kinetic coefficients of terminal eutectic phases. This qualitative criterion, albeit crude with several approximations and assumptions, can elucidate most of the published experimental results with the correct order of magnitude. Solidification modes in some eutectic alloys are predicted on the basis of the present criterion. Future work that may result in some probable errors is briefly directed to improve the model.

Including scattering within the room acoustics diffusion model: An analytical approach.

PubMed

Foy, Cédric; Picaut, Judicaël; Valeau, Vincent

2016-10-01

Over the last 20 years, a statistical acoustic model has been developed to predict the reverberant sound field in buildings. This model is based on the assumption that the propagation of the reverberant sound field follows a transport process and, as an approximation, a diffusion process that can be easily solved numerically. This model, initially designed and validated for rooms with purely diffuse reflections, is extended in the present study to mixed reflections, with a proportion of specular and diffuse reflections defined by a scattering coefficient. The proposed mathematical developments lead to an analytical expression of the diffusion constant that is a function of the scattering coefficient, but also on the absorption coefficient of the walls. The results obtained with this extended diffusion model are then compared with the classical diffusion model, as well as with a sound particles tracing approach considering mixed wall reflections. The comparison shows a good agreement for long rooms with uniform low absorption (α = 0.01) and uniform scattering. For a larger absorption (α = 0.1), the agreement is moderate, due to the fact that the proposed expression of the diffusion coefficient does not vary spatially. In addition, the proposed model is for now limited to uniform diffusion and should be extended in the future to more general cases.

A quantitative property-property relationship for the internal diffusion coefficients of organic compounds in solid materials.

PubMed

Huang, L; Fantke, P; Ernstoff, A; Jolliet, O

2017-11-01

Indoor releases of organic chemicals encapsulated in solid materials are major contributors to human exposures and are directly related to the internal diffusion coefficient in solid materials. Existing correlations to estimate the diffusion coefficient are only valid for a limited number of chemical-material combinations. This paper develops and evaluates a quantitative property-property relationship (QPPR) to predict diffusion coefficients for a wide range of organic chemicals and materials. We first compiled a training dataset of 1103 measured diffusion coefficients for 158 chemicals in 32 consolidated material types. Following a detailed analysis of the temperature influence, we developed a multiple linear regression model to predict diffusion coefficients as a function of chemical molecular weight (MW), temperature, and material type (adjusted R 2 of .93). The internal validations showed the model to be robust, stable and not a result of chance correlation. The external validation against two separate prediction datasets demonstrated the model has good predicting ability within its applicability domain (Rext2>.8), namely MW between 30 and 1178 g/mol and temperature between 4 and 180°C. By covering a much wider range of organic chemicals and materials, this QPPR facilitates high-throughput estimates of human exposures for chemicals encapsulated in solid materials. © 2017 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd.

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.

Computer Aided Design of Integrated Circuit Fabrication Processes for VLSI Devices

DTIC Science & Technology

1980-01-01

diffusion coefficient and surface conc,,tration of the chlorine as well as any field present; X is related to the ratio ol the diffusion coefficient to...with polysilicon gat(. .ed contacts, the interaction of oxidation, segregation and diffusion in all regions of the simulation space is a critical

Microscopic Interpretation and Generalization of the Bloch-Torrey Equation for Diffusion Magnetic Resonance

PubMed Central

Seroussi, Inbar; Grebenkov, Denis S.; Pasternak, Ofer; Sochen, Nir

2017-01-01

In order to bridge microscopic molecular motion with macroscopic diffusion MR signal in complex structures, we propose a general stochastic model for molecular motion in a magnetic field. The Fokker-Planck equation of this model governs the probability density function describing the diffusion-magnetization propagator. From the propagator we derive a generalized version of the Bloch-Torrey equation and the relation to the random phase approach. This derivation does not require assumptions such as a spatially constant diffusion coefficient, or ad-hoc selection of a propagator. In particular, the boundary conditions that implicitly incorporate the microstructure into the diffusion MR signal can now be included explicitly through a spatially varying diffusion coefficient. While our generalization is reduced to the conventional Bloch-Torrey equation for piecewise constant diffusion coefficients, it also predicts scenarios in which an additional term to the equation is required to fully describe the MR signal. PMID:28242566

Secondary Ion Mass Spectrometry for Mg Tracer Diffusion: Issues and Solutions

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

Tuggle, Jay; Giordani, Andrew; Kulkarni, Nagraj S

2014-01-01

A Secondary Ion Mass Spectrometry (SIMS) method has been developed to measure stable Mg isotope tracer diffusion. This SIMS method was then used to calculate Mg self- diffusivities and the data was verified against historical data measured using radio tracers. The SIMS method has been validated as a reliable alternative to the radio-tracer technique for the measurement of Mg self-diffusion coefficients and can be used as a routine method for determining diffusion coefficients.

Diffuse reflectance relations based on diffusion dipole theory for large absorption and reduced scattering

NASA Astrophysics Data System (ADS)

Bremmer, Rolf H.; van Gemert, Martin J. C.; Faber, Dirk J.; van Leeuwen, Ton G.; Aalders, Maurice C. G.

2013-08-01

Diffuse reflectance spectra are used to determine the optical properties of biological samples. In medicine and forensic science, the turbid objects under study often possess large absorption and/or scattering properties. However, data analysis is frequently based on the diffusion approximation to the radiative transfer equation, implying that it is limited to tissues where the reduced scattering coefficient dominates over the absorption coefficient. Nevertheless, up to absorption coefficients of 20 m at reduced scattering coefficients of 1 and 11.5 mm-1, we observed excellent agreement (r2=0.994) between reflectance measurements of phantoms and the diffuse reflectance equation proposed by Zonios et al. [Appl. Opt. 38, 6628-6637 (1999)], derived as an approximation to one of the diffusion dipole equations of Farrell et al. [Med. Phys. 19, 879-888 (1992)]. However, two parameters were fitted to all phantom experiments, including strongly absorbing samples, implying that the reflectance equation differs from diffusion theory. Yet, the exact diffusion dipole approximation at high reduced scattering and absorption also showed agreement with the phantom measurements. The mathematical structure of the diffuse reflectance relation used, derived by Zonios et al. [Appl. Opt. 38, 6628-6637 (1999)], explains this observation. In conclusion, diffuse reflectance relations derived as an approximation to the diffusion dipole theory of Farrell et al. can analyze reflectance ratios accurately, even for much larger absorption than reduced scattering coefficients. This allows calibration of fiber-probe set-ups so that the object's diffuse reflectance can be related to its absorption even when large. These findings will greatly expand the application of diffuse reflection spectroscopy. In medicine, it may allow the use of blue/green wavelengths and measurements on whole blood, and in forensic science, it may allow inclusion of objects such as blood stains and cloth at crime scenes.

Nonlinear simulations of peeling-ballooning modes with anomalous electron viscosity and their role in edge localized mode crashes

DOE PAGES

Xu, X. Q.; Dudson, B.; Snyder, P. B.; ...

2010-10-22

A minimum set of equations based on the peeling-ballooning (P-B) model with nonideal physics effects (diamagnetic drift, E×B drift, resistivity, and anomalous electron viscosity) is found to simulate pedestal collapse when using the new BOUT++ simulation code, developed in part from the original fluid edge code BOUT. Nonlinear simulations of P-B modes demonstrate that the P-B modes trigger magnetic reconnection, which leads to the pedestal collapse. With the addition of a model of the anomalous electron viscosity under the assumption that the electron viscosity is comparable to the anomalous electron thermal diffusivity, it is found from simulations using a realisticmore » high-Lundquist number that the pedestal collapse is limited to the edge region and the edge localized mode (ELM) size is about 5–10% of the pedestal stored energy. Furthermore, this is consistent with many observations of large ELMs.« less

Investigating Whistler Mode Wave Diffusion Coefficients at Mars

NASA Astrophysics Data System (ADS)

Shane, A. D.; Liemohn, M. W.; Xu, S.; Florie, C.

2017-12-01

Observations of electron pitch angle distributions have suggested collisions are not the only pitch angle scattering process occurring in the Martian ionosphere. This unknown scattering process is causing high energy electrons (>100 eV) to become isotropized. Whistler mode waves are one pitch angle scattering mechanism known to preferentially scatter high energy electrons in certain plasma regimes. The distribution of whistler mode wave diffusion coefficients are dependent on the background magnetic field strength and thermal electron density, as well as the frequency and wave normal angle of the wave. We have solved for the whistler mode wave diffusion coefficients using the quasi-linear diffusion equations and have integrated them into a superthermal electron transport (STET) model. Preliminary runs have produced results that qualitatively match the observed electron pitch angle distributions at Mars. We performed parametric sweeps over magnetic field, thermal electron density, wave frequency, and wave normal angle to understand the relationship between the plasma parameters and the diffusion coefficient distributions, but also to investigate what regimes whistler mode waves scatter only high energy electrons. Increasing the magnetic field strength and lowering the thermal electron density shifts the distribution of diffusion coefficients toward higher energies and lower pitch angles. We have created an algorithm to identify Mars Atmosphere Volatile and EvolutioN (MAVEN) observations of high energy isotropic pitch angle distributions in the Martian ionosphere. We are able to map these distributions at Mars, and compare the conditions under which these are observed at Mars with the results of our parametric sweeps. Lastly, we will also look at each term in the kinetic diffusion equation to determine if the energy and mixed diffusion coefficients are important enough to incorporate into STET as well.

Toward Precision and Reproducibility of Diffusion Tensor Imaging: A Multicenter Diffusion Phantom and Traveling Volunteer Study.

PubMed

Palacios, E M; Martin, A J; Boss, M A; Ezekiel, F; Chang, Y S; Yuh, E L; Vassar, M J; Schnyer, D M; MacDonald, C L; Crawford, K L; Irimia, A; Toga, A W; Mukherjee, P

2017-03-01

Precision medicine is an approach to disease diagnosis, treatment, and prevention that relies on quantitative biomarkers that minimize the variability of individual patient measurements. The aim of this study was to assess the intersite variability after harmonization of a high-angular-resolution 3T diffusion tensor imaging protocol across 13 scanners at the 11 academic medical centers participating in the Transforming Research and Clinical Knowledge in Traumatic Brain Injury multisite study. Diffusion MR imaging was acquired from a novel isotropic diffusion phantom developed at the National Institute of Standards and Technology and from the brain of a traveling volunteer on thirteen 3T MR imaging scanners representing 3 major vendors (GE Healthcare, Philips Healthcare, and Siemens). Means of the DTI parameters and their coefficients of variation across scanners were calculated for each DTI metric and white matter tract. For the National Institute of Standards and Technology diffusion phantom, the coefficients of variation of the apparent diffusion coefficient across the 13 scanners was <3.8% for a range of diffusivities from 0.4 to 1.1 × 10 -6 mm 2 /s. For the volunteer, the coefficients of variations across scanners of the 4 primary DTI metrics, each averaged over the entire white matter skeleton, were all <5%. In individual white matter tracts, large central pathways showed good reproducibility with the coefficients of variation consistently below 5%. However, smaller tracts showed more variability, with the coefficients of variation of some DTI metrics reaching 10%. The results suggest the feasibility of standardizing DTI across 3T scanners from different MR imaging vendors in a large-scale neuroimaging research study. © 2017 by American Journal of Neuroradiology.

Modified free volume theory of self-diffusion and molecular theory of shear viscosity of liquid carbon dioxide.

PubMed

Nasrabad, Afshin Eskandari; Laghaei, Rozita; Eu, Byung Chan

2005-04-28

In previous work on the density fluctuation theory of transport coefficients of liquids, it was necessary to use empirical self-diffusion coefficients to calculate the transport coefficients (e.g., shear viscosity of carbon dioxide). In this work, the necessity of empirical input of the self-diffusion coefficients in the calculation of shear viscosity is removed, and the theory is thus made a self-contained molecular theory of transport coefficients of liquids, albeit it contains an empirical parameter in the subcritical regime. The required self-diffusion coefficients of liquid carbon dioxide are calculated by using the modified free volume theory for which the generic van der Waals equation of state and Monte Carlo simulations are combined to accurately compute the mean free volume by means of statistical mechanics. They have been computed as a function of density along four different isotherms and isobars. A Lennard-Jones site-site interaction potential was used to model the molecular carbon dioxide interaction. The density and temperature dependence of the theoretical self-diffusion coefficients are shown to be in excellent agreement with experimental data when the minimum critical free volume is identified with the molecular volume. The self-diffusion coefficients thus computed are then used to compute the density and temperature dependence of the shear viscosity of liquid carbon dioxide by employing the density fluctuation theory formula for shear viscosity as reported in an earlier paper (J. Chem. Phys. 2000, 112, 7118). The theoretical shear viscosity is shown to be robust and yields excellent density and temperature dependence for carbon dioxide. The pair correlation function appearing in the theory has been computed by Monte Carlo simulations.

Molecular dynamics simulation of three plastic additives' diffusion in polyethylene terephthalate.

PubMed

Li, Bo; Wang, Zhi-Wei; Lin, Qin-Bao; Hu, Chang-Ying

2017-06-01

Accurate diffusion coefficient data of additives in a polymer are of paramount importance for estimating the migration of the additives over time. This paper shows how this diffusion coefficient can be estimated for three plastic additives [2-(2'-hydroxy-5'-methylphenyl) (UV-P), 2,6-di-tert-butyl-4-methylphenol (BHT) and di-(2-ethylhexyl) phthalate (DEHP)] in polyethylene terephthalate (PET) using the molecular dynamics (MD) simulation method. MD simulations were performed at temperatures of 293-433 K. The diffusion coefficient was calculated through the Einstein relationship connecting the data of mean-square displacement at different times. Comparison of the diffusion coefficients simulated by the MD simulation technique, predicted by the Piringer model and experiments, showed that, except for a few samples, the MD-simulated values were in agreement with the experimental values within one order of magnitude. Furthermore, the diffusion process for additives is discussed in detail, and four factors - the interaction energy between additive molecules and PET, fractional free volume, molecular shape and size, and self-diffusion of the polymer - are proposed to illustrate the microscopic diffusion mechanism. The movement trajectories of additives in PET cell models suggested that the additive molecules oscillate slowly rather than hopping for a long time. Occasionally, when a sufficiently large hole was created adjacently, the molecule could undergo spatial motion by jumping into the free-volume hole and consequently start a continuous oscillation and hop. The results indicate that MD simulation is a useful approach for predicting the microstructure and diffusion coefficient of plastic additives, and help to estimate the migration level of additives from PET packaging.

Fractal Theory and Field Cover Experiments: Implications for the Fractal Characteristics and Radon Diffusion Behavior of Soils and Rocks.

PubMed

Tan, Wanyu; Li, Yongmei; Tan, Kaixuan; Duan, Xianzhe; Liu, Dong; Liu, Zehua

2016-12-01

Radon diffusion and transport through different media is a complex process affected by many factors. In this study, the fractal theories and field covering experiments were used to study the fractal characteristics of particle size distribution (PSD) of six kinds of geotechnical materials (e.g., waste rock, sand, laterite, kaolin, mixture of sand and laterite, and mixture of waste rock and laterite) and their effects on radon diffusion. In addition, the radon diffusion coefficient and diffusion length were calculated. Moreover, new formulas for estimating diffusion coefficient and diffusion length functional of fractal dimension d of PSD were proposed. These results demonstrate the following points: (1) the fractal dimension d of the PSD can be used to characterize the property of soils and rocks in the studies of radon diffusion behavior; (2) the diffusion coefficient and diffusion length decrease with increasing fractal dimension of PSD; and (3) the effectiveness of final covers in reducing radon exhalation of uranium tailings impoundments can be evaluated on the basis of the fractal dimension of PSD of materials.

Viscosity and thermal conductivity coefficients of gaseous and liquid oxygen

NASA Technical Reports Server (NTRS)

Hanley, H. J. M.; Mccarty, R. D.; Sengers, J. V.

1974-01-01

Equations and tables are presented for the viscosity and thermal conductivity coefficients of gaseous and liquid oxygen at temperatures between 80 K and 400 K for pressures up to 200 atm. and at temperatures between 80 K and 2000 K for the dilute gas. A description of the anomalous behavior of the thermal conductivity in the critical region is included. The tabulated coefficients are reliable to within about 15% except for a region in the immediate vicinity of the critical point. Some possibilities for future improvements of this reliability are discussed.

Measurement of diffusion coefficients of VOCs for building materials: review and development of a calculation procedure.

PubMed

Haghighat, F; Lee, C S; Ghaly, W S

2002-06-01

The measurement and prediction of building material emission rates have been the subject of intensive research over the past decade, resulting in the development of advanced sensory and chemical analysis measurement techniques as well as the development of analytical and numerical models. One of the important input parameters for these models is the diffusion coefficient. Several experimental techniques have been applied to estimate the diffusion coefficient. An extensive literature review of the techniques used to measure this coefficient was carried out, for building materials exposed to volatile organic compounds (VOC). This paper reviews these techniques; it also analyses the results and discusses the possible causes of difference in the reported data. It was noted that the discrepancy between the different results was mainly because of the assumptions made in and the techniques used to analyze the data. For a given technique, the results show that there can be a difference of up to 700% in the reported data. Moreover, the paper proposes what is referred to as the mass exchanger method, to calculate diffusion coefficients considering both diffusion and convection. The results obtained by this mass exchanger method were compared with those obtained by the existing method considering only diffusion. It was demonstrated that, for porous materials, the convection resistance could not be ignored when compared with the diffusion resistance.

Apparent Diffusion Coefficient and Dynamic Contrast-Enhanced Magnetic Resonance Imaging in Pancreatic Cancer: Characteristics and Correlation With Histopathologic Parameters.

PubMed

Ma, Wanling; Li, Na; Zhao, Weiwei; Ren, Jing; Wei, Mengqi; Yang, Yong; Wang, Yingmei; Fu, Xin; Zhang, Zhuoli; Larson, Andrew C; Huan, Yi

2016-01-01

To clarify diffusion and perfusion abnormalities and evaluate correlation between apparent diffusion coefficient (ADC), MR perfusion and histopathologic parameters of pancreatic cancer (PC). Eighteen patients with PC underwent diffusion-weighted imaging and dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI). Parameters of DCE-MRI and ADC of cancer and non-cancerous tissue were compared. Correlation between the rate constant that represents transfer of contrast agent from the arterial blood into the extravascular extracellular space (K, volume of the extravascular extracellular space per unit volume of tissue (Ve), and ADC of PC and histopathologic parameters were analyzed. The rate constant that represents transfer of contrast agent from the extravascular extracellular space into blood plasma, K, tissue volume fraction occupied by vascular space, and ADC of PC were significantly lower than nontumoral pancreases. Ve of PC was significantly higher than that of nontumoral pancreas. Apparent diffusion coefficient and K values of PC were negatively correlated to fibrosis content and fibroblast activation protein staining score. Fibrosis content was positively correlated to Ve. Apparent diffusion coefficient values and parameters of DCE-MRI can differentiate PC from nontumoral pancreases. There are correlations between ADC, K, Ve, and fibrosis content of PC. Fibroblast activation protein staining score of PC is negatively correlated to ADC and K. Apparent diffusion coefficient, K, and Ve may be feasible to predict prognosis of PC.

An improved strip FRAP method for estimating diffusion coefficients: correcting for the degree of photobleaching.

PubMed

Yang, J; Köhler, K; Davis, D M; Burroughs, N J

2010-06-01

Fluorescence recovery after photobleaching is a widely established method for the estimation of diffusion coefficients, strip bleaching with an associated recovery curve analysis being one of the simplest techniques. However, its implementation requires near 100% bleaching in the region of interest with negligible fluorescence loss outside, both constraints being hard to achieve concomitantly for fast diffusing molecules. We demonstrate that when these requirements are not met there is an error in the estimation of the diffusion coefficient D, either an under- or overestimation depending on which assumption is violated the most. We propose a simple modification to the recovery curve analysis incorporating the concept of the relative bleached mass m giving a revised recovery time parametrization tau=m(2)w(2)/4piD for a strip of width w. This modified model removes the requirement of 100% bleaching in the region of interest and allows for limited diffusion of the fluorophore during bleaching. We validate our method by estimating the (volume) diffusion coefficient of FITC-labelled IgG in 60% glycerol solution, D= 4.09 +/- 0.21 microm(2) s(-1), and the (surface) diffusion coefficient of a green-fluorescent protein-tagged class I MHC protein expressed at the surface of a human B cell line, D= 0.32 +/- 0.03 microm(2) s(-1) for a population of cells.

Approximation of effective moisture-diffusion coefficient to characterize performance of a barrier coating

NASA Astrophysics Data System (ADS)

Nagai, Shingo

2013-11-01

We report estimation of the effective diffusion coefficient of moisture through a barrier coating to develop an encapsulation technology for the thin-film electronics industry. This investigation targeted a silicon oxide (SiOx) film that was deposited on a plastic substrate by a large-process-area web coater. Using the finite difference method based on diffusion theory, our estimation of the effective diffusion coefficient of a SiOx film corresponded to that of bulk glass that was previously reported. This result suggested that the low diffusivities of barrier films can be obtained on a mass-production level in the factory. In this investigation, experimental observations and mathematical confirmation revealed the limit of the water vapor transmission rate on the single barrier coating.

Calculation of the fractional interstitial component of boron diffusion and segregation coefficient of boron in Si0.8Ge0.2

NASA Astrophysics Data System (ADS)

Fang, Tilden T.; Fang, Wingra T. C.; Griffin, Peter B.; Plummer, James D.

1996-02-01

Investigation of boron diffusion in strained silicon germanium buried layers reveals a fractional interstitial component of boron diffusion (fBI) in Se0.8Ge0.2 approximately equal to the fBI value in silicon. In conjunction with computer-simulated boron profiles, the results yield an absolute lower-bound of fBI in Si0.8Ge0.2 of ˜0.8. In addition, the experimental methodology provides a unique vehicle for measuring the segregation coefficient; oxidation-enhanced diffusion is used instead of an extended, inert anneal to rapidly diffuse the dopant to equilibrium levels across the interface, allowing the segregation coefficient to be measured more quickly.

Towards a bootstrap approach to higher orders of epsilon expansion

NASA Astrophysics Data System (ADS)

Dey, Parijat; Kaviraj, Apratim

2018-02-01

We employ a hybrid approach in determining the anomalous dimension and OPE coefficient of higher spin operators in the Wilson-Fisher theory. First we do a large spin analysis for CFT data where we use results obtained from the usual and the Mellin bootstrap and also from Feynman diagram literature. This gives new predictions at O( ɛ 4) and O( ɛ 5) for anomalous dimensions and OPE coefficients, and also provides a cross-check for the results from Mellin bootstrap. These higher orders get contributions from all higher spin operators in the crossed channel. We also use the bootstrap in Mellin space method for ϕ 3 in d = 6 - ɛ CFT where we calculate general higher spin OPE data. We demonstrate a higher loop order calculation in this approach by summing over contributions from higher spin operators of the crossed channel in the same spirit as before.

Note on coefficient matrices from stochastic Galerkin methods for random diffusion equations

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

Zhou Tao, E-mail: tzhou@lsec.cc.ac.c; Tang Tao, E-mail: ttang@hkbu.edu.h

2010-11-01

In a recent work by Xiu and Shen [D. Xiu, J. Shen, Efficient stochastic Galerkin methods for random diffusion equations, J. Comput. Phys. 228 (2009) 266-281], the Galerkin methods are used to solve stochastic diffusion equations in random media, where some properties for the coefficient matrix of the resulting system are provided. They also posed an open question on the properties of the coefficient matrix. In this work, we will provide some results related to the open question.

Separation of Electric Fields Into Potential and Inductive Parts, and Implications for Radial Diffusion

NASA Astrophysics Data System (ADS)

Chan, A. A.; Ilie, R.; Elkington, S. R.; Albert, J.; Huie, W.

2017-12-01

It has been traditional to separate radiation belt radial-diffusion coefficients into two contributions: an "electrostatic" diffusion coefficient, which is assumed to be due to a potential (non-inductive) electric field, and an "electromagnetic" diffusion coefficient , which is assumed to be due to the combined effect of an inductive electric field and the corresponding time-dependent magnetic field. One difficulty in implementing this separation when using magnetospheric fields obtained from measurements, or from MHD simulations, is that only the total electric field is given; the separation of the electric field into potential and inductive parts is not readily available. In this work we separate the electric field using a numerical method based on the Helmholtz decomposition of the total motional electric field calculated by the BATS-R-US MHD code. The inner boundary for the electric potential is based on the Ridley Ionospheric Model solution and we assume floating boundary conditions in the solar wind. Using different idealized solar wind drivers, including a solar wind density that is oscillating at a single frequency or with a broad spectrum of frequencies, we calculate potential and inductive electric fields, electric and magnetic power spectral densities, and corresponding radial diffusion coefficients. Simulations driven by idealized solar wind conditions show a clear separation of the potential and inductive contributions to the power spectral densities and diffusion coefficients. Simulations with more realistic solar wind drivers are underway to better assess the use of electrostatic and electromagnetic diffusion coefficients in understanding ULF wave-particle interactions in Earth's radiation belts.

The Effect of a Fluorophore Photo-Physics on the Lipid Vesicle Diffusion Coefficient Studied by Fluorescence Correlation Spectroscopy.

PubMed

Drabik, Dominik; Przybyło, Magda; Sikorski, Aleksander; Langner, Marek

2016-03-01

Fluorescence Correlation Spectroscopy (FCS) is a technique, which allows determination of the diffusion coefficient and concentration of fluorescent objects suspended in the solution. The measured parameter is the fluctuation of the fluorescence signal emitted by diffusing molecules. When 100 nm DOPC vesicles labeled with various fluorescent dyes (Fluorescein-PE, NBD-PE, Atto488 DOPE or βBodipy FL) were measured, different values of diffusion coefficients have been obtained. These diffusion coefficients were different from the expected values measured using the dynamic light scattering method (DLS). The FCS was initially developed for solutions containing small fluorescent molecules therefore the observed inconsistency may result from the nature of vesicle suspension itself. The duration of the fluorescence signal may depend on the following factors: the exposure time of the labeled object to the excitation beam, the photo-physical properties (e.g., stability) of a fluorophore, the theoretical model used for the calculations of the diffusion coefficient and optical properties of the vesicle suspension. The diffusion coefficients determined for differently labeled liposomes show that its dependence on vesicle size and quantity of fluorescent probed used for labeling was significant demonstrating that the fluorescence properties of the fluorophore itself (bleaching and/or blinking) were critical factors for a correct outcome of FCS experiment. The new, based on combined FCS and DLS measurements, method for the determination of the focal volume prove itself to be useful for the evaluation of a fluorescence dye with respect to its applicability for FCS experiment.

Effects of molecular size and structure on self-diffusion coefficient and viscosity for saturated hydrocarbons having six carbon atoms.

PubMed

Iwahashi, Makio; Kasahara, Yasutoshi

2007-01-01

Self-diffusion coefficients and viscosities for the saturated hydrocarbons having six carbon atoms such as hexane, 2-methylpentane (2MP), 3-methylpentane (3MP), 2,2-dimethylbutane (22DMB), 2,3-dimethylbutane (23DMB), methylcyclopentane (McP) and cyclohexane (cH) were measured at various constant temperatures; obtained results were discussed in connection with their molar volumes, molecular structures and thermodynamic properties. The values of self-diffusion coefficients as the microscopic property were inversely proportional to those of viscosities as the macroscopic property. The order of their viscosities was almost same to those of their melting temperatures and enthalpies of fusion, which reflect the attractive interactions among their molecules. On the other hand, the order of the self-diffusion coefficients inversely related to the order of the melting temperatures and the enthalpies of the fusion. Namely, the compound having the larger attractive interaction mostly shows the less mobility in its liquid state, e.g., cyclohexane (cH), having the largest attractive interaction and the smallest molar volume exhibits an extremely large viscosity and small self-diffusion coefficient comparing with other hydrocarbons. However, a significant exception was 22DMB, being most close to a sphere: In spite of the smallest attractive interaction and the largest molar volume of 22DMB in the all samples, it has the thirdly larger viscosity and the thirdly smaller self-diffusion coefficient. Consequently, the dynamical properties such as self-diffusion and viscosity for the saturated hydrocarbons are determined not only by their attractive interactions but also by their molecular structures.

Relativistic collective diffusion in one-dimensional systems

NASA Astrophysics Data System (ADS)

Lin, Gui-Wu; Lam, Yu-Yiu; Zheng, Dong-Qin; Zhong, Wei-Rong

2018-05-01

The relativistic collective diffusion in one-dimensional molecular system is investigated through nonequilibrium molecular dynamics with Monte Carlo methods. We have proposed the relationship among the speed, the temperature, the density distribution and the collective diffusion coefficient of particles in a relativistic moving system. It is found that the relativistic speed of the system has no effect on the temperature, but the collective diffusion coefficient decreases to zero as the velocity of the system approaches to the speed of light. The collective diffusion coefficient is modified as D‧ = D(1 ‑w2 c2 )3 2 for satisfying the relativistic circumstances. The present results may contribute to the understanding of the behavior of the particles transport diffusion in a high speed system, as well as enlighten the study of biological metabolism at relativistic high speed situation.

Transport properties of carbonated silicate melt at high pressure

PubMed Central

Ghosh, Dipta B.; Karki, Bijaya B.

2017-01-01

Carbon dioxide, generally considered as the second most abundant volatile component in silicate magmas, is expected to significantly influence various melt properties. In particular, our knowledge about its dynamical effects is lacking over most of Earth’s mantle pressure regime. Here, we report the first-principles molecular dynamics results on the transport properties of carbonated MgSiO3 liquid under conditions of mantle relevance. They show that dissolved CO2 systematically enhances the diffusion rates of all elements and lowers the melt viscosity on average by factors of 1.5 to 3 over the pressure range considered. It is remarkable that CO2 has very little or no influence on the electrical conductivity of the silicate melt under most conditions. Simulations also predict anomalous dynamical behavior, increasing diffusivity and conductivity and decreasing viscosity with compression in the low-pressure regime. This anomaly and the concomitant increase of pressure and temperature with depth together make these transport coefficients vary modestly over extended portions of the mantle regime. It is possible that the melt electrical conductivity under conditions corresponding to the 410- and 660-km seismic discontinuities is at a detectable level by electromagnetic sounding observation. In addition, the low melt viscosity values of 0.2 to 0.5 Pa⋅s at these depths and near the core-mantle boundary may imply high mobility of possible melts in these regions. PMID:29226244

Coupled low-energy - ring current plasma diffusion in the Jovian magnetosphere

NASA Technical Reports Server (NTRS)

Summers, D.; Siscoe, G. L.

1985-01-01

The outwardly diffusing Iogenic plasma and the simultaneously inwardly diffusing ring current plasma in the Jovian magnetosphere are described using a coupled diffusion model which incorporates the effects of the pressure gradient of the ring current into the cross-L diffusion coefficient. The coupled diffusion coefficient is derived by calculating the total energy available to drive the diffusion process. The condition is imposed that the diffusion coefficient takes on a local minimum value at some point in the region L = 7-8, at which point the gradient of the Io plasma density is specified as ramp value given by Siscoe et al. (1981). The hypothesis that the pressure gradient of the ring current causes the diminution of radial plasma transport is tested, and solution profiles for the Iogenic and ring current plasma densities are obtained which imply that the Io plasma ramp is caused by a high-density, low-energy component of the ring current hitherto unobserved directly.

Self diffusion of alkaline-Earth in Ca-Mg-aluminosilicate melts: Experimental improvements on the determination of the self-diffusion coefficients

NASA Technical Reports Server (NTRS)

Paillat, O.; Wasserburg, G. J.

1993-01-01

Experimental studies of self-diffusion isotopes in silicate melts often have quite large uncertainties when comparing one study to another. We designed an experiment in order to improve the precision of the results by simultaneously studying several elements (Mg, Ca, Sr, Ba) during the same experiment thereby greatly reducing the relative experimental uncertainties. Results show that the uncertainties on the diffusion coefficients can be reduced to 10 percent, allowing a more reliable comparison of differences of self-diffusion coefficients of the elements. This type of experiment permits us to study precisely and simultaneously several elements with no restriction on any element. We also designed an experiment to investigate the possible effects of multicomponent diffusion during Mg self-diffusion experiments by comparing cases where the concentrations of the elements and the isotopic compositions are different. The results suggest that there are differences between the effective means of transport. This approach should allow us to investigate the importance of multicomponent diffusion in silicate melts.

Diffusion Coefficients from Molecular Dynamics Simulations in Binary and Ternary Mixtures

NASA Astrophysics Data System (ADS)

Liu, Xin; Schnell, Sondre K.; Simon, Jean-Marc; Krüger, Peter; Bedeaux, Dick; Kjelstrup, Signe; Bardow, André; Vlugt, Thijs J. H.

2013-07-01

Multicomponent diffusion in liquids is ubiquitous in (bio)chemical processes. It has gained considerable and increasing interest as it is often the rate limiting step in a process. In this paper, we review methods for calculating diffusion coefficients from molecular simulation and predictive engineering models. The main achievements of our research during the past years can be summarized as follows: (1) we introduced a consistent method for computing Fick diffusion coefficients using equilibrium molecular dynamics simulations; (2) we developed a multicomponent Darken equation for the description of the concentration dependence of Maxwell-Stefan diffusivities. In the case of infinite dilution, the multicomponent Darken equation provides an expression for [InlineEquation not available: see fulltext.] which can be used to parametrize the generalized Vignes equation; and (3) a predictive model for self-diffusivities was proposed for the parametrization of the multicomponent Darken equation. This equation accurately describes the concentration dependence of self-diffusivities in weakly associating systems. With these methods, a sound framework for the prediction of mutual diffusion in liquids is achieved.

Computational modeling of diffusion in the cerebellum.

PubMed

Marinov, Toma M; Santamaria, Fidel

2014-01-01

Diffusion is a major transport mechanism in living organisms. In the cerebellum, diffusion is responsible for the propagation of molecular signaling involved in synaptic plasticity and metabolism, both intracellularly and extracellularly. In this chapter, we present an overview of the cerebellar structure and function. We then discuss the types of diffusion processes present in the cerebellum and their biological importance. We particularly emphasize the differences between extracellular and intracellular diffusion and the presence of tortuosity and anomalous diffusion in different parts of the cerebellar cortex. We provide a mathematical introduction to diffusion and a conceptual overview of various computational modeling techniques. We discuss their scope and their limit of application. Although our focus is the cerebellum, we have aimed at presenting the biological and mathematical foundations as general as possible to be applicable to any other area in biology in which diffusion is of importance. © 2014 Elsevier Inc. All rights reserved.

Partitioning and diffusion of PBDEs through an HDPE geomembrane.

PubMed

Rowe, R Kerry; Saheli, Pooneh T; Rutter, Allison

2016-09-01

Polybrominated diphenyl ether (PBDE) has been measured in MSW landfill leachate and its migration through a modern landfill liner has not been investigated previously. To assure environmental protection, it is important to evaluate the efficacy of landfill liners for controlling the release of PBDE to the environment to a negligible level. The partitioning and diffusion of a commercial mixture of PBDEs (DE-71: predominantly containing six congeners) with respect to a high-density polyethylene (HDPE) geomembrane is examined. The results show that the partitioning coefficients of the six congeners in this mixture range from 700,000 to 7,500,000 and the diffusion coefficients range from 1.3 to 6.0×10(-15)m(2)/s depending on the congener. This combination of very high partitioning coefficients and very low diffusion coefficients suggest that a well constructed HDPE geomembrane liner will be an extremely effective barrier for PBDEs with respect to diffusion from a municipal solid waste landfill, as illustrated by an example. The results for pure diffusion scenario showed that the congeners investigated meet the guidelines by at least a factor of three for an effective geomembrane liner where diffusion is the controlling transport mechanism. Copyright © 2016 Elsevier Ltd. All rights reserved.