Turing instability in reaction-diffusion systems with nonlinear diffusion

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

Zemskov, E. P., E-mail: zemskov@ccas.ru

2013-10-15

The Turing instability is studied in two-component reaction-diffusion systems with nonlinear diffusion terms, and the regions in parametric space where Turing patterns can form are determined. The boundaries between super- and subcritical bifurcations are found. Calculations are performed for one-dimensional brusselator and oregonator models.

Investigating axial diffusion in cylindrical pores using confocal single-particle fluorescence correlation spectroscopy.

PubMed

Chen, Fang; Neupane, Bhanu; Li, Peiyuan; Su, Wei; Wang, Gufeng

2016-08-01

We explored the feasibility of using confocal fluorescence correlation spectroscopy to study small nanoparticle diffusion in hundred-nanometer-sized cylindrical pores. By modeling single particle diffusion in tube-like confined three-dimensional space aligned parallel to the confocal optical axis, we showed that two diffusion dynamics can be observed in both original intensity traces and the autocorrelation functions (ACFs): the confined two-dimensional lateral diffusion and the unconfined one-dimensional (1D) axial diffusion. The separation of the axial and confined lateral diffusion dynamics provides an opportunity to study diffusions in different dimensions separately. We further experimentally studied 45 nm carboxylated polystyrene particles diffusing in 300 nm alumina pores. The experimental data showed consistency with the simulation. To extract the accurate axial diffusion coefficient, we found that a 1D diffusion model with a Lorentzian axial collection profile needs to be used to analyze the experimental ACFs. The diffusion of the 45 nm nanoparticles in polyethyleneglycol-passivated 300 nm pores slowed down by a factor of ∼2, which can be satisfactorily explained by hydrodynamic frictions. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Mixing Regimes in a Spatially Confined, Two-Dimensional, Supersonic Shear Layer

DTIC Science & Technology

1992-07-31

MODEL ................................... 3 THE MODEL PROBLEMS .............................................. 6 THE ONE-DIMENSIONAL PROBLEM...the effects of the numerical diffusion on the spectrum. Guirguis et al.ś and Farouk et al."’ have studied spatially evolving mixing layers for equal...approximations. Physical and Numerical Model General Formulation We solve the time-dependent, two-dimensional, compressible, Navier-Stokes equations for a

Measuring and Overcoming Limits of the Saffman-Delbrück Model for Soap Film Viscosities

PubMed Central

Vivek, Skanda; Weeks, Eric R.

2015-01-01

We observe tracer particles diffusing in soap films to measure the two-dimensional (2D) viscous properties of the films. Saffman-Delbrück type models relate the single-particle diffusivity to parameters of the film (such as thickness h) for thin films, but the relation breaks down for thicker films. Notably, the diffusivity is faster than expected for thicker films, with the crossover at h/d = 5.2 ± 0.9 using the tracer particle diameter d. This indicates a crossover from purely 2D diffusion to diffusion that is more three-dimensional. We demonstrate that measuring the correlations of particle pairs as a function of their separation overcomes the limitations of the Saffman-Delbrück model and allows one to measure the viscosity of a soap film for any thickness. PMID:25822262

Measuring and overcoming limits of the Saffman-Delbrück model for soap film viscosities.

PubMed

Vivek, Skanda; Weeks, Eric R

2015-01-01

We observe tracer particles diffusing in soap films to measure the two-dimensional (2D) viscous properties of the films. Saffman-Delbrück type models relate the single-particle diffusivity to parameters of the film (such as thickness h) for thin films, but the relation breaks down for thicker films. Notably, the diffusivity is faster than expected for thicker films, with the crossover at h/d = 5.2 ± 0.9 using the tracer particle diameter d. This indicates a crossover from purely 2D diffusion to diffusion that is more three-dimensional. We demonstrate that measuring the correlations of particle pairs as a function of their separation overcomes the limitations of the Saffman-Delbrück model and allows one to measure the viscosity of a soap film for any thickness.

A one-dimensional diffusion analogy model for estimation of tide heights in selected tidal marshes in Connecticut

USGS Publications Warehouse

Bjerklie, David M.; O’Brien, Kevin; Rozsa, Ron

2013-01-01

A one-dimensional diffusion analogy model for estimating tide heights in coastal marshes was developed and calibrated by using data from previous tidal-marsh studies. The method is simpler to use than other one- and two-dimensional hydrodynamic models because it does not require marsh depth and tidal prism information; however, the one-dimensional diffusion analogy model cannot be used to estimate tide heights, flow velocities, and tide arrival times for tide conditions other than the highest tide for which it is calibrated. Limited validation of the method indicates that it has an accuracy within 0.3 feet. The method can be applied with limited calibration information that is based entirely on remote sensing or geographic information system data layers. The method can be used to estimate high-tide heights in tidal wetlands drained by tide gates where tide levels cannot be observed directly by opening the gates without risk of flooding properties and structures. A geographic information system application of the method is demonstrated for Sybil Creek marsh in Branford, Connecticut. The tidal flux into this marsh is controlled by two tide gates that prevent full tidal inundation of the marsh. The method application shows reasonable tide heights for the gates-closed condition (the normal condition) and the one-gate-open condition on the basis of comparison with observed heights. The condition with all tide gates open (two gates) was simulated with the model; results indicate where several structures would be flooded if the gates were removed as part of restoration efforts or if the tide gates were to fail.

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.

Nonequilibrium Statistical Mechanics in One Dimension

NASA Astrophysics Data System (ADS)

Privman, Vladimir

2005-08-01

Part I. Reaction-Diffusion Systems and Models of Catalysis; 1. Scaling theories of diffusion-controlled and ballistically-controlled bimolecular reactions S. Redner; 2. The coalescence process, A+A->A, and the method of interparticle distribution functions D. ben-Avraham; 3. Critical phenomena at absorbing states R. Dickman; Part II. Kinetic Ising Models; 4. Kinetic ising models with competing dynamics: mappings, correlations, steady states, and phase transitions Z. Racz; 5. Glauber dynamics of the ising model N. Ito; 6. 1D Kinetic ising models at low temperatures - critical dynamics, domain growth, and freezing S. Cornell; Part III. Ordering, Coagulation, Phase Separation; 7. Phase-ordering dynamics in one dimension A. J. Bray; 8. Phase separation, cluster growth, and reaction kinetics in models with synchronous dynamics V. Privman; 9. Stochastic models of aggregation with injection H. Takayasu and M. Takayasu; Part IV. Random Sequential Adsorption and Relaxation Processes; 10. Random and cooperative sequential adsorption: exactly solvable problems on 1D lattices, continuum limits, and 2D extensions J. W. Evans; 11. Lattice models of irreversible adsorption and diffusion P. Nielaba; 12. Deposition-evaporation dynamics: jamming, conservation laws and dynamical diversity M. Barma; Part V. Fluctuations In Particle and Surface Systems; 13. Microscopic models of macroscopic shocks S. A. Janowsky and J. L. Lebowitz; 14. The asymmetric exclusion model: exact results through a matrix approach B. Derrida and M. R. Evans; 15. Nonequilibrium surface dynamics with volume conservation J. Krug; 16. Directed walks models of polymers and wetting J. Yeomans; Part VI. Diffusion and Transport In One Dimension; 17. Some recent exact solutions of the Fokker-Planck equation H. L. Frisch; 18. Random walks, resonance, and ratchets C. R. Doering and T. C. Elston; 19. One-dimensional random walks in random environment K. Ziegler; Part VII. Experimental Results; 20. Diffusion-limited exciton kinetics in one-dimensional systems R. Kroon and R. Sprik; 21. Experimental investigations of molecular and excitonic elementary reaction kinetics in one-dimensional systems R. Kopelman and A. L. Lin; 22. Luminescence quenching as a probe of particle distribution S. H. Bossmann and L. S. Schulman; Index.

Incorporating convection into one-dimensional solute redistribution during crystal growth from the melt I. The steady-state solution

NASA Astrophysics Data System (ADS)

Yen, C. T.; Tiller, W. A.

1992-03-01

A one-dimensional mathematical analysis is made of the redistribution of solute which occurs during crystal growth from a convected melt. In this analysis, the important contribution from lateral melt convection to one-dimensional solute redistribution analysis is taken into consideration via an annihilation/creation term in the one-dimensional solute transport equation. Calculations of solute redistribution under steady-state conditions have been carried out analytically. It is found that this new solute redistribution model overcomes several weaknesses that occur when applying the Burton, Prim and Slichter solute segregation equation (1953) in real melt growth situations. It is also found that, with this correction, the diffusion coefficients for solute's in liquid silicon are now found to be in the same range as other liquid metal diffusion coefficients.

Finite Difference Formulation for Prediction of Water Pollution

NASA Astrophysics Data System (ADS)

Johari, Hanani; Rusli, Nursalasawati; Yahya, Zainab

2018-03-01

Water is an important component of the earth. Human being and living organisms are demand for the quality of water. Human activity is one of the causes of the water pollution. The pollution happened give bad effect to the physical and characteristic of water contents. It is not practical to monitor all aspects of water flow and transport distribution. So, in order to help people to access to the polluted area, a prediction of water pollution concentration must be modelled. This study proposed a one-dimensional advection diffusion equation for predicting the water pollution concentration transport. The numerical modelling will be produced in order to predict the transportation of water pollution concentration. In order to approximate the advection diffusion equation, the implicit Crank Nicolson is used. For the purpose of the simulation, the boundary condition and initial condition, the spatial steps and time steps as well as the approximations of the advection diffusion equation have been encoded. The results of one dimensional advection diffusion equation have successfully been used to predict the transportation of water pollution concentration by manipulating the velocity and diffusion parameters.

Diffusion in random networks

DOE PAGES

Zhang, Duan Z.; Padrino, Juan C.

2017-06-01

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

Relativistic analysis of stochastic kinematics

NASA Astrophysics Data System (ADS)

Giona, Massimiliano

2017-10-01

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

Experimental and Numerical Study of Ammonium Perchlorate Counterflow Diffusion Flames

NASA Technical Reports Server (NTRS)

Smooke, M. D.; Yetter, R. A.; Parr, T. P.; Hanson-Parr, D. M.; Tanoff, M. A.

1999-01-01

Many solid rocket propellants are based on a composite mixture of ammonium perchlorate (AP) oxidizer and polymeric binder fuels. In these propellants, complex three-dimensional diffusion flame structures between the AP and binder decomposition products, dependent upon the length scales of the heterogeneous mixture, drive the combustion via heat transfer back to the surface. Changing the AP crystal size changes the burn rate of such propellants. Large AP crystals are governed by the cooler AP self-deflagration flame and burn slowly, while small AP crystals are governed more by the hot diffusion flame with the binder and burn faster. This allows control of composite propellant ballistic properties via particle size variation. Previous measurements on these diffusion flames in the planar two-dimensional sandwich configuration yielded insight into controlling flame structure, but there are several drawbacks that make comparison with modeling difficult. First, the flames are two-dimensional and this makes modeling much more complex computationally than with one-dimensional problems, such as RDX self- and laser-supported deflagration. In addition, little is known about the nature, concentration, and evolution rates of the gaseous chemical species produced by the various binders as they decompose. This makes comparison with models quite difficult. Alternatively, counterflow flames provide an excellent geometric configuration within which AP/binder diffusion flames can be studied both experimentally and computationally.

Mixing of gaseous reactants in chemical generation of atomic iodine for COIL: two-dimensional study

NASA Astrophysics Data System (ADS)

Jirasek, Vit; Spalek, Otomar; Kodymova, Jarmila; Censky, Miroslav

2003-11-01

Two-dimensional CFD model was applied for the study of mixing and reaction between gaseous chlorine dioxide and nitrogen monoxide diluted with nitrogen during atomic iodine generation. The influence of molecular diffusion on the production of atomic chlorine as a precursor of atomic iodine was predominantly studied. The results were compared with one-dimensional modeling of the system.

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.

Effects of curved midline and varying width on the description of the effective diffusivity of Brownian particles

NASA Astrophysics Data System (ADS)

Chávez, Yoshua; Chacón-Acosta, Guillermo; Dagdug, Leonardo

2018-05-01

Axial diffusion in channels and tubes of smoothly-varying geometry can be approximately described as one-dimensional diffusion in the entropy potential with a position-dependent effective diffusion coefficient, by means of the modified Fick–Jacobs equation. In this work, we derive analytical expressions for the position-dependent effective diffusivity for two-dimensional asymmetric varying-width channels, and for three-dimensional curved midline tubes, formed by straight walls. To this end, we use a recently developed theoretical framework using the Frenet–Serret moving frame as the coordinate system (2016 J. Chem. Phys. 145 074105). For narrow tubes and channels, an effective one-dimensional description reducing the diffusion equation to a Fick–Jacobs-like equation in general coordinates is used. From this last equation, one can calculate the effective diffusion coefficient applying Neumann boundary conditions.

One-Dimension Diffusion Preparation of Concentration-Gradient Fe₂O₃/SiO₂ Aerogel.

PubMed

Zhang, Ting; Wang, Haoran; Zhou, Bin; Ji, Xiujie; Wang, Hongqiang; Du, Ai

2018-06-21

Concentration-gradient Fe₂O₃/SiO₂ aerogels were prepared by placing an MTMS (methyltrimethoxysilane)-derived SiO₂ aerogel on an iron gauze with an HCl atmosphere via one-dimensional diffusion, ammonia-atmosphere fixing, supercritical fluid drying and thermal treatment. The energy dispersive spectra show that the Fe/Si molar ratios change gradually from 2.14% to 18.48% with a height of 40 mm. Pore-size distribution results show that the average pore size of the sample decreases from 15.8 nm to 3.1 nm after diffusion. This corresponds well with TEM results, indicating a pore-filling effect of the Fe compound. In order to precisely control the gradient, diffusion kinetics are further studied by analyzing the influence of time and position on the concentration of the wet gel. At last, it is found that the diffusion process could be fitted well with the one-dimensional model of Fick’s second law, demonstrating the feasibility of the precise design and control of the concentration gradient.

A two-dimensional kinematic dynamo model of the ionospheric magnetic field at Venus

NASA Technical Reports Server (NTRS)

Cravens, T. E.; Wu, D.; Shinagawa, H.

1990-01-01

The results of a high-resolution, two-dimensional, time dependent, kinematic dynamo model of the ionospheric magnetic field of Venus are presented. Various one-dimensional models are considered and the two-dimensional model is then detailed. In this model, the two-dimensional magnetic induction equation, the magnetic diffusion-convection equation, is numerically solved using specified plasma velocities. Origins of the vertical velocity profile and of the horizontal velocities are discussed. It is argued that the basic features of the vertical magnetic field profile remain unaltered by horizontal flow effects and also that horizontal plasma flow can strongly affect the magnetic field for altitudes above 300 km.

Feasibility of High Energy Lasers for Interdiction Activities

DTIC Science & Technology

2017-12-01

2.3.2 Power in the Bucket Another parameter we will use in this study is the power-in-the-bucket. The “bucket” is defined as the area on the target we...the heat diffusion equation for a one -dimensional case (where the x-direction is into the target) and assuming a semi-infinite slab of material. The... studied and modeled. One of the approaches to describe these interactions is by making a one -dimensional mathematical model assuming [8]: 1. A semi

Inverse design of centrifugal compressor vaned diffusers in inlet shear flows

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

Zangeneh, M.

1996-04-01

A three-dimensional inverse design method in which the blade (or vane) geometry is designed for specified distributions of circulation and blade thickness is applied to the design of centrifugal compressor vaned diffusers. Two generic diffusers are designed, one with uniform inlet flow (equivalent to a conventional design) and the other with a sheared inlet flow. The inlet shear flow effects are modeled in the design method by using the so-called ``Secondary Flow Approximation`` in which the Bernoulli surfaces are convected by the tangentially mean inviscid flow field. The difference between the vane geometry of the uniform inlet flow and nonuniformmore » inlet flow diffusers is found to be most significant from 50 percent chord to the trailing edge region. The flows through both diffusers are computed by using Denton`s three-dimensional inviscid Euler solver and Dawes` three-dimensional Navier-Stokes solver under sheared in-flow conditions. The predictions indicate improved pressure recovery and internal flow field for the diffuser designed for shear inlet flow conditions.« less

Robust stochastic Turing patterns in the development of a one-dimensional cyanobacterial organism.

PubMed

Di Patti, Francesca; Lavacchi, Laura; Arbel-Goren, Rinat; Schein-Lubomirsky, Leora; Fanelli, Duccio; Stavans, Joel

2018-05-01

Under nitrogen deprivation, the one-dimensional cyanobacterial organism Anabaena sp. PCC 7120 develops patterns of single, nitrogen-fixing cells separated by nearly regular intervals of photosynthetic vegetative cells. We study a minimal, stochastic model of developmental patterns in Anabaena that includes a nondiffusing activator, two diffusing inhibitor morphogens, demographic fluctuations in the number of morphogen molecules, and filament growth. By tracking developing filaments, we provide experimental evidence for different spatiotemporal roles of the two inhibitors during pattern maintenance and for small molecular copy numbers, justifying a stochastic approach. In the deterministic limit, the model yields Turing patterns within a region of parameter space that shrinks markedly as the inhibitor diffusivities become equal. Transient, noise-driven, stochastic Turing patterns are produced outside this region, which can then be fixed by downstream genetic commitment pathways, dramatically enhancing the robustness of pattern formation, also in the biologically relevant situation in which the inhibitors' diffusivities may be comparable.

Assessing the inherent uncertainty of one-dimensional diffusions

NASA Astrophysics Data System (ADS)

Eliazar, Iddo; Cohen, Morrel H.

2013-01-01

In this paper we assess the inherent uncertainty of one-dimensional diffusion processes via a stochasticity classification which provides an à la Mandelbrot categorization into five states of uncertainty: infra-mild, mild, borderline, wild, and ultra-wild. Two settings are considered. (i) Stopped diffusions: the diffusion initiates from a high level and is stopped once it first reaches a low level; in this setting we analyze the inherent uncertainty of the diffusion's maximal exceedance above its initial high level. (ii) Stationary diffusions: the diffusion is in dynamical statistical equilibrium; in this setting we analyze the inherent uncertainty of the diffusion's equilibrium level. In both settings general closed-form analytic results are established, and their application is exemplified by stock prices in the stopped-diffusions setting, and by interest rates in the stationary-diffusions setting. These results provide a highly implementable decision-making tool for the classification of uncertainty in the context of one-dimensional diffusions.

Deposition on disordered substrates with precursor layer diffusion

NASA Astrophysics Data System (ADS)

Filipe, J. A. N.; Rodgers, G. J.; Tavassoli, Z.

1998-09-01

Recently we introduced a one-dimensional accelerated random sequential adsorption process as a model for chemisorption with precursor layer diffusion. In this paper we consider this deposition process on disordered or impure substrates. The problem is solved exactly on both the lattice and continuum and for various impurity distributions. The results are compared with those from the standard random sequential adsorption model.

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

NASA Astrophysics Data System (ADS)

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

2010-11-01

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

Effects of 3 dimensional crystal geometry and orientation on 1D and 2D time-scale determinations of magmatic processes using olivine and orthopyroxene

NASA Astrophysics Data System (ADS)

Shea, Thomas; Krimer, Daniel; Costa, Fidel; Hammer, Julia

2014-05-01

One of the achievements in recent years in volcanology is the determination of time-scales of magmatic processes via diffusion in minerals and its addition to the petrologists' and volcanologists' toolbox. The method typically requires one-dimensional modeling of randomly cut crystals from two-dimensional thin sections. Here we address the question whether using 1D (traverse) or 2D (surface) datasets exploited from randomly cut 3D crystals introduces a bias or dispersion in the time-scales estimated, and how this error can be improved or eliminated. Computational simulations were performed using a concentration-dependent, finite-difference solution to the diffusion equation in 3D. The starting numerical models involved simple geometries (spheres, parallelepipeds), Mg/Fe zoning patterns (either normal or reverse), and isotropic diffusion coefficients. Subsequent models progressively incorporated more complexity, 3D olivines possessing representative polyhedral morphologies, diffusion anisotropy along the different crystallographic axes, and more intricate core-rim zoning patterns. Sections and profiles used to compare 1, 2 and 3D diffusion models were selected to be (1) parallel to the crystal axes, (2) randomly oriented but passing through the olivine center, or (3) randomly oriented and sectioned. Results show that time-scales estimated on randomly cut traverses (1D) or surfaces (2D) can be widely distributed around the actual durations of 3D diffusion (~0.2 to 10 times the true diffusion time). The magnitude over- or underestimations of duration are a complex combination of the geometry of the crystal, the zoning pattern, the orientation of the cuts with respect to the crystallographic axes, and the degree of diffusion anisotropy. Errors on estimated time-scales retrieved from such models may thus be significant. Drastic reductions in the uncertainty of calculated diffusion times can be obtained by following some simple guidelines during the course of data collection (i.e. selection of crystals and concentration profiles, acquisition of crystallographic orientation data), thus allowing derivation of robust time-scales.

Exploding dissipative solitons in the cubic-quintic complex Ginzburg-Landau equation in one and two spatial dimensions. A review and a perspective

NASA Astrophysics Data System (ADS)

Cartes, C.; Descalzi, O.; Brand, H. R.

2014-10-01

We review the work on exploding dissipative solitons in one and two spatial dimensions. Features covered include: the transition from modulated to exploding dissipative solitons, the analogue of the Ruelle-Takens scenario for dissipative solitons, inducing exploding dissipative solitons by noise, two classes of exploding dissipative solitons in two spatial dimensions, diffusing asymmetric exploding dissipative solitons as a model for a two-dimensional extended chaotic system. As a perspective we outline the interaction of exploding dissipative solitons with quasi one-dimensional dissipative solitons, breathing quasi one-dimensional solutions and their possible connection with experimental results on convection, and the occurence of exploding dissipative solitons in reaction-diffusion systems. It is a great pleasure to dedicate this work to our long-time friend Hans (Prof. Dr. Hans Jürgen Herrmann) on the occasion of his 60th birthday.

Dimensional reduction of a general advection–diffusion equation in 2D channels

NASA Astrophysics Data System (ADS)

Kalinay, Pavol; Slanina, František

2018-06-01

Diffusion of point-like particles in a two-dimensional channel of varying width is studied. The particles are driven by an arbitrary space dependent force. We construct a general recurrence procedure mapping the corresponding two-dimensional advection-diffusion equation onto the longitudinal coordinate x. Unlike the previous specific cases, the presented procedure enables us to find the one-dimensional description of the confined diffusion even for non-conservative (vortex) forces, e.g. caused by flowing solvent dragging the particles. We show that the result is again the generalized Fick–Jacobs equation. Despite of non existing scalar potential in the case of vortex forces, the effective one-dimensional scalar potential, as well as the corresponding quasi-equilibrium and the effective diffusion coefficient can be always found.

Progress in MOSFET double-layer metalization

NASA Technical Reports Server (NTRS)

Gassaway, J. D.; Trotter, J. D.; Wade, T. E.

1980-01-01

Report describes one-year research effort in VLSL fabrication. Four activities are described: theoretical study of two-dimensional diffusion in SOS (silicon-on-sapphire); setup of sputtering system, furnaces, and photolithography equipment; experiments on double layer metal; and investigation of two-dimensional modeling of MOSFET's (metal-oxide-semiconductor field-effect transistors).

Diffusion of interacting particles in discrete geometries: Equilibrium and dynamical properties

NASA Astrophysics Data System (ADS)

Becker, T.; Nelissen, K.; Cleuren, B.; Partoens, B.; Van den Broeck, C.

2014-11-01

We expand on a recent study of a lattice model of interacting particles [Phys. Rev. Lett. 111, 110601 (2013), 10.1103/PhysRevLett.111.110601]. The adsorption isotherm and equilibrium fluctuations in particle number are discussed as a function of the interaction. Their behavior is similar to that of interacting particles in porous materials. Different expressions for the particle jump rates are derived from transition-state theory. Which expression should be used depends on the strength of the interparticle interactions. Analytical expressions for the self- and transport diffusion are derived when correlations, caused by memory effects in the environment, are neglected. The diffusive behavior is studied numerically with kinetic Monte Carlo (kMC) simulations, which reproduces the diffusion including correlations. The effect of correlations is studied by comparing the analytical expressions with the kMC simulations. It is found that the Maxwell-Stefan diffusion can exceed the self-diffusion. To our knowledge, this is the first time this is observed. The diffusive behavior in one-dimensional and higher-dimensional systems is qualitatively the same, with the effect of correlations decreasing for increasing dimension. The length dependence of both the self- and transport diffusion is studied for one-dimensional systems. For long lengths the self-diffusion shows a 1 /L dependence. Finally, we discuss when agreement with experiments and simulations can be expected. The assumption that particles in different cavities do not interact is expected to hold quantitatively at low and medium particle concentrations if the particles are not strongly interacting.

Ordering phase transition in the one-dimensional Axelrod model

NASA Astrophysics Data System (ADS)

Vilone, D.; Vespignani, A.; Castellano, C.

2002-12-01

We study the one-dimensional behavior of a cellular automaton aimed at the description of the formation and evolution of cultural domains. The model exhibits a non-equilibrium transition between a phase with all the system sharing the same culture and a disordered phase of coexisting regions with different cultural features. Depending on the initial distribution of the disorder the transition occurs at different values of the model parameters. This phenomenology is qualitatively captured by a mean-field approach, which maps the dynamics into a multi-species reaction-diffusion problem.

One-dimensional Turbulence Models of Type I X-ray Bursts

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

Hou, Chen

Type I X-ray bursts are caused by thermonuclear explosions occurring on the surface of an accreting neutron star in a binary star system. Observations and simulations of these phenomena are of great importance for understanding the fundamental properties of neutron stars and dense matter because the equation of state for cold dense matter can be constrained by the mass-radius relationship of neutron stars. During the bursts, turbulence plays a key role in mixing the fuels and driving the unstable nuclear burning process. This dissertation presents one-dimensional models of photospheric radius expansion bursts with a new approach to simulate turbulent advection.more » Compared with the traditional mixing length theory, the one-dimensional turbulence (ODT) model represents turbulent motions by a sequence of maps that are generated according to a stochastic process. The light curves I obtained with the ODT models are in good agreement with those of the KEPLER model in which the mixing length theory and various diffusive processes are applied. The abundance comparison, however, indicates that the differences in turbulent regions and turbulent diffusivities result in more 12C survival during the bursts in the ODT models, which can make a difference in the superbursts phenomena triggered by unstable carbon burning.« less

Cross-stream diffusion under pressure-driven flow in microchannels with arbitrary aspect ratios: a phase diagram study using a three-dimensional analytical model

PubMed Central

Song, Hongjun; Wang, Yi; Pant, Kapil

2011-01-01

This article presents a three-dimensional analytical model to investigate cross-stream diffusion transport in rectangular microchannels with arbitrary aspect ratios under pressure-driven flow. The Fourier series solution to the three-dimensional convection–diffusion equation is obtained using a double integral transformation method and associated eigensystem calculation. A phase diagram derived from the dimensional analysis is presented to thoroughly interrogate the characteristics in various transport regimes and examine the validity of the model. The analytical model is verified against both experimental and numerical models in terms of the concentration profile, diffusion scaling law, and mixing efficiency with excellent agreement (with <0.5% relative error). Quantitative comparison against other prior analytical models in extensive parameter space is also performed, which demonstrates that the present model accommodates much broader transport regimes with significantly enhanced applicability. PMID:22247719

Cross-stream diffusion under pressure-driven flow in microchannels with arbitrary aspect ratios: a phase diagram study using a three-dimensional analytical model.

PubMed

Song, Hongjun; Wang, Yi; Pant, Kapil

2012-01-01

This article presents a three-dimensional analytical model to investigate cross-stream diffusion transport in rectangular microchannels with arbitrary aspect ratios under pressure-driven flow. The Fourier series solution to the three-dimensional convection-diffusion equation is obtained using a double integral transformation method and associated eigensystem calculation. A phase diagram derived from the dimensional analysis is presented to thoroughly interrogate the characteristics in various transport regimes and examine the validity of the model. The analytical model is verified against both experimental and numerical models in terms of the concentration profile, diffusion scaling law, and mixing efficiency with excellent agreement (with <0.5% relative error). Quantitative comparison against other prior analytical models in extensive parameter space is also performed, which demonstrates that the present model accommodates much broader transport regimes with significantly enhanced applicability.

A computer model for one-dimensional mass and energy transport in and around chemically reacting particles, including complex gas-phase chemistry, multicomponent molecular diffusion, surface evaporation, and heterogeneous reaction

NASA Technical Reports Server (NTRS)

Cho, S. Y.; Yetter, R. A.; Dryer, F. L.

1992-01-01

Various chemically reacting flow problems highlighting chemical and physical fundamentals rather than flow geometry are presently investigated by means of a comprehensive mathematical model that incorporates multicomponent molecular diffusion, complex chemistry, and heterogeneous processes, in the interest of obtaining sensitivity-related information. The sensitivity equations were decoupled from those of the model, and then integrated one time-step behind the integration of the model equations, and analytical Jacobian matrices were applied to improve the accuracy of sensitivity coefficients that are calculated together with model solutions.

Spatiotemporal Patterns in a Predator-Prey Model with Cross-Diffusion Effect

NASA Astrophysics Data System (ADS)

Sambath, M.; Balachandran, K.; Guin, L. N.

The present research deals with the emergence of spatiotemporal patterns of a two-dimensional (2D) continuous predator-prey system with cross-diffusion effect. First, we work out the critical lines of Hopf and Turing bifurcations of the current model system in a 2D spatial domain by means of bifurcation theory. More specifically, the exact Turing region is specified in a two-parameter space. In effect, by choosing the cross-diffusion coefficient as one of the momentous parameter, we demonstrate that the model system undergoes a sequence of spatiotemporal patterns in a homogeneous environment through diffusion-driven instability. Our results via numerical simulation authenticate that cross-diffusion be able to create stationary patterns which enrich the findings of pattern formation in an ecosystem.

Stability and Hopf Bifurcation in a Reaction-Diffusion Model with Chemotaxis and Nonlocal Delay Effect

NASA Astrophysics Data System (ADS)

Li, Dong; Guo, Shangjiang

Chemotaxis is an observed phenomenon in which a biological individual moves preferentially toward a relatively high concentration, which is contrary to the process of natural diffusion. In this paper, we study a reaction-diffusion model with chemotaxis and nonlocal delay effect under Dirichlet boundary condition by using Lyapunov-Schmidt reduction and the implicit function theorem. The existence, multiplicity, stability and Hopf bifurcation of spatially nonhomogeneous steady state solutions are investigated. Moreover, our results are illustrated by an application to the model with a logistic source, homogeneous kernel and one-dimensional spatial domain.

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

NASA Astrophysics Data System (ADS)

Padrino, Juan C.; Zhang, Duan Z.

2016-11-01

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

Lattice Three-Species Models of the Spatial Spread of Rabies among FOXES

NASA Astrophysics Data System (ADS)

Benyoussef, A.; Boccara, N.; Chakib, H.; Ez-Zahraouy, H.

Lattice models describing the spatial spread of rabies among foxes are studied. In these models, the fox population is divided into three-species: susceptible (S), infected or incubating (I), and infectious or rabid (R). They are based on the fact that susceptible and incubating foxes are territorial while rabid foxes have lost their sense of direction and move erratically. Two different models are investigated: a one-dimensional coupled-map lattice model, and a two-dimensional automata network model. Both models take into account the short-range character of the infection process and the diffusive motion of rabid foxes. Numerical simulations show how the spatial distribution of rabies, and the speed of propagation of the epizootic front depend upon the carrying capacity of the environment and diffusion of rabid foxes out of their territory.

Illumination in diverse codimensions

NASA Technical Reports Server (NTRS)

Banks, David C.

1994-01-01

This paper derives a model of diffuse and specular illumination in arbitrarily large dimensions, based on a few characteristics of material and light in three-space. It then describes how to adjust for the anomaly of excess brightness in large codimensions. If a surface is grooved or furry, it can be illuminated with a hybrid model that incorporates both the one dimensional geometry (the grooves or fur) and the two dimensional geometry (the surface).

A fast semi-discrete Kansa method to solve the two-dimensional spatiotemporal fractional diffusion equation

NASA Astrophysics Data System (ADS)

Sun, HongGuang; Liu, Xiaoting; Zhang, Yong; Pang, Guofei; Garrard, Rhiannon

2017-09-01

Fractional-order diffusion equations (FDEs) extend classical diffusion equations by quantifying anomalous diffusion frequently observed in heterogeneous media. Real-world diffusion can be multi-dimensional, requiring efficient numerical solvers that can handle long-term memory embedded in mass transport. To address this challenge, a semi-discrete Kansa method is developed to approximate the two-dimensional spatiotemporal FDE, where the Kansa approach first discretizes the FDE, then the Gauss-Jacobi quadrature rule solves the corresponding matrix, and finally the Mittag-Leffler function provides an analytical solution for the resultant time-fractional ordinary differential equation. Numerical experiments are then conducted to check how the accuracy and convergence rate of the numerical solution are affected by the distribution mode and number of spatial discretization nodes. Applications further show that the numerical method can efficiently solve two-dimensional spatiotemporal FDE models with either a continuous or discrete mixing measure. Hence this study provides an efficient and fast computational method for modeling super-diffusive, sub-diffusive, and mixed diffusive processes in large, two-dimensional domains with irregular shapes.

A Two Species Bump-On-Tail Model With Relaxation for Energetic Particle Driven Modes

NASA Astrophysics Data System (ADS)

Aslanyan, V.; Porkolab, M.; Sharapov, S. E.; Spong, D. A.

2017-10-01

Energetic particle driven Alfvén Eigenmodes (AEs) observed in present day experiments exhibit various nonlinear behaviours varying from steady state amplitude at a fixed frequency to bursting amplitudes and sweeping frequency. Using the appropriate action-angle variables, the problem of resonant wave-particle interaction becomes effectively one-dimensional. Previously, a simple one-dimensional Bump-On-Tail (BOT) model has proven to be one of the most effective in describing characteristic nonlinear near-threshold wave evolution scenarios. In particular, dynamical friction causes bursting mode evolution, while diffusive relaxation may give steady-state, periodic or chaotic mode evolution. BOT has now been extended to include two populations of fast particles, with one dominated by dynamical friction at the resonance and the other by diffusion; the relative size of the populations determines the temporal evolution of the resulting wave. This suggests an explanation for recent observations on the TJ-II stellarator, where a transition between steady state and bursting occured as the magnetic configuration varied. The two species model is then applied to burning plasma with drag-dominated alpha particles and diffusion-dominated ICRH accelerated minority ions. This work was supported by the US DoE and the RCUK Energy Programme [Grant Number EP/P012450/1].

Sub-Fickean Diffusion in a One-Dimensional Plasma Ring

NASA Astrophysics Data System (ADS)

Theisen, W. L.

2013-12-01

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

Continuous versus discontinuous albedo representations in a simple diffusive climate model

NASA Astrophysics Data System (ADS)

Simmons, P. A.; Griffel, D. H.

1988-07-01

A one-dimensional annually and zonally averaged energy-balance model, with diffusive meridional heat transport and including icealbedo feedback, is considered. This type of model is found to be very sensitive to the form of albedo used. The solutions for a discontinuous step-function albedo are compared to those for a more realistic smoothly varying albedo. The smooth albedo gives a closer fit to present conditions, but the discontinuous form gives a better representation of climates in earlier epochs.

Optical measurement of transverse molecular diffusion in a microchannel.

PubMed Central

Kamholz, A E; Schilling, E A; Yager, P

2001-01-01

Quantitative analysis of molecular diffusion is a necessity for the efficient design of most microfluidic devices as well as an important biophysical method in its own right. This study demonstrates the rapid measurement of diffusion coefficients of large and small molecules in a microfluidic device, the T-sensor, by means of conventional epifluorescence microscopy. Data were collected by monitoring the transverse flux of analyte from a sample stream into a second stream flowing alongside it. As indicated by the low Reynolds numbers of the system (< 1), flow is laminar, and molecular transport between streams occurs only by diffusion. Quantitative determinations were made by fitting data with predictions of a one-dimensional model. Analysis was made of the flow development and its effect on the distribution of diffusing analyte using a three-dimensional modeling software package. Diffusion coefficients were measured for four fluorescently labeled molecules: fluorescein-biotin, insulin, ovalbumin, and streptavidin. The resulting values differed from accepted results by an average of 2.4%. Microfluidic system parameters can be selected to achieve accurate diffusion coefficient measurements and to optimize other microfluidic devices that rely on precise transverse transport of molecules. PMID:11259309

Phase transition of traveling waves in bacterial colony pattern

NASA Astrophysics Data System (ADS)

Wakano, Joe Yuichiro; Komoto, Atsushi; Yamaguchi, Yukio

2004-05-01

Depending on the growth condition, bacterial colonies can exhibit different morphologies. Many previous studies have used reaction diffusion equations to reproduce spatial patterns. They have revealed that nonlinear reaction term can produce diverse patterns as well as nonlinear diffusion coefficient. Typical reaction term consists of nutrient consumption, bacterial reproduction, and sporulation. Among them, the functional form of sporulation rate has not been biologically investigated. Here we report experimentally measured sporulation rate. Then, based on the result, a reaction diffusion model is proposed. One-dimensional simulation showed the existence of traveling wave solution. We study the wave form as a function of the initial nutrient concentration and find two distinct types of solution. Moreover, transition between them is very sharp, which is analogous to phase transition. The velocity of traveling wave also shows sharp transition in nonlinear diffusion model, which is consistent with the previous experimental result. The phenomenon can be explained by separatrix in reaction term dynamics. Results of two-dimensional simulation are also shown and discussed.

CITRATE 1.0: Phytoplankton continuous trait-distribution model with one-dimensional physical transport applied to the North Pacific

NASA Astrophysics Data System (ADS)

Chen, Bingzhang; Smith, Sherwood Lan

2018-02-01

Diversity plays critical roles in ecosystem functioning, but it remains challenging to model phytoplankton diversity in order to better understand those roles and reproduce consistently observed diversity patterns in the ocean. In contrast to the typical approach of resolving distinct species or functional groups, we present a ContInuous TRAiT-basEd phytoplankton model (CITRATE) that focuses on macroscopic system properties such as total biomass, mean trait values, and trait variance. This phytoplankton component is embedded within a nitrogen-phytoplankton-zooplankton-detritus-iron model that itself is coupled with a simplified one-dimensional ocean model. Size is used as the master trait for phytoplankton. CITRATE also incorporates trait diffusion for sustaining diversity and simple representations of physiological acclimation, i.e., flexible chlorophyll-to-carbon and nitrogen-to-carbon ratios. We have implemented CITRATE at two contrasting stations in the North Pacific where several years of observational data are available. The model is driven by physical forcing including vertical eddy diffusivity imported from three-dimensional general ocean circulation models (GCMs). One common set of model parameters for the two stations is optimized using the Delayed-Rejection Adaptive Metropolis-Hasting Monte Carlo (DRAM) algorithm. The model faithfully reproduces most of the observed patterns and gives robust predictions on phytoplankton mean size and size diversity. CITRATE is suitable for applications in GCMs and constitutes a prototype upon which more sophisticated continuous trait-based models can be developed.

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

Hu, Shenyang; Joshi, Vineet; Lavender, Curt A.

Experiments showed that recrystallization dramatically speeds up the gas bubble swelling kinetics in metallic UMo fuels. In this work a recrystallization model is developed to study the effect of microstructures and radiation conditions on recrystallization kinetics. The model integrates the rate theory of intra-granular gas bubble and interstitial loop evolution and a phase field model of recrystallization zone evolution. A fast passage method is employed to describe one dimensional diffusion of interstitials which have diffusivity several order magnitude larger than that of the fission gas Xe. With the model, the effect of grain sizes on recrystallization kinetics is simulated.

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.

A one-dimensional heat-transport model for conduit flow in karst aquifers

USGS Publications Warehouse

Long, Andrew J.; Gilcrease, P.C.

2009-01-01

A one-dimensional heat-transport model for conduit flow in karst aquifers is presented as an alternative to two or three-dimensional distributed-parameter models, which are data intensive and require knowledge of conduit locations. This model can be applied for cases where water temperature in a well or spring receives all or part of its water from a phreatic conduit. Heat transport in the conduit is simulated by using a physically-based heat-transport equation that accounts for inflow of diffuse flow from smaller openings and fissures in the surrounding aquifer during periods of low recharge. Additional diffuse flow that is within the zone of influence of the well or spring but has not interacted with the conduit is accounted for with a binary mixing equation to proportion these different water sources. The estimation of this proportion through inverse modeling is useful for the assessment of contaminant vulnerability and well-head or spring protection. The model was applied to 7 months of continuous temperature data for a sinking stream that recharges a conduit and a pumped well open to the Madison aquifer in western South Dakota. The simulated conduit-flow fraction to the well ranged from 2% to 31% of total flow, and simulated conduit velocity ranged from 44 to 353 m/d.

Molecular Dynamic Simulation of Water Vapor and Determination of Diffusion Characteristics in the Pore

NASA Astrophysics Data System (ADS)

Nikonov, Eduard G.; Pavluš, Miron; Popovičová, Mária

2018-02-01

One of the varieties of pores, often found in natural or artificial building materials, are the so-called blind pores of dead-end or saccate type. Three-dimensional model of such kind of pore has been developed in this work. This model has been used for simulation of water vapor interaction with individual pore by molecular dynamics in combination with the diffusion equation method. Special investigations have been done to find dependencies between thermostats implementations and conservation of thermodynamic and statistical values of water vapor - pore system. The two types of evolution of water - pore system have been investigated: drying and wetting of the pore. Full research of diffusion coefficient, diffusion velocity and other diffusion parameters has been made.

Validation of a numerical method for interface-resolving simulation of multicomponent gas-liquid mass transfer and evaluation of multicomponent diffusion models

NASA Astrophysics Data System (ADS)

Woo, Mino; Wörner, Martin; Tischer, Steffen; Deutschmann, Olaf

2018-03-01

The multicomponent model and the effective diffusivity model are well established diffusion models for numerical simulation of single-phase flows consisting of several components but are seldom used for two-phase flows so far. In this paper, a specific numerical model for interfacial mass transfer by means of a continuous single-field concentration formulation is combined with the multicomponent model and effective diffusivity model and is validated for multicomponent mass transfer. For this purpose, several test cases for one-dimensional physical or reactive mass transfer of ternary mixtures are considered. The numerical results are compared with analytical or numerical solutions of the Maxell-Stefan equations and/or experimental data. The composition-dependent elements of the diffusivity matrix of the multicomponent and effective diffusivity model are found to substantially differ for non-dilute conditions. The species mole fraction or concentration profiles computed with both diffusion models are, however, for all test cases very similar and in good agreement with the analytical/numerical solutions or measurements. For practical computations, the effective diffusivity model is recommended due to its simplicity and lower computational costs.

Alignment dynamics of diffusive scalar gradient in a two-dimensional model flow

NASA Astrophysics Data System (ADS)

Gonzalez, M.

2018-04-01

The Lagrangian two-dimensional approach of scalar gradient kinematics is revisited accounting for molecular diffusion. Numerical simulations are performed in an analytic, parameterized model flow, which enables considering different regimes of scalar gradient dynamics. Attention is especially focused on the influence of molecular diffusion on Lagrangian statistical orientations and on the dynamics of scalar gradient alignment.

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.

Transient and diffusion analysis of HgCdTe

NASA Technical Reports Server (NTRS)

Clayton, J. C.

1982-01-01

Solute redistribution during directional solidification of HgCdTe is addressed. Both one-dimensional and two-dimensional models for solute redistribution are treated and model results compared to experiment. The central problem studied is the cause of radial inhomogeneities found in directionally solidified HgCdTe. A large scale gravity-driven interface instability, termed shape instability, is postulated to be the cause of radial inhomogeneities. Recommendations for future work, along with appropriate computer programs, are included.

A theoretical model describing the one-dimensional growth of single crystals on free sustained substrates

NASA Astrophysics Data System (ADS)

Ye, Ziran; Wang, Ke; Lu, Chenxi; Jin, Ying; Sui, Chenghua; Yan, Bo; Gao, Fan; Cai, Pinggen; Lv, Bin; Li, Yun; Chen, Naibo; Sun, Guofang; Xu, Fengyun; Ye, Gaoxiang

2018-03-01

We develop a theoretical model that interprets the growth mechanism of zinc (Zn) crystal nanorods on a liquid substrate by thermal evaporation. During deposition, Zn atoms diffuse randomly on an isotropic and quasi-free sustained substrate, the nucleation of the atoms results in the primary nanorod (or seed crystal) growth. Subsequently, a characteristic one-dimensional atomic aggregation is proposed, which leads to the accelerating growth of the crystal nanorod along its preferential growth direction until the growth terminates. The theoretical results are in good agreement with the experimental findings.

A numerical solution for the diffusion equation in hydrogeologic systems

USGS Publications Warehouse

Ishii, A.L.; Healy, R.W.; Striegl, Robert G.

1989-01-01

The documentation of a computer code for the numerical solution of the linear diffusion equation in one or two dimensions in Cartesian or cylindrical coordinates is presented. Applications of the program include molecular diffusion, heat conduction, and fluid flow in confined systems. The flow media may be anisotropic and heterogeneous. The model is formulated by replacing the continuous linear diffusion equation by discrete finite-difference approximations at each node in a block-centered grid. The resulting matrix equation is solved by the method of preconditioned conjugate gradients. The conjugate gradient method does not require the estimation of iteration parameters and is guaranteed convergent in the absence of rounding error. The matrixes are preconditioned to decrease the steps to convergence. The model allows the specification of any number of boundary conditions for any number of stress periods, and the output of a summary table for selected nodes showing flux and the concentration of the flux quantity for each time step. The model is written in a modular format for ease of modification. The model was verified by comparison of numerical and analytical solutions for cases of molecular diffusion, two-dimensional heat transfer, and axisymmetric radial saturated fluid flow. Application of the model to a hypothetical two-dimensional field situation of gas diffusion in the unsaturated zone is demonstrated. The input and output files are included as a check on program installation. The definition of variables, input requirements, flow chart, and program listing are included in the attachments. (USGS)

Direct reconstruction in CT-analogous pharmacokinetic diffuse fluorescence tomography: two-dimensional simulative and experimental validations

NASA Astrophysics Data System (ADS)

Wang, Xin; Zhang, Yanqi; Zhang, Limin; Li, Jiao; Zhou, Zhongxing; Zhao, Huijuan; Gao, Feng

2016-04-01

We present a generalized strategy for direct reconstruction in pharmacokinetic diffuse fluorescence tomography (DFT) with CT-analogous scanning mode, which can accomplish one-step reconstruction of the indocyanine-green pharmacokinetic-rate images within in vivo small animals by incorporating the compartmental kinetic model into an adaptive extended Kalman filtering scheme and using an instantaneous sampling dataset. This scheme, compared with the established indirect and direct methods, eliminates the interim error of the DFT inversion and relaxes the expensive requirement of the instrument for obtaining highly time-resolved date-sets of complete 360 deg projections. The scheme is validated by two-dimensional simulations for the two-compartment model and pilot phantom experiments for the one-compartment model, suggesting that the proposed method can estimate the compartmental concentrations and the pharmacokinetic-rates simultaneously with a fair quantitative and localization accuracy, and is well suitable for cost-effective and dense-sampling instrumentation based on the highly-sensitive photon counting technique.

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

NASA Astrophysics Data System (ADS)

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

2016-06-01

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

Simulations of thermodynamics and kinetics on rough energy landscapes with milestoning.

PubMed

Bello-Rivas, Juan M; Elber, Ron

2016-03-05

We investigated by computational means the kinetics and stationary behavior of stochastic dynamics on an ensemble of rough two-dimensional energy landscapes. There are no obvious separations of temporal scales in these systems, which constitute a simple model for the behavior of glasses and some biomaterials. Even though there are significant computational challenges present in these systems due to the large number of metastable states, the Milestoning method is able to compute their kinetic and thermodynamic properties exactly. We observe two clearly distinguished regimes in the overall kinetics: one in which diffusive behavior dominates and another that follows an Arrhenius law (despite the absence of a dominant barrier). We compare our results with those obtained with an exactly-solvable one-dimensional model, and with the results from the rough one-dimensional energy model introduced by Zwanzig. © 2015 Wiley Periodicals, Inc. © 2015 Wiley Periodicals, Inc.

Reaction-diffusion systems coupled at the boundary and the Morse-Smale property

NASA Astrophysics Data System (ADS)

Broche, Rita de Cássia D. S.; de Oliveira, Luiz Augusto F.

We study an one-dimensional nonlinear reaction-diffusion system coupled on the boundary. Such system comes from modeling problems of temperature distribution on two bars of same length, jointed together, with different diffusion coefficients. We prove the transversality property of unstable and stable manifolds assuming all equilibrium points are hyperbolic. To this end, we write the system as an equation with noncontinuous diffusion coefficient. We then study the nonincreasing property of the number of zeros of a linearized nonautonomous equation as well as the Sturm-Liouville properties of the solutions of a linear elliptic problem.

Superimposed Code Theoretic Analysis of Deoxyribonucleic Acid (DNA) Codes and DNA Computing

DTIC Science & Technology

2010-01-01

partitioned by font type) of sequences are allowed to be in each position (e.g., Arial = position 0, Comic = position 1, etc. ) and within each collection...movement was modeled by a Brownian motion 3 dimensional random walk. The one dimensional diffusion coefficient D for the ellipsoid shape with 3...temperature, kB is Boltzmann’s constant, and η is the viscosity of the medium. The random walk motion is modeled by assuming the oligo is on a three

Bistable flow occurrence in the 2D model of a steam turbine valve

NASA Astrophysics Data System (ADS)

Pavel, Procházka; Václav, Uruba

2017-09-01

The internal flow inside a steam turbine valve was investigated experimentally using PIV measurement. The valve model was proposed to be two-dimensional. The model was connected to the blow-down wind tunnel. The flow conditions were set by the different position of the valve plug. Several angles of the diffuser by diverse radii were investigated concerning flow separation and flow dynamics. It was found that the flow takes one of two possible bistable modes. The first regime is characterized by a massive flow separation just at the beginning of the diffuser section on the one side. The second regime is axisymmetric and the flow separation is not detected at all.

Comparison of fluid neutral models for one-dimensional plasma edge modeling with a finite volume solution of the Boltzmann equation

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

Horsten, N., E-mail: niels.horsten@kuleuven.be; Baelmans, M.; Dekeyser, W.

2016-01-15

We derive fluid neutral approximations for a simplified 1D edge plasma model, suitable to study the neutral behavior close to the target of a nuclear fusion divertor, and compare its solutions to the solution of the corresponding kinetic Boltzmann equation. The plasma is considered as a fixed background extracted from a detached 2D simulation. We show that the Maxwellian equilibrium distribution is already obtained very close to the target, justifying the use of a fluid approximation. We compare three fluid neutral models: (i) a diffusion model; (ii) a pressure-diffusion model (i.e., a combination of a continuity and momentum equation) assumingmore » equal neutral and ion temperatures; and (iii) the pressure-diffusion model coupled to a neutral energy equation taking into account temperature differences between neutrals and ions. Partial reflection of neutrals reaching the boundaries is included in both the kinetic and fluid models. We propose two methods to obtain an incident neutral flux boundary condition for the fluid models: one based on a diffusion approximation and the other assuming a truncated Chapman-Enskog distribution. The pressure-diffusion model predicts the plasma sources very well. The diffusion boundary condition gives slightly better results overall. Although including an energy equation still improves the results, the assumption of equal ion and neutral temperature already gives a very good approximation.« less

Modeling of chemical vapor infiltration for ceramic composites reinforced with layered, woven fabrics

NASA Technical Reports Server (NTRS)

Chung, Gui-Yung; Mccoy, Benjamin J.

1991-01-01

A homogeneous model is developed for the chemical vapor infiltration by one-dimensional diffusion into a system of layered plies consisting of woven tows containing bundles of filaments. The model predictions of the amount of deposition and the porosity of the sample as a function of time are compared with the predictions of a recent nonhomogeneous model with aligned holes formed by the weave. The nonhomogeneous model allows for diffusion through the aligned holes, into the spaces between plies, and into the gaps around filaments; i.e., three diffusion equations apply. Relative to the nonhomogeneous results, the homogeneous model underestimates the amount of deposition, since the absence of holes and spaces allows earlier occlusion of gaps around filaments and restricts the vapor infiltration.

Comments on the Diffusive Behavior of Two Upwind Schemes

NASA Technical Reports Server (NTRS)

Wood, William A.; Kleb, William L.

1998-01-01

The diffusive characteristics of two upwind schemes, multi-dimensional fluctuation splitting and locally one-dimensional finite volume, are compared for scalar advection-diffusion problems. Algorithms for the two schemes are developed for node-based data representation on median-dual meshes associated with unstructured triangulations in two spatial dimensions. Four model equations are considered: linear advection, non-linear advection, diffusion, and advection-diffusion. Modular coding is employed to isolate the effects of the two approaches for upwind flux evaluation, allowing for head-to-head accuracy and efficiency comparisons. Both the stability of compressive limiters and the amount of artificial diffusion generated by the schemes is found to be grid-orientation dependent, with the fluctuation splitting scheme producing less artificial diffusion than the finite volume scheme. Convergence rates are compared for the combined advection-diffusion problem, with a speedup of 2.5 seen for fluctuation splitting versus finite volume when solved on the same mesh. However, accurate solutions to problems with small diffusion coefficients can be achieved on coarser meshes using fluctuation splitting rather than finite volume, so that when comparing convergence rates to reach a given accuracy, fluctuation splitting shows a speedup of 29 over finite volume.

An Examination of the Evolution of Radiation and Advection Fogs

DTIC Science & Technology

1993-01-01

and fog diagnostic and prediction models have developed in sophistication so that they can reproduce fairly accurate one- or two-dimensional...occurred only by molecular diffusion near the interface created between the species during the mixing process. The rate of homogenization is minimal until...of excess vapor by molecular diffusion at the interfaces of nearly saturated air mixing in eddies is faster than the relaxation time of droplet

Tailorable Exciton Transport in Doped Peptide–Amphiphile Assemblies

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

Solomon, Lee A.; Sykes, Matthew E.; Wu, Yimin A.

Light-harvesting biomaterials are an attractive target in photovoltaics, photocatalysis, and artificial photosynthesis. Through peptide self-assembly, complex nanostructures can be engineered to study the role of chromophore organization during light absorption and energy transport. To this end, we demonstrate the one-dimensional transport of excitons along naturally occurring, light-harvesting, Zn-protoporphyrin IX chromophores within self-assembled peptide-amphiphile nanofibers. The internal structure of the nanofibers induces packing of the porphyrins into linear chains. We find that this peptide assembly can enable long-range exciton diffusion, yet it also induces the formation of excimers between adjacent molecules, which serve as exciton traps. Electronic coupling between neighboring porphyrinmore » molecules is confirmed by various spectroscopic methods. The exciton diffusion process is then probed through transient photoluminescence and absorption measurements and fit to a model for one-dimensional hopping. Because excimer formation impedes exciton hopping, increasing the interchromophore spacing allows for improved diffusivity, which we control through porphyrin doping levels. We show that diffusion lengths of over 60 nm are possible at low porphyrin doping, representing an order of magnitude improvement over the highest doping fractions.« less

Tailorable Exciton Transport in Doped Peptide-Amphiphile Assemblies.

PubMed

Solomon, Lee A; Sykes, Matthew E; Wu, Yimin A; Schaller, Richard D; Wiederrecht, Gary P; Fry, H Christopher

2017-09-26

Light-harvesting biomaterials are an attractive target in photovoltaics, photocatalysis, and artificial photosynthesis. Through peptide self-assembly, complex nanostructures can be engineered to study the role of chromophore organization during light absorption and energy transport. To this end, we demonstrate the one-dimensional transport of excitons along naturally occurring, light-harvesting, Zn-protoporphyrin IX chromophores within self-assembled peptide-amphiphile nanofibers. The internal structure of the nanofibers induces packing of the porphyrins into linear chains. We find that this peptide assembly can enable long-range exciton diffusion, yet it also induces the formation of excimers between adjacent molecules, which serve as exciton traps. Electronic coupling between neighboring porphyrin molecules is confirmed by various spectroscopic methods. The exciton diffusion process is then probed through transient photoluminescence and absorption measurements and fit to a model for one-dimensional hopping. Because excimer formation impedes exciton hopping, increasing the interchromophore spacing allows for improved diffusivity, which we control through porphyrin doping levels. We show that diffusion lengths of over 60 nm are possible at low porphyrin doping, representing an order of magnitude improvement over the highest doping fractions.

Bioturbation, advection, and diffusion of a conserved tracer in a laboratory flume

NASA Astrophysics Data System (ADS)

Work, P. A.; Moore, P. R.; Reible, D. D.

2002-06-01

Laboratory experiments indicating the relative influences of advection, diffusion, and bioturbation on transport of NaCl tracer between a stream and streambed are described. Data were collected in a recirculating flume housing a box filled with test sediments. Peclet numbers ranged from 0 to 1.5. Sediment components included a medium sand (d50 = 0.31 mm), kaolinite, and topsoil. Lumbriculus variegatus were introduced as bioturbators. Conductivity probes were employed to document the flux of the tracer solution out of the bed. Measurements are compared to one-dimensional effective diffusion models assuming one or two horizontal sediment layers. These simple models provide a good indication of tracer half-life in the bed if a suitable effective diffusion coefficient is chosen but underpredict initial flux and overpredict flux at long times. Organism activity was limited to the upper reaches of the sediment test box but eventually exerts a secondary influence on flux from deeper regions.

Active colloidal propulsion over a crystalline surface

NASA Astrophysics Data System (ADS)

Choudhury, Udit; Straube, Arthur V.; Fischer, Peer; Gibbs, John G.; Höfling, Felix

2017-12-01

We study both experimentally and theoretically the dynamics of chemically self-propelled Janus colloids moving atop a two-dimensional crystalline surface. The surface is a hexagonally close-packed monolayer of colloidal particles of the same size as the mobile one. The dynamics of the self-propelled colloid reflects the competition between hindered diffusion due to the periodic surface and enhanced diffusion due to active motion. Which contribution dominates depends on the propulsion strength, which can be systematically tuned by changing the concentration of a chemical fuel. The mean-square displacements (MSDs) obtained from the experiment exhibit enhanced diffusion at long lag times. Our experimental data are consistent with a Langevin model for the effectively two-dimensional translational motion of an active Brownian particle in a periodic potential, combining the confining effects of gravity and the crystalline surface with the free rotational diffusion of the colloid. Approximate analytical predictions are made for the MSD describing the crossover from free Brownian motion at short times to active diffusion at long times. The results are in semi-quantitative agreement with numerical results of a refined Langevin model that treats translational and rotational degrees of freedom on the same footing.

Temperature gradient effects on vapor diffusion in partially-saturated porous media

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

Webb, S.W.

1999-07-01

Vapor diffusion in porous media in the presence of its own liquid may be enhanced due to pore-scale processes, such as condensation and evaporation across isolated liquid islands. Webb and Ho (1997) developed one-and two-dimensional mechanistic pore-scale models of these processes in an ideal porous medium. For isothermal and isobaric boundary conditions with a concentration gradient, the vapor diffusion rate was significantly enhanced by these liquid island processes compared to a dry porous media. The influence of a temperature gradient on the enhanced vapor diffusion rate is considered in this paper. The two-dimensional pore network model which is used inmore » the present study is shown. For partially-saturated conditions, a liquid island is introduced into the top center pore. Boundary conditions on the left and right sides of the model are specified to give the desired concentration and temperature gradients. Vapor condenses on one side of the liquid island and evaporates off the other side due to local vapor pressure lowering caused by the interface curvature, even without a temperature gradient. Rather than acting as an impediment to vapor diffusion, the liquid island actually enhances the vapor diffusion rate. The enhancement of the vapor diffusion rate can be significant depending on the liquid saturation. Vapor diffusion is enhanced by up to 40% for this single liquid island compared to a dry porous medium; enhancement factors of up to an order of magnitude have been calculated for other conditions by Webb and Ho (1997). The dominant effect on the enhancement factor is the concentration gradient; the influence of the temperature gradient is smaller. The significance of these results, which need to be confirmed by experiments, is that the dominant model of enhanced vapor diffusion (EVD) by Philip and deVries (1957) predicts that temperature gradients must exist for EVD to occur. If there is no temperature gradient, there is no enhancement. The present results indicate that EVD is predominantly driven by concentration gradients; temperature gradients are less important. Therefore, the EVD model of Philip and deVries may need to be modified to reflect these results.« less

Noise-induced drift in two-dimensional anisotropic systems

NASA Astrophysics Data System (ADS)

Farago, Oded

2017-10-01

We study the isothermal Brownian dynamics of a particle in a system with spatially varying diffusivity. Due to the heterogeneity of the system, the particle's mean displacement does not vanish even if it does not experience any physical force. This phenomenon has been termed "noise-induced drift," and has been extensively studied for one-dimensional systems. Here, we examine the noise-induced drift in a two-dimensional anisotropic system, characterized by a symmetric diffusion tensor with unequal diagonal elements. A general expression for the mean displacement vector is derived and presented as a sum of two vectors, depicting two distinct drifting effects. The first vector describes the tendency of the particle to drift toward the high diffusivity side in each orthogonal principal diffusion direction. This is a generalization of the well-known expression for the noise-induced drift in one-dimensional systems. The second vector represents a novel drifting effect, not found in one-dimensional systems, originating from the spatial rotation in the directions of the principal axes. The validity of the derived expressions is verified by using Langevin dynamics simulations. As a specific example, we consider the relative diffusion of two transmembrane proteins, and demonstrate that the average distance between them increases at a surprisingly fast rate of several tens of micrometers per second.

Electromigration of intergranular voids in metal films for microelectronic interconnects

NASA Astrophysics Data System (ADS)

Averbuch, Amir; Israeli, Moshe; Ravve, Igor

2003-04-01

Voids and cracks often occur in the interconnect lines of microelectronic devices. They increase the resistance of the circuits and may even lead to a fatal failure. Voids may occur inside a single grain, but often they appear on the boundary between two grains. In this work, we model and analyze numerically the migration and evolution of an intergranular void subjected to surface diffusion forces and external voltage applied to the interconnect. The grain-void interface is considered one-dimensional, and the physical formulation of the electromigration and diffusion model results in two coupled fourth-order one-dimensional time-dependent PDEs. The boundary conditions are specified at the triple points, which are common to both neighboring grains and the void. The solution of these equations uses a finite difference scheme in space and a Runge-Kutta integration scheme in time, and is also coupled to the solution of a static Laplace equation describing the voltage distribution throughout the grain. Since the voltage distribution is required only along the interface line, the two-dimensional discretization of the grain interior is not needed, and the static problem is solved by the boundary element method at each time step. The motion of the intergranular void was studied for different ratios between the diffusion and the electric field forces, and for different initial configurations of the void.

LETTER TO THE EDITOR: Fractal diffusion coefficient from dynamical zeta functions

NASA Astrophysics Data System (ADS)

Cristadoro, Giampaolo

2006-03-01

Dynamical zeta functions provide a powerful method to analyse low-dimensional dynamical systems when the underlying symbolic dynamics is under control. On the other hand, even simple one-dimensional maps can show an intricate structure of the grammar rules that may lead to a non-smooth dependence of global observables on parameters changes. A paradigmatic example is the fractal diffusion coefficient arising in a simple piecewise linear one-dimensional map of the real line. Using the Baladi-Ruelle generalization of the Milnor-Thurnston kneading determinant, we provide the exact dynamical zeta function for such a map and compute the diffusion coefficient from its smallest zero.

Spatiotemporal patterns in reaction-diffusion system and in a vibrated granular bed

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

Swinney, H.L.; Lee, K.J.; McCormick, W.D.

Experiments on a quasi-two-dimensional reaction-diffusion system reveal transitions from a uniform state to stationary hexagonal, striped, and rhombic spatial patterns. For other reactor conditions lamellae and self-replicating spot patterns are observed. These patterns form in continuously fed thin gel reactors that can be maintained indefinitely in well-defined nonequilibrium states. Reaction-diffusion models with two chemical species yield patterns similar to those observed in the experiments. Pattern formation is also being examined in vertically oscillated thin granular layers (typically 3-30 particle diameters deep). For small acceleration amplitudes, a granular layer is flat, but above a well-defined critical acceleration amplitude, spatial patterns spontaneouslymore » form. Disordered time-dependent granular patterns are observed as well as regular patterns of squares, stripes, and hexagons. A one-dimensional model consisting of a completely inelastic ball colliding with a sinusoidally oscillating platform provides a semi-quantitative description of most of the observed bifurcations between the different spatiotemporal regimes.« less

A stochastic multi-scale method for turbulent premixed combustion

NASA Astrophysics Data System (ADS)

Cha, Chong M.

2002-11-01

The stochastic chemistry algorithm of Bunker et al. and Gillespie is used to perform the chemical reactions in a transported probability density function (PDF) modeling approach of turbulent combustion. Recently, Kraft & Wagner have demonstrated a 100-fold gain in computational speed (for a 100 species mechanism) using the stochastic approach over the conventional, direct integration method of solving for the chemistry. Here, the stochastic chemistry algorithm is applied to develop a new transported PDF model of turbulent premixed combustion. The methodology relies on representing the relevant spatially dependent physical processes as queuing events. The canonical problem of a one-dimensional premixed flame is used for validation. For the laminar case, molecular diffusion is described by a random walk. For the turbulent case, one of two different material transport submodels can provide the necessary closure: Taylor dispersion or Kerstein's one-dimensional turbulence approach. The former exploits ``eddy diffusivity'' and hence would be much more computationally tractable for practical applications. Various validation studies are performed. Results from the Monte Carlo simulations compare well to asymptotic solutions of laminar premixed flames, both with and without high activation temperatures. The correct scaling of the turbulent burning velocity is predicted in both Damköhler's small- and large-scale turbulence limits. The effect of applying the eddy diffusivity concept in the various regimes is discussed.

Transport dissipative particle dynamics model for mesoscopic advection- diffusion-reaction problems

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

Zhen, Li; Yazdani, Alireza; Tartakovsky, Alexandre M.

2015-07-07

We present a transport dissipative particle dynamics (tDPD) model for simulating mesoscopic problems involving advection-diffusion-reaction (ADR) processes, along with a methodology for implementation of the correct Dirichlet and Neumann boundary conditions in tDPD simulations. tDPD is an extension of the classic DPD framework with extra variables for describing the evolution of concentration fields. The transport of concentration is modeled by a Fickian flux and a random flux between particles, and an analytical formula is proposed to relate the mesoscopic concentration friction to the effective diffusion coefficient. To validate the present tDPD model and the boundary conditions, we perform three tDPDmore » simulations of one-dimensional diffusion with different boundary conditions, and the results show excellent agreement with the theoretical solutions. We also performed two-dimensional simulations of ADR systems and the tDPD simulations agree well with the results obtained by the spectral element method. Finally, we present an application of the tDPD model to the dynamic process of blood coagulation involving 25 reacting species in order to demonstrate the potential of tDPD in simulating biological dynamics at the mesoscale. We find that the tDPD solution of this comprehensive 25-species coagulation model is only twice as computationally expensive as the DPD simulation of the hydrodynamics only, which is a significant advantage over available continuum solvers.« less

Transition density of one-dimensional diffusion with discontinuous drift

NASA Technical Reports Server (NTRS)

Zhang, Weijian

1990-01-01

The transition density of a one-dimensional diffusion process with a discontinuous drift coefficient is studied. A probabilistic representation of the transition density is given, illustrating the close connections between discontinuities of the drift and Brownian local times. In addition, some explicit results are obtained based on the trivariate density of Brownian motion, its occupation, and local times.

Diffusion with resetting inside a circle

NASA Astrophysics Data System (ADS)

Chatterjee, Abhinava; Christou, Christos; Schadschneider, Andreas

2018-06-01

We study the Brownian motion of a particle in a bounded circular two-dimensional domain in search for a stationary target on the boundary of the domain. The process switches between two modes: one where it performs a two-dimensional diffusion inside the circle and one where it diffuses along the one-dimensional boundary. During the process, the Brownian particle resets to its initial position with a constant rate r . The Fokker-Planck formalism allows us to calculate the mean time to absorption (MTA) as well as the optimal resetting rate for which the MTA is minimized. From the derived analytical results the parameter regions where resetting reduces the search time can be specified. We also provide a numerical method for the verification of our results.

Room-Temperature Micron-Scale Exciton Migration in a Stabilized Emissive Molecular Aggregate.

PubMed

Caram, Justin R; Doria, Sandra; Eisele, Dörthe M; Freyria, Francesca S; Sinclair, Timothy S; Rebentrost, Patrick; Lloyd, Seth; Bawendi, Moungi G

2016-11-09

We report 1.6 ± 1 μm exciton transport in self-assembled supramolecular light-harvesting nanotubes (LHNs) assembled from amphiphillic cyanine dyes. We stabilize LHNs in a sucrose glass matrix, greatly reducing light and oxidative damage and allowing the observation of exciton-exciton annihilation signatures under weak excitation flux. Fitting to a one-dimensional diffusion model, we find an average exciton diffusion constant of 55 ± 20 cm 2 /s, among the highest measured for an organic system. We develop a simple model that uses cryogenic measurements of static and dynamic energetic disorder to estimate a diffusion constant of 32 cm 2 /s, in agreement with experiment. We ascribe large exciton diffusion lengths to low static and dynamic energetic disorder in LHNs. We argue that matrix-stabilized LHNS represent an excellent model system to study coherent excitonic transport.

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.

Critical short-time dynamics in a system with interacting static and diffusive populations

NASA Astrophysics Data System (ADS)

Argolo, C.; Quintino, Yan; Gleria, Iram; Lyra, M. L.

2012-01-01

We study the critical short-time dynamical behavior of a one-dimensional model where diffusive individuals can infect a static population upon contact. The model presents an absorbing phase transition from an active to an inactive state. Previous calculations of the critical exponents based on quasistationary quantities have indicated an unusual crossover from the directed percolation to the diffusive contact process universality classes. Here we show that the critical exponents governing the slow short-time dynamic evolution of several relevant quantities, including the order parameter, its relative fluctuations, and correlation function, reinforce the lack of universality in this model. Accurate estimates show that the critical exponents are distinct in the regimes of low and high recovery rates.

Continuous time random walk model with asymptotical probability density of waiting times via inverse Mittag-Leffler function

NASA Astrophysics Data System (ADS)

Liang, Yingjie; Chen, Wen

2018-04-01

The mean squared displacement (MSD) of the traditional ultraslow diffusion is a logarithmic function of time. Recently, the continuous time random walk model is employed to characterize this ultraslow diffusion dynamics by connecting the heavy-tailed logarithmic function and its variation as the asymptotical waiting time density. In this study we investigate the limiting waiting time density of a general ultraslow diffusion model via the inverse Mittag-Leffler function, whose special case includes the traditional logarithmic ultraslow diffusion model. The MSD of the general ultraslow diffusion model is analytically derived as an inverse Mittag-Leffler function, and is observed to increase even more slowly than that of the logarithmic function model. The occurrence of very long waiting time in the case of the inverse Mittag-Leffler function has the largest probability compared with the power law model and the logarithmic function model. The Monte Carlo simulations of one dimensional sample path of a single particle are also performed. The results show that the inverse Mittag-Leffler waiting time density is effective in depicting the general ultraslow random motion.

A simplified counter diffusion method combined with a 1D simulation program for optimizing crystallization conditions.

PubMed

Tanaka, Hiroaki; Inaka, Koji; Sugiyama, Shigeru; Takahashi, Sachiko; Sano, Satoshi; Sato, Masaru; Yoshitomi, Susumu

2004-01-01

We developed a new protein crystallization method has been developed using a simplified counter-diffusion method for optimizing crystallization condition. It is composed of only a single capillary, the gel in the silicon tube and the screw-top test tube, which are readily available in the laboratory. The one capillary can continuously scan a wide range of crystallization conditions (combination of the concentrations of the precipitant and the protein) unless crystallization occurs, which means that it corresponds to many drops in the vapor-diffusion method. The amount of the precipitant and the protein solutions can be much less than in conventional methods. In this study, lysozyme and alpha-amylase were used as model proteins for demonstrating the efficiency of this method. In addition, one-dimensional (1-D) simulations of the crystal growth were performed based on the 1-D diffusion model. The optimized conditions can be applied to the initial crystallization conditions for both other counter-diffusion methods with the Granada Crystallization Box (GCB) and for the vapor-diffusion method after some modification.

A Gibbs point field model for the spatial pattern of coronary capillaries

NASA Astrophysics Data System (ADS)

Karch, R.; Neumann, M.; Neumann, F.; Ullrich, R.; Neumüller, J.; Schreiner, W.

2006-09-01

We propose a Gibbs point field model for the pattern of coronary capillaries in transverse histologic sections from human hearts, based on the physiology of oxygen supply from capillaries to tissue. To specify the potential energy function of the Gibbs point field, we draw on an analogy between the equation of steady-state oxygen diffusion from an array of parallel capillaries to the surrounding tissue and Poisson's equation for the electrostatic potential of a two-dimensional distribution of identical point charges. The influence of factors other than diffusion is treated as a thermal disturbance. On this basis, we arrive at the well-known two-dimensional one-component plasma, a system of identical point charges exhibiting a weak (logarithmic) repulsive interaction that is completely characterized by a single dimensionless parameter. By variation of this parameter, the model is able to reproduce many characteristics of real capillary patterns.

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.

Diffusion related isotopic fractionation effects with one-dimensional advective-dispersive transport.

PubMed

Xu, Bruce S; Lollar, Barbara Sherwood; Passeport, Elodie; Sleep, Brent E

2016-04-15

Aqueous phase diffusion-related isotope fractionation (DRIF) for carbon isotopes was investigated for common groundwater contaminants in systems in which transport could be considered to be one-dimensional. This paper focuses not only on theoretically observable DRIF effects in these systems but introduces the important concept of constraining "observable" DRIF based on constraints imposed by the scale of measurements in the field, and on standard limits of detection and analytical uncertainty. Specifically, constraints for the detection of DRIF were determined in terms of the diffusive fractionation factor, the initial concentration of contaminants (C0), the method detection limit (MDL) for isotopic analysis, the transport time, and the ratio of the longitudinal mechanical dispersion coefficient to effective molecular diffusion coefficient (Dmech/Deff). The results allow a determination of field conditions under which DRIF may be an important factor in the use of stable carbon isotope measurements for evaluation of contaminant transport and transformation for one-dimensional advective-dispersive transport. This study demonstrates that for diffusion-dominated transport of BTEX, MTBE, and chlorinated ethenes, DRIF effects are only detectable for the smaller molar mass compounds such as vinyl chloride for C0/MDL ratios of 50 or higher. Much larger C0/MDL ratios, corresponding to higher source concentrations or lower detection limits, are necessary for DRIF to be detectable for the higher molar mass compounds. The distance over which DRIF is observable for VC is small (less than 1m) for a relatively young diffusive plume (<100years), and DRIF will not easily be detected by using the conventional sampling approach with "typical" well spacing (at least several meters). With contaminant transport by advection, mechanical dispersion, and molecular diffusion this study suggests that in field sites where Dmech/Deff is larger than 10, DRIF effects will likely not be observable for common groundwater contaminants. Importantly, under most field conditions, Dmech/Deff≥10 is usually satisfied in the longitudinal direction, suggesting that DRIF is not likely to be observable in most groundwater systems in which contaminant transport is predominantly one-dimensional. Given the importance in the MDL it is recommended that MDL should always be explicitly reported in both modeling and field studies. Copyright © 2016. Published by Elsevier B.V.

Application of underdamped Langevin dynamics simulations for the study of diffusion from a drug-eluting stent

NASA Astrophysics Data System (ADS)

Regev, Shaked; Farago, Oded

2018-10-01

We use a one-dimensional two layer model with a semi-permeable membrane to study the diffusion of a therapeutic drug delivered from a drug-eluting stent (DES). The rate of drug transfer from the stent coating to the arterial wall is calculated by using underdamped Langevin dynamics simulations. Our results reveal that the membrane has virtually no delay effect on the rate of delivery from the DES. The work demonstrates the great potential of underdamped Langevin dynamics simulations as an easy to implement, efficient, method for solving complicated diffusion problems in systems with a spatially-dependent diffusion coefficient.

Fourier analysis of finite element preconditioned collocation schemes

NASA Technical Reports Server (NTRS)

Deville, Michel O.; Mund, Ernest H.

1990-01-01

The spectrum of the iteration operator of some finite element preconditioned Fourier collocation schemes is investigated. The first part of the paper analyses one-dimensional elliptic and hyperbolic model problems and the advection-diffusion equation. Analytical expressions of the eigenvalues are obtained with use of symbolic computation. The second part of the paper considers the set of one-dimensional differential equations resulting from Fourier analysis (in the tranverse direction) of the 2-D Stokes problem. All results agree with previous conclusions on the numerical efficiency of finite element preconditioning schemes.

Parameter extraction and transistor models

NASA Technical Reports Server (NTRS)

Rykken, Charles; Meiser, Verena; Turner, Greg; Wang, QI

1985-01-01

Using specified mathematical models of the MOSFET device, the optimal values of the model-dependent parameters were extracted from data provided by the Jet Propulsion Laboratory (JPL). Three MOSFET models, all one-dimensional were used. One of the models took into account diffusion (as well as convection) currents. The sensitivity of the models was assessed for variations of the parameters from their optimal values. Lines of future inquiry are suggested on the basis of the behavior of the devices, of the limitations of the proposed models, and of the complexity of the required numerical investigations.

Theory of bimolecular reactions in a solution with linear traps: Application to the problem of target search on DNA.

PubMed

Turkin, Alexander; van Oijen, Antoine M; Turkin, Anatoliy A

2015-01-01

One-dimensional sliding along DNA as a means to accelerate protein target search is a well-known phenomenon occurring in various biological systems. Using a biomimetic approach, we have recently demonstrated the practical use of DNA-sliding peptides to speed up bimolecular reactions more than an order of magnitude by allowing the reactants to associate not only in the solution by three-dimensional (3D) diffusion, but also on DNA via one-dimensional (1D) diffusion [A. Turkin et al., Chem. Sci. (2015)]. Here we present a mean-field kinetic model of a bimolecular reaction in a solution with linear extended sinks (e.g., DNA) that can intermittently trap molecules present in a solution. The model consists of chemical rate equations for mean concentrations of reacting species. Our model demonstrates that addition of linear traps to the solution can significantly accelerate reactant association. We show that at optimum concentrations of linear traps the 1D reaction pathway dominates in the kinetics of the bimolecular reaction; i.e., these 1D traps function as an assembly line of the reaction product. Moreover, we show that the association reaction on linear sinks between trapped reactants exhibits a nonclassical third-order behavior. Predictions of the model agree well with our experimental observations. Our model provides a general description of bimolecular reactions that are controlled by a combined 3D+1D mechanism and can be used to quantitatively describe both naturally occurring as well as biomimetic biochemical systems that reduce the dimensionality of search.

Laser one-dimensional range profile and the laser two-dimensional range profile of cylinders

NASA Astrophysics Data System (ADS)

Gong, Yanjun; Wang, Mingjun; Gong, Lei

2015-10-01

Laser one-dimensional range profile, that is scattering power from pulse laser scattering of target, is a radar imaging technology. The laser two-dimensional range profile is two-dimensional scattering imaging of pulse laser of target. Laser one-dimensional range profile and laser two-dimensional range profile are called laser range profile(LRP). The laser range profile can reflect the characteristics of the target shape and surface material. These techniques were motivated by applications of laser radar to target discrimination in ballistic missile defense. The radar equation of pulse laser is given in this paper. This paper demonstrates the analytical model of laser range profile of cylinder based on the radar equation of the pulse laser. Simulations results of laser one-dimensional range profiles of some cylinders are given. Laser range profiles of cylinder, whose surface material with diffuse lambertian reflectance, is given in this paper. Laser range profiles of different pulse width of cylinder are given in this paper. The influences of geometric parameters, pulse width, attitude on the range profiles are analyzed.

A Computational Investigation of Sooting Limits of Spherical Diffusion Flames

NASA Technical Reports Server (NTRS)

Lecoustre, V. R.; Chao, B. H.; Sunderland, P. B.; Urban, D. L.; Stocker, D. P.; Axelbaum, R. L.

2007-01-01

Limiting conditions for soot particle inception in spherical diffusion flames were investigated numerically. The flames were modeled using a one-dimensional, time accurate diffusion flame code with detailed chemistry and transport and an optically thick radiation model. Seventeen normal and inverse flames were considered, covering a wide range of stoichiometric mixture fraction, adiabatic flame temperature, and residence time. These flames were previously observed to reach their sooting limits after 2 s of microgravity. Sooting-limit diffusion flames with residence times longer than 200 ms were found to have temperatures near 1190 K where C/O = 0.6, whereas flames with shorter residence times required increased temperatures. Acetylene was found to be a reasonable surrogate for soot precursor species in these flames, having peak mole fractions of about 0.01.

Effects of C/O Ratio and Temperature on Sooting Limits of Spherical Diffusion Flames

NASA Technical Reports Server (NTRS)

Lecoustre, V. R.; Sunderland, P. B.; Chao, B. H.; Urban, D. L.; Stocker, D. P.; Axelbaum, R. L.

2008-01-01

Limiting conditions for soot particle inception in spherical diffusion flames were investigated numerically. The flames were modeled using a one-dimensional, time accurate diffusion flame code with detailed chemistry and transport and an optically thick radiation model. Seventeen normal and inverse flames were considered, covering a wide range of stoichiometric mixture fraction, adiabatic flame temperature, residence time and scalar dissipation rate. These flames were previously observed to reach their sooting limits after 2 s of microgravity. Sooting-limit diffusion flames with scalar dissipation rate lower than 2/s were found to have temperatures near 1400 K where C/O = 0.51, whereas flames with greater scalar dissipation rate required increased temperatures. This finding was valid across a broad range of fuel and oxidizer compositions and convection directions.

Barriers to front propagation in laminar, three-dimensional fluid flows

NASA Astrophysics Data System (ADS)

Doan, Minh; Simons, J. J.; Lilienthal, Katherine; Solomon, Tom; Mitchell, Kevin A.

2018-03-01

We present experiments on one-way barriers that block reaction fronts in a fully three-dimensional (3D) fluid flow. Fluorescent Belousov-Zhabotinsky reaction fronts are imaged with laser-scanning in a laminar, overlapping vortex flow. The barriers are analyzed with a 3D extension to burning invariant manifold (BIM) theory that was previously applied to two-dimensional advection-reaction-diffusion processes. We discover tube and sheet barriers that guide the front evolution. The experimentally determined barriers are explained by BIMs calculated from a model of the flow.

DMM: A MULTIGROUP, MULTIREGION ONE-SPACE-DIMENSIONAL COMPUTER PROGRAM USING NEUTRON DIFFUSION THEORY. PART II. DMM PROGRAM DESCRIPTION

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

Kavanagh, D.L.; Antchagno, M.J.; Egawa, E.K.

1960-12-31

Operating instructions are presented for DMM, a Remington Rand 1103A program using one-space-dimensional multigroup diffusion theory to calculate the reactivity or critical conditions and flux distribution of a multiregion reactor. Complete descriptions of the routines and problem input and output specifications are also included. (D.L.C.)

Roles of Diffusion Dynamics in Stem Cell Signaling and Three-Dimensional Tissue Development.

PubMed

McMurtrey, Richard J

2017-09-15

Recent advancements in the ability to construct three-dimensional (3D) tissues and organoids from stem cells and biomaterials have not only opened abundant new research avenues in disease modeling and regenerative medicine but also have ignited investigation into important aspects of molecular diffusion in 3D cellular architectures. This article describes fundamental mechanics of diffusion with equations for modeling these dynamic processes under a variety of scenarios in 3D cellular tissue constructs. The effects of these diffusion processes and resultant concentration gradients are described in the context of the major molecular signaling pathways in stem cells that both mediate and are influenced by gas and nutrient concentrations, including how diffusion phenomena can affect stem cell state, cell differentiation, and metabolic states of the cell. The application of these diffusion models and pathways is of vital importance for future studies of developmental processes, disease modeling, and tissue regeneration.

Two-dimensional numerical simulation of boron diffusion for pyramidally textured silicon

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

Ma, Fa-Jun, E-mail: Fajun.Ma@nus.edu.sg; Duttagupta, Shubham; Department of Electrical and Computer Engineering, National University of Singapore, 4 Engineering Drive 3, 117576

2014-11-14

Multidimensional numerical simulation of boron diffusion is of great relevance for the improvement of industrial n-type crystalline silicon wafer solar cells. However, surface passivation of boron diffused area is typically studied in one dimension on planar lifetime samples. This approach neglects the effects of the solar cell pyramidal texture on the boron doping process and resulting doping profile. In this work, we present a theoretical study using a two-dimensional surface morphology for pyramidally textured samples. The boron diffusivity and segregation coefficient between oxide and silicon in simulation are determined by reproducing measured one-dimensional boron depth profiles prepared using different boronmore » diffusion recipes on planar samples. The established parameters are subsequently used to simulate the boron diffusion process on textured samples. The simulated junction depth is found to agree quantitatively well with electron beam induced current measurements. Finally, chemical passivation on planar and textured samples is compared in device simulation. Particularly, a two-dimensional approach is adopted for textured samples to evaluate chemical passivation. The intrinsic emitter saturation current density, which is only related to Auger and radiative recombination, is also simulated for both planar and textured samples. The differences between planar and textured samples are discussed.« less

Macroscopic Modeling of a One-Dimensional Electrochemical Cell using the Poisson-Nernst-Planck Equations

NASA Astrophysics Data System (ADS)

Yan, David

This thesis presents the one-dimensional equations, numerical method and simulations of a model to characterize the dynamical operation of an electrochemical cell. This model extends the current state-of-the art in that it accounts, in a primitive way, for the physics of the electrolyte/electrode interface and incorporates diffuse-charge dynamics, temperature coupling, surface coverage, and polarization phenomena. The one-dimensional equations account for a system with one or two mobile ions of opposite charge, and the electrode reaction we consider (when one is needed) is a one-electron electrodeposition reaction. Though the modeled system is far from representing a realistic electrochemical device, our results show a range of dynamics and behaviors which have not been observed previously, and explore the numerical challenges required when adding more complexity to a model. Furthermore, the basic transport equations (which are developed in three spatial dimensions) can in future accomodate the inclusion of additional physics, and coupling to more complex boundary conditions that incorporate two-dimensional surface phenomena and multi-rate reactions. In the model, the Poisson-Nernst-Planck equations are used to model diffusion and electromigration in an electrolyte, and the generalized Frumkin-Butler-Volmer equation is used to model reaction kinetics at electrodes. An energy balance equation is derived and coupled to the diffusion-migration equation. The model also includes dielectric polarization effects by introducing different values of the dielectric permittivity in different regions of the bulk, as well as accounting for surface coverage effects due to adsorption, and finite size "crowding", or steric effects. Advection effects are not modeled but could in future be incorporated. In order to solve the coupled PDE's, we use a variable step size second order scheme in time and finite differencing in space. Numerical tests are performed on a simplified system and the scheme's stability and convergence properties are discussed. While evaluating different methods for discretizing the coupled flux boundary condition, we discover a thresholding behaviour in the adaptive time stepper, and perform additional tests to investigate it. Finally, a method based on ghost points is chosen for its favorable numerical properties compared to the alternatives. With this method, we are able to run simulations with a large range of parameters, including any value of the nondimensionalized Debye length epsilon. The numerical code is first used to run simulations to explore the effects of polarization, surface coverage, and temperature. The code is also used to perform frequency sweeps of input signals in order to mimic impedance spectroscopy experiments. Finally, in Chapter 5, we use our model to apply ramped voltages to electrochemical systems, and show theoretical and simulated current-voltage curves for liquid and solid thin films, cells with blocking (polarized) electrodes, and electrolytes with background charge. Linear sweep and cyclic voltammetry techniques are important tools for electrochemists and have a variety of applications in engineering. Voltammetry has classically been treated with the Randles-Sevcik equation, which assumes an electroneutral supported electrolyte. No general theory of linear-sweep voltammetry is available, however, for unsupported electrolytes and for other situations where diffuse charge effects play a role. We show theoretical and simulated current-voltage curves for liquid and solid thin films, cells with blocking electrodes, and membranes with fixed background charge. The analysis focuses on the coupling of Faradaic reactions and diffuse charge dynamics, but capacitive charging of the double layers is also studied, for early time transients at reactive electrodes and for non-reactive blocking electrodes. The final chapter highlights the role of diffuse charge in the context of voltammetry, and illustrates which regimes can be approximated using simple analytical expressions and which require more careful consideration.

Diffuse optical correlation tomography of cerebral blood flow during cortical spreading depression in rat brain

NASA Astrophysics Data System (ADS)

Zhou, Chao; Yu, Guoqiang; Furuya, Daisuke; Greenberg, Joel; Yodh, Arjun; Durduran, Turgut

2006-02-01

Diffuse optical correlation methods were adapted for three-dimensional (3D) tomography of cerebral blood flow (CBF) in small animal models. The image reconstruction was optimized using a noise model for diffuse correlation tomography which enabled better data selection and regularization. The tomographic approach was demonstrated with simulated data and during in-vivo cortical spreading depression (CSD) in rat brain. Three-dimensional images of CBF were obtained through intact skull in tissues(~4mm) deep below the cortex.

Convergence to a pulsating travelling wave for an epidemic reaction-diffusion system with non-diffusive susceptible population.

PubMed

Ducrot, Arnaud; Giletti, Thomas

2014-09-01

In this work we study the asymptotic behaviour of the Kermack-McKendrick reaction-diffusion system in a periodic environment with non-diffusive susceptible population. This problem was proposed by Kallen et al. as a model for the spatial spread for epidemics, where it can be reasonable to assume that the susceptible population is motionless. For arbitrary dimensional space we prove that large classes of solutions of such a system have an asymptotic spreading speed in large time, and that the infected population has some pulse-like asymptotic shape. The analysis of the one-dimensional problem is more developed, as we are able to uncover a much more accurate description of the profile of solutions. Indeed, we will see that, for some initially compactly supported infected population, the profile of the solution converges to some pulsating travelling wave with minimal speed, that is to some entire solution moving at a constant positive speed and whose profile's shape is periodic in time.

Thermal conductivity in one-dimensional nonlinear systems

NASA Astrophysics Data System (ADS)

Politi, Antonio; Giardinà, Cristian; Livi, Roberto; Vassalli, Massimo

2000-03-01

Thermal conducitivity of one-dimensional nonlinear systems typically diverges in the thermodynamic limit, whenever the momentum is conserved (i.e. in the absence of interactions with an external substrate). Evidence comes from detailed studies of Fermi-Pasta-Ulam and diatomic Toda chains. Here, we discuss the first example of a one-dimensional system obeying Fourier law : a chain of coupled rotators. Numerical estimates of the thermal conductivity obtained by simulating a chain in contact with two thermal baths at different temperatures are found to be consistent with those ones based on linear response theory. The dynamics of the Fourier modes provides direct evidence of energy diffusion. The finiteness of the conductivity is traced back to the occurrence of phase-jumps. Our conclusions are confirmed by the analysis of two variants of the rotator model.

Finite element modeling of diffusion and partitioning in biological systems: the infinite composite medium problem.

PubMed

Missel, P J

2000-01-01

Four methods are proposed for modeling diffusion in heterogeneous media where diffusion and partition coefficients take on differing values in each subregion. The exercise was conducted to validate finite element modeling (FEM) procedures in anticipation of modeling drug diffusion with regional partitioning into ocular tissue, though the approach can be useful for other organs, or for modeling diffusion in laminate devices. Partitioning creates a discontinuous value in the dependent variable (concentration) at an intertissue boundary that is not easily handled by available general-purpose FEM codes, which allow for only one value at each node. The discontinuity is handled using a transformation on the dependent variable based upon the region-specific partition coefficient. Methods were evaluated by their ability to reproduce a known exact result, for the problem of the infinite composite medium (Crank, J. The Mathematics of Diffusion, 2nd ed. New York: Oxford University Press, 1975, pp. 38-39.). The most physically intuitive method is based upon the concept of chemical potential, which is continuous across an interphase boundary (method III). This method makes the equation of the dependent variable highly nonlinear. This can be linearized easily by a change of variables (method IV). Results are also given for a one-dimensional problem simulating bolus injection into the vitreous, predicting time disposition of drug in vitreous and retina.

An axisymmetric single-path model for gas transport in the conducting airways.

PubMed

Madasu, Srinath; Borhan, All; Ultman, James S

2006-02-01

In conventional one-dimensional single-path models, radially averaged concentration is calculated as a function of time and longitudinal position in the lungs, and coupled convection and diffusion are accounted for with a dispersion coefficient. The axisymmetric single-path model developed in this paper is a two-dimensional model that incorporates convective-diffusion processes in a more fundamental manner by simultaneously solving the Navier-Stokes and continuity equations with the convection-diffusion equation. A single airway path was represented by a series of straight tube segments interconnected by leaky transition regions that provide for flow loss at the airway bifurcations. As a sample application, the model equations were solved by a finite element method to predict the unsteady state dispersion of an inhaled pulse of inert gas along an airway path having dimensions consistent with Weibel's symmetric airway geometry. Assuming steady, incompressible, and laminar flow, a finite element analysis was used to solve for the axisymmetric pressure, velocity and concentration fields. The dispersion calculated from these numerical solutions exhibited good qualitative agreement with the experimental values, but quantitatively was in error by 20%-30% due to the assumption of axial symmetry and the inability of the model to capture the complex recirculatory flows near bifurcations.

Universal time-dependent dispersion properties for diffusion in a one-dimensional critically tilted potential

NASA Astrophysics Data System (ADS)

Guérin, T.; Dean, D. S.

2017-01-01

We consider the time-dependent dispersion properties of overdamped tracer particles diffusing in a one-dimensional periodic potential under the influence of an additional constant tilting force F . The system is studied in the region where the force is close to the critical value Fc at which the barriers separating neighboring potential wells disappear. We show that, when F crosses the critical value, the shape of the mean-square displacement (MSD) curves is strongly modified. We identify a diffusive regime at intermediate-time scales with an effective diffusion coefficient which is much larger than the late-time diffusion coefficient for F >Fc , whereas for F

Homogenization of a Directed Dispersal Model for Animal Movement in a Heterogeneous Environment.

PubMed

Yurk, Brian P

2016-10-01

The dispersal patterns of animals moving through heterogeneous environments have important ecological and epidemiological consequences. In this work, we apply the method of homogenization to analyze an advection-diffusion (AD) model of directed movement in a one-dimensional environment in which the scale of the heterogeneity is small relative to the spatial scale of interest. We show that the large (slow) scale behavior is described by a constant-coefficient diffusion equation under certain assumptions about the fast-scale advection velocity, and we determine a formula for the slow-scale diffusion coefficient in terms of the fast-scale parameters. We extend the homogenization result to predict invasion speeds for an advection-diffusion-reaction (ADR) model with directed dispersal. For periodic environments, the homogenization approximation of the solution of the AD model compares favorably with numerical simulations. Invasion speed approximations for the ADR model also compare favorably with numerical simulations when the spatial period is sufficiently small.

A three-dimensional spin-diffusion model for micromagnetics

PubMed Central

Abert, Claas; Ruggeri, Michele; Bruckner, Florian; Vogler, Christoph; Hrkac, Gino; Praetorius, Dirk; Suess, Dieter

2015-01-01

We solve a time-dependent three-dimensional spin-diffusion model coupled to the Landau-Lifshitz-Gilbert equation numerically. The presented model is validated by comparison to two established spin-torque models: The model of Slonzewski that describes spin-torque in multi-layer structures in the presence of a fixed layer and the model of Zhang and Li that describes current driven domain-wall motion. It is shown that both models are incorporated by the spin-diffusion description, i.e., the nonlocal effects of the Slonzewski model are captured as well as the spin-accumulation due to magnetization gradients as described by the model of Zhang and Li. Moreover, the presented method is able to resolve the time dependency of the spin-accumulation. PMID:26442796

Finite-dimensional approximation for optimal fixed-order compensation of distributed parameter systems

NASA Technical Reports Server (NTRS)

Bernstein, Dennis S.; Rosen, I. G.

1988-01-01

In controlling distributed parameter systems it is often desirable to obtain low-order, finite-dimensional controllers in order to minimize real-time computational requirements. Standard approaches to this problem employ model/controller reduction techniques in conjunction with LQG theory. In this paper we consider the finite-dimensional approximation of the infinite-dimensional Bernstein/Hyland optimal projection theory. This approach yields fixed-finite-order controllers which are optimal with respect to high-order, approximating, finite-dimensional plant models. The technique is illustrated by computing a sequence of first-order controllers for one-dimensional, single-input/single-output, parabolic (heat/diffusion) and hereditary systems using spline-based, Ritz-Galerkin, finite element approximation. Numerical studies indicate convergence of the feedback gains with less than 2 percent performance degradation over full-order LQG controllers for the parabolic system and 10 percent degradation for the hereditary system.

Theoretical investigation of microstructure evolution and deformation of zirconium under neutron irradiation

DOE PAGES

Barashev, A. V.; Golubov, S. I.; Stoller, R. E.

2015-06-01

We studied the radiation growth of zirconium using a reaction–diffusion model which takes into account intra-cascade clustering of self-interstitial atoms and one-dimensional diffusion of interstitial clusters. The observed dose dependence of strain rates is accounted for by accumulation of sessile dislocation loops during irradiation. Moreover, the computational model developed and fitted to available experimental data is applied to study deformation of Zr single crystals under irradiation up to hundred dpa. Finally, the effect of cold work and the reasons for negative prismatic strains and co-existence of vacancy and interstitial loops are elucidated.

Aquitard contaminant storage and flux resulting from dense nonaqueous phase liquid source zone dissolution and remediation

EPA Science Inventory

A one-dimensional diffusion model was used to investigate the effects of dense non-aqueous phase liquid (DNAPL) source zone dissolution and remediation on the storage and release of contaminants from aquitards. Source zone dissolution was represented by a power-law source depleti...

Transport dissipative particle dynamics model for mesoscopic advection-diffusion-reaction problems

PubMed Central

Yazdani, Alireza; Tartakovsky, Alexandre; Karniadakis, George Em

2015-01-01

We present a transport dissipative particle dynamics (tDPD) model for simulating mesoscopic problems involving advection-diffusion-reaction (ADR) processes, along with a methodology for implementation of the correct Dirichlet and Neumann boundary conditions in tDPD simulations. tDPD is an extension of the classic dissipative particle dynamics (DPD) framework with extra variables for describing the evolution of concentration fields. The transport of concentration is modeled by a Fickian flux and a random flux between tDPD particles, and the advection is implicitly considered by the movements of these Lagrangian particles. An analytical formula is proposed to relate the tDPD parameters to the effective diffusion coefficient. To validate the present tDPD model and the boundary conditions, we perform three tDPD simulations of one-dimensional diffusion with different boundary conditions, and the results show excellent agreement with the theoretical solutions. We also performed two-dimensional simulations of ADR systems and the tDPD simulations agree well with the results obtained by the spectral element method. Finally, we present an application of the tDPD model to the dynamic process of blood coagulation involving 25 reacting species in order to demonstrate the potential of tDPD in simulating biological dynamics at the mesoscale. We find that the tDPD solution of this comprehensive 25-species coagulation model is only twice as computationally expensive as the conventional DPD simulation of the hydrodynamics only, which is a significant advantage over available continuum solvers. PMID:26156459

Polymer diffusion in the interphase between surface and solution.

PubMed

Weger, Lukas; Weidmann, Monika; Ali, Wael; Hildebrandt, Marcus; Gutmann, Jochen Stefan; Hoffmann-Jacobsen, Kerstin

2018-05-22

Total internal reflection fluorescence correlation spectroscopy (TIR-FCS) is applied to study the self-diffusion of polyethylene glycol solutions in the presence of weakly attractive interfaces. Glass coverslips modified with aminopropyl- and propyl-terminated silanes are used to study the influence of solid surfaces on polymer diffusion. A model of three phases of polymer diffusion allows to describe the experimental fluorescence autocorrelation functions. Besides the two-dimensional diffusion of adsorbed polymer on the substrate and three-dimensional free diffusion in bulk solution, a third diffusion time scale is observed with intermediate diffusion times. This retarded three-dimensional diffusion in solution is assigned to long range effects of solid surfaces on diffusional dynamics of polymers. The respective diffusion constants show Rouse scaling (D~N -1 ) indicating a screening of hydrodynamic interactions by the presence of the surface. Hence, the presented TIR-FCS method proves to be a valuable tool to investigate the effect of surfaces on polymer diffusion beyond the first adsorbed polymer layer on the 100 nm length scale.

Experimental determination of the turbulence in a liquid rocket combustion chamber

NASA Technical Reports Server (NTRS)

Hara, J.; Smith, L. O.; Partus, F. P.

1972-01-01

The intensity of turbulence and the Lagrangian correlation coefficient for a liquid rocket combustion chamber were determined experimentally using the tracer gas diffusion method. The results indicate that the turbulent diffusion process can be adequately modeled by the one-dimensional Taylor theory; however, the numerical values show significant disagreement with previously accepted values. The intensity of turbulence is higher by a factor of about two, while the Lagrangian correlation coefficient which was assumed to be unity in the past is much less than unity.

Modeling snow-crystal growth: a three-dimensional mesoscopic approach.

PubMed

Gravner, Janko; Griffeath, David

2009-01-01

We introduce a three-dimensional, computationally feasible, mesoscopic model for snow-crystal growth, based on diffusion of vapor, anisotropic attachment, and a boundary layer. Several case studies are presented that faithfully replicate most observed snow-crystal morphology, an unusual achievement for a mathematical model. In particular, many of the most striking physical specimens feature both facets and branches, and our model provides an explanation for this phenomenon. We also duplicate many other observed traits, including ridges, ribs, sandwich plates, and hollow columns, as well as various dynamic instabilities. The concordance of observed phenomena suggests that the ingredients in our model are the most important ones in the development of physical snow crystals.

Modeling and experimental examination of water level effects on radon exhalation from fragmented uranium ore.

PubMed

Ye, Yong-Jun; Dai, Xin-Tao; Ding, De-Xin; Zhao, Ya-Li

2016-12-01

In this study, a one-dimensional steady-state mathematical model of radon transport in fragmented uranium ore was established according to Fick's law and radon transfer theory in an air-water interface. The model was utilized to obtain an analytical solution for radon concentration in the air-water, two-phase system under steady state conditions, as well as a corresponding radon exhalation rate calculation formula. We also designed a one-dimensional experimental apparatus for simulating radon diffusion migration in the uranium ore with various water levels to verify the mathematical model. The predicted results were in close agreement with the measured results, suggesting that the proposed model can be readily used to determine radon concentrations and exhalation rates in fragmented uranium ore with varying water levels. Copyright © 2016. Published by Elsevier Ltd.

Modeling the Role of Incisures in Vertebrate Phototransduction

PubMed Central

Caruso, Giovanni; Bisegna, Paolo; Shen, Lixin; Andreucci, Daniele; Hamm, Heidi E.; DiBenedetto, Emmanuele

2006-01-01

Phototransduction is mediated by a G-protein-coupled receptor-mediated cascade, activated by light and localized to rod outer segment (ROS) disk membranes, which, in turn, drives a diffusion process of the second messengers cGMP and Ca2+ in the ROS cytosol. This process is hindered by disks—which, however, bear physical cracks, known as incisures, believed to favor the longitudinal diffusion of cGMP and Ca2+. This article is aimed at highlighting the biophysical functional role and significance of incisures, and their effect on the local and global response of the photocurrent. Previous work on this topic regarded the ROS as well stirred in the radial variables, lumped the diffusion mechanism on the longitudinal axis of the ROS, and replaced the cytosolic diffusion coefficients by effective ones, accounting for incisures through their total patent area only. The fully spatially resolved model recently published by our group is a natural tool to take into account other significant details of incisures, including their geometry and distribution. Using mathematical theories of homogenization and concentrated capacity, it is shown here that the complex diffusion process undergone by the second messengers cGMP and Ca2+ in the ROS bearing incisures can be modeled by a family of two-dimensional diffusion processes on the ROS cross sections, glued together by other two-dimensional diffusion processes, accounting for diffusion in the ROS outer shell and in the bladelike regions comprised by the stack of incisures. Based on this mathematical model, a code has been written, capable of incorporating an arbitrary number of incisures and activation sites, with any given arbitrary distribution within the ROS. The code is aimed at being an operational tool to perform numerical experiments of phototransduction, in rods with incisures of different geometry and structure, under a wide spectrum of operating conditions. The simulation results show that incisures have a dual biophysical function. On the one hand, since incisures line up from disk to disk, they create vertical cytoplasmic channels crossing the disks, thus facilitating diffusion of second messengers; on the other hand, at least in those species bearing multiple incisures, they divide the disks into lobes like the petals of a flower, thus confining the diffusion of activated phosphodiesterase and localizing the photon response. Accordingly, not only the total area of incisures, but their geometrical shape and distribution as well, significantly influence the global photoresponse. PMID:16714347

Ducted turbine theory with right angled ducts

NASA Astrophysics Data System (ADS)

McLaren-Gow, S.; Jamieson, P.; Graham, J. M. R.

2014-06-01

This paper describes the use of an inviscid approach to model a ducted turbine - also known as a diffuser augmented turbine - and a comparison of results with a particular one-dimensional theory. The aim of the investigation was to gain a better understanding of the relationship between a real duct and the ideal diffuser, which is a concept that is developed in the theory. A range of right angled ducts, which have a rim for a 90° exit angle, were modelled. As a result, the performance of right angled ducts has been characterised in inviscid flow. It was concluded that right angled ducts cannot match the performance of their associated ideal diffuser and that the optimum rotor loading for these turbines varies with the duct dimensions.

A two-dimensional, time-dependent model of suspended sediment transport and bed reworking for continental shelves

USGS Publications Warehouse

Harris, C.K.; Wiberg, P.L.

2001-01-01

A two-dimensional, time-dependent solution to the transport equation is formulated to account for advection and diffusion of sediment suspended in the bottom boundary layer of continental shelves. This model utilizes a semi-implicit, upwind-differencing scheme to solve the advection-diffusion equation across a two-dimensional transect that is configured so that one dimension is the vertical, and the other is a horizontal dimension usually aligned perpendicular to shelf bathymetry. The model calculates suspended sediment concentration and flux; and requires as input wave properties, current velocities, sediment size distributions, and hydrodynamic sediment properties. From the calculated two-dimensional suspended sediment fluxes, we quantify the redistribution of shelf sediment, bed erosion, and deposition for several sediment sizes during resuspension events. The two-dimensional, time-dependent approach directly accounts for cross-shelf gradients in bed shear stress and sediment properties, as well as transport that occurs before steady-state suspended sediment concentrations have been attained. By including the vertical dimension in the calculations, we avoid depth-averaging suspended sediment concentrations and fluxes, and directly account for differences in transport rates and directions for fine and coarse sediment in the bottom boundary layer. A flux condition is used as the bottom boundary condition for the transport equation in order to capture time-dependence of the suspended sediment field. Model calculations demonstrate the significance of both time-dependent and spatial terms on transport and depositional patterns on continental shelves. ?? 2001 Elsevier Science Ltd. All rights reserved.

Fractional calculus phenomenology in two-dimensional plasma models

NASA Astrophysics Data System (ADS)

Gustafson, Kyle; Del Castillo Negrete, Diego; Dorland, Bill

2006-10-01

Transport processes in confined plasmas for fusion experiments, such as ITER, are not well-understood at the basic level of fully nonlinear, three-dimensional kinetic physics. Turbulent transport is invoked to describe the observed levels in tokamaks, which are orders of magnitude greater than the theoretical predictions. Recent results show the ability of a non-diffusive transport model to describe numerical observations of turbulent transport. For example, resistive MHD modeling of tracer particle transport in pressure-gradient driven turbulence for a three-dimensional plasma reveals that the superdiffusive (2̂˜t^α where α> 1) radial transport in this system is described quantitatively by a fractional diffusion equation Fractional calculus is a generalization involving integro-differential operators, which naturally describe non-local behaviors. Our previous work showed the quantitative agreement of special fractional diffusion equation solutions with numerical tracer particle flows in time-dependent linearized dynamics of the Hasegawa-Mima equation (for poloidal transport in a two-dimensional cold-ion plasma). In pursuit of a fractional diffusion model for transport in a gyrokinetic plasma, we now present numerical results from tracer particle transport in the nonlinear Hasegawa-Mima equation and a planar gyrokinetic model. Finite Larmor radius effects will be discussed. D. del Castillo Negrete, et al, Phys. Rev. Lett. 94, 065003 (2005).

Divergence of the long-wavelength collective diffusion coefficient in quasi-one- and quasi-two-dimensional colloidal suspensions.

PubMed

Lin, Binhua; Cui, Bianxiao; Xu, Xinliang; Zangi, Ronen; Diamant, Haim; Rice, Stuart A

2014-02-01

We report the results of experimental studies of the short-time-long-wavelength behavior of collective particle displacements in quasi-one-dimensional (q1D) and quasi-two-dimensional (q2D) colloid suspensions. Our results are reported via the q → 0 behavior of the hydrodynamic function H(q) that relates the effective collective diffusion coefficient D(e)(q), with the static structure factor S(q) and the self-diffusion coefficient of isolated particles D(0): H(q) ≡ D(e)(q)S(q)/D(0). We find an apparent divergence of H(q) as q → 0 with the form H(q) ∝ q(-γ) (1.7 < γ < 1.9) for both q1D and q2D colloid suspensions. Given that S(q) does not diverge as q → 0 we infer that D(e)(q) does. This behavior is qualitatively different from that of the three-dimensional H(q) and D(e)(q) as q → 0, and the divergence is of a different functional form from that predicted for the diffusion coefficient in one-component one-dimensional and two-dimensional fluids not subject to boundary conditions that define the dimensionality of the system. We provide support for the contention that the boundary conditions that define a confined system play a very important role in determining the long-wavelength behavior of the collective diffusion coefficient from two sources: (i) the results of simulations of H(q) and D(e)(q) in quasi-1D and quasi-2D systems and (ii) verification, using data from the work of Lin, Rice and Weitz [Phys. Rev. E 51, 423 (1995)], of the prediction by Bleibel et al., arXiv:1305.3715, that D(e)(q) for a monolayer of colloid particles constrained to lie in the interface between two fluids diverges as q(-1) as q → 0.

Diffusiophoresis in one-dimensional solute gradients

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

Ault, Jesse T.; Warren, Patrick B.; Shin, Sangwoo

Here, the diffusiophoretic motion of suspended colloidal particles under one-dimensional solute gradients is solved using numerical and analytical techniques. Similarity solutions are developed for the injection and withdrawal dynamics of particles into semi-infinite pores. Furthermore, a method of characteristics formulation of the diffusion-free particle transport model is presented and integrated to realize particle trajectories. Analytical solutions are presented for the limit of small particle diffusiophoretic mobility Γ p relative to the solute diffusivity D s for particle motions in both semi-infinite and finite domains. Results confirm the build up of local maxima and minima in the propagating particle front dynamics.more » The method of characteristics is shown to successfully predict particle motions and the position of the particle front, although it fails to accurately predict suspended particle concentrations in the vicinity of sharp gradients, such as at the particle front peak seen in some injection cases, where particle diffusion inevitably plays an important role. Results inform the design of applications in which the use of applied solute gradients can greatly enhance particle injection into and withdrawal from pores.« less

Universality-class crossover by a nonorder field introduced to the pair contact process with diffusion

NASA Astrophysics Data System (ADS)

Park, Su-Chan

2017-09-01

The one-dimensional pair contact process with diffusion (PCPD), an interacting particle system with diffusion, pair annihilation, and creation by pairs, has defied consensus about the universality class to which it belongs. An argument by Hinrichsen [Physica A 361, 457 (2006), 10.1016/j.physa.2005.06.101] claims that freely diffusing particles in the PCPD should play the same role as frozen particles when it comes to the critical behavior. Therefore, the PCPD is claimed to have the same critical phenomena as a model with infinitely many absorbing states that belongs to the directed percolation (DP) universality class. To investigate if diffusing particles are really indistinguishable from frozen particles in the sense of the renormalization group, we study numerically a variation of the PCPD by introducing a nonorder field associated with infinitely many absorbing states. We find that a crossover from the PCPD to DP occurs due to the nonorder field. By studying a similar model, we exclude the possibility that the mere introduction of a nonorder field to one model can entail a nontrivial crossover to another model in the same universality class, thus we attribute the observed crossover to the difference of the universality class of the PCPD from the DP class.

Corrected simulations for one-dimensional diffusion processes with naturally occurring boundaries.

PubMed

Shafiey, Hassan; Gan, Xinjun; Waxman, David

2017-11-01

To simulate a diffusion process, a usual approach is to discretize the time in the associated stochastic differential equation. This is the approach used in the Euler method. In the present work we consider a one-dimensional diffusion process where the terms occurring, within the stochastic differential equation, prevent the process entering a region. The outcome is a naturally occurring boundary (which may be absorbing or reflecting). A complication occurs in a simulation of this situation. The term involving a random variable, within the discretized stochastic differential equation, may take a trajectory across the boundary into a "forbidden region." The naive way of dealing with this problem, which we refer to as the "standard" approach, is simply to reset the trajectory to the boundary, based on the argument that crossing the boundary actually signifies achieving the boundary. In this work we show, within the framework of the Euler method, that such resetting introduces a spurious force into the original diffusion process. This force may have a significant influence on trajectories that come close to a boundary. We propose a corrected numerical scheme, for simulating one-dimensional diffusion processes with naturally occurring boundaries. This involves correcting the standard approach, so that an exact property of the diffusion process is precisely respected. As a consequence, the proposed scheme does not introduce a spurious force into the dynamics. We present numerical test cases, based on exactly soluble one-dimensional problems with one or two boundaries, which suggest that, for a given value of the discrete time step, the proposed scheme leads to substantially more accurate results than the standard approach. Alternatively, the standard approach needs considerably more computation time to obtain a comparable level of accuracy to the proposed scheme, because the standard approach requires a significantly smaller time step.

Corrected simulations for one-dimensional diffusion processes with naturally occurring boundaries

NASA Astrophysics Data System (ADS)

Shafiey, Hassan; Gan, Xinjun; Waxman, David

2017-11-01

To simulate a diffusion process, a usual approach is to discretize the time in the associated stochastic differential equation. This is the approach used in the Euler method. In the present work we consider a one-dimensional diffusion process where the terms occurring, within the stochastic differential equation, prevent the process entering a region. The outcome is a naturally occurring boundary (which may be absorbing or reflecting). A complication occurs in a simulation of this situation. The term involving a random variable, within the discretized stochastic differential equation, may take a trajectory across the boundary into a "forbidden region." The naive way of dealing with this problem, which we refer to as the "standard" approach, is simply to reset the trajectory to the boundary, based on the argument that crossing the boundary actually signifies achieving the boundary. In this work we show, within the framework of the Euler method, that such resetting introduces a spurious force into the original diffusion process. This force may have a significant influence on trajectories that come close to a boundary. We propose a corrected numerical scheme, for simulating one-dimensional diffusion processes with naturally occurring boundaries. This involves correcting the standard approach, so that an exact property of the diffusion process is precisely respected. As a consequence, the proposed scheme does not introduce a spurious force into the dynamics. We present numerical test cases, based on exactly soluble one-dimensional problems with one or two boundaries, which suggest that, for a given value of the discrete time step, the proposed scheme leads to substantially more accurate results than the standard approach. Alternatively, the standard approach needs considerably more computation time to obtain a comparable level of accuracy to the proposed scheme, because the standard approach requires a significantly smaller time step.

A Review of the Ginzburg-Syrovatskii's Galactic Cosmic-Ray Propagation Model and its Leaky-Box Limit

NASA Technical Reports Server (NTRS)

Barghouty, A. F.

2012-01-01

Phenomenological models of galactic cosmic-ray propagation are based on a diffusion equation known as the Ginzburg-Syrovatskii s equation, or variants (or limits) of this equation. Its one-dimensional limit in a homogeneous volume, known as the leaky-box limit or model, is sketched here. The justification, utility, limitations, and a typical numerical implementation of the leaky-box model are examined in some detail.

Coarse analysis of collective behaviors: Bifurcation analysis of the optimal velocity model for traffic jam formation

NASA Astrophysics Data System (ADS)

Miura, Yasunari; Sugiyama, Yuki

2017-12-01

We present a general method for analyzing macroscopic collective phenomena observed in many-body systems. For this purpose, we employ diffusion maps, which are one of the dimensionality-reduction techniques, and systematically define a few relevant coarse-grained variables for describing macroscopic phenomena. The time evolution of macroscopic behavior is described as a trajectory in the low-dimensional space constructed by these coarse variables. We apply this method to the analysis of the traffic model, called the optimal velocity model, and reveal a bifurcation structure, which features a transition to the emergence of a moving cluster as a traffic jam.

Nonequilibrium two-dimensional Ising model with stationary uphill diffusion.

PubMed

Colangeli, Matteo; Giardinà, Cristian; Giberti, Claudio; Vernia, Cecilia

2018-03-01

Usually, in a nonequilibrium setting, a current brings mass from the highest density regions to the lowest density ones. Although rare, the opposite phenomenon (known as "uphill diffusion") has also been observed in multicomponent systems, where it appears as an artificial effect of the interaction among components. We show here that uphill diffusion can be a substantial effect, i.e., it may occur even in single component systems as a consequence of some external work. To this aim we consider the two-dimensional ferromagnetic Ising model in contact with two reservoirs that fix, at the left and the right boundaries, magnetizations of the same magnitude but of opposite signs.We provide numerical evidence that a class of nonequilibrium steady states exists in which, by tuning the reservoir magnetizations, the current in the system changes from "downhill" to "uphill". Moreover, we also show that, in such nonequilibrium setup, the current vanishes when the reservoir magnetization attains a value approaching, in the large volume limit, the magnetization of the equilibrium dynamics, thus establishing a relation between equilibrium and nonequilibrium properties.

Nonequilibrium two-dimensional Ising model with stationary uphill diffusion

NASA Astrophysics Data System (ADS)

Colangeli, Matteo; Giardinà, Cristian; Giberti, Claudio; Vernia, Cecilia

2018-03-01

Usually, in a nonequilibrium setting, a current brings mass from the highest density regions to the lowest density ones. Although rare, the opposite phenomenon (known as "uphill diffusion") has also been observed in multicomponent systems, where it appears as an artificial effect of the interaction among components. We show here that uphill diffusion can be a substantial effect, i.e., it may occur even in single component systems as a consequence of some external work. To this aim we consider the two-dimensional ferromagnetic Ising model in contact with two reservoirs that fix, at the left and the right boundaries, magnetizations of the same magnitude but of opposite signs.We provide numerical evidence that a class of nonequilibrium steady states exists in which, by tuning the reservoir magnetizations, the current in the system changes from "downhill" to "uphill". Moreover, we also show that, in such nonequilibrium setup, the current vanishes when the reservoir magnetization attains a value approaching, in the large volume limit, the magnetization of the equilibrium dynamics, thus establishing a relation between equilibrium and nonequilibrium properties.

Analytical modeling of operating characteristics of premixing-prevaporizing fuel-air mixing passages. Volume 1: Analysis and results

NASA Technical Reports Server (NTRS)

Anderson, O. L.; Chiappetta, L. M.; Edwards, D. E.; Mcvey, J. B.

1982-01-01

A model for predicting the distribution of liquid fuel droplets and fuel vapor in premixing-prevaporizing fuel-air mixing passages of the direct injection type is reported. This model consists of three computer programs; a calculation of the two dimensional or axisymmetric air flow field neglecting the effects of fuel; a calculation of the three dimensional fuel droplet trajectories and evaporation rates in a known, moving air flow; a calculation of fuel vapor diffusing into a moving three dimensional air flow with source terms dependent on the droplet evaporation rates. The fuel droplets are treated as individual particle classes each satisfying Newton's law, a heat transfer, and a mass transfer equation. This fuel droplet model treats multicomponent fuels and incorporates the physics required for the treatment of elastic droplet collisions, droplet shattering, droplet coalescence and droplet wall interactions. The vapor diffusion calculation treats three dimensional, gas phase, turbulent diffusion processes. The analysis includes a model for the autoignition of the fuel air mixture based upon the rate of formation of an important intermediate chemical species during the preignition period.

Universal time-dependent dispersion properties for diffusion in a one-dimensional critically tilted potential.

PubMed

Guérin, T; Dean, D S

2017-01-01

We consider the time-dependent dispersion properties of overdamped tracer particles diffusing in a one-dimensional periodic potential under the influence of an additional constant tilting force F. The system is studied in the region where the force is close to the critical value F_{c} at which the barriers separating neighboring potential wells disappear. We show that, when F crosses the critical value, the shape of the mean-square displacement (MSD) curves is strongly modified. We identify a diffusive regime at intermediate-time scales with an effective diffusion coefficient which is much larger than the late-time diffusion coefficient for F>F_{c}, whereas for F

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.

Effect of cation ordering on oxygen vacancy diffusion pathways in double perovskites

DOE PAGES

Uberuaga, Blas Pedro; Pilania, Ghanshyam

2015-07-08

Perovskite structured oxides (ABO 3) are attractive for a number of technological applications, including as superionics because of the high oxygen conductivities they exhibit. Double perovskites (AA’BB’O 6) provide even more flexibility for tailoring properties. Using accelerated molecular dynamics, we examine the role of cation ordering on oxygen vacancy mobility in one model double perovskite SrLaTiAlO 6. We find that the mobility of the vacancy is very sensitive to the cation ordering, with a migration energy that varies from 0.6 to 2.7 eV. In the extreme cases, the mobility is both higher and lower than either of the two endmore » member single perovskites. Further, the nature of oxygen vacancy diffusion, whether one-dimensional, two-dimensional, or three-dimensional, also varies with cation ordering. We correlate the dependence of oxygen mobility on cation structure to the distribution of Ti 4+ cations, which provide unfavorable environments for the positively charged oxygen vacancy. The results demonstrate the potential of using tailored double perovskite structures to precisely control the behavior of oxygen vacancies in these materials.« less

Diffusion of One-Dimensional Crystals in Channels of Single-Walled Carbon Nanotubes

NASA Astrophysics Data System (ADS)

Zhigalina, V. G.; Kumskov, A. S.; Falaleev, N. S.; Vasiliev, A. L.; Kiselev, N. A.

2018-05-01

The transport of one-dimensional CuI crystals in channels of single-walled carbon nanotubes (SWCNTs) has been studied by high resolution electron microscopy. The diffusion kinetics has been investigated by counting the number of CuI atoms escaping from the nanotube channel. The diffusivity is calculated to be 6.8 × 10-21 m2/s, which corresponds to an activation-barrier height of 1 eV/atom. A comparison with the theoretically estimated height of the energy barrier for molecular transport through a graphene layer is indicative of mass transfer through vacancy defects in graphene.

A novel model of photothermal diffusion (PTD) for polymer nano-composite semiconducting of thin circular plate

NASA Astrophysics Data System (ADS)

Lotfy, Kh.

2018-05-01

In this article, theoretical discussions for a novel mathematical-physical Photothermal diffusion (PTD) model in the generalized thermoelasticity theory with photothermal processes and chemical action are introduced. The mean idea of this model depends on the interaction between quasi-particles (plasma waves) that depends on the kind of the used materials, the mechanical forces acting on the surface, the generalized thermo and mass diffusion (due to coupling of temperature fields with thermal waves and chemical potential) and the elastic waves. The one dimensional Laplace transforms is used to obtain the exact solution for some physical and chemical quantities for a thin circular plate of a semiconducting polymer nanocomposite such as silicon (Si). New variables are deduced and discussed. The obtained results of the physical quantities are presented analytically and illustrated graphically with some important applications.

Cosmic Ray Hysteresis as Evidence for Time-dependent Diffusive Processes in the Long Term Solar Modulation

NASA Technical Reports Server (NTRS)

Ogallagher, J. J.

1973-01-01

A simple one-dimensional time-dependent diffusion-convection model for the modulation of cosmic rays is presented. This model predicts that the observed intensity at a given time is approximately equal to the intensity given by the time independent diffusion convection solution under interplanetary conditions which existed a time iota in the past, (U(t sub o) = U sub s(t sub o - tau)) where iota is the average time spent by a particle inside the modulating cavity. Delay times in excess of several hundred days are possible with reasonable modulation parameters. Interpretation of phase lags observed during the 1969 to 1970 solar maximum in terms of this model suggests that the modulating region is probably not less than 10 a.u. and maybe as much as 35 a.u. in extent.

The Interplay between Proto--Neutron Star Convection and Neutrino Transport in Core-Collapse Supernovae

NASA Astrophysics Data System (ADS)

Mezzacappa, A.; Calder, A. C.; Bruenn, S. W.; Blondin, J. M.; Guidry, M. W.; Strayer, M. R.; Umar, A. S.

1998-01-01

We couple two-dimensional hydrodynamics to realistic one-dimensional multigroup flux-limited diffusion neutrino transport to investigate proto-neutron star convection in core-collapse supernovae, and more specifically, the interplay between its development and neutrino transport. Our initial conditions, time-dependent boundary conditions, and neutrino distributions for computing neutrino heating, cooling, and deleptonization rates are obtained from one-dimensional simulations that implement multigroup flux-limited diffusion and one-dimensional hydrodynamics. The development and evolution of proto-neutron star convection are investigated for both 15 and 25 M⊙ models, representative of the two classes of stars with compact and extended iron cores, respectively. For both models, in the absence of neutrino transport, the angle-averaged radial and angular convection velocities in the initial Ledoux unstable region below the shock after bounce achieve their peak values in ~20 ms, after which they decrease as the convection in this region dissipates. The dissipation occurs as the gradients are smoothed out by convection. This initial proto-neutron star convection episode seeds additional convectively unstable regions farther out beneath the shock. The additional proto-neutron star convection is driven by successive negative entropy gradients that develop as the shock, in propagating out after core bounce, is successively strengthened and weakened by the oscillating inner core. The convection beneath the shock distorts its sphericity, but on the average the shock radius is not boosted significantly relative to its radius in our corresponding one-dimensional models. In the presence of neutrino transport, proto-neutron star convection velocities are too small relative to bulk inflow velocities to result in any significant convective transport of entropy and leptons. This is evident in our two-dimensional entropy snapshots, which in this case appear spherically symmetric. The peak angle-averaged radial and angular convection velocities are orders of magnitude smaller than they are in the corresponding ``hydrodynamics-only'' models. A simple analytical model supports our numerical results, indicating that the inclusion of neutrino transport reduces the entropy-driven (lepton-driven) convection growth rates and asymptotic velocities by a factor ~3 (50) at the neutrinosphere and a factor ~250 (1000) at ρ = 1012 g cm-3, for both our 15 and 25 M⊙ models. Moreover, when transport is included, the initial postbounce entropy gradient is smoothed out by neutrino diffusion, whereas the initial lepton gradient is maintained by electron capture and neutrino escape near the neutrinosphere. Despite the maintenance of the lepton gradient, proto-neutron star convection does not develop over the 100 ms duration typical of all our simulations, except in the instance where ``low-test'' intial conditions are used, which are generated by core-collapse and bounce simulations that neglect neutrino-electron scattering and ion-ion screening corrections to neutrino-nucleus elastic scattering. Models favoring the development of proto-neutron star convection either by starting with more favorable, albeit artificial (low-test), initial conditions or by including transport corrections that were ignored in our ``fiducial'' models were considered. Our conclusions nonetheless remained the same. Evidence of proto-neutron star convection in our two-dimensional entropy snapshots was minimal, and, as in our fiducial models, the angle-averaged convective velocities when neutrino transport was included remained orders of magnitude smaller than their counterparts in the corresponding hydrodynamics-only models.

A Kronecker product splitting preconditioner for two-dimensional space-fractional diffusion equations

NASA Astrophysics Data System (ADS)

Chen, Hao; Lv, Wen; Zhang, Tongtong

2018-05-01

We study preconditioned iterative methods for the linear system arising in the numerical discretization of a two-dimensional space-fractional diffusion equation. Our approach is based on a formulation of the discrete problem that is shown to be the sum of two Kronecker products. By making use of an alternating Kronecker product splitting iteration technique we establish a class of fixed-point iteration methods. Theoretical analysis shows that the new method converges to the unique solution of the linear system. Moreover, the optimal choice of the involved iteration parameters and the corresponding asymptotic convergence rate are computed exactly when the eigenvalues of the system matrix are all real. The basic iteration is accelerated by a Krylov subspace method like GMRES. The corresponding preconditioner is in a form of a Kronecker product structure and requires at each iteration the solution of a set of discrete one-dimensional fractional diffusion equations. We use structure preserving approximations to the discrete one-dimensional fractional diffusion operators in the action of the preconditioning matrix. Numerical examples are presented to illustrate the effectiveness of this approach.

Analytical approach for collective diffusion: One-dimensional lattice with the nearest neighbor and the next nearest neighbor lateral interactions

NASA Astrophysics Data System (ADS)

Tarasenko, Alexander

2018-01-01

Diffusion of particles adsorbed on a homogeneous one-dimensional lattice is investigated using a theoretical approach and MC simulations. The analytical dependencies calculated in the framework of approach are tested using the numerical data. The perfect coincidence of the data obtained by these different methods demonstrates that the correctness of the approach based on the theory of the non-equilibrium statistical operator.

An incompressible two-dimensional multiphase particle-in-cell model for dense particle flows

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

Snider, D.M.; O`Rourke, P.J.; Andrews, M.J.

1997-06-01

A two-dimensional, incompressible, multiphase particle-in-cell (MP-PIC) method is presented for dense particle flows. The numerical technique solves the governing equations of the fluid phase using a continuum model and those of the particle phase using a Lagrangian model. Difficulties associated with calculating interparticle interactions for dense particle flows with volume fractions above 5% have been eliminated by mapping particle properties to a Eulerian grid and then mapping back computed stress tensors to particle positions. This approach utilizes the best of Eulerian/Eulerian continuum models and Eulerian/Lagrangian discrete models. The solution scheme allows for distributions of types, sizes, and density of particles,more » with no numerical diffusion from the Lagrangian particle calculations. The computational method is implicit with respect to pressure, velocity, and volume fraction in the continuum solution thus avoiding courant limits on computational time advancement. MP-PIC simulations are compared with one-dimensional problems that have analytical solutions and with two-dimensional problems for which there are experimental data.« less

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.

Mean apparent propagator (MAP) MRI: a novel diffusion imaging method for mapping tissue microstructure.

PubMed

Özarslan, Evren; Koay, Cheng Guan; Shepherd, Timothy M; Komlosh, Michal E; İrfanoğlu, M Okan; Pierpaoli, Carlo; Basser, Peter J

2013-09-01

Diffusion-weighted magnetic resonance (MR) signals reflect information about underlying tissue microstructure and cytoarchitecture. We propose a quantitative, efficient, and robust mathematical and physical framework for representing diffusion-weighted MR imaging (MRI) data obtained in "q-space," and the corresponding "mean apparent propagator (MAP)" describing molecular displacements in "r-space." We also define and map novel quantitative descriptors of diffusion that can be computed robustly using this MAP-MRI framework. We describe efficient analytical representation of the three-dimensional q-space MR signal in a series expansion of basis functions that accurately describes diffusion in many complex geometries. The lowest order term in this expansion contains a diffusion tensor that characterizes the Gaussian displacement distribution, equivalent to diffusion tensor MRI (DTI). Inclusion of higher order terms enables the reconstruction of the true average propagator whose projection onto the unit "displacement" sphere provides an orientational distribution function (ODF) that contains only the orientational dependence of the diffusion process. The representation characterizes novel features of diffusion anisotropy and the non-Gaussian character of the three-dimensional diffusion process. Other important measures this representation provides include the return-to-the-origin probability (RTOP), and its variants for diffusion in one- and two-dimensions-the return-to-the-plane probability (RTPP), and the return-to-the-axis probability (RTAP), respectively. These zero net displacement probabilities measure the mean compartment (pore) volume and cross-sectional area in distributions of isolated pores irrespective of the pore shape. MAP-MRI represents a new comprehensive framework to model the three-dimensional q-space signal and transform it into diffusion propagators. Experiments on an excised marmoset brain specimen demonstrate that MAP-MRI provides several novel, quantifiable parameters that capture previously obscured intrinsic features of nervous tissue microstructure. This should prove helpful for investigating the functional organization of normal and pathologic nervous tissue. Copyright © 2013 Elsevier Inc. All rights reserved.

Two-dimensional dynamics of elasto-inertial turbulence and its role in polymer drag reduction

NASA Astrophysics Data System (ADS)

Sid, S.; Terrapon, V. E.; Dubief, Y.

2018-02-01

The goal of the present study is threefold: (i) to demonstrate the two-dimensional nature of the elasto-inertial instability in elasto-inertial turbulence (EIT), (ii) to identify the role of the bidimensional instability in three-dimensional EIT flows, and (iii) to establish the role of the small elastic scales in the mechanism of self-sustained EIT. Direct numerical simulations of viscoelastic fluid flows are performed in both two- and three-dimensional straight periodic channels using the Peterlin finitely extensible nonlinear elastic model (FENE-P). The Reynolds number is set to Reτ=85 , which is subcritical for two-dimensional flows but beyond the transition for three-dimensional ones. The polymer properties selected correspond to those of typical dilute polymer solutions, and two moderate Weissenberg numbers, Wiτ=40 ,100 , are considered. The simulation results show that sustained turbulence can be observed in two-dimensional subcritical flows, confirming the existence of a bidimensional elasto-inertial instability. The same type of instability is also observed in three-dimensional simulations where both Newtonian and elasto-inertial turbulent structures coexist. Depending on the Wi number, one type of structure can dominate and drive the flow. For large Wi values, the elasto-inertial instability tends to prevail over the Newtonian turbulence. This statement is supported by (i) the absence of typical Newtonian near-wall vortices and (ii) strong similarities between two- and three-dimensional flows when considering larger Wi numbers. The role of small elastic scales is investigated by introducing global artificial diffusion (GAD) in the hyperbolic transport equation for polymers. The aim is to measure how the flow reacts when the smallest elastic scales are progressively filtered out. The study results show that the introduction of large polymer diffusion in the system strongly damps a significant part of the elastic scales that are necessary to feed turbulence, eventually leading to flow laminarization. A sufficiently high Schmidt number (weakly diffusive polymers) is necessary to allow self-sustained turbulence to settle. Although EIT can withstand a low amount of diffusion and remains in a nonlaminar chaotic state, adding a finite amount of GAD in the system can have an impact on the dynamics and lead to important quantitative changes, even for Schmidt numbers as large as 102. The use of GAD should therefore be avoided in viscoelastic flow simulations.

Probability and Cumulative Density Function Methods for the Stochastic Advection-Reaction Equation

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

Barajas-Solano, David A.; Tartakovsky, Alexandre M.

We present a cumulative density function (CDF) method for the probabilistic analysis of $d$-dimensional advection-dominated reactive transport in heterogeneous media. We employ a probabilistic approach in which epistemic uncertainty on the spatial heterogeneity of Darcy-scale transport coefficients is modeled in terms of random fields with given correlation structures. Our proposed CDF method employs a modified Large-Eddy-Diffusivity (LED) approach to close and localize the nonlocal equations governing the one-point PDF and CDF of the concentration field, resulting in a $(d + 1)$ dimensional PDE. Compared to the classsical LED localization, the proposed modified LED localization explicitly accounts for the mean-field advectivemore » dynamics over the phase space of the PDF and CDF. To illustrate the accuracy of the proposed closure, we apply our CDF method to one-dimensional single-species reactive transport with uncertain, heterogeneous advection velocities and reaction rates modeled as random fields.« less

Diffuse scattering in relaxor ferroelectrics: true three-dimensional mapping, experimental artefacts and modelling.

PubMed

Bosak, A; Chernyshov, D; Vakhrushev, Sergey; Krisch, M

2012-01-01

The available body of experimental data in terms of the relaxor-specific component of diffuse scattering is critically analysed and a collection of related models is reviewed; the sources of experimental artefacts and consequent failures of modelling efforts are enumerated. Furthermore, it is shown that the widely used concept of polar nanoregions as individual static entities is incompatible with the experimental diffuse scattering results. Based on the synchrotron diffuse scattering three-dimensional data set taken for the prototypical ferroelectric relaxor lead magnesium niobate-lead titanate (PMN-PT), a new parameterization of diffuse scattering in relaxors is presented and a simple phenomenological picture is proposed to explain the unusual properties of the relaxor behaviour. The model assumes a specific slowly changing displacement pattern, which is indirectly controlled by the low-energy acoustic phonons of the system. The model provides a qualitative but rather detailed explanation of temperature, pressure and electric-field dependence of diffuse neutron and X-ray scattering, as well as of the existence of a hierarchy in the relaxation times of these materials.

Modeling of long range frequency sweeping for energetic particle modes

NASA Astrophysics Data System (ADS)

Nyqvist, R. M.; Breizman, B. N.

2013-04-01

Long range frequency sweeping events are simulated numerically within a one-dimensional, electrostatic bump-on-tail model with fast particle sources and collisions. The numerical solution accounts for fast particle trapping and detrapping in an evolving wave field with a fixed wavelength, and it includes three distinct collisions operators: Drag (dynamical friction on the background electrons), Krook-type collisions, and velocity space diffusion. The effects of particle trapping and diffusion on the evolution of holes and clumps are investigated, and the occurrence of non-monotonic (hooked) frequency sweeping and asymptotically steady holes is discussed. The presented solution constitutes a step towards predictive modeling of frequency sweeping events in more realistic geometries.

High-fidelity meshes from tissue samples for diffusion MRI simulations.

PubMed

Panagiotaki, Eleftheria; Hall, Matt G; Zhang, Hui; Siow, Bernard; Lythgoe, Mark F; Alexander, Daniel C

2010-01-01

This paper presents a method for constructing detailed geometric models of tissue microstructure for synthesizing realistic diffusion MRI data. We construct three-dimensional mesh models from confocal microscopy image stacks using the marching cubes algorithm. Random-walk simulations within the resulting meshes provide synthetic diffusion MRI measurements. Experiments optimise simulation parameters and complexity of the meshes to achieve accuracy and reproducibility while minimizing computation time. Finally we assess the quality of the synthesized data from the mesh models by comparison with scanner data as well as synthetic data from simple geometric models and simplified meshes that vary only in two dimensions. The results support the extra complexity of the three-dimensional mesh compared to simpler models although sensitivity to the mesh resolution is quite robust.

Avalanches, breathers, and flow reversal in a continuous Lorenz-96 model

NASA Astrophysics Data System (ADS)

Blender, R.; Wouters, J.; Lucarini, V.

2013-07-01

For the discrete model suggested by Lorenz in 1996, a one-dimensional long-wave approximation with nonlinear excitation and diffusion is derived. The model is energy conserving but non-Hamiltonian. In a low-order truncation, weak external forcing of the zonal mean flow induces avalanchelike breather solutions which cause reversal of the mean flow by a wave-mean flow interaction. The mechanism is an outburst-recharge process similar to avalanches in a sandpile model.

Computational Analyses of Complex Flows with Chemical Reactions

NASA Astrophysics Data System (ADS)

Bae, Kang-Sik

The heat and mass transfer phenomena in micro-scale for the mass transfer phenomena on drug in cylindrical matrix system, the simulation of oxygen/drug diffusion in a three dimensional capillary network, and a reduced chemical kinetic modeling of gas turbine combustion for Jet propellant-10 have been studied numerically. For the numerical analysis of the mass transfer phenomena on drug in cylindrical matrix system, the governing equations are derived from the cylindrical matrix systems, Krogh cylinder model, which modeling system is comprised of a capillary to a surrounding cylinder tissue along with the arterial distance to veins. ADI (Alternative Direction Implicit) scheme and Thomas algorithm are applied to solve the nonlinear partial differential equations (PDEs). This study shows that the important factors which have an effect on the drug penetration depth to the tissue are the mass diffusivity and the consumption of relevant species during the time allowed for diffusion to the brain tissue. Also, a computational fluid dynamics (CFD) model has been developed to simulate the blood flow and oxygen/drug diffusion in a three dimensional capillary network, which are satisfied in the physiological range of a typical capillary. A three dimensional geometry has been constructed to replicate the one studied by Secomb et al. (2000), and the computational framework features a non-Newtonian viscosity model for blood, the oxygen transport model including in oxygen-hemoglobin dissociation and wall flux due to tissue absorption, as well as an ability to study the diffusion of drugs and other materials in the capillary streams. Finally, a chemical kinetic mechanism of JP-10 has been compiled and validated for a wide range of combustion regimes, covering pressures of 1atm to 40atm with temperature ranges of 1,200 K--1,700 K, which is being studied as a possible Jet propellant for the Pulse Detonation Engine (PDE) and other high-speed flight applications such as hypersonic missiles. The comprehensive skeletal mechanism consists of 58 species and 315 reactions including in CPD, Benzene formation process by the theory for polycyclic aromatic hydrocarbons (PAH) and soot formation process on the constant volume combustor, premixed flame characteristics.

Stochastic modeling and simulation of reaction-diffusion system with Hill function dynamics.

PubMed

Chen, Minghan; Li, Fei; Wang, Shuo; Cao, Young

2017-03-14

Stochastic simulation of reaction-diffusion systems presents great challenges for spatiotemporal biological modeling and simulation. One widely used framework for stochastic simulation of reaction-diffusion systems is reaction diffusion master equation (RDME). Previous studies have discovered that for the RDME, when discretization size approaches zero, reaction time for bimolecular reactions in high dimensional domains tends to infinity. In this paper, we demonstrate that in the 1D domain, highly nonlinear reaction dynamics given by Hill function may also have dramatic change when discretization size is smaller than a critical value. Moreover, we discuss methods to avoid this problem: smoothing over space, fixed length smoothing over space and a hybrid method. Our analysis reveals that the switch-like Hill dynamics reduces to a linear function of discretization size when the discretization size is small enough. The three proposed methods could correctly (under certain precision) simulate Hill function dynamics in the microscopic RDME system.

Random walk on lattices: Graph-theoretic approach to simulating long-range diffusion-attachment growth models

NASA Astrophysics Data System (ADS)

Limkumnerd, Surachate

2014-03-01

Interest in thin-film fabrication for industrial applications have driven both theoretical and computational aspects of modeling its growth. One of the earliest attempts toward understanding the morphological structure of a film's surface is through a class of solid-on-solid limited-mobility growth models such as the Family, Wolf-Villain, or Das Sarma-Tamborenea models, which have produced fascinating surface roughening behaviors. These models, however, restrict the motion of an incidence atom to be within the neighborhood of its landing site, which renders them inept for simulating long-distance surface diffusion such as that observed in thin-film growth using a molecular-beam epitaxy technique. Naive extension of these models by repeatedly applying the local diffusion rules for each hop to simulate large diffusion length can be computationally very costly when certain statistical aspects are demanded. We present a graph-theoretic approach to simulating a long-range diffusion-attachment growth model. Using the Markovian assumption and given a local diffusion bias, we derive the transition probabilities for a random walker to traverse from one lattice site to the others after a large, possibly infinite, number of steps. Only computation with linear-time complexity is required for the surface morphology calculation without other probabilistic measures. The formalism is applied, as illustrations, to simulate surface growth on a two-dimensional flat substrate and around a screw dislocation under the modified Wolf-Villain diffusion rule. A rectangular spiral ridge is observed in the latter case with a smooth front feature similar to that obtained from simulations using the well-known multiple registration technique. An algorithm for computing the inverse of a class of substochastic matrices is derived as a corollary.

Cerium Ion Mobility and Diffusivity Rates in Perfluorosulfonic Acid Membranes Measured via Hydrogen Pump Operation

DOE PAGES

Baker, Andrew M.; Babu, Siddharth Komini; Mukundan, Rangachary; ...

2017-09-21

Ion mobility and diffusivity coefficients were determined for cerium ions in Nafion XL perfluorosulfonic acid ionomer membranes at 100% and 50% relative humidity in a conductivity cell using a hydrogen pump. We quantified Ce ion migration profiles as a function of charge transfer through the cell using X-ray fluorescence (XRF). To decouple simultaneous effects of Ce ion mobility and back-diffusion which occur due to potential and concentration gradients, respectively, a one-dimensional model was developed and fit to these intermittent XRF profiles. The resulting mobility and diffusivity coefficients demonstrate the dramatic effects of potential and concentration gradients on Ce ion migrationmore » during PEM fuel cell operation.« less

Cerium Ion Mobility and Diffusivity Rates in Perfluorosulfonic Acid Membranes Measured via Hydrogen Pump Operation

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

Baker, Andrew M.; Babu, Siddharth Komini; Mukundan, Rangachary

Ion mobility and diffusivity coefficients were determined for cerium ions in Nafion XL perfluorosulfonic acid ionomer membranes at 100% and 50% relative humidity in a conductivity cell using a hydrogen pump. We quantified Ce ion migration profiles as a function of charge transfer through the cell using X-ray fluorescence (XRF). To decouple simultaneous effects of Ce ion mobility and back-diffusion which occur due to potential and concentration gradients, respectively, a one-dimensional model was developed and fit to these intermittent XRF profiles. The resulting mobility and diffusivity coefficients demonstrate the dramatic effects of potential and concentration gradients on Ce ion migrationmore » during PEM fuel cell operation.« less

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

PubMed

Lenarda, P; Paggi, M

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

Magnetic Field Line Random Walk in Arbitrarily Stretched Isotropic Turbulence

NASA Astrophysics Data System (ADS)

Wongpan, P.; Ruffolo, D.; Matthaeus, W. H.; Rowlands, G.

2006-12-01

Many types of space and laboratory plasmas involve turbulent fluctuations with an approximately uniform mean magnetic field B_0, and the field line random walk plays an important role in guiding particle motions. Much of the relevant literature concerns isotropic turbulence, and has mostly been perturbative, i.e., for small fluctuations, or based on numerical simulations for specific conditions. On the other hand, solar wind turbulence is apparently anisotropic, and has been modeled as a sum of idealized two-dimensional and one dimensional (slab) components, but with the deficiency of containing no oblique wave vectors. In the present work, we address the above issues with non-perturbative analytic calculations of diffusive field line random walks for unpolarized, arbitrarily stretched isotropic turbulence, including the limits of nearly one-dimensional (highly stretched) and nearly two-dimensional (highly squashed) turbulence. We develop implicit analytic formulae for the diffusion coefficients D_x and D_z, two coupled integral equations in which D_x and D_z appear inside 3-dimensional integrals over all k-space, are solved numerically with the aid of Mathematica routines for specific cases. We can vary the parameters B0 and β, the stretching along z for constant turbulent energy. Furthermore, we obtain analytic closed-form solutions in all extreme cases. We obtain 0.54 < D_z/D_x < 2, indicating an approximately isotropic random walk even for very anisotropic (unpolarized) turbulence, a surprising result. For a given β, the diffusion coefficient vs. B0 can be described by a Padé approximant. We find quasilinear behavior at high B0 and percolative behavior at low B_0. Partially supported by a Sritrangthong Scholarship from the Faculty of Science, Mahidol University; the Thailand Research Fund; NASA Grant NNG05GG83G; and Thailand's Commission for Higher Education.

A Model for Selection of Eyespots on Butterfly Wings.

PubMed

Sekimura, Toshio; Venkataraman, Chandrasekhar; Madzvamuse, Anotida

2015-01-01

The development of eyespots on the wing surface of butterflies of the family Nympalidae is one of the most studied examples of biological pattern formation.However, little is known about the mechanism that determines the number and precise locations of eyespots on the wing. Eyespots develop around signaling centers, called foci, that are located equidistant from wing veins along the midline of a wing cell (an area bounded by veins). A fundamental question that remains unsolved is, why a certain wing cell develops an eyespot, while other wing cells do not. We illustrate that the key to understanding focus point selection may be in the venation system of the wing disc. Our main hypothesis is that changes in morphogen concentration along the proximal boundary veins of wing cells govern focus point selection. Based on previous studies, we focus on a spatially two-dimensional reaction-diffusion system model posed in the interior of each wing cell that describes the formation of focus points. Using finite element based numerical simulations, we demonstrate that variation in the proximal boundary condition is sufficient to robustly select whether an eyespot focus point forms in otherwise identical wing cells. We also illustrate that this behavior is robust to small perturbations in the parameters and geometry and moderate levels of noise. Hence, we suggest that an anterior-posterior pattern of morphogen concentration along the proximal vein may be the main determinant of the distribution of focus points on the wing surface. In order to complete our model, we propose a two stage reaction-diffusion system model, in which an one-dimensional surface reaction-diffusion system, posed on the proximal vein, generates the morphogen concentrations that act as non-homogeneous Dirichlet (i.e., fixed) boundary conditions for the two-dimensional reaction-diffusion model posed in the wing cells. The two-stage model appears capable of generating focus point distributions observed in nature. We therefore conclude that changes in the proximal boundary conditions are sufficient to explain the empirically observed distribution of eyespot focus points on the entire wing surface. The model predicts, subject to experimental verification, that the source strength of the activator at the proximal boundary should be lower in wing cells in which focus points form than in those that lack focus points. The model suggests that the number and locations of eyespot foci on the wing disc could be largely controlled by two kinds of gradients along two different directions, that is, the first one is the gradient in spatially varying parameters such as the reaction rate along the anterior-posterior direction on the proximal boundary of the wing cells, and the second one is the gradient in source values of the activator along the veins in the proximal-distal direction of the wing cell.

Convective drying of osmo-dehydrated apple slices: kinetics and spatial behavior of effective mass diffusivity and moisture content

NASA Astrophysics Data System (ADS)

de Farias Aires, Juarez Everton; da Silva, Wilton Pereira; de Almeida Farias Aires, Kalina Lígia Cavalcante; da Silva Júnior, Aluízio Freire; da Silva e Silva, Cleide Maria Diniz Pereira

2018-04-01

The main objective of this study is the presentation of a numerical model of liquid diffusion for the description of the convective drying of apple slices submitted to pretreatment of osmotic dehydration able of predicting the spatial distribution of effective mass diffusivity values in apple slabs. Two models that use numerical solutions of the two-dimensional diffusion equation in Cartesian coordinates with the boundary condition of third kind were proposed to describe drying. The first one does not consider the shrinkage of the product and assumes that the process parameters remain constant along the convective drying. The second one considers the shrinkage of the product and assumes that the effective mass diffusivity of water varies according to the local value of the water content in the apple samples. Process parameters were estimated from experimental data through an optimizer coupled to the numerical solutions. The osmotic pretreatment did not reduce the drying time in relation to the fresh fruits when the drying temperature was equal to 40 °C. The use of the temperature of 60 °C led to a reduction in the drying time. The model that considers the variations in the dimensions of the product and the variation in the effective mass diffusivity proved to be more adequate to describe the process.

Facilitated diffusion in chromatin lattices: mechanistic diversity and regulatory potential.

PubMed

Kampmann, Martin

2005-08-01

The interaction between a protein and a specific DNA site is the molecular basis for vital processes in all organisms. Location of the DNA target site by the protein commonly involves facilitated diffusion. Mechanisms of facilitated diffusion vary among proteins; they include one- and two-dimensional sliding along DNA, direct transfer between uncorrelated sites, as well as combinations of these mechanisms. Facilitated diffusion has almost exclusively been studied in vitro. This review discusses facilitated diffusion in the context of the living cell and proposes a theoretical model for facilitated diffusion in chromatin lattices. Chromatin structure differentially affects proteins in different modes of diffusion. The interplay of facilitated diffusion and chromatin structure can determine the rate of protein association with the target site, the frequency of association-dissociation events at the target site, and, under particular conditions, the occupancy of the target site. Facilitated diffusion is required in vivo for efficient DNA repair and bacteriophage restriction and has potential roles in fine-tuning gene regulatory networks and kinetically compartmentalizing the eukaryotic nucleus.

An axisymmetric non-hydrostatic model for double-diffusive water systems

NASA Astrophysics Data System (ADS)

Hilgersom, Koen; Zijlema, Marcel; van de Giesen, Nick

2018-02-01

The three-dimensional (3-D) modelling of water systems involving double-diffusive processes is challenging due to the large computation times required to solve the flow and transport of constituents. In 3-D systems that approach axisymmetry around a central location, computation times can be reduced by applying a 2-D axisymmetric model set-up. This article applies the Reynolds-averaged Navier-Stokes equations described in cylindrical coordinates and integrates them to guarantee mass and momentum conservation. The discretized equations are presented in a way that a Cartesian finite-volume model can be easily extended to the developed framework, which is demonstrated by the implementation into a non-hydrostatic free-surface flow model. This model employs temperature- and salinity-dependent densities, molecular diffusivities, and kinematic viscosity. One quantitative case study, based on an analytical solution derived for the radial expansion of a dense water layer, and two qualitative case studies demonstrate a good behaviour of the model for seepage inflows with contrasting salinities and temperatures. Four case studies with respect to double-diffusive processes in a stratified water body demonstrate that turbulent flows are not yet correctly modelled near the interfaces and that an advanced turbulence model is required.

Far-field analysis of coupled bulk and boundary layer diffusion toward an ion channel entrance.

PubMed Central

Schumaker, M F; Kentler, C J

1998-01-01

We present a far-field analysis of ion diffusion toward a channel embedded in a membrane with a fixed charge density. The Smoluchowski equation, which represents the 3D problem, is approximated by a system of coupled three- and two-dimensional diffusions. The 2D diffusion models the quasi-two-dimensional diffusion of ions in a boundary layer in which the electrical potential interaction with the membrane surface charge is important. The 3D diffusion models ion transport in the bulk region outside the boundary layer. Analytical expressions for concentration and flux are developed that are accurate far from the channel entrance. These provide boundary conditions for a numerical solution of the problem. Our results are used to calculate far-field ion flows corresponding to experiments of Bell and Miller (Biophys. J. 45:279, 1984). PMID:9591651

Low temperature exciton dynamics and structural changes in perylene bisimide aggregates

NASA Astrophysics Data System (ADS)

Wolter, Steffen; Magnus Westphal, Karl; Hempel, Magdalena; Würthner, Frank; Kühn, Oliver; Lochbrunner, Stefan

2017-09-01

The temperature dependent exciton dynamics of J-aggregates formed by a perylene bisimide dye is investigated down to liquid nitrogen temperature (77 K) by femtosecond pump-probe spectroscopy. The analysis of the transient absorption data using a diffusion model for the excitons does not only reveal an overall decrease of the exciton mobility, but also a change in the dimensionality of the exciton transport at low temperatures. This change in dimensionality is further investigated by kinetic Monte Carlo simulations, identifying weakly interlinked one-dimensional aggregate chains as the most likely structure at low temperatures. This causes the exciton transport to be highly anisotropic.

Post-earthquake dilatancy recovery

NASA Technical Reports Server (NTRS)

Scholz, C. H.

1974-01-01

Geodetic measurements of the 1964 Niigata, Japan earthquake and of three other examples are briefly examined. They show exponentially decaying subsidence for a year after the quakes. The observations confirm the dilatancy-fluid diffusion model of earthquake precursors and clarify the extent and properties of the dilatant zone. An analysis using one-dimensional consolidation theory is included which agrees well with this interpretation.

Diffusion of a Concentrated Lattice Gas in a Regular Comb Structure

NASA Astrophysics Data System (ADS)

Garcia, Paul; Wentworth, Christopher

2008-10-01

Understanding diffusion in constrained geometries is of interest in a variety of contexts as varied as mass transport in disordered solids, such as a percolation cluster, or intercellular transport of water molecules in biological tissue. In this investigation we explore diffusion in a very simple constrained geometry: a comb-like structure involving a one-dimensional backbone of lattice sites with regularly spaced teeth of fixed length. The model considered assumes a fixed concentration of diffusing particles can hop to nearest-neighbor sites only, and they do not interact with each other except that double occupancy is not allowed. The system is simulated using a Monte Carlo simulation procedure. The mean-square displacement of a tagged particle is calculated from the simulation as a function of time. The simulation shows normal diffusive behavior after a period of anomalous diffusion that increases as the tooth size increases.

Forward and back diffusion through argillaceous formations

NASA Astrophysics Data System (ADS)

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

2017-05-01

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

Users manual for a one-dimensional Lagrangian transport model

USGS Publications Warehouse

Schoellhamer, D.H.; Jobson, H.E.

1986-01-01

A Users Manual for the Lagrangian Transport Model (LTM) is presented. The LTM uses Lagrangian calculations that are based on a reference frame moving with the river flow. The Lagrangian reference frame eliminates the need to numerically solve the convective term of the convection-diffusion equation and provides significant numerical advantages over the more commonly used Eulerian reference frame. When properly applied, the LTM can simulate riverine transport and decay processes within the accuracy required by most water quality studies. The LTM is applicable to steady or unsteady one-dimensional unidirectional flows in fixed channels with tributary and lateral inflows. Application of the LTM is relatively simple and optional capabilities improve the model 's convenience. Appendices give file formats and three example LTM applications that include the incorporation of the QUAL II water quality model 's reaction kinetics into the LTM. (Author 's abstract)

Homotopy decomposition method for solving one-dimensional time-fractional diffusion equation

NASA Astrophysics Data System (ADS)

Abuasad, Salah; Hashim, Ishak

2018-04-01

In this paper, we present the homotopy decomposition method with a modified definition of beta fractional derivative for the first time to find exact solution of one-dimensional time-fractional diffusion equation. In this method, the solution takes the form of a convergent series with easily computable terms. The exact solution obtained by the proposed method is compared with the exact solution obtained by using fractional variational homotopy perturbation iteration method via a modified Riemann-Liouville derivative.

Quantum Hamilton equations of motion for bound states of one-dimensional quantum systems

NASA Astrophysics Data System (ADS)

Köppe, J.; Patzold, M.; Grecksch, W.; Paul, W.

2018-06-01

On the basis of Nelson's stochastic mechanics derivation of the Schrödinger equation, a formal mathematical structure of non-relativistic quantum mechanics equivalent to the one in classical analytical mechanics has been established in the literature. We recently were able to augment this structure by deriving quantum Hamilton equations of motion by finding the Nash equilibrium of a stochastic optimal control problem, which is the generalization of Hamilton's principle of classical mechanics to quantum systems. We showed that these equations allow a description and numerical determination of the ground state of quantum problems without using the Schrödinger equation. We extend this approach here to deliver the complete discrete energy spectrum and related eigenfunctions for bound states of one-dimensional stationary quantum systems. We exemplify this analytically for the one-dimensional harmonic oscillator and numerically by analyzing a quartic double-well potential, a model of broad importance in many areas of physics. We furthermore point out a relation between the tunnel splitting of such models and mean first passage time concepts applied to Nelson's diffusion paths in the ground state.

Free-energy landscape for cage breaking of three hard disks.

PubMed

Hunter, Gary L; Weeks, Eric R

2012-03-01

We investigate cage breaking in dense hard-disk systems using a model of three Brownian disks confined within a circular corral. This system has a six-dimensional configuration space, but can be equivalently thought to explore a symmetric one-dimensional free-energy landscape containing two energy minima separated by an energy barrier. The exact free-energy landscape can be calculated as a function of system size by a direct enumeration of states. Results of simulations show the average time between cage breaking events follows an Arrhenius scaling when the energy barrier is large. We also discuss some of the consequences of using a one-dimensional representation to understand dynamics through a multidimensional space, such as diffusion acquiring spatial dependence and discontinuities in spatial derivatives of free energy.

Hydrodynamic fingering instability induced by a precipitation reaction

NASA Astrophysics Data System (ADS)

De Wit, Anne; Nagatsu, Yuichiro

2014-05-01

We experimentally demonstrate that a precipitation reaction at the miscible interface between two reactive solutions can trigger a hydrodynamic instability due to the build-up of a locally adverse mobility gradient related to a decrease in permeability. The precipitate results from an A+B → C type of reaction when a solution containing one of the reactant is injected into a solution of the other reactant in a porous medium or a Hele-Shaw cell. Finger-like precipitation patterns are observed upon displacement, the properties of which depend on whether A displaces B or vice-versa. A mathematical modeling of the underlying mobility profile in the cell reconstructed on the basis of one-dimensional reaction-diffusion concentration profiles confirms that the instability originates from a local decrease in mobility driven by the precipitation. Nonlinear simulations of the related reaction-diffusion-convection model reproduce the properties of the instability observed experimentally. In particular, the simulations suggest that differences in diffusivity between A and B may contribute to the asymmetric characteristics of the fingering precipitation patterns.

Designing herbicide formulation characteristics to maximize efficacy and minimize rice injury in paddy environments.

PubMed

Cryer, S A; Mann, R K; Erhardt-Zabik, S; Keeney, F N; Handy, P R

2001-06-01

Mathematical descriptors, coupled with experimental observations, are used to quantify differential uptake of an experimental herbicide in Japonica and Indica rice (Oryza sativa, non-target) and barnyardgrass (Echinochloa crus-galli, target). Partitioning, degradation, plant uptake and metabolism are described using mass-balance conservation equations in the form of kinetic approximations. Estimated environmental concentrations, governed by the pesticide formulation, are described using superimposed analytical solutions for the one-dimensional diffusion equation in spherical coordinates and by a finite difference representation of the two-dimensional diffusion equation in Cartesian coordinates. Formulation attributes from granules include active ingredient release rates, particle sizes, pesticide loading, and granule spacing. The diffusion model for pesticide transport is coupled with the compartment model to follow the fate and transport of a pesticide from its initial application location to various environmental matrices of interest. Formulation effects, partitioning and degradation in the various environmental matrices, differential plant uptake and metabolism, and dose-response information for plants are accounted for. This novel model provides a mechanism for selecting formulation delivery systems that optimize specific attributes (such as weed control or the therapeutic index) for risk-assessment procedures. In this report we describe how this methodology was used to explore the factors affecting herbicide efficacy and to define an optimal release rate for a granule formulation.

Effects of calcium leaching on diffusion properties of hardened and altered cement pastes

NASA Astrophysics Data System (ADS)

Kurumisawa, Kiyofumi; Haga, Kazuko; Hayashi, Daisuke; Owada, Hitoshi

2017-06-01

It is very important to predict alterations in the concrete used for fabricating disposal containers for radioactive waste. Therefore, it is necessary to understand the alteration of cementitious materials caused by calcium leaching when they are in contact with ground water in the long term. To evaluate the long-term transport characteristics of cementitious materials, the microstructural behavior of these materials should be considered. However, many predictive models of transport characteristics focus on the pore structure, while only few such models consider both, the spatial distribution of calcium silicate hydrate (C-S-H), portlandite, and the pore spaces. This study focused on the spatial distribution of these cement phases. The auto-correlation function of each phase of cementitious materials was calculated from two-dimensional backscattered electron imaging, and the three-dimensional spatial image of the cementitious material was produced using these auto-correlation functions. An attempt was made to estimate the diffusion coefficient of chloride from the three-dimensional spatial image. The estimated diffusion coefficient of the altered sample from the three-dimensional spatial image was found to be comparable to the measured value. This demonstrated that it is possible to predict the diffusion coefficient of the altered cement paste by using the proposed model.

Generalized fourier analyses of the advection-diffusion equation - Part II: two-dimensional domains

NASA Astrophysics Data System (ADS)

Voth, Thomas E.; Martinez, Mario J.; Christon, Mark A.

2004-07-01

Part I of this work presents a detailed multi-methods comparison of the spatial errors associated with the one-dimensional finite difference, finite element and finite volume semi-discretizations of the scalar advection-diffusion equation. In Part II we extend the analysis to two-dimensional domains and also consider the effects of wave propagation direction and grid aspect ratio on the phase speed, and the discrete and artificial diffusivities. The observed dependence of dispersive and diffusive behaviour on propagation direction makes comparison of methods more difficult relative to the one-dimensional results. For this reason, integrated (over propagation direction and wave number) error and anisotropy metrics are introduced to facilitate comparison among the various methods. With respect to these metrics, the consistent mass Galerkin and consistent mass control-volume finite element methods, and their streamline upwind derivatives, exhibit comparable accuracy, and generally out-perform their lumped mass counterparts and finite-difference based schemes. While this work can only be considered a first step in a comprehensive multi-methods analysis and comparison, it serves to identify some of the relative strengths and weaknesses of multiple numerical methods in a common mathematical framework. Published in 2004 by John Wiley & Sons, Ltd.

Mathematical analysis of a sharp-diffuse interfaces model for seawater intrusion

NASA Astrophysics Data System (ADS)

Choquet, C.; Diédhiou, M. M.; Rosier, C.

2015-10-01

We consider a new model mixing sharp and diffuse interface approaches for seawater intrusion phenomena in free aquifers. More precisely, a phase field model is introduced in the boundary conditions on the virtual sharp interfaces. We thus include in the model the existence of diffuse transition zones but we preserve the simplified structure allowing front tracking. The three-dimensional problem then reduces to a two-dimensional model involving a strongly coupled system of partial differential equations of parabolic type describing the evolution of the depths of the two free surfaces, that is the interface between salt- and freshwater and the water table. We prove the existence of a weak solution for the model completed with initial and boundary conditions. We also prove that the depths of the two interfaces satisfy a coupled maximum principle.

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.

Approximate series solution of multi-dimensional, time fractional-order (heat-like) diffusion equations using FRDTM.

PubMed

Singh, Brajesh K; Srivastava, Vineet K

2015-04-01

The main goal of this paper is to present a new approximate series solution of the multi-dimensional (heat-like) diffusion equation with time-fractional derivative in Caputo form using a semi-analytical approach: fractional-order reduced differential transform method (FRDTM). The efficiency of FRDTM is confirmed by considering four test problems of the multi-dimensional time fractional-order diffusion equation. FRDTM is a very efficient, effective and powerful mathematical tool which provides exact or very close approximate solutions for a wide range of real-world problems arising in engineering and natural sciences, modelled in terms of differential equations.

Approximate series solution of multi-dimensional, time fractional-order (heat-like) diffusion equations using FRDTM

PubMed Central

Singh, Brajesh K.; Srivastava, Vineet K.

2015-01-01

The main goal of this paper is to present a new approximate series solution of the multi-dimensional (heat-like) diffusion equation with time-fractional derivative in Caputo form using a semi-analytical approach: fractional-order reduced differential transform method (FRDTM). The efficiency of FRDTM is confirmed by considering four test problems of the multi-dimensional time fractional-order diffusion equation. FRDTM is a very efficient, effective and powerful mathematical tool which provides exact or very close approximate solutions for a wide range of real-world problems arising in engineering and natural sciences, modelled in terms of differential equations. PMID:26064639

Two dimensional finite element modelling for dynamic water diffusion through stratum corneum.

PubMed

Xiao, Perry; Imhof, Robert E

2012-10-01

Solvents penetration through in vivo human stratum corneum (SC) has always been an interesting research area for trans-dermal drug delivery studies, and the importance of intercellular routes (diffuse in between corneocytes) and transcellular routes (diffuse through corneocytes) during diffusion is often debatable. In this paper, we have developed a two dimensional finite element model to simulate the dynamic water diffusion through the SC. It is based on the brick-and-mortar model, with brick represents corneocytes and mortar represents lipids, respectively. It simulates the dynamic water diffusion process through the SC from pre-defined initial conditions and boundary conditions. Although the simulation is based on water diffusions, the principles can also be applied to the diffusions of other topical applied substances. The simulation results show that both intercellular routes and transcellular routes are important for water diffusion. Although intercellular routes have higher flux rates, most of the water still diffuse through transcellular routes because of the high cross area ratio of corneocytes and lipids. The diffusion water flux, or trans-epidermal water loss (TEWL), is reversely proportional to corneocyte size, i.e. the larger the corneocyte size, the lower the TEWL, and vice versa. There is also an effect of the SC thickness, external air conditions and diffusion coefficients on the water diffusion through SC on the resulting TEWL. Copyright © 2012 Elsevier B.V. All rights reserved.

Na Diffusion in Quasi One-Dimensional Ion Conductor NaMn2O4 Observed by μ+SR

NASA Astrophysics Data System (ADS)

Umegaki, Izumi; Nozaki, Hiroshi; Harada, Masashi; Månsson, Martin; Sakurai, Hiroya; Kawasaki, Ikuto; Watanabe, Isao; Sugiyama, Jun

A quasi one-dimensional (1D) compound, NaMn2O4, in which Mn2O4 zigzag chains form a 1D channel along the b-axis and Na ions locate at the center of the channel, is thought to be a good Na ionic conductor. In order to study Na-ion diffusion, we have measured μ+SR spectra using a powder sample in the temperature range between 100 and 500 K. A diffusive behavior was clearly observed above 325 K. Assuming a thermal activate process for jump diffusion of Na-ion between two nearest neighboring sites, a self diffusion coefficient of Na ion (DNa) and its activation energy (Ea) were estimated as DNa = (3.1 ± 0.2) × 10 - 11 cm2/s at 350 K and Ea = 180(9) meV.

From analytical solutions of solute transport equations to multidimensional time-domain random walk (TDRW) algorithms

NASA Astrophysics Data System (ADS)

Bodin, Jacques

2015-03-01

In this study, new multi-dimensional time-domain random walk (TDRW) algorithms are derived from approximate one-dimensional (1-D), two-dimensional (2-D), and three-dimensional (3-D) analytical solutions of the advection-dispersion equation and from exact 1-D, 2-D, and 3-D analytical solutions of the pure-diffusion equation. These algorithms enable the calculation of both the time required for a particle to travel a specified distance in a homogeneous medium and the mass recovery at the observation point, which may be incomplete due to 2-D or 3-D transverse dispersion or diffusion. The method is extended to heterogeneous media, represented as a piecewise collection of homogeneous media. The particle motion is then decomposed along a series of intermediate checkpoints located on the medium interface boundaries. The accuracy of the multi-dimensional TDRW method is verified against (i) exact analytical solutions of solute transport in homogeneous media and (ii) finite-difference simulations in a synthetic 2-D heterogeneous medium of simple geometry. The results demonstrate that the method is ideally suited to purely diffusive transport and to advection-dispersion transport problems dominated by advection. Conversely, the method is not recommended for highly dispersive transport problems because the accuracy of the advection-dispersion TDRW algorithms degrades rapidly for a low Péclet number, consistent with the accuracy limit of the approximate analytical solutions. The proposed approach provides a unified methodology for deriving multi-dimensional time-domain particle equations and may be applicable to other mathematical transport models, provided that appropriate analytical solutions are available.

Directly measuring of thermal pulse transfer in one-dimensional highly aligned carbon nanotubes

PubMed Central

Zhang, Guang; Liu, Changhong; Fan, Shoushan

2013-01-01

Using a simple and precise instrument system, we directly measured the thermo-physical properties of one-dimensional highly aligned carbon nanotubes (CNTs). A kind of CNT-based macroscopic materials named super aligned carbon nanotube (SACNT) buckypapers was measured in our experiment. We defined a new one-dimensional parameter, the “thermal transfer speed” to characterize the thermal damping mechanisms in the SACNT buckypapers. Our results indicated that the SACNT buckypapers with different densities have obviously different thermal transfer speeds. Furthermore, we found that the thermal transfer speed of high-density SACNT buckypapers may have an obvious damping factor along the CNTs aligned direction. The anisotropic thermal diffusivities of SACNT buckypapers could be calculated by the thermal transfer speeds. The thermal diffusivities obviously increase as the buckypaper-density increases. For parallel SACNT buckypapers, the thermal diffusivity could be as high as 562.2 ± 55.4 mm2/s. The thermal conductivities of these SACNT buckypapers were also calculated by the equation k = Cpαρ. PMID:23989589

Directly measuring of thermal pulse transfer in one-dimensional highly aligned carbon nanotubes.

PubMed

Zhang, Guang; Liu, Changhong; Fan, Shoushan

2013-01-01

Using a simple and precise instrument system, we directly measured the thermo-physical properties of one-dimensional highly aligned carbon nanotubes (CNTs). A kind of CNT-based macroscopic materials named super aligned carbon nanotube (SACNT) buckypapers was measured in our experiment. We defined a new one-dimensional parameter, the "thermal transfer speed" to characterize the thermal damping mechanisms in the SACNT buckypapers. Our results indicated that the SACNT buckypapers with different densities have obviously different thermal transfer speeds. Furthermore, we found that the thermal transfer speed of high-density SACNT buckypapers may have an obvious damping factor along the CNTs aligned direction. The anisotropic thermal diffusivities of SACNT buckypapers could be calculated by the thermal transfer speeds. The thermal diffusivities obviously increase as the buckypaper-density increases. For parallel SACNT buckypapers, the thermal diffusivity could be as high as 562.2 ± 55.4 mm(2)/s. The thermal conductivities of these SACNT buckypapers were also calculated by the equation k = Cpαρ.

Thermal Pollution Mathematical Model. Volume 2; Verification of One-Dimensional Numerical Model at Lake Keowee

NASA Technical Reports Server (NTRS)

Lee, S. S.; Sengupta, S.; Nwadike, E. V.

1980-01-01

A one dimensional model for studying the thermal dynamics of cooling lakes was developed and verified. The model is essentially a set of partial differential equations which are solved by finite difference methods. The model includes the effects of variation of area with depth, surface heating due to solar radiation absorbed at the upper layer, and internal heating due to the transmission of solar radiation to the sub-surface layers. The exchange of mechanical energy between the lake and the atmosphere is included through the coupling of thermal diffusivity and wind speed. The effects of discharge and intake by power plants are also included. The numerical model was calibrated by applying it to Cayuga Lake. The model was then verified through a long term simulation using Lake Keowee data base. The comparison between measured and predicted vertical temperature profiles for the nine years is good. The physical limnology of Lake Keowee is presented through a set of graphical representations of the measured data base.

Limit theorems for Lévy walks in d dimensions: rare and bulk fluctuations

NASA Astrophysics Data System (ADS)

Fouxon, Itzhak; Denisov, Sergey; Zaburdaev, Vasily; Barkai, Eli

2017-04-01

We consider super-diffusive Lévy walks in d≥slant 2 dimensions when the duration of a single step, i.e. a ballistic motion performed by a walker, is governed by a power-law tailed distribution of infinite variance and finite mean. We demonstrate that the probability density function (PDF) of the coordinate of the random walker has two different scaling limits at large times. One limit describes the bulk of the PDF. It is the d-dimensional generalization of the one-dimensional Lévy distribution and is the counterpart of the central limit theorem (CLT) for random walks with finite dispersion. In contrast with the one-dimensional Lévy distribution and the CLT this distribution does not have a universal shape. The PDF reflects anisotropy of the single-step statistics however large the time is. The other scaling limit, the so-called ‘infinite density’, describes the tail of the PDF which determines second (dispersion) and higher moments of the PDF. This limit repeats the angular structure of the PDF of velocity in one step. A typical realization of the walk consists of anomalous diffusive motion (described by anisotropic d-dimensional Lévy distribution) interspersed with long ballistic flights (described by infinite density). The long flights are rare but due to them the coordinate increases so much that their contribution determines the dispersion. We illustrate the concept by considering two types of Lévy walks, with isotropic and anisotropic distributions of velocities. Furthermore, we show that for isotropic but otherwise arbitrary velocity distributions the d-dimensional process can be reduced to a one-dimensional Lévy walk. We briefly discuss the consequences of non-universality for the d  >  1 dimensional fractional diffusion equation, in particular the non-uniqueness of the fractional Laplacian.

Continuum models of cohesive stochastic swarms: The effect of motility on aggregation patterns

NASA Astrophysics Data System (ADS)

Hughes, Barry D.; Fellner, Klemens

2013-10-01

Mathematical models of swarms of moving agents with non-local interactions have many applications and have been the subject of considerable recent interest. For modest numbers of agents, cellular automata or related algorithms can be used to study such systems, but in the present work, instead of considering discrete agents, we discuss a class of one-dimensional continuum models, in which the agents possess a density ρ(x,t) at location x at time t. The agents are subject to a stochastic motility mechanism and to a global cohesive inter-agent force. The motility mechanisms covered include classical diffusion, nonlinear diffusion (which may be used to model, in a phenomenological way, volume exclusion or other short-range local interactions), and a family of linear redistribution operators related to fractional diffusion equations. A variety of exact analytic results are discussed, including equilibrium solutions and criteria for unimodality of equilibrium distributions, full time-dependent solutions, and transitions between asymptotic collapse and asymptotic escape. We address the behaviour of the system for diffusive motility in the low-diffusivity limit for both smooth and singular interaction potentials and show how this elucidates puzzling behaviour in fully deterministic non-local particle interaction models. We conclude with speculative remarks about extensions and applications of the models.

A non-linear dimension reduction methodology for generating data-driven stochastic input models

NASA Astrophysics Data System (ADS)

Ganapathysubramanian, Baskar; Zabaras, Nicholas

2008-06-01

Stochastic analysis of random heterogeneous media (polycrystalline materials, porous media, functionally graded materials) provides information of significance only if realistic input models of the topology and property variations are used. This paper proposes a framework to construct such input stochastic models for the topology and thermal diffusivity variations in heterogeneous media using a data-driven strategy. Given a set of microstructure realizations (input samples) generated from given statistical information about the medium topology, the framework constructs a reduced-order stochastic representation of the thermal diffusivity. This problem of constructing a low-dimensional stochastic representation of property variations is analogous to the problem of manifold learning and parametric fitting of hyper-surfaces encountered in image processing and psychology. Denote by M the set of microstructures that satisfy the given experimental statistics. A non-linear dimension reduction strategy is utilized to map M to a low-dimensional region, A. We first show that M is a compact manifold embedded in a high-dimensional input space Rn. An isometric mapping F from M to a low-dimensional, compact, connected set A⊂Rd(d≪n) is constructed. Given only a finite set of samples of the data, the methodology uses arguments from graph theory and differential geometry to construct the isometric transformation F:M→A. Asymptotic convergence of the representation of M by A is shown. This mapping F serves as an accurate, low-dimensional, data-driven representation of the property variations. The reduced-order model of the material topology and thermal diffusivity variations is subsequently used as an input in the solution of stochastic partial differential equations that describe the evolution of dependant variables. A sparse grid collocation strategy (Smolyak algorithm) is utilized to solve these stochastic equations efficiently. We showcase the methodology by constructing low-dimensional input stochastic models to represent thermal diffusivity in two-phase microstructures. This model is used in analyzing the effect of topological variations of two-phase microstructures on the evolution of temperature in heat conduction processes.

Evaluation of Full Reynolds Stress Turbulence Models in FUN3D

NASA Technical Reports Server (NTRS)

Dudek, Julianne C.; Carlson, Jan-Renee

2017-01-01

Full seven-equation Reynolds stress turbulence models are promising tools for today’s aerospace technology challenges. This paper examines two such models for computing challenging turbulent flows including shock-wave boundary layer interactions, separation and mixing layers. The Wilcox and the SSG/LRR full second-moment Reynolds stress models have been implemented into the FUN3D (Fully Unstructured Navier-Stokes Three Dimensional) unstructured Navier-Stokes code and were evaluated for four problems: a transonic two-dimensional diffuser, a supersonic axisymmetric compression corner, a compressible planar shear layer, and a subsonic axisymmetric jet. Simulation results are compared with experimental data and results computed using the more commonly used Spalart-Allmaras (SA) one-equation and the Menter Shear Stress Transport (SST-V) two-equation turbulence models.

Evaluation of Full Reynolds Stress Turbulence Models in FUN3D

NASA Technical Reports Server (NTRS)

Dudek, Julianne C.; Carlson, Jan-Renee

2017-01-01

Full seven-equation Reynolds stress turbulence models are a relatively new and promising tool for todays aerospace technology challenges. This paper uses two stress-omega full Reynolds stress models to evaluate challenging flows including shock-wave boundary layer interactions, separation and mixing layers. The Wilcox and the SSG/LRR full second-moment Reynolds stress models have been implemented into the FUN3D (Fully Unstructured Navier-Stokes Three Dimensional) unstructured Navier-Stokes code and are evaluated for four problems: a transonic two-dimensional diffuser, a supersonic axisymmetric compression corner, a compressible planar shear layer, and a subsonic axisymmetric jet. Simulation results are compared with experimental data and results using the more commonly used Spalart-Allmaras (SA) one-equation and the Menter Shear Stress Transport (SST-V) two-equation turbulence models.

Models of inertial range spectra of interplanetary magnetohydrodynamic turbulence

NASA Technical Reports Server (NTRS)

Zhou, YE; Matthaeus, William H.

1990-01-01

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

Application of Paramagnetically Tagged Molecules for Magnetic Resonance Imaging of Biofilm Mass Transport Processes▿

PubMed Central

Ramanan, B.; Holmes, W. M.; Sloan, W. T.; Phoenix, V. R.

2010-01-01

Molecules become readily visible by magnetic resonance imaging (MRI) when labeled with a paramagnetic tag. Consequently, MRI can be used to image their transport through porous media. In this study, we demonstrated that this method could be applied to image mass transport processes in biofilms. The transport of a complex of gadolinium and diethylenetriamine pentaacetic acid (Gd-DTPA), a commercially available paramagnetic molecule, was imaged both in agar (as a homogeneous test system) and in a phototrophic biofilm. The images collected were T1 weighted, where T1 is an MRI property of the biofilm and is dependent on Gd-DTPA concentration. A calibration protocol was applied to convert T1 parameter maps into concentration maps, thus revealing the spatially resolved concentrations of this tracer at different time intervals. Comparing the data obtained from the agar experiment with data from a one-dimensional diffusion model revealed that transport of Gd-DTPA in agar was purely via diffusion, with a diffusion coefficient of 7.2 × 10−10 m2 s−1. In contrast, comparison of data from the phototrophic biofilm experiment with data from a two-dimensional diffusion model revealed that transport of Gd-DTPA inside the biofilm was by both diffusion and advection, equivalent to a diffusion coefficient of 1.04 × 10−9 m2 s−1. This technology can be used to further explore mass transport processes in biofilms, either by using the wide range of commercially available paramagnetically tagged molecules and nanoparticles or by using bespoke tagged molecules. PMID:20435773

Sparse learning of stochastic dynamical equations

NASA Astrophysics Data System (ADS)

Boninsegna, Lorenzo; Nüske, Feliks; Clementi, Cecilia

2018-06-01

With the rapid increase of available data for complex systems, there is great interest in the extraction of physically relevant information from massive datasets. Recently, a framework called Sparse Identification of Nonlinear Dynamics (SINDy) has been introduced to identify the governing equations of dynamical systems from simulation data. In this study, we extend SINDy to stochastic dynamical systems which are frequently used to model biophysical processes. We prove the asymptotic correctness of stochastic SINDy in the infinite data limit, both in the original and projected variables. We discuss algorithms to solve the sparse regression problem arising from the practical implementation of SINDy and show that cross validation is an essential tool to determine the right level of sparsity. We demonstrate the proposed methodology on two test systems, namely, the diffusion in a one-dimensional potential and the projected dynamics of a two-dimensional diffusion process.

Colony patterning and collective hyphal growth of filamentous fungi

NASA Astrophysics Data System (ADS)

Matsuura, Shu

2002-11-01

Colony morphology of wild and mutant strains of Aspergillus nidulans at various nutrient and agar levels was investigated. Two types of colony patterning were found for these strains. One type produced uniform colonies at all nutrient and agar levels tested, and the other exhibited morphological change into disordered ramified colonies at low nutrient levels. Both types showed highly condensed compact colonies at high nutrient levels on low agar media that was highly diffusive. Disordered colonies were found to develop with low hyphal extension rates at low nutrient levels. To understand basic pattern selection rules, a colony model with three parameters, i.e., the initial nutrient level and the step length of nutrient random walk as the external parameters, and the frequency of nutrient uptake as an internal parameter, was constructed. At low nutrient levels, with decreasing nutrient uptake frequency under diffusive conditions, the model colony exhibited onsets of disordered ramification. Further, in the growth process of A. nidulans, reduction of hyphal extension rate due to a population effect of hyphae was found when hyphae form three-dimensional dense colonies, as compared to the case in which hyphal growth was restricted into two-dimensional space. A hyphal population effect was introduced in the colony model. Thickening of colony periphery due to the population effect became distinctive as the nutrient diffusion effect was raised at high nutrient levels with low hyphal growth rate. It was considered that colony patterning and onset of disorder were strongly governed by the combination of nutrient diffusion and hyphal growth rate.

Fingering convection induced by atomic diffusion in stars: 3D numerical computations and applications to stellar models

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

Zemskova, Varvara; Garaud, Pascale; Deal, Morgan

2014-11-10

Iron-rich layers are known to form in the stellar subsurface through a combination of gravitational settling and radiative levitation. Their presence, nature, and detailed structure can affect the excitation process of various stellar pulsation modes and must therefore be modeled carefully in order to better interpret Kepler asteroseismic data. In this paper, we study the interplay between atomic diffusion and fingering convection in A-type stars, as well as its role in the establishment and evolution of iron accumulation layers. To do so, we use a combination of three-dimensional idealized numerical simulations of fingering convection (which neglect radiative transfer and complexmore » opacity effects) and one-dimensional realistic stellar models. Using the three-dimensional simulations, we first validate the mixing prescription for fingering convection recently proposed by Brown et al. (within the scope of the aforementioned approximation) and identify what system parameters (total mass of iron, iron diffusivity, thermal diffusivity, etc.) play a role in the overall evolution of the layer. We then implement the Brown et al. prescription in the Toulouse-Geneva Evolution Code to study the evolution of the iron abundance profile beneath the stellar surface. We find, as first discussed by Théado et al., that when the concurrent settling of helium is ignored, this accumulation rapidly causes an inversion in the mean molecular weight profile, which then drives fingering convection. The latter mixes iron with the surrounding material very efficiently, and the resulting iron layer is very weak. However, taking helium settling into account partially stabilizes the iron profile against fingering convection, and a large iron overabundance can accumulate. The opacity also increases significantly as a result, and in some cases it ultimately triggers dynamical convection. The direct effects of radiative acceleration on the dynamics of fingering convection (especially in the nonlinear regime) remain to be added in the future to improve the quantitative predictions of the model.« less

Determination of spatially dependent diffusion parameters in bovine bone using Kalman filter.

PubMed

Shokry, Abdallah; Ståhle, Per; Svensson, Ingrid

2015-11-07

Although many studies have been made for homogenous constant diffusion, bone is an inhomogeneous material. It has been suggested that bone porosity decreases from the inner boundaries to the outer boundaries of the long bones. The diffusivity of substances in the bone matrix is believed to increase as the bone porosity increases. In this study, an experimental set up is used where bovine bone samples, saturated with potassium chloride (KCl), were put into distilled water and the conductivity of the water was followed. Chloride ions in the bone samples escaped out in the water through diffusion and the increase of the conductivity was measured. A one-dimensional, spatially dependent mathematical model describing the diffusion process is used. The diffusion parameters in the model are determined using a Kalman filter technique. The parameters for spatially dependent at endosteal and periosteal surfaces are found to be (12.8 ± 4.7) × 10(-11) and (5 ± 3.5) × 10(-11)m(2)/s respectively. The mathematical model function using the obtained diffusion parameters fits very well with the experimental data with mean square error varies from 0.06 × 10(-6) to 0.183 × 10(-6) (μS/m)(2). Copyright © 2015 Elsevier Ltd. All rights reserved.

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

NASA Astrophysics Data System (ADS)

Beck, Margaret; Wayne, C. Eugene

2009-01-01

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

A splitting scheme based on the space-time CE/SE method for solving multi-dimensional hydrodynamical models of semiconductor devices

NASA Astrophysics Data System (ADS)

Nisar, Ubaid Ahmed; Ashraf, Waqas; Qamar, Shamsul

2016-08-01

Numerical solutions of the hydrodynamical model of semiconductor devices are presented in one and two-space dimension. The model describes the charge transport in semiconductor devices. Mathematically, the models can be written as a convection-diffusion type system with a right hand side describing the relaxation effects and interaction with a self consistent electric field. The proposed numerical scheme is a splitting scheme based on the conservation element and solution element (CE/SE) method for hyperbolic step, and a semi-implicit scheme for the relaxation step. The numerical results of the suggested scheme are compared with the splitting scheme based on Nessyahu-Tadmor (NT) central scheme for convection step and the same semi-implicit scheme for the relaxation step. The effects of various parameters such as low field mobility, device length, lattice temperature and voltages for one-space dimensional hydrodynamic model are explored to further validate the generic applicability of the CE/SE method for the current model equations. A two dimensional simulation is also performed by CE/SE method for a MESFET device, producing results in good agreement with those obtained by NT-central scheme.

One-dimensional energetic particle quasilinear diffusion for realistic TAE instabilities

NASA Astrophysics Data System (ADS)

Duarte, Vinicius; Ghantous, Katy; Berk, Herbert; Gorelenkov, Nikolai

2014-10-01

Owing to the proximity of the characteristic phase (Alfvén) velocity and typical energetic particle (EP) superthermal velocities, toroidicity-induced Alfvén eigenmodes (TAEs) can be resonantly destabilized endangering the plasma performance. Thus, it is of ultimate importance to understand the deleterious effects on the confinement resulting from fast ion driven instabilities expected in fusion-grade plasmas. We propose to study the interaction of EPs and TAEs using a line broadened quasilinear model, which captures the interaction in both regimes of isolated and overlapping modes. The resonance particles diffuse in the phase space where the problem essentially reduces to one dimension with constant kinetic energy and the diffusion mainly along the canonical toroidal angular momentum. Mode structure and wave particle resonances are computed by the NOVA code and are used in a quasilinear diffusion code that is being written to study the evolution of the distribution function, under the assumption that they can be considered virtually unalterable during the diffusion. A new scheme for the resonant particle diffusion is being proposed that builds on the 1-D nature of the diffusion from a single mode, which leads to a momentum conserving difference scheme even when there is mode overlap.

One-dimensional model of interacting-step fluctuations on vicinal surfaces: Analytical formulas and kinetic Monte Carlo simulations

NASA Astrophysics Data System (ADS)

Patrone, Paul N.; Einstein, T. L.; Margetis, Dionisios

2010-12-01

We study analytically and numerically a one-dimensional model of interacting line defects (steps) fluctuating on a vicinal crystal. Our goal is to formulate and validate analytical techniques for approximately solving systems of coupled nonlinear stochastic differential equations (SDEs) governing fluctuations in surface motion. In our analytical approach, the starting point is the Burton-Cabrera-Frank (BCF) model by which step motion is driven by diffusion of adsorbed atoms on terraces and atom attachment-detachment at steps. The step energy accounts for entropic and nearest-neighbor elastic-dipole interactions. By including Gaussian white noise to the equations of motion for terrace widths, we formulate large systems of SDEs under different choices of diffusion coefficients for the noise. We simplify this description via (i) perturbation theory and linearization of the step interactions and, alternatively, (ii) a mean-field (MF) approximation whereby widths of adjacent terraces are replaced by a self-consistent field but nonlinearities in step interactions are retained. We derive simplified formulas for the time-dependent terrace-width distribution (TWD) and its steady-state limit. Our MF analytical predictions for the TWD compare favorably with kinetic Monte Carlo simulations under the addition of a suitably conservative white noise in the BCF equations.

Diagnostic analysis of two-dimensional monthly average ozone balance with Chapman chemistry

NASA Technical Reports Server (NTRS)

Stolarski, Richard S.; Jackman, Charles H.; Kaye, Jack A.

1986-01-01

Chapman chemistry has been used in a two-dimensional model to simulate ozone balance phenomenology. The similarity between regions of ozone production and loss calculated using Chapman chemistry and those computed using LIMS and SAMS data with a photochemical equilibrium model indicate that such simplified chemistry is useful in studying gross features in stratospheric ozone balance. Net ozone production or loss rates are brought about by departures from the photochemical equilibrium (PCE) condition. If transport drives ozone above its PCE condition, then photochemical loss dominates production. If transport drives ozone below its PCE condition, then photochemical production dominates loss. Gross features of ozone loss/production (L/P) inferred for the real atmosphere from data are also simulated using only eddy diffusion. This indicates that one must be careful in assigning a transport scheme for a two-dimensional model that mimics only behavior of the observed ozone L/P.

Putting atomic diffusion theory of magnetic ApBp stars to the test: evaluation of the predictions of time-dependent diffusion models

NASA Astrophysics Data System (ADS)

Kochukhov, O.; Ryabchikova, T. A.

2018-02-01

A series of recent theoretical atomic diffusion studies has address the challenging problem of predicting inhomogeneous vertical and horizontal chemical element distributions in the atmospheres of magnetic ApBp stars. Here we critically assess the most sophisticated of such diffusion models - based on a time-dependent treatment of the atomic diffusion in a magnetized stellar atmosphere - by direct comparison with observations as well by testing the widely used surface mapping tools with the spectral line profiles predicted by this theory. We show that the mean abundances of Fe and Cr are grossly underestimated by the time-dependent theoretical diffusion model, with discrepancies reaching a factor of 1000 for Cr. We also demonstrate that Doppler imaging inversion codes, based either on modelling of individual metal lines or line-averaged profiles simulated according to theoretical three-dimensional abundance distribution, are able to reconstruct correct horizontal chemical spot maps despite ignoring the vertical abundance variation. These numerical experiments justify a direct comparison of the empirical two-dimensional Doppler maps with theoretical diffusion calculations. This comparison is generally unfavourable for the current diffusion theory, as very few chemical elements are observed to form overabundance rings in the horizontal field regions as predicted by the theory and there are numerous examples of element accumulations in the vicinity of radial field zones, which cannot be explained by diffusion calculations.

Analysis of Molecular Diffusion by First-Passage Time Variance Identifies the Size of Confinement Zones

PubMed Central

Rajani, Vishaal; Carrero, Gustavo; Golan, David E.; de Vries, Gerda; Cairo, Christopher W.

2011-01-01

The diffusion of receptors within the two-dimensional environment of the plasma membrane is a complex process. Although certain components diffuse according to a random walk model (Brownian diffusion), an overwhelming body of work has found that membrane diffusion is nonideal (anomalous diffusion). One of the most powerful methods for studying membrane diffusion is single particle tracking (SPT), which records the trajectory of a label attached to a membrane component of interest. One of the outstanding problems in SPT is the analysis of data to identify the presence of heterogeneity. We have adapted a first-passage time (FPT) algorithm, originally developed for the interpretation of animal movement, for the analysis of SPT data. We discuss the general application of the FPT analysis to molecular diffusion, and use simulations to test the method against data containing known regions of confinement. We conclude that FPT can be used to identify the presence and size of confinement within trajectories of the receptor LFA-1, and these results are consistent with previous reports on the size of LFA-1 clusters. The analysis of trajectory data for cell surface receptors by FPT provides a robust method to determine the presence and size of confined regions of diffusion. PMID:21402028

A comparison of Fick and Maxwell-Stefan diffusion formulations in PEMFC gas diffusion layers

NASA Astrophysics Data System (ADS)

Lindstrom, Michael; Wetton, Brian

2017-01-01

This paper explores the mathematical formulations of Fick and Maxwell-Stefan diffusion in the context of polymer electrolyte membrane fuel cell cathode gas diffusion layers. The simple Fick law with a diagonal diffusion matrix is an approximation of Maxwell-Stefan. Formulations of diffusion combined with mass-averaged Darcy flow are considered for three component gases. For this application, the formulations can be compared computationally in a simple, one dimensional setting. Despite the models' seemingly different structure, it is observed that the predictions of the formulations are very similar on the cathode when air is used as oxidant. The two formulations give quite different results when the Nitrogen in the air oxidant is replaced by helium (this is often done as a diagnostic for fuel cells designs). The two formulations also give quite different results for the anode with a dilute Hydrogen stream. These results give direction to when Maxwell-Stefan diffusion, which is more complicated to implement computationally in many codes, should be used in fuel cell simulations.

Brownian motion of arbitrarily shaped particles in two dimensions.

PubMed

Chakrabarty, Ayan; Konya, Andrew; Wang, Feng; Selinger, Jonathan V; Sun, Kai; Wei, Qi-Huo

2014-11-25

We implement microfabricated boomerang particles with unequal arm lengths as a model for nonsymmetric particles and study their Brownian motion in a quasi-two-dimensional geometry by using high-precision single-particle motion tracking. We show that because of the coupling between translation and rotation, the mean squared displacements of a single asymmetric boomerang particle exhibit a nonlinear crossover from short-time faster to long-time slower diffusion, and the mean displacements for fixed initial orientation are nonzero and saturate out at long times. The measured anisotropic diffusion coefficients versus the tracking point position indicate that there exists one unique point, i.e., the center of hydrodynamic stress (CoH), at which all coupled diffusion coefficients vanish. This implies that in contrast to motion in three dimensions where the CoH exists only for high-symmetry particles, the CoH always exists for Brownian motion in two dimensions. We develop an analytical model based on Langevin theory to explain the experimental results and show that among the six anisotropic diffusion coefficients only five are independent because the translation-translation coupling originates from the translation-rotation coupling. Finally, we classify the behavior of two-dimensional Brownian motion of arbitrarily shaped particles into four groups based on the particle shape symmetry group and discussed potential applications of the CoH in simplifying understanding of the circular motions of microswimmers.

Effect of Soret diffusion on lean hydrogen/air flames at normal and elevated pressure and temperature

NASA Astrophysics Data System (ADS)

Zhou, Zhen; Hernández-Pérez, Francisco E.; Shoshin, Yuriy; van Oijen, Jeroen A.; de Goey, Laurentius P. H.

2017-09-01

The influence of Soret diffusion on lean premixed flames propagating in hydrogen/air mixtures is numerically investigated with a detailed chemical and transport models at normal and elevated pressure and temperature. The Soret diffusion influence on the one-dimensional (1D) flame mass burning rate and two-dimensional (2D) flame propagating characteristics is analysed, revealing a strong dependency on flame stretch rate, pressure and temperature. For 1D flames, at normal pressure and temperature, with an increase of Karlovitz number from 0 to 0.4, the mass burning rate is first reduced and then enhanced by Soret diffusion of H2 while it is reduced by Soret diffusion of H. The influence of Soret diffusion of H2 is enhanced by pressure and reduced by temperature. On the contrary, the influence of Soret diffusion of H is reduced by pressure and enhanced by temperature. For 2D flames, at normal pressure and temperature, during the early phase of flame evolution, flames with Soret diffusion display more curved flame cells. Pressure enhances this effect, while temperature reduces it. The influence of Soret diffusion of H2 on the global consumption speed is enhanced at elevated pressure. The influence of Soret diffusion of H on the global consumption speed is enhanced at elevated temperature. The flame evolution is more affected by Soret diffusion in the early phase of propagation than in the long run due to the local enrichment of H2 caused by flame curvature effects. The present study provides new insights into the Soret diffusion effect on the characteristics of lean hydrogen/air flames at conditions that are relevant to practical applications, e.g. gas engines and turbines.

Evaluating BTEX concentration in soil using a simple one-dimensional vado zone model: application to a new fuel station in Valencia (Spain)

NASA Astrophysics Data System (ADS)

Rodrigo-Ilarri, Javier; Rodrigo-Clavero, María-Elena

2017-04-01

Specific studies of the impact of fuel spills on the vadose zone are currently required when trying to obtain the environmental permits for new fuel stations. The development of One-Dimensional mathematical models of fate and transport of BTEX on the vadose zone can therefore be used to understand the behavior of the pollutants under different scenarios. VLEACH - a simple One-Dimensional Finite Different Vadose Zone Leaching Model - uses an numerical approximation of the Millington Equation, a theoretical based model for gaseous diffusion in porous media. This equation has been widely used in the fields of soil physics and hydrology to calculate the gaseous or vapor diffusion in porous media. The model describes the movement of organic contaminants within and between three different phases: (1) as a solute dissolved in water, (2) as a gas in the vapor phase, and (3) as an absorbed compound in the soil phase. Initially, the equilibrium distribution of contaminant mass between liquid, gas and sorbed phases is calculated. Transport processes are then simulated. Liquid advective transport is calculated based on values defined by the user for infiltration and soil water content. The contaminant in the vapor phase migrates into or out of adjacent cells based on the calculated concentration gradients that exist between adjacent cells. After the mass is exchanged between the cells, the total mass in each cell is recalculated and re-equilibrated between the different phases. At the end of the simulation, (1) an overall area-weighted groundwater impact for the entire modeled area and (2) the concentration profile of BTEX on the vadose zone are calculated. This work shows the results obtained when applying VLEACH to analyze the contamination scenario caused by a BTEX spill coming from a set of future underground storage tanks located on a new fuel station in Aldaia (Valencia region - Spain).

Modeling Diffusion as a Result of Observing Salinity, Water Temperature and Mixing of the Norwalk River into Long Island Sound

NASA Astrophysics Data System (ADS)

Giuliano, A. L.; Gillotte, C. N.; Wooldridge, T. R.

2016-02-01

This project investigates the space and time variability of salinity and temperature in the lower Norwalk River using a one-dimensional numerical model. The project uses surface measurements taken at two locations, one at the Norwalk Maritime Museum (NMM) and the other at the mouth of the river as it drains into the Norwalk Islands region adjacent to Long Island Sound (LIS). The model covers a relatively small distance of 1-2km. The size of the upriver neck and the first buoy is approximately five times smaller than the mouth between the second buoy site and Peach Island. The instrumentation will be responsible for generally characterizing the thermal physics occurring at the river-ocean environment. A one-dimensional advection-diffusion model will be used to simulate results. The data points will measure the salinity, water temperature, and pressure during a series of deployments in the river during a three-season period between 2013 and 2014. Further processes will ultimately show the overall advection occurring in the river. The upriver site is maintained by the Norwalk River Museum. A YSI XXX attached to a tether buoy is used to measure salinity and temperature at the surface.Preliminary results suggest typical temperature range at the upriver site is greater than at the mouth of the Norwalk River, and the daily peak temperature lag depends upon several factors, such as tidal state. The phenomenon of a salt wedge will also be considered.

Non-Markovian effects in the first-passage dynamics of obstructed tracer particle diffusion in one-dimensional systems

NASA Astrophysics Data System (ADS)

Forsling, Robin; Sanders, Lloyd P.; Ambjörnsson, Tobias; Lizana, Ludvig

2014-09-01

The standard setup for single-file diffusion is diffusing particles in one dimension which cannot overtake each other, where the dynamics of a tracer (tagged) particle is of main interest. In this article, we generalize this system and investigate first-passage properties of a tracer particle when flanked by identical crowder particles which may, besides diffuse, unbind (rebind) from (to) the one-dimensional lattice with rates koff (kon). The tracer particle is restricted to diffuse with rate kD on the lattice and the density of crowders is constant (on average). The unbinding rate koff is our key parameter and it allows us to systematically study the non-trivial transition between the completely Markovian case (koff ≫ kD) to the non-Markovian case (koff ≪ kD) governed by strong memory effects. This has relevance for several quasi one-dimensional systems. One example is gene regulation where regulatory proteins are searching for specific binding sites on a crowded DNA. We quantify the first-passage time distribution, f (t) (t is time), numerically using the Gillespie algorithm, and estimate f (t) analytically. In terms of koff (keeping kD fixed), we study the transition between the two known regimes: (i) when koff ≫ kD the particles may effectively pass each other and we recover the single particle result f (t) ˜ t-3/2, with a reduced diffusion constant; (ii) when koff ≪ kD unbinding is rare and we obtain the single-file result f (t) ˜ t-7/4. The intermediate region displays rich dynamics where both the characteristic f (t) - peak and the long-time power-law slope are sensitive to koff.

Leapfrog Diffusion Mechanism for One-Dimensional Chains on Missing-Row Reconstructed Surfaces

NASA Astrophysics Data System (ADS)

Montalenti, F.; Ferrando, R.

1999-02-01

We analyze the in-channel diffusion of dimers and longer n-adatom chains on Au and Pt (110) \\(1×2\\) surfaces by molecular dynamics simulations. From our calculations it arises that, on the missing-row reconstructed surface, a novel diffusion process, called leapfrog, dominates over concerted jumps, thus becoming the most frequent diffusion mechanism.

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

NASA Astrophysics Data System (ADS)

Huveneers, François

2018-04-01

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

First-passage and escape problems in the Feller process

NASA Astrophysics Data System (ADS)

Masoliver, Jaume; Perelló, Josep

2012-10-01

The Feller process is an one-dimensional diffusion process with linear drift and state-dependent diffusion coefficient vanishing at the origin. The process is positive definite and it is this property along with its linear character that have made Feller process a convenient candidate for the modeling of a number of phenomena ranging from single-neuron firing to volatility of financial assets. While general properties of the process have long been well known, less known are properties related to level crossing such as the first-passage and the escape problems. In this work we thoroughly address these questions.

Surge dynamics coupled to pore-pressure evolution in debris flows

USGS Publications Warehouse

Savage, S.B.; Iverson, R.M.; ,

2003-01-01

Temporally and spatially varying pore-fluid pressures exert strong controls on debris-flow motion by mediating internal and basal friction at grain contacts. We analyze these effects by deriving a one-dimensional model of pore-pressure diffusion explicitly coupled to changes in debris-flow thickness. The new pore-pressure equation is combined with Iverson's (1997) extension of the depth-averaged Savage-Hutter (1989, 1991) granular avalanche equations to predict motion of unsteady debris-flow surges with evolving pore-pressure distributions. Computational results illustrate the profound effects of pore-pressure diffusivities on debris-flow surge depths and velocities. ?? 2003 Millpress,.

Numerical simulations of the transport and diffusion during the 1991 Winter Validation Study along the front range in Colorado

NASA Astrophysics Data System (ADS)

Fast, J. D.; Osteen, B. L.

An important aspect of the U.S. Department of Energy's Atmospheric Studies in Complex Terrain (ASCOT) program is the development and evaluation of numerical models that predict transport and diffusion of pollutants in complex terrain. Operational mesoscale modeling of the transport of pollutants in complex terrain will become increasingly practical as computational costs decrease and additional data from high-resolution remote sensing instrumentation networks become available during the 1990s. Four-dimensional data assimilation (4DDA) techniques are receiving a great deal of attention recently not only to improve the initial conditions of mesoscale forecast models, but to create high-quality four-dimensional mesoscale analysis fields that can be used as input to air-quality models. In this study, a four-dimensional data assimilation technique based on Newtonian relaxation is incorporated into the Colorado State University (CSU) Regional Atmospheric Modeling System (RAMS) and evaluated using data taken from one experiment of the 1991 ASCOT field study along the front range of the Rockies in Colorado. The main objective of this study is to compare the observed surface concentrations with those predicted by a Lagrangian particle dispersion model and to demonstrate the effect of data assimilation on the simulated plume. In contrast to previous studies in which the smallest horizontal grid spacing was 10 km (Stauffer and Seaman, 1991) and 8 km (Yamada and Hermi, 1991), data assimilation is applied in this study to domains with a horizontal grid spacing as small as 1 km.

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.

Linking basin-scale and pore-scale gas hydrate distribution patterns in diffusion-dominated marine hydrate systems: DIFFUSION-DRIVEN HYDRATE GROWTH IN SANDS

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

Nole, Michael; Daigle, Hugh; Cook, Ann E.

The goal of this study is to computationally determine the potential distribution patterns of diffusion-driven methane hydrate accumulations in coarse-grained marine sediments. Diffusion of dissolved methane in marine gas hydrate systems has been proposed as a potential transport mechanism through which large concentrations of hydrate can preferentially accumulate in coarse-grained sediments over geologic time. Using one-dimensional compositional reservoir simulations, we examine hydrate distribution patterns at the scale of individual sand layers (1 to 20 m thick) that are deposited between microbially active fine-grained material buried through the gas hydrate stability zone (GHSZ). We then extrapolate to two- dimensional and basin-scalemore » three-dimensional simulations, where we model dipping sands and multilayered systems. We find that properties of a sand layer including pore size distribution, layer thickness, dip, and proximity to other layers in multilayered systems all exert control on diffusive methane fluxes toward and within a sand, which in turn impact the distribution of hydrate throughout a sand unit. In all of these simulations, we incorporate data on physical properties and sand layer geometries from the Terrebonne Basin gas hydrate system in the Gulf of Mexico. We demonstrate that diffusion can generate high hydrate saturations (upward of 90%) at the edges of thin sands at shallow depths within the GHSZ, but that it is ineffective at producing high hydrate saturations throughout thick (greater than 10 m) sands buried deep within the GHSZ. As a result, we find that hydrate in fine-grained material can preserve high hydrate saturations in nearby thin sands with burial.« less

Linking basin-scale and pore-scale gas hydrate distribution patterns in diffusion-dominated marine hydrate systems: DIFFUSION-DRIVEN HYDRATE GROWTH IN SANDS

DOE PAGES

Nole, Michael; Daigle, Hugh; Cook, Ann E.; ...

2017-02-01

The goal of this study is to computationally determine the potential distribution patterns of diffusion-driven methane hydrate accumulations in coarse-grained marine sediments. Diffusion of dissolved methane in marine gas hydrate systems has been proposed as a potential transport mechanism through which large concentrations of hydrate can preferentially accumulate in coarse-grained sediments over geologic time. Using one-dimensional compositional reservoir simulations, we examine hydrate distribution patterns at the scale of individual sand layers (1 to 20 m thick) that are deposited between microbially active fine-grained material buried through the gas hydrate stability zone (GHSZ). We then extrapolate to two- dimensional and basin-scalemore » three-dimensional simulations, where we model dipping sands and multilayered systems. We find that properties of a sand layer including pore size distribution, layer thickness, dip, and proximity to other layers in multilayered systems all exert control on diffusive methane fluxes toward and within a sand, which in turn impact the distribution of hydrate throughout a sand unit. In all of these simulations, we incorporate data on physical properties and sand layer geometries from the Terrebonne Basin gas hydrate system in the Gulf of Mexico. We demonstrate that diffusion can generate high hydrate saturations (upward of 90%) at the edges of thin sands at shallow depths within the GHSZ, but that it is ineffective at producing high hydrate saturations throughout thick (greater than 10 m) sands buried deep within the GHSZ. As a result, we find that hydrate in fine-grained material can preserve high hydrate saturations in nearby thin sands with burial.« less

Diffusion Characteristics of Upwind Schemes on Unstructured Triangulations

NASA Technical Reports Server (NTRS)

Wood, William A.; Kleb, William L.

1998-01-01

The diffusive characteristics of two upwind schemes, multi-dimensional fluctuation splitting and dimensionally-split finite volume, are compared for scalar advection-diffusion problems. Algorithms for the two schemes are developed for node-based data representation on median-dual meshes associated with unstructured triangulations in two spatial dimensions. Four model equations are considered: linear advection, non-linear advection, diffusion, and advection-diffusion. Modular coding is employed to isolate the effects of the two approaches for upwind flux evaluation, allowing for head-to-head accuracy and efficiency comparisons. Both the stability of compressive limiters and the amount of artificial diffusion generated by the schemes is found to be grid-orientation dependent, with the fluctuation splitting scheme producing less artificial diffusion than the dimensionally-split finite volume scheme. Convergence rates are compared for the combined advection-diffusion problem, with a speedup of 2-3 seen for fluctuation splitting versus finite volume when solved on the same mesh. However, accurate solutions to problems with small diffusion coefficients can be achieved on coarser meshes using fluctuation splitting rather than finite volume, so that when comparing convergence rates to reach a given accuracy, fluctuation splitting shows a 20-25 speedup over finite volume.

Design of a variable area diffuser for a 15-inch Mach 6 open-jet tunnel

NASA Technical Reports Server (NTRS)

Loney, Norman W.

1994-01-01

The Langley 15-inch Mach 6 High Temperature Tunnel was recently converted from a Mach 10 Hypersonic Flow Apparatus. This conversion was effected to improve the capability of testing in Mach 6 air at relatively high reservoir temperatures not previously possible at Langley. Elevated temperatures allow the matching of the Mach numbers, Reynolds numbers, and ratio of wall-to-adiabatic-wall temperatures (TW/Taw) between this and the Langley 20-inch Mach 6 CF4 Tunnel. This ratio is also matched for Langley's 31-inch Mach 10 Tunnel and is an important parameter useful in the simulation of slender bodies such as National Aerospace Plane (NASP) configurations currently being studied. Having established the nozzle's operating characteristics, the decision was made to install another test section to provide model injection capability. This test section is an open-jet type, with an injection system capable of injecting a model from retracted position to nozzle centerline between 0.5 and 2 seconds. Preliminary calibrations with the new test section resulted in Tunnel blockage. This blockage phenomenon was eliminated when the conical center body in the diffuser was replaced. The issue then, is to provide a new and more efficient variable area diffuser configuration with the capability to withstand testing of larger models without sending the Tunnel into an unstart condition. Use of the 1-dimensional steady flow equation with due regard to friction and heat transfer was employed to estimate the required area ratios (exit area / throat area) in a variable area diffuser. Correlations between diffuser exit Mach number and area ratios, relative to the stagnation pressure ratios and diffuser inlet Mach number were derived. From these correlations, one can set upper and lower operating pressures and temperatures for a given diffuser throat area. In addition, they will provide appropriate input conditions for the full 3-dimensional computational fluid dynamics (CFD) code for further simulation studies.

Three species one-dimensional kinetic model for weakly ionized plasmas

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

Gonzalez, J., E-mail: jorge.gonzalez@upm.es; Donoso, J. M.; Tierno, S. P.

2016-06-15

A three species one-dimensional kinetic model is presented for a spatially homogeneous weakly ionized plasma subjected to the action of a time varying electric field. Planar geometry is assumed, which means that the plasma evolves in the privileged direction of the field. The energy transmitted to the electric charges is channelized to the neutrals thanks to collisions, a mechanism that influences the plasma dynamics. Charge-charge interactions have been designed as a one-dimensional collision term equivalent to the Landau operator used for fully ionized plasmas. Charge-neutral collisions are modelled by a conservative drift-diffusion operator in the Dougherty's form. The resulting setmore » of coupled integro-differential equations is solved with the stable and robust propagator integral method. This semi–analytical method feasibility accounts for non–linear effects without appealing to linearisation or simplifications, providing conservative physically meaningful solutions even for initial or emerging sharp velocity distribution function profiles. It is found that charge-neutral collisions exert a significant effect since a quite different plasma evolution arises if compared to the collisionless limit. In addition, substantial differences in the system motion are found for constant and temperature dependent collision frequencies cases.« less

LBQ2D, Extending the Line Broadened Quasilinear Model to TAE-EP Interaction

NASA Astrophysics Data System (ADS)

Ghantous, Katy; Gorelenkov, Nikolai; Berk, Herbert

2012-10-01

The line broadened quasilinear model was proposed and tested on the one dimensional electrostatic case of the bump on tailfootnotetextH.L Berk, B. Breizman and J. Fitzpatrick, Nucl. Fusion, 35:1661, 1995 to study the wave particle interaction. In conventional quasilinear theory, the sea of overlapping modes evolve with time as the particle distribution function self consistently undergo diffusion in phase space. The line broadened quasilinear model is an extension to the conventional theory in a way that allows treatment of isolated modes as well as overlapping modes by broadening the resonant line in phase space. This makes it possible to treat the evolution of modes self consistently from onset to saturation in either case. We describe here the model denoted by LBQ2D which is an extension of the proposed one dimensional line broadened quasilinear model to the case of TAEs interacting with energetic particles in two dimensional phase space, energy as well as canonical angular momentum. We study the saturation of isolated modes in various regimes and present the analytical derivation and numerical results. Finally, we present, using ITER parameters, the case where multiple modes overlap and describe the techniques used for the numerical treatment.

A one-dimensional photochemical model of the troposphere with planetary boundary-layer parameterization

NASA Technical Reports Server (NTRS)

Fishman, J.; Carney, T. A.

1984-01-01

A time-dependent, one-dimensional photochemical model of the troposphere is used to describe the vertical distribution of atmospheric trace constituents for summer-time conditions at midlatitudes in the Northern Hemisphere. The model incorporates a planetary boundary layer (PBL) parametrization and a detailed chemical mechanism that includes the photochemistry of important nonmethane hydrocarbon species formed during the oxidation process. One result of the parametrized PBL is that the concentrations of some trace species in the free troposphere are 20-30 percent higher than when mixing processes are described by a vertical eddy diffusion coefficient which is held constant with respect to height and time. The lifetime of the oxides of nitrogen against photochemical conversion to nitric acid during summertime conditions is on the order of six hours. This lifetime is short enough to deplete most of the NO(x) in the PBL so that other reactive nitrogen species are more abundant than NO(x) throughout the free troposphere.

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

NASA Astrophysics Data System (ADS)

Siems, Ullrich; Nielaba, Peter

2018-04-01

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

Isopycnal mixing by mesoscale eddies significantly impacts oceanic anthropogenic carbon uptake

NASA Astrophysics Data System (ADS)

Gnanadesikan, Anand; Pradal, Marie-Aude; Abernathey, Ryan

2015-06-01

Anthropogenic carbon dioxide uptake varies across Earth System Models for reasons that have remained obscure. When varied within a single model, the lateral eddy mixing coefficient ARedi produces a range of uptake similar to the modeled range. The highest uptake, resulting from a simulation with a constant ARedi of 2400 m2/s, simulates 15% more historical carbon uptake than a model with ARedi = 400 m2/s. A sudden doubling in carbon dioxide produces a 21% range in carbon uptake across the models. Two spatially dependent representations of ARedi produce uptake that lies in the middle of the range of constant values despite predicting very large values in the subtropical gyres. One-dimensional diffusive models of the type used for integrated assessments can be fit to the simulations, with ARedi accounting for a substantial fraction of the effective vertical diffusion. Such models, however, mask significant regional changes in stratification and biological carbon storage.

Linear and non-linear infrared response of one-dimensional vibrational Holstein polarons in the anti-adiabatic limit: Optical and acoustical phonon models

NASA Astrophysics Data System (ADS)

Falvo, Cyril

2018-02-01

The theory of linear and non-linear infrared response of vibrational Holstein polarons in one-dimensional lattices is presented in order to identify the spectral signatures of self-trapping phenomena. Using a canonical transformation, the optical response is computed from the small polaron point of view which is valid in the anti-adiabatic limit. Two types of phonon baths are considered: optical phonons and acoustical phonons, and simple expressions are derived for the infrared response. It is shown that for the case of optical phonons, the linear response can directly probe the polaron density of states. The model is used to interpret the experimental spectrum of crystalline acetanilide in the C=O range. For the case of acoustical phonons, it is shown that two bound states can be observed in the two-dimensional infrared spectrum at low temperature. At high temperature, analysis of the time-dependence of the two-dimensional infrared spectrum indicates that bath mediated correlations slow down spectral diffusion. The model is used to interpret the experimental linear-spectroscopy of model α-helix and β-sheet polypeptides. This work shows that the Davydov Hamiltonian cannot explain the observations in the NH stretching range.

Simulation of Deep Convective Clouds with the Dynamic Reconstruction Turbulence Closure

NASA Astrophysics Data System (ADS)

Shi, X.; Chow, F. K.; Street, R. L.; Bryan, G. H.

2017-12-01

The terra incognita (TI), or gray zone, in simulations is a range of grid spacing comparable to the most energetic eddy diameter. Spacing in mesoscale and simulations is much larger than the eddies, and turbulence is parameterized with one-dimensional vertical-mixing. Large eddy simulations (LES) have grid spacing much smaller than the energetic eddies, and use three-dimensional models of turbulence. Studies of convective weather use convection-permitting resolutions, which are in the TI. Neither mesoscale-turbulence nor LES models are designed for the TI, so TI turbulence parameterization needs to be discussed. Here, the effects of sub-filter scale (SFS) closure schemes on the simulation of deep tropical convection are evaluated by comparing three closures, i.e. Smagorinsky model, Deardorff-type TKE model and the dynamic reconstruction model (DRM), which partitions SFS turbulence into resolvable sub-filter scales (RSFS) and unresolved sub-grid scales (SGS). The RSFS are reconstructed, and the SGS are modeled with a dynamic eddy viscosity/diffusivity model. The RSFS stresses/fluxes allow backscatter of energy/variance via counter-gradient stresses/fluxes. In high-resolution (100m) simulations of tropical convection use of these turbulence models did not lead to significant differences in cloud water/ice distribution, precipitation flux, or vertical fluxes of momentum and heat. When model resolutions are coarsened, the Smagorinsky and TKE models overestimate cloud ice and produces large-amplitude downward heat flux in the middle troposphere (not found in the high-resolution simulations). This error is a result of unrealistically large eddy diffusivities, i.e., the eddy diffusivity of the DRM is on the order of 1 for the coarse resolution simulations, the eddy diffusivity of the Smagorinsky and TKE model is on the order of 100. Splitting the eddy viscosity/diffusivity scalars into vertical and horizontal components by using different length scales and strain rate components helps to reduce the errors, but does not completely remedy the problem. In contrast, the coarse resolution simulations using the DRM produce results that are more consistent with the high-resolution results, suggesting that the DRM is a more appropriate turbulence model for simulating convection in the TI.

SkyFACT: high-dimensional modeling of gamma-ray emission with adaptive templates and penalized likelihoods

NASA Astrophysics Data System (ADS)

Storm, Emma; Weniger, Christoph; Calore, Francesca

2017-08-01

We present SkyFACT (Sky Factorization with Adaptive Constrained Templates), a new approach for studying, modeling and decomposing diffuse gamma-ray emission. Like most previous analyses, the approach relies on predictions from cosmic-ray propagation codes like GALPROP and DRAGON. However, in contrast to previous approaches, we account for the fact that models are not perfect and allow for a very large number (gtrsim 105) of nuisance parameters to parameterize these imperfections. We combine methods of image reconstruction and adaptive spatio-spectral template regression in one coherent hybrid approach. To this end, we use penalized Poisson likelihood regression, with regularization functions that are motivated by the maximum entropy method. We introduce methods to efficiently handle the high dimensionality of the convex optimization problem as well as the associated semi-sparse covariance matrix, using the L-BFGS-B algorithm and Cholesky factorization. We test the method both on synthetic data as well as on gamma-ray emission from the inner Galaxy, |l|<90o and |b|<20o, as observed by the Fermi Large Area Telescope. We finally define a simple reference model that removes most of the residual emission from the inner Galaxy, based on conventional diffuse emission components as well as components for the Fermi bubbles, the Fermi Galactic center excess, and extended sources along the Galactic disk. Variants of this reference model can serve as basis for future studies of diffuse emission in and outside the Galactic disk.

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

NASA Astrophysics Data System (ADS)

Ginn, T. R.

2018-01-01

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

Subdiffusion in Membrane Permeation of Small Molecules.

PubMed

Chipot, Christophe; Comer, Jeffrey

2016-11-02

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

Purging of multilayer insulation by gas diffusion

NASA Technical Reports Server (NTRS)

Sumner, I. E.; Spuckler, C. M.

1976-01-01

An experimental investigation was conducted to determine the time required to purge a multilayer insulation (MLI) panel with gaseous helium by means of gas diffusion to obtain a condensable (nitrogen) gas concentration of less than 1 percent within the panel. Two flat, rectangular MLI panel configurations, one incorporating a butt joint, were tested. The insulation panels consisted of 15 double-aluminized Mylar radiation shields separated by double silk net spacers. The test results indicated that the rate which the condensable gas concentration at the edge or at the butt joint of an MLI panel was reduced was a significant factor in the total time required to reduce the condensable gas concentration within the panel to less than 1 percent. The experimental data agreed well with analytical predictions made by using a simple, one-dimensional gas diffusion model in which the boundary conditions at the edge of the MLI panel were time dependent.

Radiation transfer in plant canopies - Scattering of solar radiation and canopy reflectance

NASA Technical Reports Server (NTRS)

Verstraete, Michel M.

1988-01-01

The one-dimensional vertical model of radiation transfer in a plant canopy described by Verstraete (1987) is extended to account for the transfer of diffuse radiation. This improved model computes the absorption and scattering of both visible and near-infrared radiation in a multilayer canopy as a function of solar position and leaf orientation distribution. Multiple scattering is allowed, and the spectral reflectance of the vegetation stand is predicted. The results of the model are compared to those of other models and actual observations.

Dynamic Displacement Disorder of Cubic BaTiO3

NASA Astrophysics Data System (ADS)

Paściak, M.; Welberry, T. R.; Kulda, J.; Leoni, S.; Hlinka, J.

2018-04-01

The three-dimensional distribution of the x-ray diffuse scattering intensity of BaTiO3 has been recorded in a synchrotron experiment and simultaneously computed using molecular dynamics simulations of a shell model. Together, these have allowed the details of the disorder in paraelectric BaTiO3 to be clarified. The narrow sheets of diffuse scattering, related to the famous anisotropic longitudinal correlations of Ti ions, are shown to be caused by the overdamped anharmonic soft phonon branch. This finding demonstrates that the occurrence of narrow sheets of diffuse scattering agrees with a displacive picture of the cubic phase of this textbook ferroelectric material. The presented methodology allows one to go beyond the harmonic approximation in the analysis of phonons and phonon-related scattering.

Global Search of a Three-dimensional Low Solidity Circular Cascade Diffuser for Centrifugal Blowers by Meta-model Assisted Optimization

NASA Astrophysics Data System (ADS)

Sakaguchi, Daisaku; Sakue, Daiki; Tun, Min Thaw

2018-04-01

A three-dimensional blade of a low solidity circular cascade diffuser in centrifugal blowers is designed by means of a multi-point optimization technique. The optimization aims at improving static pressure coefficient at a design point and at a small flow rate condition. Moreover, a clear definition of secondary flow expressed by positive radial velocity at hub side is taken into consideration in constraints. The number of design parameters for three-dimensional blade reaches to 10 in this study, such as a radial gap, a radial chord length and mean camber angle distribution of the LSD blade with five control points, control point between hub and shroud with two design freedom. Optimization results show clear Pareto front and selected optimum design shows good improvement of pressure rise in diffuser at small flow rate conditions. It is found that three-dimensional blade has advantage to stabilize the secondary flow effect with improving pressure recovery of the low solidity circular cascade diffuser.

Surface Diffusion in Systems of Interacting Brownian Particles

NASA Astrophysics Data System (ADS)

Mazroui, M'hammed; Boughaleb, Yahia

The paper reviews recent results on diffusive phenomena in two-dimensional periodic potential. Specifically, static and dynamic properties are investigated by calculating different correlation functions. Diffusion process is first studied for one-dimensional system by using the Fokker-Planck equation which is solved numerically by the matrix continued fraction method in the case of bistable potential. The transition from hopping to liquid-like diffusion induced by variation of some parameters is discussed. This study will therefore serve to demonstrate the influence of this form of potential. Further, an analytical approximation for the dc-conductivity is derived for a wide damping range in the framework of the Linear Response Theory. On the basis of this expression, calculations of the ac conductivity of two-dimensional system with Frenkel-Kontorova pair interaction in the intermediate friction regime is performed by using the continued fraction expansion method. The dc-conductivity expression is used to determine the rest of the development. By varying the density of mobile ions we discuss commensurability effects. To get information about the diffusion mechanism, the full width at half maximum λω(q), of the quasi-elastic line of the dynamical structure factor S(q,ω) is computed. The calculations are extended up to large values of q covering several Brillouin zones. The analysis of λω(q) with different parameters shows that the most probable diffusion process in good two-dimensional superionic conductors consists of a competition between a back correlated hopping in one direction and forward correlated hopping in addition to liquid-like motions in the other direction.

On the Effective Thermal Conductivity of Frost Considering Mass Diffusion and Eddy Convection

NASA Technical Reports Server (NTRS)

Kandula, Max

2010-01-01

A physical model for the effective thermal conductivity of water frost is proposed for application to the full range of frost density. The proposed model builds on the Zehner-Schlunder one-dimensional formulation for porous media appropriate for solid-to-fluid thermal conductivity ratios less than about 1000. By superposing the effects of mass diffusion and eddy convection on stagnant conduction in the fluid, the total effective thermal conductivity of frost is shown to be satisfactorily described. It is shown that the effects of vapor diffusion and eddy convection on the frost conductivity are of the same order. The results also point out that idealization of the frost structure by cylindrical inclusions offers a better representation of the effective conductivity of frost as compared to spherical inclusions. Satisfactory agreement between the theory and the measurements for the effective thermal conductivity of frost is demonstrated for a wide range of frost density and frost temperature.

Complex Geometric Models of Diffusion and Relaxation in Healthy and Damaged White Matter

PubMed Central

Farrell, Jonathan A.D.; Smith, Seth A.; Reich, Daniel S.; Calabresi, Peter A.; van Zijl, Peter C.M.

2010-01-01

Which aspects of tissue microstructure affect diffusion weighted MRI signals? Prior models, many of which use Monte-Carlo simulations, have focused on relatively simple models of the cellular microenvironment and have not considered important anatomic details. With the advent of higher-order analysis models for diffusion imaging, such as high-angular-resolution diffusion imaging (HARDI), more realistic models are necessary. This paper presents and evaluates the reproducibility of simulations of diffusion in complex geometries. Our framework is quantitative, does not require specialized hardware, is easily implemented with little programming experience, and is freely available as open-source software. Models may include compartments with different diffusivities, permeabilities, and T2 time constants using both parametric (e.g., spheres and cylinders) and arbitrary (e.g., mesh-based) geometries. Three-dimensional diffusion displacement-probability functions are mapped with high reproducibility, and thus can be readily used to assess reproducibility of diffusion-derived contrasts. PMID:19739233

On the source of stochastic volatility: Evidence from CAC40 index options during the subprime crisis

NASA Astrophysics Data System (ADS)

Slim, Skander

2016-12-01

This paper investigates the performance of time-changed Lévy processes with distinct sources of return volatility variation for modeling cross-sectional option prices on the CAC40 index during the subprime crisis. Specifically, we propose a multi-factor stochastic volatility model: one factor captures the diffusion component dynamics and two factors capture positive and negative jump variations. In-sample and out-of-sample tests show that our full-fledged model significantly outperforms nested lower-dimensional specifications. We find that all three sources of return volatility variation, with different persistence, are needed to properly account for market pricing dynamics across moneyness, maturity and volatility level. Besides, the model estimation reveals negative risk premium for both diffusive volatility and downward jump intensity whereas a positive risk premium is found to be attributed to upward jump intensity.

Polarization radiation in the planetary atmosphere delimited by a heterogeneous diffusely reflecting surface

NASA Technical Reports Server (NTRS)

Strelkov, S. A.; Sushkevich, T. A.

1983-01-01

Spatial frequency characteristics (SFC) and the scattering functions were studied in the two cases of a uniform horizontal layer with absolutely black bottom, and an isolated layer. The mathematical model for these examples describes the horizontal heterogeneities in a light field with regard to radiation polarization in a three dimensional planar atmosphere, delimited by a heterogeneous surface with diffuse reflection. The perturbation method was used to obtain vector transfer equations which correspond to the linear and nonlinear systems of polarization radiation transfer. The boundary value tasks for the vector transfer equation that is a parametric set and one dimensional are satisfied by the SFC of the nonlinear system, and are expressed through the SFC of linear approximation. As a consequence of the developed theory, formulas were obtained for analytical calculation of albedo in solving the task of dissemination of polarization radiation in the planetary atmosphere with uniform Lambert bottom.

Analytical approximations for spatial stochastic gene expression in single cells and tissues

PubMed Central

Smith, Stephen; Cianci, Claudia; Grima, Ramon

2016-01-01

Gene expression occurs in an environment in which both stochastic and diffusive effects are significant. Spatial stochastic simulations are computationally expensive compared with their deterministic counterparts, and hence little is currently known of the significance of intrinsic noise in a spatial setting. Starting from the reaction–diffusion master equation (RDME) describing stochastic reaction–diffusion processes, we here derive expressions for the approximate steady-state mean concentrations which are explicit functions of the dimensionality of space, rate constants and diffusion coefficients. The expressions have a simple closed form when the system consists of one effective species. These formulae show that, even for spatially homogeneous systems, mean concentrations can depend on diffusion coefficients: this contradicts the predictions of deterministic reaction–diffusion processes, thus highlighting the importance of intrinsic noise. We confirm our theory by comparison with stochastic simulations, using the RDME and Brownian dynamics, of two models of stochastic and spatial gene expression in single cells and tissues. PMID:27146686

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.

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.

A Non Local Electron Heat Transport Model for Multi-Dimensional Fluid Codes

NASA Astrophysics Data System (ADS)

Schurtz, Guy

2000-10-01

Apparent inhibition of thermal heat flow is one of the most ancient problems in computational Inertial Fusion and flux-limited Spitzer-Harm conduction has been a mainstay in multi-dimensional hydrodynamic codes for more than 25 years. Theoretical investigation of the problem indicates that heat transport in laser produced plasmas has to be considered as a non local process. Various authors contributed to the non local theory and proposed convolution formulas designed for practical implementation in one-dimensional fluid codes. Though the theory, confirmed by kinetic calculations, actually predicts a reduced heat flux, it fails to explain the very small limiters required in two-dimensional simulations. Fokker-Planck simulations by Epperlein, Rickard and Bell [PRL 61, 2453 (1988)] demonstrated that non local effects could lead to a strong reduction of heat flow in two dimensions, even in situations where a one-dimensional analysis suggests that the heat flow is nearly classical. We developed at CEA/DAM a non local electron heat transport model suitable for implementation in our two-dimensional radiation hydrodynamic code FCI2. This model may be envisionned as the first step of an iterative solution of the Fokker-Planck equations; it takes the mathematical form of multigroup diffusion equations, the solution of which yields both the heat flux and the departure of the electron distribution function to the Maxwellian. Although direct implementation of the model is straightforward, formal solutions of it can be expressed in convolution form, exhibiting a three-dimensional tensor propagator. Reduction to one dimension retrieves the original formula of Luciani, Mora and Virmont [PRL 51, 1664 (1983)]. Intense magnetic fields may be generated by thermal effects in laser targets; these fields, as well as non local effects, will inhibit electron conduction. We present simulations where both effects are taken into account and shortly discuss the coupling strategy between them.

Cadmium biosorption rate in protonated Sargassum biomass

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

Yang, J.; Volesky, B.

1999-03-01

Biosorption of the heavy metal ion Cd{sup 2+} by protonated nonliving brown alga Sargassum fluitans biomass was accompanied by the release of hydrogen protons from the biomass. The uptake of cadmium and the release of proton matched each other throughout the biosorption process. The end-point titration methodology was used to maintain the constant pH 4.0 for developing the dynamic sorption rate. The sorption isotherm could be well represented by the Langmuir sorption model. A mass transfer model assuming the intraparticle diffusion in a one-dimensional thin plate as a controlling step was developed to describe the overall biosorption rate of cadmiummore » ions in flat seaweed biomass particles. The overall biosorption mathematical model equations were solved numerically yielding the effective diffusion coefficient D{sub e} about 3.5 {times} 10{sup {minus}6} cm{sup 2}/s. This value matches that obtained for the desorption process and is approximately half of that of the molecular diffusion coefficient for cadmium ions in aqueous solution.« less

Applications of an exponential finite difference technique

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

Handschuh, R.F.; Keith, T.G. Jr.

1988-07-01

An exponential finite difference scheme first presented by Bhattacharya for one dimensional unsteady heat conduction problems in Cartesian coordinates was extended. The finite difference algorithm developed was used to solve the unsteady diffusion equation in one dimensional cylindrical coordinates and was applied to two and three dimensional conduction problems in Cartesian coordinates. Heat conduction involving variable thermal conductivity was also investigated. The method was used to solve nonlinear partial differential equations in one and two dimensional Cartesian coordinates. Predicted results are compared to exact solutions where available or to results obtained by other numerical methods.

O'Connell's process as a vicious Brownian motion.

PubMed

Katori, Makoto

2011-12-01

Vicious Brownian motion is a diffusion scaling limit of Fisher's vicious walk model, which is a system of Brownian particles in one dimension such that if two motions meet they kill each other. We consider the vicious Brownian motions conditioned never to collide with each other and call it noncolliding Brownian motion. This conditional diffusion process is equivalent to the eigenvalue process of the Hermitian-matrix-valued Brownian motion studied by Dyson [J. Math. Phys. 3, 1191 (1962)]. Recently, O'Connell [Ann. Probab. (to be published)] introduced a generalization of the noncolliding Brownian motion by using the eigenfunctions (the Whittaker functions) of the quantum Toda lattice in order to analyze a directed polymer model in 1 + 1 dimensions. We consider a system of one-dimensional Brownian motions with a long-ranged killing term as a generalization of the vicious Brownian motion and construct the O'Connell process as a conditional process of the killing Brownian motions to survive forever.

Development of morphogen gradient: The role of dimension and discreteness

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

Teimouri, Hamid; Kolomeisky, Anatoly B.

2014-02-28

The fundamental processes of biological development are governed by multiple signaling molecules that create non-uniform concentration profiles known as morphogen gradients. It is widely believed that the establishment of morphogen gradients is a result of complex processes that involve diffusion and degradation of locally produced signaling molecules. We developed a multi-dimensional discrete-state stochastic approach for investigating the corresponding reaction-diffusion models. It provided a full analytical description for stationary profiles and for important dynamic properties such as local accumulation times, variances, and mean first-passage times. The role of discreteness in developing of morphogen gradients is analyzed by comparing with available continuummore » descriptions. It is found that the continuum models prediction about multiple time scales near the source region in two-dimensional and three-dimensional systems is not supported in our analysis. Using ideas that view the degradation process as an effective potential, the effect of dimensionality on establishment of morphogen gradients is also discussed. In addition, we investigated how these reaction-diffusion processes are modified with changing the size of the source region.« less

Stability Test for Transient-Temperature Calculations

NASA Technical Reports Server (NTRS)

Campbell, W.

1984-01-01

Graphical test helps assure numerical stability of calculations of transient temperature or diffusion in composite medium. Rectangular grid forms basis of two-dimensional finite-difference model for heat conduction or other diffusion like phenomena. Model enables calculation of transient heat transfer among up to four different materials that meet at grid point.

Single-Molecule Test for Markovianity of the Dynamics along a Reaction Coordinate.

PubMed

Berezhkovskii, Alexander M; Makarov, Dmitrii E

2018-05-03

In an effort to answer the much-debated question of whether the time evolution of common experimental observables can be described as one-dimensional diffusion in the potential of mean force, we propose a simple criterion that allows one to test whether the Markov assumption is applicable to a single-molecule trajectory x( t). This test does not involve fitting of the data to any presupposed model and can be applied to experimental data with relatively low temporal resolution.

Testing a one-dimensional prescription of dynamical shear mixing with a two-dimensional hydrodynamic simulation

NASA Astrophysics Data System (ADS)

Edelmann, P. V. F.; Röpke, F. K.; Hirschi, R.; Georgy, C.; Jones, S.

2017-07-01

Context. The treatment of mixing processes is still one of the major uncertainties in 1D stellar evolution models. This is mostly due to the need to parametrize and approximate aspects of hydrodynamics in hydrostatic codes. In particular, the effect of hydrodynamic instabilities in rotating stars, for example, dynamical shear instability, evades consistent description. Aims: We intend to study the accuracy of the diffusion approximation to dynamical shear in hydrostatic stellar evolution models by comparing 1D models to a first-principle hydrodynamics simulation starting from the same initial conditions. Methods: We chose an initial model calculated with the stellar evolution code GENEC that is just at the onset of a dynamical shear instability but does not show any other instabilities (e.g., convection). This was mapped to the hydrodynamics code SLH to perform a 2D simulation in the equatorial plane. We compare the resulting profiles in the two codes and compute an effective diffusion coefficient for the hydro simulation. Results: Shear instabilities develop in the 2D simulation in the regions predicted by linear theory to become unstable in the 1D stellar evolution model. Angular velocity and chemical composition is redistributed in the unstable region, thereby creating new unstable regions. After a period of time, the system settles in a symmetric, steady state, which is Richardson stable everywhere in the 2D simulation, whereas the instability remains for longer in the 1D model due to the limitations of the current implementation in the 1D code. A spatially resolved diffusion coefficient is extracted by comparing the initial and final profiles of mean atomic mass. Conclusions: The presented simulation gives a first insight on hydrodynamics of shear instabilities in a real stellar environment and even allows us to directly extract an effective diffusion coefficient. We see evidence for a critical Richardson number of 0.25 as regions above this threshold remain stable for the course of the simulation. The movie of the simulation is available at http://www.aanda.org

The twin cell model and its excellence in determining the glass transition temperature of thin film metallic glass

NASA Astrophysics Data System (ADS)

Kanjilal, Baishali; Iram, Samreen; Das, Atreyee; Chakrabarti, Haimanti

2018-05-01

This work reports a novel two dimensional approach to the theoretical computation of the glass transition temperature in simple hypothetical icosahedral packed structures based on Thin Film metallic glasses using liquid state theories in the realm of transport properties. The model starts from Navier-Stokes equation and evaluates the statistical average velocity of each different species of atom under the condition of ensemble equality to compute diffusion lengths and the diffusion coefficients as a function of temperature. The additional correction brought in is that of the limited states due to tethering of one nodule vis -a-vis the others. The movement of the molecules use our Twin Cell Model a typical model pertinent for modeling chain motions. A temperature viscosity correction by Cohen and Grest is included through the temperature dependence of the relaxation times for glass formers.

A Rate-Theory-Phase-Field Model of Irradiation-Induced Recrystallization in UMo Nuclear Fuels

NASA Astrophysics Data System (ADS)

Hu, Shenyang; Joshi, Vineet; Lavender, Curt A.

2017-12-01

In this work, we developed a recrystallization model to study the effect of microstructures and radiation conditions on recrystallization kinetics in UMo fuels. The model integrates the rate theory of intragranular gas bubble and interstitial loop evolutions and a phase-field model of recrystallization zone evolution. A first passage method is employed to describe one-dimensional diffusion of interstitials with a diffusivity value several orders of magnitude larger than that of fission gas xenons. With the model, the effect of grain sizes on recrystallization kinetics is simulated. The results show that (1) recrystallization in large grains starts earlier than that in small grains, (2) the recrystallization kinetics (recrystallization volume fraction) decrease as the grain size increases, (3) the predicted recrystallization kinetics are consistent with the experimental results, and (4) the recrystallization kinetics can be described by the modified Avrami equation, but the parameters of the Avrami equation strongly depend on the grain size.

A Maximum Entropy Method for Particle Filtering

NASA Astrophysics Data System (ADS)

Eyink, Gregory L.; Kim, Sangil

2006-06-01

Standard ensemble or particle filtering schemes do not properly represent states of low priori probability when the number of available samples is too small, as is often the case in practical applications. We introduce here a set of parametric resampling methods to solve this problem. Motivated by a general H-theorem for relative entropy, we construct parametric models for the filter distributions as maximum-entropy/minimum-information models consistent with moments of the particle ensemble. When the prior distributions are modeled as mixtures of Gaussians, our method naturally generalizes the ensemble Kalman filter to systems with highly non-Gaussian statistics. We apply the new particle filters presented here to two simple test cases: a one-dimensional diffusion process in a double-well potential and the three-dimensional chaotic dynamical system of Lorenz.

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

A non-linear dimension reduction methodology for generating data-driven stochastic input models

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

Ganapathysubramanian, Baskar; Zabaras, Nicholas

Stochastic analysis of random heterogeneous media (polycrystalline materials, porous media, functionally graded materials) provides information of significance only if realistic input models of the topology and property variations are used. This paper proposes a framework to construct such input stochastic models for the topology and thermal diffusivity variations in heterogeneous media using a data-driven strategy. Given a set of microstructure realizations (input samples) generated from given statistical information about the medium topology, the framework constructs a reduced-order stochastic representation of the thermal diffusivity. This problem of constructing a low-dimensional stochastic representation of property variations is analogous to the problem ofmore » manifold learning and parametric fitting of hyper-surfaces encountered in image processing and psychology. Denote by M the set of microstructures that satisfy the given experimental statistics. A non-linear dimension reduction strategy is utilized to map M to a low-dimensional region, A. We first show that M is a compact manifold embedded in a high-dimensional input space R{sup n}. An isometric mapping F from M to a low-dimensional, compact, connected set A is contained in R{sup d}(d<

One-Dimensional Brownian Motion of Charged Nanoparticles along Microtubules: A Model System for Weak Binding Interactions

PubMed Central

Minoura, Itsushi; Katayama, Eisaku; Sekimoto, Ken; Muto, Etsuko

2010-01-01

Abstract Various proteins are known to exhibit one-dimensional Brownian motion along charged rodlike polymers, such as microtubules (MTs), actin, and DNA. The electrostatic interaction between the proteins and the rodlike polymers appears to be crucial for one-dimensional Brownian motion, although the underlying mechanism has not been fully clarified. We examined the interactions of positively-charged nanoparticles composed of polyacrylamide gels with MTs. These hydrophilic nanoparticles bound to MTs and displayed one-dimensional Brownian motion in a charge-dependent manner, which indicates that nonspecific electrostatic interaction is sufficient for one-dimensional Brownian motion. The diffusion coefficient decreased exponentially with an increasing particle charge (with the exponent being 0.10 kBT per charge), whereas the duration of the interaction increased exponentially (exponent of 0.22 kBT per charge). These results can be explained semiquantitatively if one assumes that a particle repeats a cycle of binding to and movement along an MT until it finally dissociates from the MT. During the movement, a particle is still electrostatically constrained in the potential valley surrounding the MT. This entire process can be described by a three-state model analogous to the Michaelis-Menten scheme, in which the two parameters of the equilibrium constant between binding and movement, and the rate of dissociation from the MT, are derived as a function of the particle charge density. This study highlights the possibility that the weak binding interactions between proteins and rodlike polymers, e.g., MTs, are mediated by a similar, nonspecific charge-dependent mechanism. PMID:20409479

One-dimensional Brownian motion of charged nanoparticles along microtubules: a model system for weak binding interactions.

PubMed

Minoura, Itsushi; Katayama, Eisaku; Sekimoto, Ken; Muto, Etsuko

2010-04-21

Various proteins are known to exhibit one-dimensional Brownian motion along charged rodlike polymers, such as microtubules (MTs), actin, and DNA. The electrostatic interaction between the proteins and the rodlike polymers appears to be crucial for one-dimensional Brownian motion, although the underlying mechanism has not been fully clarified. We examined the interactions of positively-charged nanoparticles composed of polyacrylamide gels with MTs. These hydrophilic nanoparticles bound to MTs and displayed one-dimensional Brownian motion in a charge-dependent manner, which indicates that nonspecific electrostatic interaction is sufficient for one-dimensional Brownian motion. The diffusion coefficient decreased exponentially with an increasing particle charge (with the exponent being 0.10 kBT per charge), whereas the duration of the interaction increased exponentially (exponent of 0.22 kBT per charge). These results can be explained semiquantitatively if one assumes that a particle repeats a cycle of binding to and movement along an MT until it finally dissociates from the MT. During the movement, a particle is still electrostatically constrained in the potential valley surrounding the MT. This entire process can be described by a three-state model analogous to the Michaelis-Menten scheme, in which the two parameters of the equilibrium constant between binding and movement, and the rate of dissociation from the MT, are derived as a function of the particle charge density. This study highlights the possibility that the weak binding interactions between proteins and rodlike polymers, e.g., MTs, are mediated by a similar, nonspecific charge-dependent mechanism. Copyright 2010 Biophysical Society. Published by Elsevier Inc. All rights reserved.

An electrical circuit model for simulation of indoor radon concentration.

PubMed

Musavi Nasab, S M; Negarestani, A

2013-01-01

In this study, a new model based on electric circuit theory was introduced to simulate the behaviour of indoor radon concentration. In this model, a voltage source simulates radon generation in walls, conductivity simulates migration through walls and voltage across a capacitor simulates radon concentration in a room. This simulation considers migration of radon through walls by diffusion mechanism in one-dimensional geometry. Data reported in a typical Greek house were employed to examine the application of this technique of simulation to the behaviour of radon.

A simplified model for tritium permeation transient predictions when trapping is active*1

NASA Astrophysics Data System (ADS)

Longhurst, G. R.

1994-09-01

This report describes a simplified one-dimensional tritium permeation and retention model. The model makes use of the same physical mechanisms as more sophisticated, time-transient codes such as implantation, recombination, diffusion, trapping and thermal gradient effects. It takes advantage of a number of simplifications and approximations to solve the steady-state problem and then provides interpolating functions to make estimates of intermediate states based on the steady-state solution. Comparison calculations with the verified and validated TMAP4 transient code show good agreement.

Bioheat model evaluations of laser effects on tissues: role of water evaporation and diffusion

NASA Astrophysics Data System (ADS)

Nagulapally, Deepthi; Joshi, Ravi P.; Thomas, Robert J.

2011-03-01

A two-dimensional, time-dependent bioheat model is applied to evaluate changes in temperature and water content in tissues subjected to laser irradiation. Our approach takes account of liquid-to-vapor phase changes and a simple diffusive flow of water within the biotissue. An energy balance equation considers blood perfusion, metabolic heat generation, laser absorption, and water evaporation. The model also accounts for the water dependence of tissue properties (both thermal and optical), and variations in blood perfusion rates based on local tissue injury. Our calculations show that water diffusion would reduce the local temperature increases and hot spots in comparison to simple models that ignore the role of water in the overall thermal and mass transport. Also, the reduced suppression of perfusion rates due to tissue heating and damage with water diffusion affect the necrotic depth. Two-dimensional results for the dynamic temperature, water content, and damage distributions will be presented for skin simulations. It is argued that reduction in temperature gradients due to water diffusion would mitigate local refractive index variations, and hence influence the phenomenon of thermal lensing. Finally, simple quantitative evaluations of pressure increases within the tissue due to laser absorption are presented.

Time-dependent transport of energetic particles in magnetic turbulence: computer simulations versus analytical theory

NASA Astrophysics Data System (ADS)

Arendt, V.; Shalchi, A.

2018-06-01

We explore numerically the transport of energetic particles in a turbulent magnetic field configuration. A test-particle code is employed to compute running diffusion coefficients as well as particle distribution functions in the different directions of space. Our numerical findings are compared with models commonly used in diffusion theory such as Gaussian distribution functions and solutions of the cosmic ray Fokker-Planck equation. Furthermore, we compare the running diffusion coefficients across the mean magnetic field with solutions obtained from the time-dependent version of the unified non-linear transport theory. In most cases we find that particle distribution functions are indeed of Gaussian form as long as a two-component turbulence model is employed. For turbulence setups with reduced dimensionality, however, the Gaussian distribution can no longer be obtained. It is also shown that the unified non-linear transport theory agrees with simulated perpendicular diffusion coefficients as long as the pure two-dimensional model is excluded.

Rationalizing long-lived photo-excited carriers in photocatalyst (La5Ti2CuS5O7) in terms of one-dimensional carrier transport

NASA Astrophysics Data System (ADS)

Suzuki, Yohichi; Singh, Rupashree Balia; Matsuzaki, Hiroyuki; Furube, Akihiro; Ma, Guijun; Hisatomi, Takashi; Domen, Kazunari; Seki, Kazuhiko

2016-09-01

The semiconductor La5Ti2CuS5O7 (LTC) is a potential photocatalyst capable of operating under visible light irradiation and behaves both as a photocathode and anode when embedded onto metal layers. Time-resolved diffuse reflectance (TRDR) measurements were carried out on LTC powder and LTC deposited on Au as the back contact using the particle-transfer method. Results of TRDR measurements of powdered LTC indicated the existence of long-lived photo-excited carriers, and suggested the existence of a mechanism for preventing carrier loss in LTC. Prior research has reported that LTC has a rod-shaped crystal structure and that electrons and holes are transported through different, spatially separated channels. Based on this, we introduced a one-dimensional carrier transport model. By analyzing TRDR data, we extracted material parameters such as the diffusion coefficient of LTC. Theoretical results indicated that a micron-sized LTC particle would be preferable if carriers trapped at the top-surface do contribute to photocatalytic gas generation.

Collective dissolution of microbubbles

NASA Astrophysics Data System (ADS)

Michelin, Sébastien; Guérin, Etienne; Lauga, Eric

2018-04-01

A microscopic bubble of soluble gas always dissolves in finite time in an undersaturated fluid. This diffusive process is driven by the difference between the gas concentration near the bubble, whose value is governed by the internal pressure through Henry's law, and the concentration in the far field. The presence of neighboring bubbles can significantly slow down this process by increasing the effective background concentration and reducing the diffusing flux of dissolved gas experienced by each bubble. We develop theoretical modeling of such diffusive shielding process in the case of small microbubbles whose internal pressure is dominated by Laplace pressure. We first use an exact semianalytical solution to capture the case of two bubbles and analyze in detail the shielding effect as a function of the distance between the bubbles and their size ratio. While we also solve exactly for the Stokes flow around the bubble, we show that hydrodynamic effects are mostly negligible except in the case of almost-touching bubbles. In order to tackle the case of multiple bubbles, we then derive and validate two analytical approximate yet generic frameworks, first using the method of reflections and then by proposing a self-consistent continuum description. Using both modeling frameworks, we examine the dissolution of regular one-, two-, and three-dimensional bubble lattices. Bubbles located at the edge of the lattices dissolve first, while innermost bubbles benefit from the diffusive shielding effect, leading to the inward propagation of a dissolution front within the lattice. We show that diffusive shielding leads to severalfold increases in the dissolution time, which grows logarithmically with the number of bubbles in one-dimensional lattices and algebraically in two and three dimensions, scaling respectively as its square root and 2 /3 power. We further illustrate the sensitivity of the dissolution patterns to initial fluctuations in bubble size or arrangement in the case of large and dense lattices, as well as nonintuitive oscillatory effects.

Viscous diffusion of vorticity in unsteady wall layers using the diffusion velocity concept

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

Strickland, J.H.; Kempka, S.N.; Wolfe, W.P.

1995-03-01

The primary purpose of this paper is to provide a careful evaluation of the diffusion velocity concept with regard to its ability to predict the diffusion of vorticity near a moving wall. A computer code BDIF has been written which simulates the evolution of the vorticity field near a wall of infinite length which is moving in an arbitrary fashion. The simulations generated by this code are found to give excellent results when compared to several exact solutions. We also outline a two-dimensional unsteady viscous boundary layer model which utilizes the diffusion velocity concept and is compatible with vortex methods.more » A primary goal of this boundary layer model is to minimize the number of vortices generated on the surface at each time step while achieving good resolution of the vorticity field near the wall. Preliminary results have been obtained for simulating a simple two-dimensional laminar boundary layer.« less

Analysis of the discontinuous Galerkin method applied to the European option pricing problem

NASA Astrophysics Data System (ADS)

Hozman, J.

2013-12-01

In this paper we deal with a numerical solution of a one-dimensional Black-Scholes partial differential equation, an important scalar nonstationary linear convection-diffusion-reaction equation describing the pricing of European vanilla options. We present a derivation of the numerical scheme based on the space semidiscretization of the model problem by the discontinuous Galerkin method with nonsymmetric stabilization of diffusion terms and with the interior and boundary penalty. The main attention is paid to the investigation of a priori error estimates for the proposed scheme. The appended numerical experiments illustrate the theoretical results and the potency of the method, consequently.

Application of the Hilbert space average method on heat conduction models.

PubMed

Michel, Mathias; Gemmer, Jochen; Mahler, Günter

2006-01-01

We analyze closed one-dimensional chains of weakly coupled many level systems, by means of the so-called Hilbert space average method (HAM). Subject to some concrete conditions on the Hamiltonian of the system, our theory predicts energy diffusion with respect to a coarse-grained description for almost all initial states. Close to the respective equilibrium, we investigate this behavior in terms of heat transport and derive the heat conduction coefficient. Thus, we are able to show that both heat (energy) diffusive behavior as well as Fourier's law follows from and is compatible with a reversible Schrödinger dynamics on the complete level of description.

Diffuse optical tomography and spectroscopy of breast cancer and fetal brain

NASA Astrophysics Data System (ADS)

Choe, Regine

Diffuse optical techniques utilize light in the near infrared spectral range to measure tissue physiology non-invasively. Based on these measurements, either on average or a three-dimensional spatial map of tissue properties such as total hemoglobin concentration, blood oxygen saturation and scattering can be obtained using model-based reconstruction algorithms. In this thesis, diffuse optical techniques were applied for in vivo breast cancer imaging and trans-abdominal fetal brain oxygenation monitoring. For in vivo breast cancer imaging, clinical diffuse optical tomography and related instrumentation was developed and used in several contexts. Bulk physiological properties were quantified for fifty-two healthy subjects in the parallel-plate transmission geometry. Three-dimensional images of breast were reconstructed for subjects with breast tumors and, tumor contrast with respect to normal tissue was found in total hemoglobin concentration and scattering and was quantified for twenty-two breast carcinomas. Tumor contrast and tumor volume changes during neoadjuvant chemotherapy were tracked for one subject and compared to the dynamic contrast-enhanced MRI. Finally, the feasibility for measuring blood flow of breast tumors using optical methods was demonstrated for seven subjects. In a qualitatively different set of experiments, the feasibility for trans-abdominal fetal brain oxygenation monitoring was demonstrated on pregnant ewes with induced fetal hypoxia. Preliminary clinical experiences were discussed to identify future directions. In total, this research has translated diffuse optical tomography techniques into clinical research environment.

Results of tests performed on the Acoustic Quiet Flow Facility Three-Dimensional Model Tunnel: Report on the Modified D.S.M.A. Design

NASA Technical Reports Server (NTRS)

Barna, P. S.

1996-01-01

Numerous tests were performed on the original Acoustic Quiet Flow Facility Three-Dimensional Model Tunnel, scaled down from the full-scale plans. Results of tests performed on the original scale model tunnel were reported in April 1995, which clearly showed that this model was lacking in performance. Subsequently this scale model was modified to attempt to possibly improve the tunnel performance. The modifications included: (a) redesigned diffuser; (b) addition of a collector; (c) addition of a Nozzle-Diffuser; (d) changes in location of vent-air. Tests performed on the modified tunnel showed a marked improvement in performance amounting to a nominal increase of pressure recovery in the diffuser from 34 percent to 54 percent. Results obtained in the tests have wider application. They may also be applied to other tunnels operating with an open test section not necessarily having similar geometry as the model under consideration.

Position-Dependent Diffusion Tensors in Anisotropic Media from Simulation: Oxygen Transport in and through Membranes.

PubMed

Ghysels, An; Venable, Richard M; Pastor, Richard W; Hummer, Gerhard

2017-06-13

A Bayesian-based methodology is developed to estimate diffusion tensors from molecular dynamics simulations of permeants in anisotropic media, and is applied to oxygen in lipid bilayers. By a separation of variables in the Smoluchowski diffusion equation, the multidimensional diffusion is reduced to coupled one-dimensional diffusion problems that are treated by discretization. The resulting diffusivity profiles characterize the membrane transport dynamics as a function of the position across the membrane, discriminating between diffusion normal and parallel to the membrane. The methodology is first validated with neat water, neat hexadecane, and a hexadecane slab surrounded by water, the latter being a simple model for a lipid membrane. Next, a bilayer consisting of pure 1-palmitoyl 2-oleoylphosphatidylcholine (POPC), and a bilayer mimicking the lipid composition of the inner mitochondrial membrane, including cardiolipin, are investigated. We analyze the detailed time evolution of oxygen molecules, in terms of both normal diffusion through and radial diffusion inside the membrane. Diffusion is fast in the more loosely packed interleaflet region, and anisotropic, with oxygen spreading more rapidly in the membrane plane than normal to it. Visualization of the propagator shows that oxygen enters the membrane rapidly, reaching its thermodynamically favored center in about 1 ns, despite the free energy barrier at the headgroup region. Oxygen transport is quantified by computing the oxygen permeability of the membranes and the average radial diffusivity, which confirm the anisotropy of the diffusion. The position-dependent diffusion constants and free energies are used to construct compartmental models and test assumptions used in estimating permeability, including Overton's rule. In particular, a hexadecane slab surrounded by water is found to be a poor model of oxygen transport in membranes because the relevant energy barriers differ substantially.

HARDI DATA DENOISING USING VECTORIAL TOTAL VARIATION AND LOGARITHMIC BARRIER

PubMed Central

Kim, Yunho; Thompson, Paul M.; Vese, Luminita A.

2010-01-01

In this work, we wish to denoise HARDI (High Angular Resolution Diffusion Imaging) data arising in medical brain imaging. Diffusion imaging is a relatively new and powerful method to measure the three-dimensional profile of water diffusion at each point in the brain. These images can be used to reconstruct fiber directions and pathways in the living brain, providing detailed maps of fiber integrity and connectivity. HARDI data is a powerful new extension of diffusion imaging, which goes beyond the diffusion tensor imaging (DTI) model: mathematically, intensity data is given at every voxel and at any direction on the sphere. Unfortunately, HARDI data is usually highly contaminated with noise, depending on the b-value which is a tuning parameter pre-selected to collect the data. Larger b-values help to collect more accurate information in terms of measuring diffusivity, but more noise is generated by many factors as well. So large b-values are preferred, if we can satisfactorily reduce the noise without losing the data structure. Here we propose two variational methods to denoise HARDI data. The first one directly denoises the collected data S, while the second one denoises the so-called sADC (spherical Apparent Diffusion Coefficient), a field of radial functions derived from the data. These two quantities are related by an equation of the form S = SSexp (−b · sADC) (in the noise-free case). By applying these two different models, we will be able to determine which quantity will most accurately preserve data structure after denoising. The theoretical analysis of the proposed models is presented, together with experimental results and comparisons for denoising synthetic and real HARDI data. PMID:20802839

High-Dimensional Intrinsic Interpolation Using Gaussian Process Regression and Diffusion Maps

DOE PAGES

Thimmisetty, Charanraj A.; Ghanem, Roger G.; White, Joshua A.; ...

2017-10-10

This article considers the challenging task of estimating geologic properties of interest using a suite of proxy measurements. The current work recast this task as a manifold learning problem. In this process, this article introduces a novel regression procedure for intrinsic variables constrained onto a manifold embedded in an ambient space. The procedure is meant to sharpen high-dimensional interpolation by inferring non-linear correlations from the data being interpolated. The proposed approach augments manifold learning procedures with a Gaussian process regression. It first identifies, using diffusion maps, a low-dimensional manifold embedded in an ambient high-dimensional space associated with the data. Itmore » relies on the diffusion distance associated with this construction to define a distance function with which the data model is equipped. This distance metric function is then used to compute the correlation structure of a Gaussian process that describes the statistical dependence of quantities of interest in the high-dimensional ambient space. The proposed method is applicable to arbitrarily high-dimensional data sets. Here, it is applied to subsurface characterization using a suite of well log measurements. The predictions obtained in original, principal component, and diffusion space are compared using both qualitative and quantitative metrics. Considerable improvement in the prediction of the geological structural properties is observed with the proposed method.« less

High-Dimensional Intrinsic Interpolation Using Gaussian Process Regression and Diffusion Maps

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

Thimmisetty, Charanraj A.; Ghanem, Roger G.; White, Joshua A.

This article considers the challenging task of estimating geologic properties of interest using a suite of proxy measurements. The current work recast this task as a manifold learning problem. In this process, this article introduces a novel regression procedure for intrinsic variables constrained onto a manifold embedded in an ambient space. The procedure is meant to sharpen high-dimensional interpolation by inferring non-linear correlations from the data being interpolated. The proposed approach augments manifold learning procedures with a Gaussian process regression. It first identifies, using diffusion maps, a low-dimensional manifold embedded in an ambient high-dimensional space associated with the data. Itmore » relies on the diffusion distance associated with this construction to define a distance function with which the data model is equipped. This distance metric function is then used to compute the correlation structure of a Gaussian process that describes the statistical dependence of quantities of interest in the high-dimensional ambient space. The proposed method is applicable to arbitrarily high-dimensional data sets. Here, it is applied to subsurface characterization using a suite of well log measurements. The predictions obtained in original, principal component, and diffusion space are compared using both qualitative and quantitative metrics. Considerable improvement in the prediction of the geological structural properties is observed with the proposed method.« less

Verification of a One-Dimensional Model of CO2 Atmospheric Transport Inside and Above a Forest Canopy Using Observations at the Norunda Research Station

NASA Astrophysics Data System (ADS)

Kovalets, Ivan; Avila, Rodolfo; Mölder, Meelis; Kovalets, Sophia; Lindroth, Anders

2018-02-01

A model of CO2 atmospheric transport in vegetated canopies is tested against measurements of the flow, as well as CO2 concentrations at the Norunda research station located inside a mixed pine-spruce forest. We present the results of simulations of wind-speed profiles and CO2 concentrations inside and above the forest canopy with a one-dimensional model of profiles of the turbulent diffusion coefficient above the canopy accounting for the influence of the roughness sub-layer on turbulent mixing according to Harman and Finnigan (Boundary-Layer Meteorol 129:323-351, 2008; hereafter HF08). Different modelling approaches are used to define the turbulent exchange coefficients for momentum and concentration inside the canopy: (1) the modified HF08 theory—numerical solution of the momentum and concentration equations with a non-constant distribution of leaf area per unit volume; (2) empirical parametrization of the turbulent diffusion coefficient using empirical data concerning the vertical profiles of the Lagrangian time scale and root-mean-square deviation of the vertical velocity component. For neutral, daytime conditions, the second-order turbulence model is also used. The flexibility of the empirical model enables the best fit of the simulated CO2 concentrations inside the canopy to the observations, with the results of simulations for daytime conditions inside the canopy layer only successful provided the respiration fluxes are properly considered. The application of the developed model for radiocarbon atmospheric transport released in the form of ^{14}CO2 is presented and discussed.

Verification of a One-Dimensional Model of CO2 Atmospheric Transport Inside and Above a Forest Canopy Using Observations at the Norunda Research Station

NASA Astrophysics Data System (ADS)

Kovalets, Ivan; Avila, Rodolfo; Mölder, Meelis; Kovalets, Sophia; Lindroth, Anders

2018-07-01

A model of CO2 atmospheric transport in vegetated canopies is tested against measurements of the flow, as well as CO2 concentrations at the Norunda research station located inside a mixed pine-spruce forest. We present the results of simulations of wind-speed profiles and CO2 concentrations inside and above the forest canopy with a one-dimensional model of profiles of the turbulent diffusion coefficient above the canopy accounting for the influence of the roughness sub-layer on turbulent mixing according to Harman and Finnigan (Boundary-Layer Meteorol 129:323-351, 2008; hereafter HF08). Different modelling approaches are used to define the turbulent exchange coefficients for momentum and concentration inside the canopy: (1) the modified HF08 theory—numerical solution of the momentum and concentration equations with a non-constant distribution of leaf area per unit volume; (2) empirical parametrization of the turbulent diffusion coefficient using empirical data concerning the vertical profiles of the Lagrangian time scale and root-mean-square deviation of the vertical velocity component. For neutral, daytime conditions, the second-order turbulence model is also used. The flexibility of the empirical model enables the best fit of the simulated CO2 concentrations inside the canopy to the observations, with the results of simulations for daytime conditions inside the canopy layer only successful provided the respiration fluxes are properly considered. The application of the developed model for radiocarbon atmospheric transport released in the form of ^{14}CO2 is presented and discussed.

Diffusive-convective physical vapor transport of PbTe from a Te-rich solid source

NASA Technical Reports Server (NTRS)

Zoutendyk, J.; Akutagawa, W.

1982-01-01

Crystal growth of PbTe by physical vapor transport (sublimation) in a closed ampoule is governed by the vapor species in thermal equilibrium with the solid compound. Deviations from stoichiometry in the source material cause diffusion limitation of the transport rate, which can be modified by natural (gravity-driven) convection. Mass-transport experiments have been performed using Te-rich material wherein sublimation rates have been measured in order to study the effects of natural convection in diffusion-limited vapor transport. Linear velocities for both crystal growth and evaporation (back sublimation) have been measured for transport in the direction of gravity, horizontally, and opposite to gravity. The experimental results are discussed in terms of both the one-dimensional diffusive-advective model and current, more sophisticated theory which includes natural convection. There is some evidence that convection effects from radial temperature gradients and solutal density gradients have been observed.

Development and application of a three dimensional numerical model for predicting pollutant and sediment transport using an Eulerian-Lagrangian marker particle technique

NASA Technical Reports Server (NTRS)

Pavish, D. L.; Spaulding, M. L.

1977-01-01

A computer coded Lagrangian marker particle in Eulerian finite difference cell solution to the three dimensional incompressible mass transport equation, Water Advective Particle in Cell Technique, WAPIC, was developed, verified against analytic solutions, and subsequently applied in the prediction of long term transport of a suspended sediment cloud resulting from an instantaneous dredge spoil release. Numerical results from WAPIC were verified against analytic solutions to the three dimensional incompressible mass transport equation for turbulent diffusion and advection of Gaussian dye releases in unbounded uniform and uniformly sheared uni-directional flow, and for steady-uniform plug channel flow. WAPIC was utilized to simulate an analytic solution for non-equilibrium sediment dropout from an initially vertically uniform particle distribution in one dimensional turbulent channel flow.

Simulation of whistler waves excited in the presence of a cold plasma cloud - Implications for the CRRES mission. [Combined Release and Radiation Effects Satellite

NASA Technical Reports Server (NTRS)

Pritchett, P. L.; Schriver, D.; Ashour-Abdalla, M.

1991-01-01

A one-dimensional electromagnetic particle simulation model is constructed to study the excitation of whistler waves in the presence of a cold plasma cloud for conditions representative of those after the release of lithium in the inner plasma sheet during the Combined Release and Radiation Effect Satellite mission. The results indicate that a standing-wave pattern with discrete wave frequencies is formed within the cloud. The magnetic wave amplitude inside the cloud, which is limited by quasi-linear diffusion, is of the order of several nanoteslas. Assuming a magnetospheric loss cone of 5 deg, the observed pitch angle diffusion produced by the whistler waves is sufficient to put the electrons on strong diffusion.

Prediction of oxygen distribution in aortic valve leaflet considering diffusion and convection.

PubMed

Wang, Ling; Korossis, Sotirios; Fisher, John; Ingham, Eileen; Jin, Zhongmin

2011-07-01

Oxygen supply and transport is an important consideration in the development of tissue engineered constructs. Previous studies from our group have focused on the effect of tissue thickness on the oxygen diffusion within a three-dimensional aortic valve leaflet model, and highlighted the necessity for additional transport mechanisms such as oxygen convection. The aims of this study were to investigate the effect of interstitial fluid flow within the aortic valve leaflet, induced by the cyclic loading of the leaflet, on oxygen transport. Indentation testing and finite element modelings were employed to derive the biphasic properties of the leaflet tissue. The biphasic properties were subsequently used in the computational modeling of oxygen convection in the leaflet, which was based on the effective interstitial fluid velocity and the tissue deformation. Subsequently, the oxygen profile was predicted within the valve leaflet model by solving the diffusion and convection equation simultaneously utilizing the finite difference method. The compression modulus (E) and hydraulic permeability were determined by adapting a finite element model to the experimental indentation test on valvular tissue, E = 0.05MPa, and k =2.0 mm4/Ns. Finite element model of oxygen convection in valvular tissue incorporating the predicted biphasic properties was developed and the interstitial fluid flow rate was calculated falling in range of 0.025-0.25 mm/s depending on the tissue depth. Oxygen distribution within valvular tissue was predicted using one-dimensional oxygen diffusion model taking into consider the interstitial fluid effect. It was found that convection did enhance the oxygen transport in valvular tissue by up to 68% increase in the minimum oxygen tension within the tissue, depending on the strain level of the tissue as reaction of the magnitude and frequencies of the cardiac loading. The effective interstitial fluid velocity was found to play an important role in enhancing the oxygen transport within the valve leaflet. Such an understanding is important in the development of valvular tissue engineered constructs.

Progress of High Efficiency Centrifugal Compressor Simulations Using TURBO

NASA Technical Reports Server (NTRS)

Kulkarni, Sameer; Beach, Timothy A.

2017-01-01

Three-dimensional, time-accurate, and phase-lagged computational fluid dynamics (CFD) simulations of the High Efficiency Centrifugal Compressor (HECC) stage were generated using the TURBO solver. Changes to the TURBO Parallel Version 4 source code were made in order to properly model the no-slip boundary condition along the spinning hub region for centrifugal impellers. A startup procedure was developed to generate a converged flow field in TURBO. This procedure initialized computations on a coarsened mesh generated by the Turbomachinery Gridding System (TGS) and relied on a method of systematically increasing wheel speed and backpressure. Baseline design-speed TURBO results generally overpredicted total pressure ratio, adiabatic efficiency, and the choking flow rate of the HECC stage as compared with the design-intent CFD results of Code Leo. Including diffuser fillet geometry in the TURBO computation resulted in a 0.6 percent reduction in the choking flow rate and led to a better match with design-intent CFD. Diffuser fillets reduced annulus cross-sectional area but also reduced corner separation, and thus blockage, in the diffuser passage. It was found that the TURBO computations are somewhat insensitive to inlet total pressure changing from the TURBO default inlet pressure of 14.7 pounds per square inch (101.35 kilopascals) down to 11.0 pounds per square inch (75.83 kilopascals), the inlet pressure of the component test. Off-design tip clearance was modeled in TURBO in two computations: one in which the blade tip geometry was trimmed by 12 mils (0.3048 millimeters), and another in which the hub flow path was moved to reflect a 12-mil axial shift in the impeller hub, creating a step at the hub. The one-dimensional results of these two computations indicate non-negligible differences between the two modeling approaches.

Improved model for the design and analysis of centrifugal compressor volutes

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

Van den Braembussche, R.A.; Ayder, E.; Hagelstein, D.

1999-07-01

This paper describes a new model for the analysis of the flow in volutes of centrifugal compressors. It explicitly takes into account the vortical structure of the flow that has been observed during detailed three-dimensional flow measurements. It makes use of an impeller and diffuser response model to predict the nonuniformity of the volute inlet flow due, to the circumferential variation of the pressure at the volute inlet, and is therefore applicable also at off-design operation of the volute. Predicted total pressure loss and static pressure rise coefficients at design and off-design operation have been compared with experimental data formore » different volute geometries but only one test case is presented here. Good agreement in terms of losses and pressure rise is observed at most operating points and confirms the validity of the impeller and diffuser response model.« less

Linearized finite-element method solution of the ion-exchange nonlinear diffusion model

NASA Astrophysics Data System (ADS)

Badr, Mohamed M.; Swillam, Mohamed A.

2017-04-01

Ion-exchange process is one of the most common techniques used in glass waveguide fabrication. This has many advantages, such as low cost, ease of implementation, and simple equipment requirements. The technology is based on the substitution of some of the host ions in the glass (typically Na+) with other ions that possess different characteristics in terms of size and polarizability. The newly diffused ions produce a region with a relatively higher refractive index in which the light could be guided. A critical issue arises when it comes to designing such waveguides, which is carefully and precisely determining the resultant index profile. This task has been proven to be hideous as the process is generally governed by a nonlinear diffusion model with no direct general analytical solution. Furthermore, numerical solutions become unreliable-in terms of stability and mean squared error-in some cases, especially the K+-Na+ ion-exchanged waveguide, which is the best candidate to produce waveguides with refractive index differences compatible with those of the commercially available optical fibers. Linearized finite-element method formulations were used to provide a reliable tool that could solve the nonlinear diffusion model of the ion-exchange in both one- and two-dimensional spaces. Additionally, the annealed channel waveguide case has been studied. In all cases, unprecedented stability and minimum mean squared error could be achieved.

SkyFACT: high-dimensional modeling of gamma-ray emission with adaptive templates and penalized likelihoods

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

Storm, Emma; Weniger, Christoph; Calore, Francesca, E-mail: e.m.storm@uva.nl, E-mail: c.weniger@uva.nl, E-mail: francesca.calore@lapth.cnrs.fr

We present SkyFACT (Sky Factorization with Adaptive Constrained Templates), a new approach for studying, modeling and decomposing diffuse gamma-ray emission. Like most previous analyses, the approach relies on predictions from cosmic-ray propagation codes like GALPROP and DRAGON. However, in contrast to previous approaches, we account for the fact that models are not perfect and allow for a very large number (∼> 10{sup 5}) of nuisance parameters to parameterize these imperfections. We combine methods of image reconstruction and adaptive spatio-spectral template regression in one coherent hybrid approach. To this end, we use penalized Poisson likelihood regression, with regularization functions that aremore » motivated by the maximum entropy method. We introduce methods to efficiently handle the high dimensionality of the convex optimization problem as well as the associated semi-sparse covariance matrix, using the L-BFGS-B algorithm and Cholesky factorization. We test the method both on synthetic data as well as on gamma-ray emission from the inner Galaxy, |ℓ|<90{sup o} and | b |<20{sup o}, as observed by the Fermi Large Area Telescope. We finally define a simple reference model that removes most of the residual emission from the inner Galaxy, based on conventional diffuse emission components as well as components for the Fermi bubbles, the Fermi Galactic center excess, and extended sources along the Galactic disk. Variants of this reference model can serve as basis for future studies of diffuse emission in and outside the Galactic disk.« less

A variable turbulent Prandtl and Schmidt number model study for scramjet applications

NASA Astrophysics Data System (ADS)

Keistler, Patrick

A turbulence model that allows for the calculation of the variable turbulent Prandtl (Prt) and Schmidt (Sct) numbers as part of the solution is presented. The model also accounts for the interactions between turbulence and chemistry by modeling the corresponding terms. Four equations are added to the baseline k-zeta turbulence model: two equations for enthalpy variance and its dissipation rate to calculate the turbulent diffusivity, and two equations for the concentrations variance and its dissipation rate to calculate the turbulent diffusion coefficient. The underlying turbulence model already accounts for compressibility effects. The variable Prt /Sct turbulence model is validated and tuned by simulating a wide variety of experiments. Included in the experiments are two-dimensional, axisymmetric, and three-dimensional mixing and combustion cases. The combustion cases involved either hydrogen and air, or hydrogen, ethylene, and air. Two chemical kinetic models are employed for each of these situations. For the hydrogen and air cases, a seven species/seven reaction model where the reaction rates are temperature dependent and a nine species/nineteen reaction model where the reaction rates are dependent on both pressure and temperature are used. For the cases involving ethylene, a 15 species/44 reaction reduced model that is both pressure and temperature dependent is used, along with a 22 species/18 global reaction reduced model that makes use of the quasi-steady-state approximation. In general, fair to good agreement is indicated for all simulated experiments. The turbulence/chemistry interaction terms are found to have a significant impact on flame location for the two-dimensional combustion case, with excellent experimental agreement when the terms are included. In most cases, the hydrogen chemical mechanisms behave nearly identically, but for one case, the pressure dependent model would not auto-ignite at the same conditions as the experiment and the other chemical model. The model was artificially ignited in that case. For the cases involving ethylene combustion, the chemical model has a profound impact on the flame size, shape, and ignition location. However, without quantitative experimental data, it is difficult to determine which one is more suitable for this particular application.

Parametric analysis of diffuser requirements for high expansion ratio space engine

NASA Technical Reports Server (NTRS)

Wojciechowski, C. J.; Anderson, P. G.

1981-01-01

A supersonic diffuser ejector design computer program was developed. Using empirically modified one dimensional flow methods the diffuser ejector geometry is specified by the code. The design code results for calculations up to the end of the diffuser second throat were verified. Diffuser requirements for sea level testing of high expansion ratio space engines were defined. The feasibility of an ejector system using two commonly available turbojet engines feeding two variable area ratio ejectors was demonstrated.

Competitive or weak cooperative stochastic Lotka-Volterra systems conditioned on non-extinction.

PubMed

Cattiaux, Patrick; Méléard, Sylvie

2010-06-01

We are interested in the long time behavior of a two-type density-dependent biological population conditioned on non-extinction, in both cases of competition or weak cooperation between the two species. This population is described by a stochastic Lotka-Volterra system, obtained as limit of renormalized interacting birth and death processes. The weak cooperation assumption allows the system not to blow up. We study the existence and uniqueness of a quasi-stationary distribution, that is convergence to equilibrium conditioned on non-extinction. To this aim we generalize in two-dimensions spectral tools developed for one-dimensional generalized Feller diffusion processes. The existence proof of a quasi-stationary distribution is reduced to the one for a d-dimensional Kolmogorov diffusion process under a symmetry assumption. The symmetry we need is satisfied under a local balance condition relying the ecological rates. A novelty is the outlined relation between the uniqueness of the quasi-stationary distribution and the ultracontractivity of the killed semi-group. By a comparison between the killing rates for the populations of each type and the one of the global population, we show that the quasi-stationary distribution can be either supported by individuals of one (the strongest one) type or supported by individuals of the two types. We thus highlight two different long time behaviors depending on the parameters of the model: either the model exhibits an intermediary time scale for which only one type (the dominant trait) is surviving, or there is a positive probability to have coexistence of the two species.

Load Diffusion in Composite and Smart Structures

NASA Technical Reports Server (NTRS)

Horgan, C. O.

2003-01-01

The research carried out here builds on our previous NASA supported research on the general topic of edge effects and load diffusion in composite structures. Further fundamental solid mechanics studies were carried out to provide a basis for assessing the complicated modeling necessary for the multi-functional large scale structures used by NASA. An understanding of the fundamental mechanisms of load diffusion in composite subcomponents is essential in developing primary composite structures. Some specific problems recently considered were those of end effects in smart materials and structures, study of the stress response of pressurized linear piezoelectric cylinders for both static and steady rotating configurations, an analysis of the effect of pre-stressing and pre-polarization on the decay of end effects in piezoelectric solids and investigation of constitutive models for hardening rubber-like materials. Our goal in the study of load diffusion is the development of readily applicable results for the decay lengths in terms of non-dimensional material and geometric parameters. Analytical models of load diffusion behavior are extremely valuable in building an intuitive base for developing refined modeling strategies and assessing results from finite element analyses. The decay behavior of stresses and other field quantities provides a significant aid towards this process. The analysis is also amenable to parameter study with a large parameter space and should be useful in structural tailoring studies. Special purpose analytical models of load diffusion behavior are extremely valuable in building an intuitive base for developing refined modeling strategies and in assessing results from general purpose finite element analyses. For example, a rational basis is needed in choosing where to use three-dimensional to two-dimensional transition finite elements in analyzing stiffened plates and shells. The decay behavior of stresses and other field quantities furnished by this research provides a significant aid towards this element transition issue. A priori knowledge of the extent of boundary-layers induced by edge effects is also useful in determination of the instrumentation location in structural verification tests or in material characterization tests.

Pulsed electrodeposition of two-dimensional Ag nanostructures on Au(111).

PubMed

Borissov, D; Tsekov, R; Freyland, W

2006-08-17

One-step pulsed potential electrodeposition of Ag on Au(111) in the underpotential deposition (UPD) region has been studied in 0.5 mM Ag2SO4 + 0.1 M H2SO4 aqueous electrolyte at various pulse durations from 0.2 to 500 ms. Evolution of the deposited Ag nanostructures was followed by in situ scanning tunneling microscopy (STM) and by measurement of the respective current transients. At short pulse durations a relatively high number density (4 x 10(11) cm(-2)) of two-dimensional Ag clusters with a narrow size and distance distribution is observed. They exhibit a remarkably high stability characterized by a dissolution potential which lies about 200 mV more anodically than the typical potential of Ag-(1 x 1) monolayer dissolution. To elucidate the underlying nucleation and growth mechanism, two models have been considered: two-dimensional lattice incorporation and a newly developed coupled diffusion-adsorption model. The first one yields a qualitative description of the current transients, whereas the second one is in nearly quantitative agreement with the experimental data. In this model the transformation of a Ag-(3 x 3) into a Ag-(1 x 1) structure indicated in the cyclic voltammogram (peaks at 520 vs 20 mV) is taken into account.

Fractional Steps methods for transient problems on commodity computer architectures

NASA Astrophysics Data System (ADS)

Krotkiewski, M.; Dabrowski, M.; Podladchikov, Y. Y.

2008-12-01

Fractional Steps methods are suitable for modeling transient processes that are central to many geological applications. Low memory requirements and modest computational complexity facilitates calculations on high-resolution three-dimensional models. An efficient implementation of Alternating Direction Implicit/Locally One-Dimensional schemes for an Opteron-based shared memory system is presented. The memory bandwidth usage, the main bottleneck on modern computer architectures, is specially addressed. High efficiency of above 2 GFlops per CPU is sustained for problems of 1 billion degrees of freedom. The optimized sequential implementation of all 1D sweeps is comparable in execution time to copying the used data in the memory. Scalability of the parallel implementation on up to 8 CPUs is close to perfect. Performing one timestep of the Locally One-Dimensional scheme on a system of 1000 3 unknowns on 8 CPUs takes only 11 s. We validate the LOD scheme using a computational model of an isolated inclusion subject to a constant far field flux. Next, we study numerically the evolution of a diffusion front and the effective thermal conductivity of composites consisting of multiple inclusions and compare the results with predictions based on the differential effective medium approach. Finally, application of the developed parabolic solver is suggested for a real-world problem of fluid transport and reactions inside a reservoir.

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

NASA Technical Reports Server (NTRS)

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

1987-01-01

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

Studies in premixed combustion. [Benjamin Levich Inst. for Physico-Chemical Hydrodynamics, City College of CUNY, New York, New York

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

Sivashinsky, G.I.

1993-01-01

During the period under review, significant progress was been made in studying the intrinsic dynamics of premixed flames and the problems of flame-flow interaction. (1) A weakly nonlinear model for Bunsen burner stabilized flames was proposed and employed for the simulation of three-dimensional polyhedral flames -- one of the most graphic manifestations of thermal-diffusive instability in premixed combustion. (2) A high-precision large-scale numerical simulation of Bunsen burner tip structure was conducted. The results obtained supported the earlier conjecture that the tip opening observed in low Lewis number systems is a purely optical effect not involving either flame extinction or leakagemore » of unburned fuel. (3) A one-dimensional model describing a reaction wave moving through a unidirectional periodic flow field is proposed and studied numerically. For long-wavelength fields the system exhibits a peculiar non-uniqueness of possible propagation regimes. The transition from one regime to another occurs in a manner of hysteresis.« less

Simulation of Helical Flow Hydrodynamics in Meanders and Advection-Turbulent Diffusion Using Smoothed Particle Hydrodynamics

NASA Astrophysics Data System (ADS)

Gusti, T. P.; Hertanti, D. R.; Bahsan, E.; Soeryantono, H.

2013-12-01

Particle-based numerical methods, such as Smoothed Particle Hydrodynamics (SPH), may be able to simulate some hydrodynamic and morphodynamic behaviors better than grid-based numerical methods. This study simulates hydrodynamics in meanders and advection and turbulent diffusion in straight river channels using Microsoft Excel and Visual Basic. The simulators generate three-dimensional data for hydrodynamics and one-dimensional data for advection-turbulent diffusion. Fluid at rest, sloshing, and helical flow are simulated in the river meanders. Spill loading and step loading are done to simulate concentration patterns associated with advection-turbulent diffusion. Results indicate that helical flow is formed due to disturbance in morphology and particle velocity in the stream and the number of particles does not have a significant effect on the pattern of advection-turbulent diffusion concentration.

Liquid water breakthrough location distances on a gas diffusion layer of polymer electrolyte membrane fuel cells

NASA Astrophysics Data System (ADS)

Yu, Junliang; Froning, Dieter; Reimer, Uwe; Lehnert, Werner

2018-06-01

The lattice Boltzmann method is adopted to simulate the three dimensional dynamic process of liquid water breaking through the gas diffusion layer (GDL) in the polymer electrolyte membrane fuel cell. 22 micro-structures of Toray GDL are built based on a stochastic geometry model. It is found that more than one breakthrough locations are formed randomly on the GDL surface. Breakthrough location distance (BLD) are analyzed statistically in two ways. The distribution is evaluated statistically by the Lilliefors test. It is concluded that the BLD can be described by the normal distribution with certain statistic characteristics. Information of the shortest neighbor breakthrough location distance can be the input modeling setups on the cell-scale simulations in the field of fuel cell simulation.

Sliding of proteins non-specifically bound to DNA: Brownian dynamics studies with coarse-grained protein and DNA models.

PubMed

Ando, Tadashi; Skolnick, Jeffrey

2014-12-01

DNA binding proteins efficiently search for their cognitive sites on long genomic DNA by combining 3D diffusion and 1D diffusion (sliding) along the DNA. Recent experimental results and theoretical analyses revealed that the proteins show a rotation-coupled sliding along DNA helical pitch. Here, we performed Brownian dynamics simulations using newly developed coarse-grained protein and DNA models for evaluating how hydrodynamic interactions between the protein and DNA molecules, binding affinity of the protein to DNA, and DNA fluctuations affect the one dimensional diffusion of the protein on the DNA. Our results indicate that intermolecular hydrodynamic interactions reduce 1D diffusivity by 30%. On the other hand, structural fluctuations of DNA give rise to steric collisions between the CG-proteins and DNA, resulting in faster 1D sliding of the protein. Proteins with low binding affinities consistent with experimental estimates of non-specific DNA binding show hopping along the CG-DNA. This hopping significantly increases sliding speed. These simulation studies provide additional insights into the mechanism of how DNA binding proteins find their target sites on the genome.

Linking a one-dimensional pesticide fate model to a three-dimensional groundwater model to simulate pollution risks of shallow and deep groundwater underlying fractured till.

PubMed

Stenemo, Fredrik; Jørgensen, Peter R; Jarvis, Nicholas

2005-09-01

The one-dimensional pesticide fate model MACRO was loose-linked to the three-dimensional discrete fracture/matrix diffusion model FRAC3DVS to describe transport of the pesticide mecoprop in a fractured moraine till and local sand aquifer (5-5.5 m depth) overlying a regional limestone aquifer (16 m depth) at Havdrup, Denmark. Alternative approaches to describe the upper boundary in the groundwater model were examined. Field-scale simulations were run to compare a uniform upper boundary condition with a spatially variable upper boundary derived from Monte-Carlo simulations with MACRO. Plot-scale simulations were run to investigate the influence of the temporal resolution of the upper boundary conditions for fluxes in the groundwater model and the effects of different assumptions concerning the macropore/fracture connectivity between the two models. The influence of within-field variability of leaching on simulated mecoprop concentrations in the local aquifer was relatively small. A fully transient simulation with FRAC3DVS gave 20 times larger leaching to the regional aquifer compared to the case with steady-state water flow, assuming full connectivity with respect to macropores/fractures across the boundary between the two models. For fully transient simulations 'disconnecting' the macropores/fractures at the interface between the two models reduced leaching by a factor 24. A fully connected, transient simulation with FRAC3DVS, with spatially uniform upper boundary fluxes derived from a MACRO simulation with 'effective' parameters is therefore recommended for assessing leaching risks to the regional aquifer, at this, and similar sites.

Exact Solutions of Linear Reaction-Diffusion Processes on a Uniformly Growing Domain: Criteria for Successful Colonization

PubMed Central

Simpson, Matthew J

2015-01-01

Many processes during embryonic development involve transport and reaction of molecules, or transport and proliferation of cells, within growing tissues. Mathematical models of such processes usually take the form of a reaction-diffusion partial differential equation (PDE) on a growing domain. Previous analyses of such models have mainly involved solving the PDEs numerically. Here, we present a framework for calculating the exact solution of a linear reaction-diffusion PDE on a growing domain. We derive an exact solution for a general class of one-dimensional linear reaction—diffusion process on 0

Exact solutions of linear reaction-diffusion processes on a uniformly growing domain: criteria for successful colonization.

PubMed

Simpson, Matthew J

2015-01-01

Many processes during embryonic development involve transport and reaction of molecules, or transport and proliferation of cells, within growing tissues. Mathematical models of such processes usually take the form of a reaction-diffusion partial differential equation (PDE) on a growing domain. Previous analyses of such models have mainly involved solving the PDEs numerically. Here, we present a framework for calculating the exact solution of a linear reaction-diffusion PDE on a growing domain. We derive an exact solution for a general class of one-dimensional linear reaction-diffusion process on 0

Mass spectrometric analysis of electrophoretically separated allergens and proteases in grass pollen diffusates

PubMed Central

Raftery, Mark J; Saldanha, Rohit G; Geczy, Carolyn L; Kumar, Rakesh K

2003-01-01

Background Pollens are important triggers for allergic asthma and seasonal rhinitis, and proteases released by major allergenic pollens can injure airway epithelial cells in vitro. Disruption of mucosal epithelial integrity by proteases released by inhaled pollens could promote allergic sensitisation. Methods Pollen diffusates from Kentucky blue grass (Poa pratensis), rye grass (Lolium perenne) and Bermuda grass (Cynodon dactylon) were assessed for peptidase activity using a fluorogenic substrate, as well as by gelatin zymography. Following one- or two-dimensional gel electrophoresis, Coomassie-stained individual bands/spots were excised, subjected to tryptic digestion and analysed by mass spectrometry, either MALDI reflectron TOF or microcapillary liquid chromatography MS-MS. Database searches were used to identify allergens and other plant proteins in pollen diffusates. Results All pollen diffusates tested exhibited peptidase activity. Gelatin zymography revealed high Mr proteolytic activity at ~ 95,000 in all diffusates and additional proteolytic bands in rye and Bermuda grass diffusates, which appeared to be serine proteases on the basis of inhibition studies. A proteolytic band at Mr ~ 35,000 in Bermuda grass diffusate, which corresponded to an intense band detected by Western blotting using a monoclonal antibody to the timothy grass (Phleum pratense) group 1 allergen Phl p 1, was identified by mass spectrometric analysis as the group 1 allergen Cyn d 1. Two-dimensional analysis similarly demonstrated proteolytic activity corresponding to protein spots identified as Cyn d 1. Conclusion One- and two-dimensional electrophoretic separation, combined with analysis by mass spectrometry, is useful for rapid determination of the identities of pollen proteins. A component of the proteolytic activity in Bermuda grass diffusate is likely to be related to the allergen Cyn d 1. PMID:14577842

Update on Advection-Diffusion Purge Flow Model

NASA Technical Reports Server (NTRS)

Brieda, Lubos

2015-01-01

Gaseous purge is commonly used in sensitive spacecraft optical or electronic instruments to prevent infiltration of contaminants and/or water vapor. Typically, purge is sized using simplistic zero-dimensional models that do not take into account instrument geometry, surface effects, and the dependence of diffusive flux on the concentration gradient. For this reason, an axisymmetric computational fluid dynamics (CFD) simulation was recently developed to model contaminant infiltration and removal by purge. The solver uses a combined Navier-Stokes and Advection-Diffusion approach. In this talk, we report on updates in the model, namely inclusion of a particulate transport model.

Scrape-off layer modeling with kinetic or diffusion description of charge-exchange atoms

NASA Astrophysics Data System (ADS)

Tokar, M. Z.

2016-12-01

Hydrogen isotope atoms, generated by charge-exchange (c-x) of neutral particles recycling from the first wall of a fusion reactor, are described either kinetically or in a diffusion approximation. In a one-dimensional (1-D) geometry, kinetic calculations are accelerated enormously by applying an approximate pass method for the assessment of integrals in the velocity space. This permits to perform an exhaustive comparison of calculations done with both approaches. The diffusion approximation is deduced directly from the velocity distribution function of c-x atoms in the limit of charge-exchanges with ions occurring much more frequently than ionization by electrons. The profiles across the flux surfaces of the plasma parameters averaged along the main part of the scrape-off layer (SOL), beyond the X-point and divertor regions, are calculated from the one-dimensional equations where parallel flows of charged particles and energy towards the divertor are taken into account as additional loss terms. It is demonstrated that the heat losses can be firmly estimated from the SOL averaged parameters only; for the particle loss the conditions in the divertor are of importance and the sensitivity of the results to the so-called "divertor impact factor" is investigated. The coupled 1-D models for neutral and charged species, with c-x atoms described either kinetically or in the diffusion approximation, are applied to assess the SOL conditions in a fusion reactor, with the input parameters from the European DEMO project. It is shown that the diffusion approximation provides practically the same profiles across the flux surfaces for the plasma density, electron, and ion temperatures, as those obtained with the kinetic description for c-x atoms. The main difference between the two approaches is observed in the characteristics of these species themselves. In particular, their energy flux onto the wall is underestimated in calculations with the diffusion approximation by 20 % - 30 % . This discrepancy can be significantly reduced if after the convergence of coupled plasma-neutral calculations, the final computation for c-x atoms is done kinetically.

Equivalence of Fluctuation Splitting and Finite Volume for One-Dimensional Gas Dynamics

NASA Technical Reports Server (NTRS)

Wood, William A.

1997-01-01

The equivalence of the discretized equations resulting from both fluctuation splitting and finite volume schemes is demonstrated in one dimension. Scalar equations are considered for advection, diffusion, and combined advection/diffusion. Analysis of systems is performed for the Euler and Navier-Stokes equations of gas dynamics. Non-uniform mesh-point distributions are included in the analyses.

Generalized Fourier analyses of the advection-diffusion equation - Part I: one-dimensional domains

NASA Astrophysics Data System (ADS)

Christon, Mark A.; Martinez, Mario J.; Voth, Thomas E.

2004-07-01

This paper presents a detailed multi-methods comparison of the spatial errors associated with finite difference, finite element and finite volume semi-discretizations of the scalar advection-diffusion equation. The errors are reported in terms of non-dimensional phase and group speed, discrete diffusivity, artificial diffusivity, and grid-induced anisotropy. It is demonstrated that Fourier analysis provides an automatic process for separating the discrete advective operator into its symmetric and skew-symmetric components and characterizing the spectral behaviour of each operator. For each of the numerical methods considered, asymptotic truncation error and resolution estimates are presented for the limiting cases of pure advection and pure diffusion. It is demonstrated that streamline upwind Petrov-Galerkin and its control-volume finite element analogue, the streamline upwind control-volume method, produce both an artificial diffusivity and a concomitant phase speed adjustment in addition to the usual semi-discrete artifacts observed in the phase speed, group speed and diffusivity. The Galerkin finite element method and its streamline upwind derivatives are shown to exhibit super-convergent behaviour in terms of phase and group speed when a consistent mass matrix is used in the formulation. In contrast, the CVFEM method and its streamline upwind derivatives yield strictly second-order behaviour. In Part II of this paper, we consider two-dimensional semi-discretizations of the advection-diffusion equation and also assess the affects of grid-induced anisotropy observed in the non-dimensional phase speed, and the discrete and artificial diffusivities. Although this work can only be considered a first step in a comprehensive multi-methods analysis and comparison, it serves to identify some of the relative strengths and weaknesses of multiple numerical methods in a common analysis framework. Published in 2004 by John Wiley & Sons, Ltd.

A HIGHWAY MODEL FOR THE ADVECTION, DIFFUSION AND CHEMICAL REACTION OF POLLUTANTS RELEASED BY AUTOMOBILES: PART I. ADVECTION AND DIFFUSION OF SF6 TRACER GAS

EPA Science Inventory

A two-dimensional, finite-difference model simulating a highway has been developed which is able to handle linear and nonlinear chemical reactions. Transport of the pollutants is accomplished by use of an upstream-flux-corrected algorithm developed at the Naval Research Laborator...

A stratospheric aerosol model with perturbations induced by the space shuttle particulate effluents

NASA Technical Reports Server (NTRS)

Rosen, J. M.; Hofmann, D. J.

1977-01-01

A one dimensional steady state stratospheric aerosol model is developed that considers the subsequent perturbations caused by including the expected space shuttle particulate effluents. Two approaches to the basic modeling effort were made: in one, enough simplifying assumptions were introduced so that a more or less exact solution to the descriptive equations could be obtained; in the other approach very few simplifications were made and a computer technique was used to solve the equations. The most complex form of the model contains the effects of sedimentation, diffusion, particle growth and coagulation. Results of the perturbation calculations show that there will probably be an immeasurably small increase in the stratospheric aerosol concentration for particles larger than about 0.15 micrometer radius.

Purging of a multilayer insulation with dacron tuft spacer by gas diffusion

NASA Technical Reports Server (NTRS)

Sumner, I. E.; Fisk, W. J.

1976-01-01

The time and purge gas usage required to purge a multilayer insulation (MLI) panel with gaseous helium by means of gas diffusion to obtain a condensable gas (nitrogen) concentration of less than 1 percent within the panel are stipulated. Two different, flat, rectangular MLI panels, one incorporating a butt joint, were constructed of of 11 double-aluminized Mylar (DAM) radiation shields separated by Dacron tuft spacers. The DAM/Dacron tuft concept is known commercially as Superfloc. The nitrogen gas concentration as a function of time within the MLI panel could be adequately predicted by using a simple, one dimensional gas diffusion model in which the boundary conditions at the edge of the MLI panel were time dependent. The time and purge gas usage required to achieve 1 percent nitrogen gas concentration within the MLI panel varied from 208 to 86 minutes and 34.1 to 56.5 MLI panel purge volumes, respectively, for gaseous helium purge rates from 10 to 40 MLI panel volumes per hour.

A model to predict radon exhalation from walls to indoor air based on the exhalation from building material samples.

PubMed

Sahoo, B K; Sapra, B K; Gaware, J J; Kanse, S D; Mayya, Y S

2011-06-01

In recognition of the fact that building materials are an important source of indoor radon, second only to soil, surface radon exhalation fluxes have been extensively measured from the samples of these materials. Based on this flux data, several researchers have attempted to predict the inhalation dose attributable to radon emitted from walls and ceilings made up of these materials. However, an important aspect not considered in this methodology is the enhancement of the radon flux from the wall or the ceiling constructed using the same building material. This enhancement occurs mainly because of the change in the radon diffusion process from the former to the latter configuration. To predict the true radon flux from the wall based on the flux data of building material samples, we now propose a semi-empirical model involving radon diffusion length and the physical dimensions of the samples as well as wall thickness as other input parameters. This model has been established by statistically fitting the ratio of the solution to radon diffusion equations for the cases of three-dimensional cuboidal shaped building materials (such as brick, concrete block) and one dimensional wall system to a simple mathematical function. The model predictions have been validated against the measurements made at a new construction site. This model provides an alternative tool (substitute to conventional 1-D model) to estimate radon flux from a wall without relying on ²²⁶Ra content, radon emanation factor and bulk density of the samples. Moreover, it may be very useful in the context of developing building codes for radon regulation in new buildings. Copyright © 2011 Elsevier B.V. All rights reserved.

Massively Parallel Simulations of Diffusion in Dense Polymeric Structures

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

Faulon, Jean-Loup, Wilcox, R.T.

1997-11-01

An original computational technique to generate close-to-equilibrium dense polymeric structures is proposed. Diffusion of small gases are studied on the equilibrated structures using massively parallel molecular dynamics simulations running on the Intel Teraflops (9216 Pentium Pro processors) and Intel Paragon(1840 processors). Compared to the current state-of-the-art equilibration methods this new technique appears to be faster by some orders of magnitude.The main advantage of the technique is that one can circumvent the bottlenecks in configuration space that inhibit relaxation in molecular dynamics simulations. The technique is based on the fact that tetravalent atoms (such as carbon and silicon) fit in themore » center of a regular tetrahedron and that regular tetrahedrons can be used to mesh the three-dimensional space. Thus, the problem of polymer equilibration described by continuous equations in molecular dynamics is reduced to a discrete problem where solutions are approximated by simple algorithms. Practical modeling applications include the constructing of butyl rubber and ethylene-propylene-dimer-monomer (EPDM) models for oxygen and water diffusion calculations. Butyl and EPDM are used in O-ring systems and serve as sealing joints in many manufactured objects. Diffusion coefficients of small gases have been measured experimentally on both polymeric systems, and in general the diffusion coefficients in EPDM are an order of magnitude larger than in butyl. In order to better understand the diffusion phenomena, 10, 000 atoms models were generated and equilibrated for butyl and EPDM. The models were submitted to a massively parallel molecular dynamics simulation to monitor the trajectories of the diffusing species.« less

CRASH: A BLOCK-ADAPTIVE-MESH CODE FOR RADIATIVE SHOCK HYDRODYNAMICS-IMPLEMENTATION AND VERIFICATION

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

Van der Holst, B.; Toth, G.; Sokolov, I. V.

We describe the Center for Radiative Shock Hydrodynamics (CRASH) code, a block-adaptive-mesh code for multi-material radiation hydrodynamics. The implementation solves the radiation diffusion model with a gray or multi-group method and uses a flux-limited diffusion approximation to recover the free-streaming limit. Electrons and ions are allowed to have different temperatures and we include flux-limited electron heat conduction. The radiation hydrodynamic equations are solved in the Eulerian frame by means of a conservative finite-volume discretization in either one-, two-, or three-dimensional slab geometry or in two-dimensional cylindrical symmetry. An operator-split method is used to solve these equations in three substeps: (1)more » an explicit step of a shock-capturing hydrodynamic solver; (2) a linear advection of the radiation in frequency-logarithm space; and (3) an implicit solution of the stiff radiation diffusion, heat conduction, and energy exchange. We present a suite of verification test problems to demonstrate the accuracy and performance of the algorithms. The applications are for astrophysics and laboratory astrophysics. The CRASH code is an extension of the Block-Adaptive Tree Solarwind Roe Upwind Scheme (BATS-R-US) code with a new radiation transfer and heat conduction library and equation-of-state and multi-group opacity solvers. Both CRASH and BATS-R-US are part of the publicly available Space Weather Modeling Framework.« less

Diffusion theory of decision making in continuous report.

PubMed

Smith, Philip L

2016-07-01

I present a diffusion model for decision making in continuous report tasks, in which a continuous, circularly distributed, stimulus attribute in working memory is matched to a representation of the attribute in the stimulus display. Memory retrieval is modeled as a 2-dimensional diffusion process with vector-valued drift on a disk, whose bounding circle represents the decision criterion. The direction and magnitude of the drift vector describe the identity of the stimulus and the quality of its representation in memory, respectively. The point at which the diffusion exits the disk determines the reported value of the attribute and the time to exit the disk determines the decision time. Expressions for the joint distribution of decision times and report outcomes are obtained by means of the Girsanov change-of-measure theorem, which allows the properties of the nonzero-drift diffusion process to be characterized as a function of a Euclidian-distance Bessel process. Predicted report precision is equal to the product of the decision criterion and the drift magnitude and follows a von Mises distribution, in agreement with the treatment of precision in the working memory literature. Trial-to-trial variability in criterion and drift rate leads, respectively, to direct and inverse relationships between report accuracy and decision times, in agreement with, and generalizing, the standard diffusion model of 2-choice decisions. The 2-dimensional model provides a process account of working memory precision and its relationship with the diffusion model, and a new way to investigate the properties of working memory, via the distributions of decision times. (PsycINFO Database Record (c) 2016 APA, all rights reserved).

Studies of the phase gradient at the boundary of the phase diffusion equation, motivated by peculiar wave patterns of rhythmic contraction in the amoeboid movement of Physarum polycephalum

NASA Astrophysics Data System (ADS)

Iima, Makoto; Kori, Hiroshi; Nakagaki, Toshiyuki

2017-04-01

The boundary of a cell is the interface with its surroundings and plays a key role in controlling the cell movement adaptations to different environments. We propose a study of the boundary effects on the patterns and waves of the rhythmic contractions in plasmodia of Physarum polycephalum, a tractable model organism of the amoeboid type. Boundary effects are defined as the effects of both the boundary conditions and the boundary shape. The rhythmicity of contraction can be modulated by local stimulation of temperature, light and chemicals, and by local deformation of cell shape via mechanosensitive ion channels as well. First, we examined the effects of boundary cell shapes in the case of a special shape resembling a tadpole, while requiring that the natural frequency in the proximity of the boundary is slightly higher and uniform. The simulation model reproduced the approximate propagated wave, from the tail to the head, while the inward waves were observed only near the periphery of the head section of the tadpole-shape. A key finding was that the frequency of the rhythmic contractions depended on the local shape of cell boundary. This implies that the boundary conditions of the phase were not always homogeneous. To understand the dependency, we reduced the two-dimensional model into a one-dimensional continuum model with Neumann boundary conditions. Here, the boundary conditions reflect the frequency distribution at the boundary. We described the analytic solutions and calculated the relationship between the boundary conditions and the wave propagation for a one-dimensional model of the continuous oscillatory field and a discrete coupled oscillator system. The results obtained may not be limited to cell movement of Physarum, but may be applicable to the other physical systems since the analysis used a generic phase diffusion equation.

Surface evolution in bare bamboo-type metal lines under diffusion and electric field effects

NASA Astrophysics Data System (ADS)

Averbuch, Amir; Israeli, Moshe; Nathan, Menachem; Ravve, Igor

2003-07-01

Irregularities such as voids and cracks often occur in bamboo-type metal lines of microelectronic interconnects. They increase the resistance of the circuits, and may even lead to a fatal failure. In this work, we analyze numerically the electromigration of an unpassivated bamboo-type line with pre-existing irregularities in its top surface (also called a grain-void interface). The bamboo line is subjected to surface diffusion forces and external electric fields. Under these forces, initial defects may either heal or become worse. The grain-void interface is considered to be one-dimensional, and the physical formulation of an electromigration and diffusion model results in two coupled, fourth order, one-dimensional time-dependent PDEs, with the boundary conditions imposed at the electrode points and at the triple point, which belongs to two neighboring grains and the void. These equations are discretized by finite differences on a regular grid in space, and by a Runge-Kutta integration scheme in time, and solved simultaneously with a static Laplace equation describing the voltage distribution throughout each grain, when the substrate conductivity is neglected. Since the voltage distribution is required only along an interface line, the two-dimensional discretization of the grain interior is not needed, and the static problem is solved by the boundary element method at each time step. The motion of the interface line is studied for different ratios between diffusion and electric field forces, and for different initial configurations of the grain-void interface. We study plain and tilted contour lines, considering positive and negative tilts with respect to the external electric field, a stepped contour with field lines entering or exiting the 'step', and a number of modifications of the classical Mullins problem of thermal grooving. We also consider a two-grain Mullins problem with a normal and tilted boundary between the grains, examining positive and negative tilts.

Evaluation of Full Reynolds Stress Turbulence Models in FUN3D

NASA Technical Reports Server (NTRS)

Dudek, Julianne C.; Carlson, Jan-Renee

2017-01-01

Full seven-equation Reynolds stress turbulence models are a relatively new and promising tool for todays aerospace technology challenges. This paper uses two stress-omega full Reynolds stress models to evaluate challenging flows including shock-wave boundary layer interactions, separation and mixing layers. The Wilcox and the SSGLRR full second-moment Reynolds stress models are evaluated for four problems: a transonic two-dimensional diffuser, a supersonic axisymmetric compression corner, a compressible planar shear layer, and a subsonic axisymmetric jet. Simulation results are compared with experimental data and results using the more commonly used Spalart-Allmaras (SA) one-equation and the Menter Shear Stress Transport (SST) two-equation models.

On the Maxwell-Stefan approach to diffusion: a general resolution in the transient regime for one-dimensional systems.

PubMed

Leonardi, Erminia; Angeli, Celestino

2010-01-14

The diffusion process in a multicomponent system can be formulated in a general form by the generalized Maxwell-Stefan equations. This formulation is able to describe the diffusion process in different systems, such as, for instance, bulk diffusion (in the gas, liquid, and solid phase) and diffusion in microporous materials (membranes, zeolites, nanotubes, etc.). The Maxwell-Stefan equations can be solved analytically (only in special cases) or by numerical approaches. Different numerical strategies have been previously presented, but the number of diffusing species is normally restricted, with only few exceptions, to three in bulk diffusion and to two in microporous systems, unless simplifications of the Maxwell-Stefan equations are considered. In the literature, a large effort has been devoted to the derivation of the analytic expression of the elements of the Fick-like diffusion matrix and therefore to the symbolic inversion of a square matrix with dimensions n x n (n being the number of independent components). This step, which can be easily performed for n = 2 and remains reasonable for n = 3, becomes rapidly very complex in problems with a large number of components. This paper addresses the problem of the numerical resolution of the Maxwell-Stefan equations in the transient regime for a one-dimensional system with a generic number of components, avoiding the definition of the analytic expression of the elements of the Fick-like diffusion matrix. To this aim, two approaches have been implemented in a computational code; the first is the simple finite difference second-order accurate in time Crank-Nicolson scheme for which the full mathematical derivation and the relevant final equations are reported. The second is based on the more accurate backward differentiation formulas, BDF, or Gear's method (Shampine, L. F. ; Gear, C. W. SIAM Rev. 1979, 21, 1.), as implemented in the Livermore solver for ordinary differential equations, LSODE (Hindmarsh, A. C. Serial Fortran Solvers for ODE Initial Value Problems, Technical Report; https://computation.llnl.gov/casc/odepack/odepack_ home.html (2006).). Both methods have been applied to a series of specific problems, such as bulk diffusion of acetone and methanol through stagnant air, uptake of two components on a microporous material in a model system, and permeation across a microporous membrane in model systems, both with the aim to validate the method and to add new information to the comprehension of the peculiar behavior of these systems. The approach is validated by comparison with different published results and with analytic expressions for the steady-state concentration profiles or fluxes in particular systems. The possibility to treat a generic number of components (the limitation being essentially the computational power) is also tested, and results are reported on the permeation of a five component mixture through a membrane in a model system. It is worth noticing that the algorithm here reported can be applied also to the Fick formulation of the diffusion problem with concentration-dependent diffusion coefficients.

A reappraisal of drug release laws using Monte Carlo simulations: the prevalence of the Weibull function.

PubMed

Kosmidis, Kosmas; Argyrakis, Panos; Macheras, Panos

2003-07-01

To verify the Higuchi law and study the drug release from cylindrical and spherical matrices by means of Monte Carlo computer simulation. A one-dimensional matrix, based on the theoretical assumptions of the derivation of the Higuchi law, was simulated and its time evolution was monitored. Cylindrical and spherical three-dimensional lattices were simulated with sites at the boundary of the lattice having been denoted as leak sites. Particles were allowed to move inside it using the random walk model. Excluded volume interactions between the particles was assumed. We have monitored the system time evolution for different lattice sizes and different initial particle concentrations. The Higuchi law was verified using the Monte Carlo technique in a one-dimensional lattice. It was found that Fickian drug release from cylindrical matrices can be approximated nicely with the Weibull function. A simple linear relation between the Weibull function parameters and the specific surface of the system was found. Drug release from a matrix, as a result of a diffusion process assuming excluded volume interactions between the drug molecules, can be described using a Weibull function. This model, although approximate and semiempirical, has the benefit of providing a simple physical connection between the model parameters and the system geometry, which was something missing from other semiempirical models.

Three-dimensional stochastic modeling of radiation belts in adiabatic invariant coordinates

NASA Astrophysics Data System (ADS)

Zheng, Liheng; Chan, Anthony A.; Albert, Jay M.; Elkington, Scot R.; Koller, Josef; Horne, Richard B.; Glauert, Sarah A.; Meredith, Nigel P.

2014-09-01

A 3-D model for solving the radiation belt diffusion equation in adiabatic invariant coordinates has been developed and tested. The model, named Radbelt Electron Model, obtains a probabilistic solution by solving a set of Itô stochastic differential equations that are mathematically equivalent to the diffusion equation. This method is capable of solving diffusion equations with a full 3-D diffusion tensor, including the radial-local cross diffusion components. The correct form of the boundary condition at equatorial pitch angle α0=90° is also derived. The model is applied to a simulation of the October 2002 storm event. At α0 near 90°, our results are quantitatively consistent with GPS observations of phase space density (PSD) increases, suggesting dominance of radial diffusion; at smaller α0, the observed PSD increases are overestimated by the model, possibly due to the α0-independent radial diffusion coefficients, or to insufficient electron loss in the model, or both. Statistical analysis of the stochastic processes provides further insights into the diffusion processes, showing distinctive electron source distributions with and without local acceleration.

Thermionic emission current in a single barrier varactor

NASA Technical Reports Server (NTRS)

Hjelmgren, Hans; East, Jack; Kollberg, Erik

1992-01-01

From I-V measurements on Single Barrier Varactors (SBV) at different temperatures we concluded that thermionic emission across the barrier of the actual device is mainly due to transport through the X band. The same structure was also modeled with a one-dimensional drift-diffusion model, including a 'boundary condition' for thermionic emission across the heterojunction interface. By including thermionic field emission through the top of the triangular barrier of a biased diode and the effect of a non-abrupt interface at the heterojunction, we obtained good agreement between the modeled and measured I-V characteristics.

Numerical calculation on a two-step subdiffusion behavior of lateral protein movement in plasma membranes

NASA Astrophysics Data System (ADS)

Sumi, Tomonari; Okumoto, Atsushi; Goto, Hitoshi; Sekino, Hideo

2017-10-01

A two-step subdiffusion behavior of lateral movement of transmembrane proteins in plasma membranes has been observed by using single-molecule experiments. A nested double-compartment model where large compartments are divided into several smaller ones has been proposed in order to explain this observation. These compartments are considered to be delimited by membrane-skeleton "fences" and membrane-protein "pickets" bound to the fences. We perform numerical simulations of a master equation using a simple two-dimensional lattice model to investigate the heterogeneous diffusion dynamics behavior of transmembrane proteins within plasma membranes. We show that the experimentally observed two-step subdiffusion process can be described using fence and picket models combined with decreased local diffusivity of transmembrane proteins in the vicinity of the pickets. This allows us to explain the two-step subdiffusion behavior without explicitly introducing nested double compartments.

Transport equations in an enzymatic glucose fuel cell

NASA Astrophysics Data System (ADS)

Jariwala, Soham; Krishnamurthy, Balaji

2018-01-01

A mathematical model is developed to study the effects of convective flux and operating temperature on the performance of an enzymatic glucose fuel cell with a membrane. The model assumes isothermal operating conditions and constant feed rate of glucose. The glucose fuel cell domain is divided into five sections, with governing equations describing transport characteristics in each region, namely - anode diffusion layer, anode catalyst layer (enzyme layer), membrane, cathode catalyst layer and cathode diffusion layer. The mass transport is assumed to be one-dimensional and the governing equations are solved numerically. The effects flow rate of glucose feed on the performance of the fuel cell are studied as it contributes significantly to the convective flux. The effects of operating temperature on the performance of a glucose fuel cell are also modeled. The cell performances are compared using cell polarization curves, which were found compliant with experimental observations.

Plasma transport in the Io torus - The importance of microscopic diffusion

NASA Technical Reports Server (NTRS)

Mei, YI; Thorne, Richard M.

1991-01-01

This paper considers the question of whether the distribution of mass in the Io plasma torus is consistent with the concept of interchange eddy transport. Specifically, the flux tube content exhibits a gradual decrease with increasing radial distance from the source near Io without any evidence for substantial density irregularity associated with the plasma source or loss. Using a simple one-dimensional numerical model to simulate macroscopic interchange eddy transport, it is demonstrated that this smooth equilibrium distribution of mass can occur but only with the inclusion of a minimal level of small scale microscopic mixing at a rate approaching Bohm diffusion. Otherwise, the system exhibits a chaotic appearance which never approaches an equilibrium distribution. Various physical mechanisms for the microscopic diffusion process which is required to provide a sufficiently rapid mixing of material between the macroscopic eddies are discussed.

Atomistics of vapour–liquid–solid nanowire growth

PubMed Central

Wang, Hailong; Zepeda-Ruiz, Luis A.; Gilmer, George H.; Upmanyu, Moneesh

2013-01-01

Vapour–liquid–solid route and its variants are routinely used for scalable synthesis of semiconducting nanowires, yet the fundamental growth processes remain unknown. Here we employ atomic-scale computations based on model potentials to study the stability and growth of gold-catalysed silicon nanowires. Equilibrium studies uncover segregation at the solid-like surface of the catalyst particle, a liquid AuSi droplet, and a silicon-rich droplet–nanowire interface enveloped by heterogeneous truncating facets. Supersaturation of the droplets leads to rapid one-dimensional growth on the truncating facets and much slower nucleation-controlled two-dimensional growth on the main facet. Surface diffusion is suppressed and the excess Si flux occurs through the droplet bulk which, together with the Si-rich interface and contact line, lowers the nucleation barrier on the main facet. The ensuing step flow is modified by Au diffusion away from the step edges. Our study highlights key interfacial characteristics for morphological and compositional control of semiconducting nanowire arrays. PMID:23752586

DSA Image Blood Vessel Skeleton Extraction Based on Anti-concentration Diffusion and Level Set Method

NASA Astrophysics Data System (ADS)

Xu, Jing; Wu, Jian; Feng, Daming; Cui, Zhiming

Serious types of vascular diseases such as carotid stenosis, aneurysm and vascular malformation may lead to brain stroke, which are the third leading cause of death and the number one cause of disability. In the clinical practice of diagnosis and treatment of cerebral vascular diseases, how to do effective detection and description of the vascular structure of two-dimensional angiography sequence image that is blood vessel skeleton extraction has been a difficult study for a long time. This paper mainly discussed two-dimensional image of blood vessel skeleton extraction based on the level set method, first do the preprocessing to the DSA image, namely uses anti-concentration diffusion model for the effective enhancement and uses improved Otsu local threshold segmentation technology based on regional division for the image binarization, then vascular skeleton extraction based on GMM (Group marching method) with fast sweeping theory was actualized. Experiments show that our approach not only improved the time complexity, but also make a good extraction results.

Quantitative diffusion and swelling kinetic measurements using large-angle interferometric refractometry.

PubMed

Saunders, John E; Chen, Hao; Brauer, Chris; Clayton, McGregor; Chen, Weijian; Barnes, Jack A; Loock, Hans-Peter

2015-12-07

The uptake and release of sorbates into films and coatings is typically accompanied by changes of the films' refractive index and thickness. We provide a comprehensive model to calculate the concentration of the sorbate from the average refractive index and the film thickness, and validate the model experimentally. The mass fraction of the analyte partitioned into a film is described quantitatively by the Lorentz-Lorenz equation and the Clausius-Mosotti equation. To validate the model, the uptake kinetics of water and other solvents into SU-8 films (d = 40-45 μm) were explored. Large-angle interferometric refractometry measurements can be used to characterize films that are between 15 μm to 150 μm thick and, Fourier analysis, is used to determine independently the thickness, the average refractive index and the refractive index at the film-substrate interface at one-second time intervals. From these values the mass fraction of water in SU-8 was calculated. The kinetics were best described by two independent uptake processes having different rates. Each process followed one-dimensional Fickian diffusion kinetics with diffusion coefficients for water into SU-8 photoresist film of 5.67 × 10(-9) cm(2) s(-1) and 61.2 × 10(-9) cm(2) s(-1).

Diffusion in quasi-one-dimensional channels: A small system n, p, T, transition state theory for hopping times.

PubMed

Ahmadi, Sheida; Bowles, Richard K

2017-04-21

Particles confined to a single file, in a narrow quasi-one-dimensional channel, exhibit a dynamic crossover from single file diffusion to Fickian diffusion as the channel radius increases and the particles begin to pass each other. The long time diffusion coefficient for a system in the crossover regime can be described in terms of a hopping time, which measures the time it takes for a particle to escape the cage formed by its neighbours. In this paper, we develop a transition state theory approach to the calculation of the hopping time, using the small system isobaric-isothermal ensemble to rigorously account for the volume fluctuations associated with the size of the cage. We also describe a Monte Carlo simulation scheme that can be used to calculate the free energy barrier for particle hopping. The theory and simulation method correctly predict the hopping times for a two-dimensional confined ideal gas system and a system of confined hard discs over a range of channel radii, but the method breaks down for wide channels in the hard discs' case, underestimating the height of the hopping barrier due to the neglect of interactions between the small system and its surroundings.

Time-dependent computational studies of flames in microgravity

NASA Technical Reports Server (NTRS)

Oran, Elaine S.; Kailasanath, K.

1989-01-01

The research performed at the Center for Reactive Flow and Dynamical Systems in the Laboratory for Computational Physics and Fluid Dynamics, at the Naval Research Laboratory, in support of the NASA Microgravity Science and Applications Program is described. The primary focus was on investigating fundamental questions concerning the propagation and extinction of premixed flames in Earth gravity and in microgravity environments. The approach was to use detailed time-dependent, multispecies, numerical models as tools to simulate flames in different gravity environments. The models include a detailed chemical kinetics mechanism consisting of elementary reactions among the eight reactive species involved in hydrogen combustion, coupled to algorithms for convection, thermal conduction, viscosity, molecular and thermal diffusion, and external forces. The external force, gravity, can be put in any direction relative to flame propagation and can have a range of values. A combination of one-dimensional and two-dimensional simulations was used to investigate the effects of curvature and dilution on ignition and propagation of flames, to help resolve fundamental questions on the existence of flammability limits when there are no external losses or buoyancy forces in the system, to understand the mechanism leading to cellular instability, and to study the effects of gravity on the transition to cellular structure. A flame in a microgravity environment can be extinguished without external losses, and the mechanism leading to cellular structure is not preferential diffusion but a thermo-diffusive instability. The simulations have also lead to a better understanding of the interactions between buoyancy forces and the processes leading to thermo-diffusive instability.

PIV measurements in a compact return diffuser under multi-conditions

NASA Astrophysics Data System (ADS)

Zhou, L.; Lu, W. G.; Shi, W. D.

2013-12-01

Due to the complex three-dimensional geometries of impellers and diffusers, their design is a delicate and difficult task. Slight change could lead to significant changes in hydraulic performance and internal flow structure. Conversely, the grasp of the pump's internal flow pattern could benefit from pump design improvement. The internal flow fields in a compact return diffuser have been investigated experimentally under multi-conditions. A special Particle Image Velocimetry (PIV) test rig is designed, and the two-dimensional PIV measurements are successfully conducted in the diffuser mid-plane to capture the complex flow patterns. The analysis of the obtained results has been focused on the flow structure in diffuser, especially under part-load conditions. The vortex and recirculation flow patterns in diffuser are captured and analysed accordingly. Strong flow separation and back flow appeared at the part-load flow rates. Under the design and over-load conditions, the flow fields in diffuser are uniform, and the flow separation and back flow appear at the part-load flow rates, strong back flow is captured at one diffuser passage under 0.2Qdes.

Transport of cosmic-ray protons in intermittent heliospheric turbulence: Model and simulations

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

Alouani-Bibi, Fathallah; Le Roux, Jakobus A., E-mail: fb0006@uah.edu

The transport of charged energetic particles in the presence of strong intermittent heliospheric turbulence is computationally analyzed based on known properties of the interplanetary magnetic field and solar wind plasma at 1 astronomical unit. The turbulence is assumed to be static, composite, and quasi-three-dimensional with a varying energy distribution between a one-dimensional Alfvénic (slab) and a structured two-dimensional component. The spatial fluctuations of the turbulent magnetic field are modeled either as homogeneous with a Gaussian probability distribution function (PDF), or as intermittent on large and small scales with a q-Gaussian PDF. Simulations showed that energetic particle diffusion coefficients both parallelmore » and perpendicular to the background magnetic field are significantly affected by intermittency in the turbulence. This effect is especially strong for parallel transport where for large-scale intermittency results show an extended phase of subdiffusive parallel transport during which cross-field transport diffusion dominates. The effects of intermittency are found to depend on particle rigidity and the fraction of slab energy in the turbulence, yielding a perpendicular to parallel mean free path ratio close to 1 for large-scale intermittency. Investigation of higher order transport moments (kurtosis) indicates that non-Gaussian statistical properties of the intermittent turbulent magnetic field are present in the parallel transport, especially for low rigidity particles at all times.« less

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.

Least-squares model-based halftoning

NASA Astrophysics Data System (ADS)

Pappas, Thrasyvoulos N.; Neuhoff, David L.

1992-08-01

A least-squares model-based approach to digital halftoning is proposed. It exploits both a printer model and a model for visual perception. It attempts to produce an 'optimal' halftoned reproduction, by minimizing the squared error between the response of the cascade of the printer and visual models to the binary image and the response of the visual model to the original gray-scale image. Conventional methods, such as clustered ordered dither, use the properties of the eye only implicitly, and resist printer distortions at the expense of spatial and gray-scale resolution. In previous work we showed that our printer model can be used to modify error diffusion to account for printer distortions. The modified error diffusion algorithm has better spatial and gray-scale resolution than conventional techniques, but produces some well known artifacts and asymmetries because it does not make use of an explicit eye model. Least-squares model-based halftoning uses explicit eye models and relies on printer models that predict distortions and exploit them to increase, rather than decrease, both spatial and gray-scale resolution. We have shown that the one-dimensional least-squares problem, in which each row or column of the image is halftoned independently, can be implemented with the Viterbi's algorithm. Unfortunately, no closed form solution can be found in two dimensions. The two-dimensional least squares solution is obtained by iterative techniques. Experiments show that least-squares model-based halftoning produces more gray levels and better spatial resolution than conventional techniques. We also show that the least- squares approach eliminates the problems associated with error diffusion. Model-based halftoning can be especially useful in transmission of high quality documents using high fidelity gray-scale image encoders. As we have shown, in such cases halftoning can be performed at the receiver, just before printing. Apart from coding efficiency, this approach permits the halftoner to be tuned to the individual printer, whose characteristics may vary considerably from those of other printers, for example, write-black vs. write-white laser printers.

Thermal drift is enough to drive a single microtubule along its axis even in the absence of motor proteins.

PubMed Central

Nakata, T; Sato-Yoshitake, R; Okada, Y; Noda, Y; Hirokawa, N

1993-01-01

One-dimensional diffusion of microtubules (MTs), a back-and-forth motion of MTs due to thermal diffusion, was reported in dynein motility assay. The interaction between MTs and dynein that allows such motion was implicated in its importance in the force generating cycle of dynein ATPase cycle. However, it was not known whether the phenomenon is special to motor proteins. Here we show two independent examples of one-dimensional diffusion of MTs in the absence of motor proteins. Dynamin, a MT-activated GTPase, causes a nucleotide dependent back-and-forth movement of single MT up to 1 micron along the longitudinal axes, although the MT never showed unidirectional consistent movement. Quantitative analysis of the motion and its nucleotide condition indicates that the motion is due to a thermal driven diffusion, restricted to one dimension, under the weak interaction between MT and dynamin. However, specific protein-protein interaction is not essential for the motion, because similar back-and-forth movement of MT was achieved on coverslips coated with only 0.8% methylcellulose. Both cases demonstrate that thermal diffusion could provide a considerable sliding of MTs only if MTs are restricted on the surface appropriately. Images FIGURE 1 FIGURE 2 FIGURE 3 PMID:7906153

Dynamic properties of molecular motors in burnt-bridge models

NASA Astrophysics Data System (ADS)

Artyomov, Maxim N.; Morozov, Alexander Yu; Pronina, Ekaterina; Kolomeisky, Anatoly B.

2007-08-01

Dynamic properties of molecular motors that fuel their motion by actively interacting with underlying molecular tracks are studied theoretically via discrete-state stochastic 'burnt-bridge' models. The transport of the particles is viewed as an effective diffusion along one-dimensional lattices with periodically distributed weak links. When an unbiased random walker passes the weak link it can be destroyed ('burned') with probability p, providing a bias in the motion of the molecular motor. We present a theoretical approach that allows one to calculate exactly all dynamic properties of motor proteins, such as velocity and dispersion, under general conditions. It is found that dispersion is a decreasing function of the concentration of bridges, while the dependence of dispersion on the burning probability is more complex. Our calculations also show a gap in dispersion for very low concentrations of weak links or for very low burning probabilities which indicates a dynamic phase transition between unbiased and biased diffusion regimes. Theoretical findings are supported by Monte Carlo computer simulations.

O'Connell's process as a vicious Brownian motion

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

Katori, Makoto

Vicious Brownian motion is a diffusion scaling limit of Fisher's vicious walk model, which is a system of Brownian particles in one dimension such that if two motions meet they kill each other. We consider the vicious Brownian motions conditioned never to collide with each other and call it noncolliding Brownian motion. This conditional diffusion process is equivalent to the eigenvalue process of the Hermitian-matrix-valued Brownian motion studied by Dyson [J. Math. Phys. 3, 1191 (1962)]. Recently, O'Connell [Ann. Probab. (to be published)] introduced a generalization of the noncolliding Brownian motion by using the eigenfunctions (the Whittaker functions) of themore » quantum Toda lattice in order to analyze a directed polymer model in 1 + 1 dimensions. We consider a system of one-dimensional Brownian motions with a long-ranged killing term as a generalization of the vicious Brownian motion and construct the O'Connell process as a conditional process of the killing Brownian motions to survive forever.« less

Structure and Dynamics of Solvent Landscapes in Charge-Transfer Reactions

NASA Astrophysics Data System (ADS)

Leite, Vitor B. Pereira

The dynamics of solvent polarization plays a major role in the control of charge transfer reactions. The success of Marcus theory describing the solvent influence via a single collective quadratic polarization coordinate has been remarkable. Onuchic and Wolynes have recently proposed (J. Chem Phys 98 (3) 2218, 1993) a simple model demonstrating how a many-dimensional-complex model composed by several dipole moments (representing solvent molecules or polar groups in proteins) can be reduced under the appropriate limits into the Marcus Model. This work presents a dynamical study of the same model, which is characterized by two parameters, an average dipole-dipole interaction as a term associated with the potential energy landscape roughness. It is shown why the effective potential, obtained using a thermodynamic approach, is appropriate for the dynamics of the system. At high temperatures, the system exhibits effective diffusive one-dimensional dynamics, where the Born-Marcus limit is recovered. At low temperatures, a glassy phase appears with a slow non-self-averaging dynamics. At intermediate temperatures, the concept of equivalent diffusion paths and polarization dependence effects are discussed. This approach is extended to treat more realistic solvent models. Real solvents are discussed in terms of simple parameters described above, and an analysis of how different regimes affect the rate of charge transfer is presented. Finally, these ideas are correlated to analogous problems in other areas.

Logarithmic Superdiffusion in Two Dimensional Driven Lattice Gases

NASA Astrophysics Data System (ADS)

Krug, J.; Neiss, R. A.; Schadschneider, A.; Schmidt, J.

2018-03-01

The spreading of density fluctuations in two-dimensional driven diffusive systems is marginally anomalous. Mode coupling theory predicts that the diffusivity in the direction of the drive diverges with time as (ln t)^{2/3} with a prefactor depending on the macroscopic current-density relation and the diffusion tensor of the fluctuating hydrodynamic field equation. Here we present the first numerical verification of this behavior for a particular version of the two-dimensional asymmetric exclusion process. Particles jump strictly asymmetrically along one of the lattice directions and symmetrically along the other, and an anisotropy parameter p governs the ratio between the two rates. Using a novel massively parallel coupling algorithm that strongly reduces the fluctuations in the numerical estimate of the two-point correlation function, we are able to accurately determine the exponent of the logarithmic correction. In addition, the variation of the prefactor with p provides a stringent test of mode coupling theory.

Speeding up biomolecular interactions by molecular sledding

DOE PAGES

Turkin, Alexander; Zhang, Lei; Marcozzi, Alessio; ...

2015-10-07

In numerous biological processes associations involve a protein with its binding partner, an event that is preceded by a diffusion-mediated search bringing the two partners together. Often hindered by crowding in biologically relevant environments, three-dimensional diffusion can be slow and result in long bimolecular association times. Moreover, the initial association step between two binding partners often represents a rate-limiting step in biotechnologically relevant reactions. We also demonstrate the practical use of an 11-a.a. DNA-interacting peptide derived from adenovirus to reduce the dimensionality of diffusional search processes and speed up associations between biological macromolecules. We functionalize binding partners with the peptidemore » and demonstrate that the ability of the peptide to one-dimensionally diffuse along DNA results in a 20-fold reduction in reaction time. We also show that modifying PCR primers with the peptide sled enables significant acceleration of standard PCR reactions.« less

Generalization of one-dimensional solute transport: A stochastic-convective flow conceptualization

NASA Astrophysics Data System (ADS)

Simmons, C. S.

1986-04-01

A stochastic-convective representation of one-dimensional solute transport is derived. It is shown to conceptually encompass solutions of the conventional convection-dispersion equation. This stochastic approach, however, does not rely on the assumption that dispersive flux satisfies Fick's diffusion law. Observable values of solute concentration and flux, which together satisfy a conservation equation, are expressed as expectations over a flow velocity ensemble, representing the inherent random processess that govern dispersion. Solute concentration is determined by a Lagrangian pdf for random spatial displacements, while flux is determined by an equivalent Eulerian pdf for random travel times. A condition for such equivalence is derived for steady nonuniform flow, and it is proven that both Lagrangian and Eulerian pdfs are required to account for specified initial and boundary conditions on a global scale. Furthermore, simplified modeling of transport is justified by proving that an ensemble of effectively constant velocities always exists that constitutes an equivalent representation. An example of how a two-dimensional transport problem can be reduced to a single-dimensional stochastic viewpoint is also presented to further clarify concepts.

Permeability and kinetic coefficients for mesoscale BCF surface step dynamics: Discrete two-dimensional deposition-diffusion equation analysis

DOE PAGES

Zhao, Renjie; Evans, James W.; Oliveira, Tiago J.

2016-04-08

Here, a discrete version of deposition-diffusion equations appropriate for description of step flow on a vicinal surface is analyzed for a two-dimensional grid of adsorption sites representing the stepped surface and explicitly incorporating kinks along the step edges. Model energetics and kinetics appropriately account for binding of adatoms at steps and kinks, distinct terrace and edge diffusion rates, and possible additional barriers for attachment to steps. Analysis of adatom attachment fluxes as well as limiting values of adatom densities at step edges for nonuniform deposition scenarios allows determination of both permeability and kinetic coefficients. Behavior of these quantities is assessedmore » as a function of key system parameters including kink density, step attachment barriers, and the step edge diffusion rate.« less

Permeability and kinetic coefficients for mesoscale BCF surface step dynamics: Discrete two-dimensional deposition-diffusion equation analysis

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

Zhao, Renjie; Evans, James W.; Oliveira, Tiago J.

Here, a discrete version of deposition-diffusion equations appropriate for description of step flow on a vicinal surface is analyzed for a two-dimensional grid of adsorption sites representing the stepped surface and explicitly incorporating kinks along the step edges. Model energetics and kinetics appropriately account for binding of adatoms at steps and kinks, distinct terrace and edge diffusion rates, and possible additional barriers for attachment to steps. Analysis of adatom attachment fluxes as well as limiting values of adatom densities at step edges for nonuniform deposition scenarios allows determination of both permeability and kinetic coefficients. Behavior of these quantities is assessedmore » as a function of key system parameters including kink density, step attachment barriers, and the step edge diffusion rate.« less

Assessment of ion kinetic effects in shock-driven inertial confinement fusion implosions using fusion burn imaging

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

Rosenberg, M. J., E-mail: mros@lle.rochester.edu; Séguin, F. H.; Rinderknecht, H. G.

The significance and nature of ion kinetic effects in D{sup 3}He-filled, shock-driven inertial confinement fusion implosions are assessed through measurements of fusion burn profiles. Over this series of experiments, the ratio of ion-ion mean free path to minimum shell radius (the Knudsen number, N{sub K}) was varied from 0.3 to 9 in order to probe hydrodynamic-like to strongly kinetic plasma conditions; as the Knudsen number increased, hydrodynamic models increasingly failed to match measured yields, while an empirically-tuned, first-step model of ion kinetic effects better captured the observed yield trends [Rosenberg et al., Phys. Rev. Lett. 112, 185001 (2014)]. Here, spatiallymore » resolved measurements of the fusion burn are used to examine kinetic ion transport effects in greater detail, adding an additional dimension of understanding that goes beyond zero-dimensional integrated quantities to one-dimensional profiles. In agreement with the previous findings, a comparison of measured and simulated burn profiles shows that models including ion transport effects are able to better match the experimental results. In implosions characterized by large Knudsen numbers (N{sub K} ∼ 3), the fusion burn profiles predicted by hydrodynamics simulations that exclude ion mean free path effects are peaked far from the origin, in stark disagreement with the experimentally observed profiles, which are centrally peaked. In contrast, a hydrodynamics simulation that includes a model of ion diffusion is able to qualitatively match the measured profile shapes. Therefore, ion diffusion or diffusion-like processes are identified as a plausible explanation of the observed trends, though further refinement of the models is needed for a more complete and quantitative understanding of ion kinetic effects.« less

Assessment of ion kinetic effects in shock-driven inertial confinement fusion (ICF) implosions using fusion burn imaging

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

Rosenberg, M. J.; Séguin, F. H.; Amendt, P. A.

The significance and nature of ion kinetic effects in D³He-filled, shock-driven inertial confinement fusion implosions are assessed through measurements of fusion burn profiles. Over this series of experiments, the ratio of ion-ion mean free path to minimum shell radius (the Knudsen number, N K) was varied from 0.3 to 9 in order to probe hydrodynamic-like to strongly kinetic plasma conditions; as the Knudsen number increased, hydrodynamic models increasingly failed to match measured yields, while an empirically-tuned, first-step model of ion kinetic effects better captured the observed yield trends [Rosenberg et al., Phys. Rev. Lett. 112, 185001 (2014)]. Here, spatially resolvedmore » measurements of the fusion burn are used to examine kinetic ion transport effects in greater detail, adding an additional dimension of understanding that goes beyond zero-dimensional integrated quantities to one-dimensional profiles. In agreement with the previous findings, a comparison of measured and simulated burn profiles shows that models including ion transport effects are able to better match the experimental results. In implosions characterized by large Knudsen numbers (N K ~ 3), the fusion burn profiles predicted by hydrodynamics simulations that exclude ion mean free path effects are peaked far from the origin, in stark disagreement with the experimentally observed profiles, which are centrally peaked. In contrast, a hydrodynamics simulation that includes a model of ion diffusion is able to qualitatively match the measured profile shapes. Therefore, ion diffusion or diffusion-like processes are identified as a plausible explanation of the observed trends, though further refinement of the models is needed for a more complete and quantitative understanding of ion kinetic effects.« less

Assessment of ion kinetic effects in shock-driven inertial confinement fusion implosions using fusion burn imaging

NASA Astrophysics Data System (ADS)

Rosenberg, M. J.; Séguin, F. H.; Amendt, P. A.; Atzeni, S.; Rinderknecht, H. G.; Hoffman, N. M.; Zylstra, A. B.; Li, C. K.; Sio, H.; Gatu Johnson, M.; Frenje, J. A.; Petrasso, R. D.; Glebov, V. Yu.; Stoeckl, C.; Seka, W.; Marshall, F. J.; Delettrez, J. A.; Sangster, T. C.; Betti, R.; Wilks, S. C.; Pino, J.; Kagan, G.; Molvig, K.; Nikroo, A.

2015-06-01

The significance and nature of ion kinetic effects in D3He-filled, shock-driven inertial confinement fusion implosions are assessed through measurements of fusion burn profiles. Over this series of experiments, the ratio of ion-ion mean free path to minimum shell radius (the Knudsen number, NK) was varied from 0.3 to 9 in order to probe hydrodynamic-like to strongly kinetic plasma conditions; as the Knudsen number increased, hydrodynamic models increasingly failed to match measured yields, while an empirically-tuned, first-step model of ion kinetic effects better captured the observed yield trends [Rosenberg et al., Phys. Rev. Lett. 112, 185001 (2014)]. Here, spatially resolved measurements of the fusion burn are used to examine kinetic ion transport effects in greater detail, adding an additional dimension of understanding that goes beyond zero-dimensional integrated quantities to one-dimensional profiles. In agreement with the previous findings, a comparison of measured and simulated burn profiles shows that models including ion transport effects are able to better match the experimental results. In implosions characterized by large Knudsen numbers (NK ˜ 3), the fusion burn profiles predicted by hydrodynamics simulations that exclude ion mean free path effects are peaked far from the origin, in stark disagreement with the experimentally observed profiles, which are centrally peaked. In contrast, a hydrodynamics simulation that includes a model of ion diffusion is able to qualitatively match the measured profile shapes. Therefore, ion diffusion or diffusion-like processes are identified as a plausible explanation of the observed trends, though further refinement of the models is needed for a more complete and quantitative understanding of ion kinetic effects.

Assessment of ion kinetic effects in shock-driven inertial confinement fusion (ICF) implosions using fusion burn imaging

DOE PAGES

Rosenberg, M. J.; Séguin, F. H.; Amendt, P. A.; ...

2015-06-02

The significance and nature of ion kinetic effects in D³He-filled, shock-driven inertial confinement fusion implosions are assessed through measurements of fusion burn profiles. Over this series of experiments, the ratio of ion-ion mean free path to minimum shell radius (the Knudsen number, N K) was varied from 0.3 to 9 in order to probe hydrodynamic-like to strongly kinetic plasma conditions; as the Knudsen number increased, hydrodynamic models increasingly failed to match measured yields, while an empirically-tuned, first-step model of ion kinetic effects better captured the observed yield trends [Rosenberg et al., Phys. Rev. Lett. 112, 185001 (2014)]. Here, spatially resolvedmore » measurements of the fusion burn are used to examine kinetic ion transport effects in greater detail, adding an additional dimension of understanding that goes beyond zero-dimensional integrated quantities to one-dimensional profiles. In agreement with the previous findings, a comparison of measured and simulated burn profiles shows that models including ion transport effects are able to better match the experimental results. In implosions characterized by large Knudsen numbers (N K ~ 3), the fusion burn profiles predicted by hydrodynamics simulations that exclude ion mean free path effects are peaked far from the origin, in stark disagreement with the experimentally observed profiles, which are centrally peaked. In contrast, a hydrodynamics simulation that includes a model of ion diffusion is able to qualitatively match the measured profile shapes. Therefore, ion diffusion or diffusion-like processes are identified as a plausible explanation of the observed trends, though further refinement of the models is needed for a more complete and quantitative understanding of ion kinetic effects.« less

Mathematical Modeling the Geometric Regularity in Proteus Mirabilis Colonies

NASA Astrophysics Data System (ADS)

Zhang, Bin; Jiang, Yi; Minsu Kim Collaboration

Proteus Mirabilis colony exhibits striking spatiotemporal regularity, with concentric ring patterns with alternative high and low bacteria density in space, and periodicity for repetition process of growth and swarm in time. We present a simple mathematical model to explain the spatiotemporal regularity of P. Mirabilis colonies. We study a one-dimensional system. Using a reaction-diffusion model with thresholds in cell density and nutrient concentration, we recreated periodic growth and spread patterns, suggesting that the nutrient constraint and cell density regulation might be sufficient to explain the spatiotemporal periodicity in P. Mirabilis colonies. We further verify this result using a cell based model.

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.

Some remarks on relativistic diffusion and the spectral dimension criterion

NASA Astrophysics Data System (ADS)

Muniz, C. R.; Cunha, M. S.; Filho, R. N. Costa; Bezerra, V. B.

2015-01-01

The spectral dimension ds for high energies is calculated using the Relativistic Schrödinger Equation Analytically Continued (RSEAC) instead of the so-called Telegraph's equation (TE), in both ultraviolet (UV) and infrared (IR) regimens. Regarding the TE, the recent literature presents difficulties related to its stochastic derivation and interpretation, advocating the use of the RSEAC to properly describe the relativistic diffusion phenomena. Taking into account that the Lorentz symmetry is broken in UV regime at Lifshitz point, we show that there exists a degeneracy in very high energies, meaning that both the RSEAC and TE correctly describe the diffusion processes at these energy scales, at least under the spectral dimension criterion. In fact, both the equations yield the same result, namely, ds=2 , a dimensional reduction that is compatible with several theories of quantum gravity. This result is reached even when one takes into account a cosmological model, as for example, the de Sitter universe. On the other hand, in the IR regimen, such degeneracy is lifted in favor of the approach via TE, due to the fact that only this equation provides the correct value for ds, which is equal to the actual number of spacetime dimensions, i.e., ds=4 , while RSEAC yields ds=3 , so that a diffusing particle described by this method experiences a three-dimensional spacetime.

Compression Freezing Kinetics of Water to Ice VII

DOE PAGES

Gleason, A. E.; Bolme, C. A.; Galtier, E.; ...

2017-07-11

Time-resolved x-ray diffraction (XRD) of compressed liquid water shows transformation to ice VII in 6 nsec, revealing crystallization rather than amorphous solidification during compression freezing. Application of classical nucleation theory indicates heterogeneous nucleation and one-dimensional (e.g., needlelike) growth. In conclusion, these first XRD data demonstrate rapid growth kinetics of ice VII with implications for fundamental physics of diffusion-mediated crystallization and thermodynamic modeling of collision or impact events on ice-rich planetary bodies.

Compression Freezing Kinetics of Water to Ice VII

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

Gleason, A. E.; Bolme, C. A.; Galtier, E.

Time-resolved x-ray diffraction (XRD) of compressed liquid water shows transformation to ice VII in 6 nsec, revealing crystallization rather than amorphous solidification during compression freezing. Application of classical nucleation theory indicates heterogeneous nucleation and one-dimensional (e.g., needlelike) growth. In conclusion, these first XRD data demonstrate rapid growth kinetics of ice VII with implications for fundamental physics of diffusion-mediated crystallization and thermodynamic modeling of collision or impact events on ice-rich planetary bodies.

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

Aslangul, C.; Bouchaud, J.; Georges, A.

The authors present new exact results for a one-dimensional asymmetric disordered hopping model. The lattice is taken infinite from the start and they do not resort to the periodization scheme used by Derrida. An explicit resummation allows for the calculation of the velocity V and the diffusion constant D (which are found to coincide with those given by Derrida) and for demonstrating that V is indeed a self-averaging quantity; the same property is established for D in the limiting case of a directed walk.

Omnidirectional-view three-dimensional display system based on cylindrical selective-diffusing screen.

PubMed

Xia, Xinxing; Zheng, Zhenrong; Liu, Xu; Li, Haifeng; Yan, Caijie

2010-09-10

We utilized a high-frame-rate projector, a rotating mirror, and a cylindrical selective-diffusing screen to present a novel three-dimensional (3D) omnidirectional-view display system without the need for any special viewing aids. The display principle and image size are analyzed, and the common display zone is proposed. The viewing zone for one observation place is also studied. The experimental results verify this method, and a vivid color 3D scene with occlusion and smooth parallax is also demonstrated with the system.

The generation of two-dimensional vortices by transverse oscillation of a soap film

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

Afenchenko, V.O.; Ezersky, A.B.; Kiyashko, S.V.

1998-02-01

An experimental investigation of the dynamics of horizontal soap films stretched over circular or square boundaries undergoing periodic transverse oscillations at frequencies in the range 20{endash}200 Hz is reported. Concomitant with modes of transverse flexural oscillations, it was observed that two-dimensional vortices in the plane of the film are excited. The vortices may be either (i) large, scaling with the size of the cavity or (ii) small, localized at a wavelength or half-wavelength of the membrane modes. In the experiments a stable generation of one, two, {hor_ellipsis}, ten pairs of counter-rotating vortices were observed in finite regions of amplitude-frequency parametermore » space. The circulation strength of vortices in a given vortex pattern increases with increasing external forcing and with decreasing soap film thickness. A theoretical model based on the wave-boundary interaction of excited Marangoni waves reveals a vorticity generation mechanism active in vibrating soap films. This model shows that vorticity is generated throughout the entire liquid volume by viscous diffusion, and qualitatively reproduces many steady vortex patterns observed in the experiment. However, the model cannot explain the existence of the sometimes intense vortices observed far from the film boundary that do not appear to be generated by diffusive processes. {copyright} {ital 1998 American Institute of Physics.}« less

Multiple-scattering coefficients and absorption controlled diffusive processes

NASA Astrophysics Data System (ADS)

Godoy, Salvador; García-Colín, L. S.; Micenmacher, Victor

1999-11-01

Multiple-scattering transmission and reflection coefficients (T,R) are introduced in addition to the diffusion coefficient D for the description of ballistic diffusion in the presence of absorption. For 1D (one-dimensional) systems, the measurement of only one between T and D imposes restrictions on the possible values of the other. If D is measured, then T is bounded between the Landauer and Lambert-Beer equations. Measurements of both (T,D) imply the theoretical knowledge of the microscopic absorption Σa and scattering rΣs cross sections.

Regulation of a Viral Proteinase by a Peptide and DNA in One-dimensional Space

PubMed Central

Blainey, Paul C.; Graziano, Vito; Pérez-Berná, Ana J.; McGrath, William J.; Flint, S. Jane; San Martín, Carmen; Xie, X. Sunney; Mangel, Walter F.

2013-01-01

Precursor proteins used in the assembly of adenovirus virions must be processed by the virally encoded adenovirus proteinase (AVP) before the virus particle becomes infectious. An activated adenovirus proteinase, the AVP-pVIc complex, was shown to slide along viral DNA with an extremely fast one-dimensional diffusion constant, 21.0 ± 1.9 × 106 bp2/s. In principle, one-dimensional diffusion can provide a means for DNA-bound proteinases to locate and process DNA-bound substrates. Here, we show that this is correct. In vitro, AVP-pVIc complexes processed a purified virion precursor protein in a DNA-dependent reaction; in a quasi in vivo environment, heat-disrupted ts-1 virions, AVP-pVIc complexes processed five different precursor proteins in DNA-dependent reactions. Sliding of AVP-pVIc complexes along DNA illustrates a new biochemical mechanism by which a proteinase can locate its substrates, represents a new paradigm for virion maturation, and reveals a new way of exploiting the surface of DNA. PMID:23043138

Analytical and computational studies on the vacuum performance of a chevron ejector

NASA Astrophysics Data System (ADS)

Kong, F. S.; Jin, Y. Z.; Kim, H. D.

2016-11-01

The effects of chevrons on the performance of a supersonic vacuum ejector-diffuser system are investigated numerically and evaluated theoretically in this work. A three-dimensional geometrical domain is numerically solved using a fully implicit finite volume scheme based on the unsteady Reynolds stress model. A one-dimensional mathematical model provides a useful tool to reveal the steady flow physics inside the vacuum ejector-diffuser system. The effects of the chevron nozzle on the generation of recirculation regions and Reynolds stress behaviors are studied and compared with those of a conventional convergent nozzle. The present performance parameters obtained from the simulated results and the mathematical results are validated with existing experimental data and show good agreement. Primary results show that the duration of the transient period and the secondary chamber pressure at a dynamic equilibrium state depend strongly on the primary jet conditions, such as inlet pressure and primary nozzle shape. Complicated oscillatory flow, generated by the unsteady movement of recirculation, finally settles into a dynamic equilibrium state. As a vortex generator, the chevron demonstrated its strong entrainment capacity to accelerate the starting transient flows to a certain extent and reduce the dynamic equilibrium pressure of the secondary chamber significantly.

Development of a numerical model for the electric current in burner-stabilised methane-air flames

NASA Astrophysics Data System (ADS)

Speelman, N.; de Goey, L. P. H.; van Oijen, J. A.

2015-03-01

This study presents a new model to simulate the electric behaviour of one-dimensional ionised flames and to predict the electric currents in these flames. The model utilises Poisson's equation to compute the electric potential. A multi-component diffusion model, including the influence of an electric field, is used to model the diffusion of neutral and charged species. The model is incorporated into the existing CHEM1D flame simulation software. A comparison between the computed electric currents and experimental values from the literature shows good qualitative agreement for the voltage-current characteristic. Physical phenomena, such as saturation and the diodic effect, are captured by the model. The dependence of the saturation current on the equivalence ratio is also captured well for equivalence ratios between 0.6 and 1.2. Simulations show a clear relation between the saturation current and the total number of charged particles created. The model shows that the potential at which the electric field saturates is strongly dependent on the recombination rate and the diffusivity of the charged particles. The onset of saturation occurs because most created charged particles are withdrawn from the flame and because the electric field effects start dominating over mass based diffusion. It is shown that this knowledge can be used to optimise ionisation chemistry mechanisms. It is shown numerically that the so-called diodic effect is caused primarily by the distance the heavier cations have to travel to the cathode.

Analysis of the geometrical-probabilistic models of electrocrystallization

NASA Astrophysics Data System (ADS)

Isaev, V. A.; Grishenkova, O. V.; Zaykov, Yu. P.

2016-08-01

The formation of a three-dimensional electrode deposit under potentiostatic conditions, including the stages of nucleation, growth, and overlap of growing new-phase clusters and their diffusion zones, is considered. The models of electrochemical phase formation for kinetics- and diffusion-controlled growth are analyzed, and the correctness of the approximations used in these models is estimated. The possibility of application of these models to an analysis of the electrodeposition of silicon from molten salts is discussed.

Semiclassical electron transport at the edge of a two-dimensional topological insulator: Interplay of protected and unprotected modes

NASA Astrophysics Data System (ADS)

Khalaf, E.; Skvortsov, M. A.; Ostrovsky, P. M.

2016-03-01

We study electron transport at the edge of a generic disordered two-dimensional topological insulator, where some channels are topologically protected from backscattering. Assuming the total number of channels is large, we consider the edge as a quasi-one-dimensional quantum wire and describe it in terms of a nonlinear sigma model with a topological term. Neglecting localization effects, we calculate the average distribution function of transmission probabilities as a function of the sample length. We mainly focus on the two experimentally relevant cases: a junction between two quantum Hall (QH) states with different filling factors (unitary class) and a relatively thick quantum well exhibiting quantum spin Hall (QSH) effect (symplectic class). In a QH sample, the presence of topologically protected modes leads to a strong suppression of diffusion in the other channels already at scales much shorter than the localization length. On the semiclassical level, this is accompanied by the formation of a gap in the spectrum of transmission probabilities close to unit transmission, thereby suppressing shot noise and conductance fluctuations. In the case of a QSH system, there is at most one topologically protected edge channel leading to weaker transport effects. In order to describe `topological' suppression of nearly perfect transparencies, we develop an exact mapping of the semiclassical limit of the one-dimensional sigma model onto a zero-dimensional sigma model of a different symmetry class, allowing us to identify the distribution of transmission probabilities with the average spectral density of a certain random-matrix ensemble. We extend our results to other symmetry classes with topologically protected edges in two dimensions.

Passive Rocket Diffuser Theory: A Re-Examination of Minimum Second Throat Size

NASA Technical Reports Server (NTRS)

Jones, Daniel R.

2016-01-01

Second-throat diffusers serve to isolate rocket engines from the effects of ambient back pressure during testing without using active control systems. Among the most critical design parameters is the relative area of the diffuser throat to that of the nozzle throat. A smaller second throat is generally desirable because it decreases the stagnation-to-ambient pressure ratio the diffuser requires for nominal operation. There is a limit, however. Below a certain size, the second throat can cause pressure buildup within the diffuser and prevent it from reaching the start condition that protects the nozzle from side-load damage. This paper presents a method for improved estimation of the minimum second throat area which enables diffuser start. The new 3-zone model uses traditional quasi-one-dimensional compressible flow theory to approximate the structure of two distinct diffuser flow fields observed in Computational Fluid Dynamics (CFD) simulations and combines them to provide a less-conservative estimate of the second throat size limit. It is unique among second throat sizing methods in that it accounts for all major conical nozzle and second throat diffuser design parameters within its limits of application. The performance of the 3-zone method is compared to the historical normal shock and force balance methods, and verified against a large number of CFD simulations at specific heat ratios of 1.4 and 1.25. Validation is left as future work, and the model is currently intended to function only as a first-order design tool.

Influence of impeller and diffuser geometries on the lateral fluid forces of whirling centrifugal impeller

NASA Technical Reports Server (NTRS)

Ohashi, Hideo; Sakurai, Akira; Nishihama, Jiro

1989-01-01

Lateral fluid forces on two-dimensional centrifugal impellers, which whirl on a circular orbit in a vaneless diffuser, were reported. Experiments were further conducted for the cases in which a three-dimensional centrifugal impeller, a model of the boiler feed pump, whirls in vaneless and vaned diffusers. The influence of the clearance configuration between the casing and front shroud of the impeller was also investigated. The result indicated that the fluid dynamic interaction between the impeller and the guide vanes induces quite strong fluctuating fluid forces to the impeller, but nevertheless its influence on radial and tangential force components averaged over a whirling orbit is relatively small.

Lithium Depletion in Solar-like Stars: Effect of Overshooting Based on Realistic Multi-dimensional Simulations

NASA Astrophysics Data System (ADS)

Baraffe, I.; Pratt, J.; Goffrey, T.; Constantino, T.; Folini, D.; Popov, M. V.; Walder, R.; Viallet, M.

2017-08-01

We study lithium depletion in low-mass and solar-like stars as a function of time, using a new diffusion coefficient describing extra-mixing taking place at the bottom of a convective envelope. This new form is motivated by multi-dimensional fully compressible, time-implicit hydrodynamic simulations performed with the MUSIC code. Intermittent convective mixing at the convective boundary in a star can be modeled using extreme value theory, a statistical analysis frequently used for finance, meteorology, and environmental science. In this Letter, we implement this statistical diffusion coefficient in a one-dimensional stellar evolution code, using parameters calibrated from multi-dimensional hydrodynamic simulations of a young low-mass star. We propose a new scenario that can explain observations of the surface abundance of lithium in the Sun and in clusters covering a wide range of ages, from ˜50 Myr to ˜4 Gyr. Because it relies on our physical model of convective penetration, this scenario has a limited number of assumptions. It can explain the observed trend between rotation and depletion, based on a single additional assumption, namely, that rotation affects the mixing efficiency at the convective boundary. We suggest the existence of a threshold in stellar rotation rate above which rotation strongly prevents the vertical penetration of plumes and below which rotation has small effects. In addition to providing a possible explanation for the long-standing problem of lithium depletion in pre-main-sequence and main-sequence stars, the strength of our scenario is that its basic assumptions can be tested by future hydrodynamic simulations.

Lithium Depletion in Solar-like Stars: Effect of Overshooting Based on Realistic Multi-dimensional Simulations

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

Baraffe, I.; Pratt, J.; Goffrey, T.

We study lithium depletion in low-mass and solar-like stars as a function of time, using a new diffusion coefficient describing extra-mixing taking place at the bottom of a convective envelope. This new form is motivated by multi-dimensional fully compressible, time-implicit hydrodynamic simulations performed with the MUSIC code. Intermittent convective mixing at the convective boundary in a star can be modeled using extreme value theory, a statistical analysis frequently used for finance, meteorology, and environmental science. In this Letter, we implement this statistical diffusion coefficient in a one-dimensional stellar evolution code, using parameters calibrated from multi-dimensional hydrodynamic simulations of a youngmore » low-mass star. We propose a new scenario that can explain observations of the surface abundance of lithium in the Sun and in clusters covering a wide range of ages, from ∼50 Myr to ∼4 Gyr. Because it relies on our physical model of convective penetration, this scenario has a limited number of assumptions. It can explain the observed trend between rotation and depletion, based on a single additional assumption, namely, that rotation affects the mixing efficiency at the convective boundary. We suggest the existence of a threshold in stellar rotation rate above which rotation strongly prevents the vertical penetration of plumes and below which rotation has small effects. In addition to providing a possible explanation for the long-standing problem of lithium depletion in pre-main-sequence and main-sequence stars, the strength of our scenario is that its basic assumptions can be tested by future hydrodynamic simulations.« less

Existence of negative differential thermal conductance in one-dimensional diffusive thermal transport

NASA Astrophysics Data System (ADS)

Hu, Jiuning; Chen, Yong P.

2013-06-01

We show that in a finite one-dimensional (1D) system with diffusive thermal transport described by the Fourier's law, negative differential thermal conductance (NDTC) cannot occur when the temperature at one end is fixed and there are no abrupt junctions. We demonstrate that NDTC in this case requires the presence of junction(s) with temperature-dependent thermal contact resistance (TCR). We derive a necessary and sufficient condition for the existence of NDTC in terms of the properties of the TCR for systems with a single junction. We show that under certain circumstances we even could have infinite (negative or positive) differential thermal conductance in the presence of the TCR. Our predictions provide theoretical basis for constructing NDTC-based devices, such as thermal amplifiers, oscillators, and logic devices.

Rarefaction-driven Rayleigh–Taylor instability. Part 1. Diffuse-interface linear stability measurements and theory

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

Morgan, R. V.; Likhachev, O. A.; Jacobs, J. W.

Theory and experiments are reported that explore the behaviour of the Rayleigh–Taylor instability initiated with a diffuse interface. Experiments are performed in which an interface between two gases of differing density is made unstable by acceleration generated by a rarefaction wave. Well-controlled, diffuse, two-dimensional and three-dimensional, single-mode perturbations are generated by oscillating the gases either side to side, or vertically for the three-dimensional perturbations. The puncturing of a diaphragm separating a vacuum tank beneath the test section generates a rarefaction wave that travels upwards and accelerates the interface downwards. This rarefaction wave generates a large, but non-constant, acceleration of the order ofmore » $$1000g_{0}$$, where$$g_{0}$$is the acceleration due to gravity. Initial interface thicknesses are measured using a Rayleigh scattering diagnostic and the instability is visualized using planar laser-induced Mie scattering. Growth rates agree well with theoretical values, and with the inviscid, dynamic diffusion model of Duffet al. (Phys. Fluids, vol. 5, 1962, pp. 417–425) when diffusion thickness is accounted for, and the acceleration is weighted using inviscid Rayleigh–Taylor theory. The linear stability formulation of Chandrasekhar (Proc. Camb. Phil. Soc., vol. 51, 1955, pp. 162–178) is solved numerically with an error function diffusion profile using the Riccati method. This technique exhibits good agreement with the dynamic diffusion model of Duffet al. for small wavenumbers, but produces larger growth rates for large-wavenumber perturbations. Asymptotic analysis shows a$$1/k^{2}$$decay in growth rates as$$k\\rightarrow \\infty$$for large-wavenumber perturbations.« less

Rarefaction-driven Rayleigh–Taylor instability. Part 1. Diffuse-interface linear stability measurements and theory

DOE PAGES

Morgan, R. V.; Likhachev, O. A.; Jacobs, J. W.

2016-02-15

Theory and experiments are reported that explore the behaviour of the Rayleigh–Taylor instability initiated with a diffuse interface. Experiments are performed in which an interface between two gases of differing density is made unstable by acceleration generated by a rarefaction wave. Well-controlled, diffuse, two-dimensional and three-dimensional, single-mode perturbations are generated by oscillating the gases either side to side, or vertically for the three-dimensional perturbations. The puncturing of a diaphragm separating a vacuum tank beneath the test section generates a rarefaction wave that travels upwards and accelerates the interface downwards. This rarefaction wave generates a large, but non-constant, acceleration of the order ofmore » $$1000g_{0}$$, where$$g_{0}$$is the acceleration due to gravity. Initial interface thicknesses are measured using a Rayleigh scattering diagnostic and the instability is visualized using planar laser-induced Mie scattering. Growth rates agree well with theoretical values, and with the inviscid, dynamic diffusion model of Duffet al. (Phys. Fluids, vol. 5, 1962, pp. 417–425) when diffusion thickness is accounted for, and the acceleration is weighted using inviscid Rayleigh–Taylor theory. The linear stability formulation of Chandrasekhar (Proc. Camb. Phil. Soc., vol. 51, 1955, pp. 162–178) is solved numerically with an error function diffusion profile using the Riccati method. This technique exhibits good agreement with the dynamic diffusion model of Duffet al. for small wavenumbers, but produces larger growth rates for large-wavenumber perturbations. Asymptotic analysis shows a$$1/k^{2}$$decay in growth rates as$$k\\rightarrow \\infty$$for large-wavenumber perturbations.« less

Non-Arrhenius temperature dependence of the island density of one-dimensional Al chains on Si(100): A kinetic Monte Carlo study

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

Albia, Jason R.; Albao, Marvin A., E-mail: maalbao@uplb.edu.ph

Classical nucleation theory predicts that the evolution of mean island density with temperature during growth in one-dimensional systems obeys the Arrhenius relation. In this study, kinetic Monte Carlo simulations of a suitable atomistic lattice-gas model were performed to investigate the experimentally observed non-Arrhenius scaling behavior of island density in the case of one-dimensional Al islands grown on Si(100). Previously, it was proposed that adatom desorption resulted in a transition temperature signaling the departure from classical predictions. Here, the authors demonstrate that desorption above the transition temperature is not possible. Instead, the authors posit that the existence of a transition temperaturemore » is due to a combination of factors such as reversibility of island growth, presence of C-defects, adatom diffusion rates, as well as detachment rates at island ends. In addition, the authors show that the anomalous non-Arrhenius behavior vanishes when adatom binds irreversibly with C-defects as observed in In on Si(100) studies.« less

Stochastic modeling of experimental chaotic time series.

PubMed

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

2007-01-26

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

Mathematical Modeling and Optimization Studies on Development of Fuel Cells for Multifarious Applications

DTIC Science & Technology

2010-05-12

multicomponent steady-state model for liquid -feed solid polymer electrolyte DBFCs. These fuel cells use sodium borohydride (NaBH4) in alkaline media...layers, diffusion layers and the polymer electrolyte membrane for a liquid feed DBFC. Diffusion of reactants within and between the pores is accounted...projected for futuristic portable applications. In this project we developed a three- dimensional, multicomponent steady-state model for liquid -feed solid

Surface relief model for photopolymers without cover plating.

PubMed

Gallego, S; Márquez, A; Ortuño, M; Francés, J; Marini, S; Beléndez, A; Pascual, I

2011-05-23

Relief surface changes provide interesting possibilities for storing diffractive optical elements on photopolymers and are an important source of information to characterize and understand the material behaviour. In this paper we present a 3-dimensional model based on direct measurements of parameters to predict the relief structures generated on the material. This model is successfully applied to different photopolymers with different values of monomer diffusion. The importance of monomer diffusion in depth is also discussed.

Scaling characteristics of one-dimensional fractional diffusion processes in the presence of power-law distributed random noise

NASA Astrophysics Data System (ADS)

Nezhadhaghighi, Mohsen Ghasemi

2017-08-01

Here, we present results of numerical simulations and the scaling characteristics of one-dimensional random fluctuations with heavy-tailed probability distribution functions. Assuming that the distribution function of the random fluctuations obeys Lévy statistics with a power-law scaling exponent, we investigate the fractional diffusion equation in the presence of μ -stable Lévy noise. We study the scaling properties of the global width and two-point correlation functions and then compare the analytical and numerical results for the growth exponent β and the roughness exponent α . We also investigate the fractional Fokker-Planck equation for heavy-tailed random fluctuations. We show that the fractional diffusion processes in the presence of μ -stable Lévy noise display special scaling properties in the probability distribution function (PDF). Finally, we numerically study the scaling properties of the heavy-tailed random fluctuations by using the diffusion entropy analysis. This method is based on the evaluation of the Shannon entropy of the PDF generated by the random fluctuations, rather than on the measurement of the global width of the process. We apply the diffusion entropy analysis to extract the growth exponent β and to confirm the validity of our numerical analysis.

Scaling characteristics of one-dimensional fractional diffusion processes in the presence of power-law distributed random noise.

PubMed

Nezhadhaghighi, Mohsen Ghasemi

2017-08-01

Here, we present results of numerical simulations and the scaling characteristics of one-dimensional random fluctuations with heavy-tailed probability distribution functions. Assuming that the distribution function of the random fluctuations obeys Lévy statistics with a power-law scaling exponent, we investigate the fractional diffusion equation in the presence of μ-stable Lévy noise. We study the scaling properties of the global width and two-point correlation functions and then compare the analytical and numerical results for the growth exponent β and the roughness exponent α. We also investigate the fractional Fokker-Planck equation for heavy-tailed random fluctuations. We show that the fractional diffusion processes in the presence of μ-stable Lévy noise display special scaling properties in the probability distribution function (PDF). Finally, we numerically study the scaling properties of the heavy-tailed random fluctuations by using the diffusion entropy analysis. This method is based on the evaluation of the Shannon entropy of the PDF generated by the random fluctuations, rather than on the measurement of the global width of the process. We apply the diffusion entropy analysis to extract the growth exponent β and to confirm the validity of our numerical analysis.

Building 1D resonance broadened quasilinear (RBQ) code for fast ions Alfvénic relaxations

NASA Astrophysics Data System (ADS)

Gorelenkov, Nikolai; Duarte, Vinicius; Berk, Herbert

2016-10-01

The performance of the burning plasma is limited by the confinement of superalfvenic fusion products, e.g. alpha particles, which are capable of resonating with the Alfvénic eigenmodes (AEs). The effect of AEs on fast ions is evaluated using a resonance line broadened diffusion coefficient. The interaction of fast ions and AEs is captured for cases where there are either isolated or overlapping modes. A new code RBQ1D is being built which constructs diffusion coefficients based on realistic eigenfunctions that are determined by the ideal MHD code NOVA. The wave particle interaction can be reduced to one-dimensional dynamics where for the Alfvénic modes typically the particle kinetic energy is nearly constant. Hence to a good approximation the Quasi-Linear (QL) diffusion equation only contains derivatives in the angular momentum. The diffusion equation is then one dimensional that is efficiently solved simultaneously for all particles with the equation for the evolution of the wave angular momentum. The evolution of fast ion constants of motion is governed by the QL diffusion equations which are adapted to find the ion distribution function.

Modeling persistence of motion in a crowded environment: The diffusive limit of excluding velocity-jump processes

NASA Astrophysics Data System (ADS)

Gavagnin, Enrico; Yates, Christian A.

2018-03-01

Persistence of motion is the tendency of an object to maintain motion in a direction for short time scales without necessarily being biased in any direction in the long term. One of the most appropriate mathematical tools to study this behavior is an agent-based velocity-jump process. In the absence of agent-agent interaction, the mean-field continuum limit of the agent-based model (ABM) gives rise to the well known hyperbolic telegraph equation. When agent-agent interaction is included in the ABM, a strictly advective system of partial differential equations (PDEs) can be derived at the population level. However, no diffusive limit of the ABM has been obtained from such a model. Connecting the microscopic behavior of the ABM to a diffusive macroscopic description is desirable, since it allows the exploration of a wider range of scenarios and establishes a direct connection with commonly used statistical tools of movement analysis. In order to connect the ABM at the population level to a diffusive PDE at the population level, we consider a generalization of the agent-based velocity-jump process on a two-dimensional lattice with three forms of agent interaction. This generalization allows us to take a diffusive limit and obtain a faithful population-level description. We investigate the properties of the model at both the individual and population levels and we elucidate some of the models' key characteristic features. In particular, we show an intrinsic anisotropy inherent to the models and we find evidence of a spontaneous form of aggregation at both the micro- and macroscales.

Multiple Scattering in Clouds: Insights from Three-Dimensional Diffusion/P{sub 1} Theory

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

Davis, Anthony B.; Marshak, Alexander

2001-03-15

In the atmosphere, multiple scattering matters nowhere more than in clouds, and being a product of its turbulence, clouds are highly variable environments. This challenges three-dimensional (3D) radiative transfer theory in a way that easily swamps any available computational resources. Fortunately, the far simpler diffusion (or P{sub 1}) theory becomes more accurate as the scattering intensifies, and allows for some analytical progress as well as computational efficiency. After surveying current approaches to 3D solar cloud-radiation problems from the diffusion standpoint, a general 3D result in steady-state diffusive transport is derived relating the variability-induced change in domain-average flux (i.e., diffuse transmittance)more » to the one-point covariance of internal fluctuations in particle density and in radiative flux. These flux variations follow specific spatial patterns in deliberately hydrodynamical language: radiative channeling. The P{sub 1} theory proves even more powerful when the photon diffusion process unfolds in time as well as space. For slab geometry, characteristic times and lengths that describe normal and transverse transport phenomena are derived. This phenomenology is used to (a) explain persistent features in satellite images of dense stratocumulus as radiative channeling, (b) set limits on current cloud remote-sensing techniques, and (c) propose new ones both active and passive.« less

Effect of electron Monte Carlo collisions on a hybrid simulation of a low-pressure capacitively coupled plasma

NASA Astrophysics Data System (ADS)

Hwang, Seok Won; Lee, Ho-Jun; Lee, Hae June

2014-12-01

Fluid models have been widely used and conducted successfully in high pressure plasma simulations where the drift-diffusion and the local-field approximation are valid. However, fluid models are not able to demonstrate non-local effects related to large electron energy relaxation mean free path in low pressure plasmas. To overcome this weakness, a hybrid model coupling electron Monte Carlo collision (EMCC) method with the fluid model is introduced to obtain precise electron energy distribution functions using pseudo-particles. Steady state simulation results by a one-dimensional hybrid model which includes EMCC method for the collisional reactions but uses drift-diffusion approximation for electron transport in a fluid model are compared with those of a conventional particle-in-cell (PIC) and a fluid model for low pressure capacitively coupled plasmas. At a wide range of pressure, the hybrid model agrees well with the PIC simulation with a reduced calculation time while the fluid model shows discrepancy in the results of the plasma density and the electron temperature.

Applications of a new wall function to turbulent flow computations

NASA Astrophysics Data System (ADS)

Chen, Y. S.

1986-01-01

A new wall function approach is developed based on a wall law suitable for incompressible turbulent boundary layers under strong adverse pressure gradients. This wall law was derived from a one-dimensional analysis of the turbulent kinetic energy equation with gradient diffusion concept employed in modeling the near-wall shear stress gradient. Numerical testing cases for the present wall functions include turbulent separating flows around an airfoil and turbulent recirculating flows in several confined regions. Improvements on the predictions using the present wall functions are illustrated. For cases of internal recirculating flows, one modification factor for improving the performance of the k-epsilon turbulence model in the flow recirculation regions is also included.

A diffusion model of protected population on bilocal habitat with generalized resource

NASA Astrophysics Data System (ADS)

Vasilyev, Maxim D.; Trofimtsev, Yuri I.; Vasilyeva, Natalya V.

2017-11-01

A model of population distribution in a two-dimensional area divided by an ecological barrier, i.e. the boundaries of natural reserve, is considered. Distribution of the population is defined by diffusion, directed migrations and areal resource. The exchange of specimens occurs between two parts of the habitat. The mathematical model is presented in the form of a boundary value problem for a system of non-linear parabolic equations with variable parameters of diffusion and growth function. The splitting space variables, sweep method and simple iteration methods were used for the numerical solution of a system. A set of programs was coded in Python. Numerical simulation results for the two-dimensional unsteady non-linear problem are analyzed in detail. The influence of migration flow coefficients and functions of natural birth/death ratio on the distributions of population densities is investigated. The results of the research would allow to describe the conditions of the stable and sustainable existence of populations in bilocal habitat containing the protected and non-protected zones.

Shock probes in a one-dimensional Katz-Lebowitz-Spohn model

NASA Astrophysics Data System (ADS)

Chatterjee, Sakuntala; Barma, Mustansir

2008-06-01

We consider shock probes in a one-dimensional driven diffusive medium with nearest-neighbor Ising interaction (KLS model). Earlier studies based on an approximate mapping of the present system to an effective zero-range process concluded that the exponents characterizing the decays of several static and dynamical correlation functions of the probes depend continuously on the strength of the Ising interaction. On the contrary, our numerical simulations indicate that over a substantial range of the interaction strength, these exponents remain constant and their values are the same as in the case of no interaction (when the medium executes an ASEP). We demonstrate this by numerical studies of several dynamical correlation functions for two probes and also for a macroscopic number of probes. Our results are consistent with the expectation that the short-ranged correlations induced by the Ising interaction should not affect the large time and large distance properties of the system, implying that scaling forms remain the same as in the medium with no interactions present.

Viscous, resistive MHD stability computed by spectral techniques

NASA Technical Reports Server (NTRS)

Dahlburg, R. B.; Zang, T. A.; Montgomery, D.; Hussaini, M. Y.

1983-01-01

Expansions in Chebyshev polynomials are used to study the linear stability of one dimensional magnetohydrodynamic (MHD) quasi-equilibria, in the presence of finite resistivity and viscosity. The method is modeled on the one used by Orszag in accurate computation of solutions of the Orr-Sommerfeld equation. Two Reynolds like numbers involving Alfven speeds, length scales, kinematic viscosity, and magnetic diffusivity govern the stability boundaries, which are determined by the geometric mean of the two Reynolds like numbers. Marginal stability curves, growth rates versus Reynolds like numbers, and growth rates versus parallel wave numbers are exhibited. A numerical result which appears general is that instability was found to be associated with inflection points in the current profile, though no general analytical proof has emerged. It is possible that nonlinear subcritical three dimensional instabilities may exist, similar to those in Poiseuille and Couette flow.

A Diffuse Interface Model with Immiscibility Preservation

PubMed Central

Tiwari, Arpit; Freund, Jonathan B.; Pantano, Carlos

2013-01-01

A new, simple, and computationally efficient interface capturing scheme based on a diffuse interface approach is presented for simulation of compressible multiphase flows. Multi-fluid interfaces are represented using field variables (interface functions) with associated transport equations that are augmented, with respect to an established formulation, to enforce a selected interface thickness. The resulting interface region can be set just thick enough to be resolved by the underlying mesh and numerical method, yet thin enough to provide an efficient model for dynamics of well-resolved scales. A key advance in the present method is that the interface regularization is asymptotically compatible with the thermodynamic mixture laws of the mixture model upon which it is constructed. It incorporates first-order pressure and velocity non-equilibrium effects while preserving interface conditions for equilibrium flows, even within the thin diffused mixture region. We first quantify the improved convergence of this formulation in some widely used one-dimensional configurations, then show that it enables fundamentally better simulations of bubble dynamics. Demonstrations include both a spherical bubble collapse, which is shown to maintain excellent symmetry despite the Cartesian mesh, and a jetting bubble collapse adjacent a wall. Comparisons show that without the new formulation the jet is suppressed by numerical diffusion leading to qualitatively incorrect results. PMID:24058207

A Rayleighian approach for modeling kinetics of ionic transport in polymeric media

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

Kumar, Rajeev

2017-02-14

Here, we report a theoretical approach for analyzing impedance of ionic liquids (ILs) and charged polymers such as polymerized ionic liquids (PolyILs) within linear response. The approach is based on the Rayleigh dissipation function formalism, which provides a computational framework for a systematic study of various factors, including polymer dynamics, in affecting the impedance. We present an analytical expression for the impedance within linear response by constructing a one-dimensional model for ionic transport in ILs/PolyILs. This expression is used to extract mutual diffusion constants, the length scale of mutual diffusion, and thicknesses of a low-dielectric layer on the electrodes frommore » the broadband dielectric spectroscopy (BDS) measurements done for an IL and three PolyILs. Also, static dielectric permittivities of the IL and the PolyILs are determined. The extracted mutual diffusion constants are compared with the self diffusion constants of ions measured using pulse field gradient (PFG) fluorine nuclear magnetic resonance (NMR). For the first time, excellent agreements between the diffusivities extracted from the Electrode Polarization spectra (EPS) of IL/PolyILs and those measured using the PFG-NMR are found, which allows the use of the EPS and the PFG-NMR techniques in a complimentary manner for a general understanding of the ionic transport.« less

Shading of a computer-generated hologram by zone plate modulation.

PubMed

Kurihara, Takayuki; Takaki, Yasuhiro

2012-02-13

We propose a hologram calculation technique that enables reconstructing a shaded three-dimensional (3D) image. The amplitude distributions of zone plates, which generate the object points that constitute a 3D object, were two-dimensionally modulated. Two-dimensional (2D) amplitude modulation was determined on the basis of the Phong reflection model developed for computer graphics, which considers the specular, diffuse, and ambient reflection light components. The 2D amplitude modulation added variable and constant modulations: the former controlled the specular light component and the latter controlled the diffuse and ambient components. The proposed calculation technique was experimentally verified. The reconstructed image showed specular reflection that varied depending on the viewing position.

Modelling Tethered Enzymatic Reactions

NASA Astrophysics Data System (ADS)

Solis Salas, Citlali; Goyette, Jesse; Coker-Gordon, Nicola; Bridge, Marcus; Isaacson, Samuel; Allard, Jun; Maini, Philip; Dushek, Omer

Enzymatic reactions are key to cell functioning, and whilst much work has been done in protein interaction in cases where diffusion is possible, interactions of tethered proteins are poorly understood. Yet, because of the large role cell membranes play in enzymatic reactions, several reactions may take place where one of the proteins is bound to a fixed point in space. We develop a model to characterize tethered signalling between the phosphatase SHP-1 interacting with a tethered, phosphorylated protein. We compare our model to experimental data obtained using surface plasmon resonance (SPR). We show that a single SPR experiment recovers 5 independent biophysical/biochemical constants. We also compare the results between a three dimensional model and a two dimensional model. The work gives the opportunity to use known techniques to learn more about signalling processes, and new insights into how enzyme tethering alters cellular signalling. With support from the Mexican Council for Science and Technology (CONACyT), the Public Education Secretariat (SEP), and the Mexican National Autonomous University's Foundation (Fundacion UNAM).

Influence of a depletion interaction on dynamical heterogeneity in a dense quasi-two-dimensional colloid liquid.

PubMed

Ho, Hau My; Cui, Bianxiao; Repel, Stephen; Lin, Binhua; Rice, Stuart A

2004-11-01

We report the results of digital video microscopy studies of the large particle displacements in a quasi-two-dimensional binary mixture of large (L) and small (S) colloid particles with diameter ratio sigma(L)/sigma(S)=4.65, as a function of the large and small colloid particle densities. As in the case of the one-component quasi-two-dimensional colloid system, the binary mixtures exhibit structural and dynamical heterogeneity. The distribution of large particle displacements over the time scale examined provides evidence for (at least) two different mechanisms of motion, one associated with particles in locally ordered regions and the other associated with particles in locally disordered regions. When rhoL*=Npisigma(L) (2)/4A< or =0.35, the addition of small colloid particles leads to a monotonic decrease in the large particle diffusion coefficient with increasing small particle volume fraction. When rhoL* > or =0.35 the addition of small colloid particles to a dense system of large colloid particles at first leads to an increase in the large particle diffusion coefficient, which is then followed by the expected decrease of the large particle diffusion coefficient with increasing small colloid particle volume fraction. The mode coupling theory of the ideal glass transition in three-dimensional systems makes a qualitative prediction that agrees with the initial increase in the large particle diffusion coefficient with increasing small particle density. Nevertheless, because the structural and dynamical heterogeneities of the quasi-two-dimensional colloid liquid occur within the field of equilibrium states, and the fluctuations generate locally ordered domains rather than just disordered regions of higher and lower density, it is suggested that mode coupling theory does not account for all classes of relevant fluctuations in a quasi-two-dimensional liquid. (c) 2004 American Institute of Physics.

A Novel Multi-scale Simulation Strategy for Turbulent Reacting Flows

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

James, Sutherland C.

In this project, a new methodology was proposed to bridge the gap between Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES). This novel methodology, titled Lattice-Based Multiscale Simulation (LBMS), creates a lattice structure of One-Dimensional Turbulence (ODT) models. This model has been shown to capture turbulent combustion with high fidelity by fully resolving interactions between turbulence and diffusion. By creating a lattice of ODT models, which are then coupled, LBMS overcomes the shortcomings of ODT, which are its inability to capture large scale three dimensional flow structures. However, by spacing these lattices significantly apart, LBMS can avoid the cursemore » of dimensionality that creates untenable computational costs associated with DNS. This project has shown that LBMS is capable of reproducing statistics of isotropic turbulent flows while coarsening the spacing between lines significantly. It also investigates and resolves issues that arise when coupling ODT lines, such as flux reconstruction perpendicular to a given ODT line, preservation of conserved quantities when eddies cross a course cell volume and boundary condition application. Robust parallelization is also investigated.« less

Pattern formation in three-dimensional reaction-diffusion systems

NASA Astrophysics Data System (ADS)

Callahan, T. K.; Knobloch, E.

1999-08-01

Existing group theoretic analysis of pattern formation in three dimensions [T.K. Callahan, E. Knobloch, Symmetry-breaking bifurcations on cubic lattices, Nonlinearity 10 (1997) 1179-1216] is used to make specific predictions about the formation of three-dimensional patterns in two models of the Turing instability, the Brusselator model and the Lengyel-Epstein model. Spatially periodic patterns having the periodicity of the simple cubic (SC), face-centered cubic (FCC) or body-centered cubic (BCC) lattices are considered. An efficient center manifold reduction is described and used to identify parameter regimes permitting stable lamellæ, SC, FCC, double-diamond, hexagonal prism, BCC and BCCI states. Both models possess a special wavenumber k* at which the normal form coefficients take on fixed model-independent ratios and both are described by identical bifurcation diagrams. This property is generic for two-species chemical reaction-diffusion models with a single activator and inhibitor.

Energy balance in the solar transition region. III - Helium emission in hydrostatic, constant-abundance models with diffusion

NASA Technical Reports Server (NTRS)

Fontenla, J. M.; Avrett, E. H.; Loeser, R.

1993-01-01

In our previous papers we described the mathematical formalism and the computed results for energy-balance hydrostatic models of the solar transition region. In this paper we discuss in some detail the limitations of the hydrostatic and one-dimensional assumptions used. Then we analyze the determination of helium emission when diffusion is included. We use transport coefficients estimated from kinetic theory to determine the helium departures from local ionization balance. We calculate the helium spectra for each of our models and evaluate the role of helium in the energy transport. Also, we investigate the effects of coronal illumination on the structure of the transition region and upper chromosphere, and show how coronal illumination affects various EUV lines and the He I 10830 A line. Comparing with both absolute intensities and detailed line profiles, we show that our models are consistent not only with the observed hydrogen spectra but also with the available helium spectra.

The influence of layering and barometric pumping on firn air transport in a 2-D model

NASA Astrophysics Data System (ADS)

Birner, Benjamin; Buizert, Christo; Wagner, Till J. W.; Severinghaus, Jeffrey P.

2018-06-01

Ancient air trapped in ice core bubbles has been paramount to developing our understanding of past climate and atmospheric composition. Before air bubbles become isolated in ice, the atmospheric signal is altered in the firn column by transport processes such as advection and diffusion. However, the influence of low-permeability layers and barometric pumping (driven by surface pressure variability) on firn air transport is not well understood and is not readily captured in conventional one-dimensional (1-D) firn air models. Here we present a two-dimensional (2-D) trace gas advection-diffusion-dispersion model that accounts for discontinuous horizontal layers of reduced permeability. We find that layering or barometric pumping individually yields too small a reduction in gravitational settling to match observations. In contrast, when both effects are active, the model's gravitational fractionation is suppressed as observed. Layering focuses airflows in certain regions in the 2-D model, which acts to amplify the dispersive mixing resulting from barometric pumping. Hence, the representation of both factors is needed to obtain a realistic emergence of the lock-in zone. In contrast to expectations, we find that the addition of barometric pumping in the layered 2-D model does not substantially change the differential kinetic fractionation of fast- and slow-diffusing trace gases. Like 1-D models, the 2-D model substantially underestimates the amount of differential kinetic fractionation seen in actual observations, suggesting that further subgrid-scale processes may be missing in the current generation of firn air transport models. However, we find robust scaling relationships between kinetic isotope fractionation of different noble gas isotope and elemental ratios. These relationships may be used to correct for kinetic fractionation in future high-precision ice core studies and can amount to a bias of up to 0.45 °C in noble-gas-based mean ocean temperature reconstructions at WAIS Divide, Antarctica.

Surface diffusion of cyclic hydrocarbons on nickel

NASA Astrophysics Data System (ADS)

Silverwood, I. P.; Armstrong, J.

2018-08-01

Surface diffusion of adsorbates is difficult to measure on realistic systems, yet it is of fundamental interest in catalysis and coating reactions. quasielastic neutron scattering (QENS) was used to investigate the diffusion of cyclohexane and benzene adsorbed on a nickel metal sponge catalyst. Molecular dynamics simulations of benzene on a model (111) nickel surface showed localised motion with diffusion by intermittent jumps. The experimental data was therefore fitted to the Singwi-Sjölander model and activation energies for diffusion of 4.0 kJ mol-1 for benzene and 4.3 kJ mol-1 for cyclohexane were calculated for the two dimensional model. Limited motion out-of plane was seen in the dynamics simulations and is discussed, although the resolution of the scattering experiment is insufficient to quantify this. Good agreement is seen between the use of a perfect crystal as a model for a disordered system over short time scales, suggesting that simple models are adequate to describe diffusion over polycrystalline metal surfaces on the timescale of QENS measurement.

Cross-diffusion-induced subharmonic spatial resonances in a predator-prey system

NASA Astrophysics Data System (ADS)

Gambino, G.; Lombardo, M. C.; Sammartino, M.

2018-01-01

In this paper we investigate the complex dynamics originated by a cross-diffusion-induced subharmonic destabilization of the fundamental subcritical Turing mode in a predator-prey reaction-diffusion system. The model we consider consists of a two-species Lotka-Volterra system with linear diffusion and a nonlinear cross-diffusion term in the predator equation. The taxis term in the search strategy of the predator is responsible for the onset of complex dynamics. In fact, our model does not exhibit any Hopf or wave instability, and on the basis of the linear analysis one should only expect stationary patterns; nevertheless, the presence of the nonlinear cross-diffusion term is able to induce a secondary instability: due to a subharmonic spatial resonance, the stationary primary branch bifurcates to an out-of-phase oscillating solution. Noticeably, the strong resonance between the harmonic and the subharmonic is able to generate the oscillating pattern albeit the subharmonic is below criticality. We show that, as the control parameter is varied, the oscillating solution (sub T mode) can undergo a sequence of secondary instabilities, generating a transition toward chaotic dynamics. Finally, we investigate the emergence of sub T -mode solutions on two-dimensional domains: when the fundamental mode describes a square pattern, subharmonic resonance originates oscillating square patterns. In the case of subcritical Turing hexagon solutions, the internal interactions with a subharmonic mode are able to generate the so-called "twinkling-eyes" pattern.

Statistical mechanics of shell models for two-dimensional turbulence

NASA Astrophysics Data System (ADS)

Aurell, E.; Boffetta, G.; Crisanti, A.; Frick, P.; Paladin, G.; Vulpiani, A.

1994-12-01

We study shell models that conserve the analogs of energy and enstrophy and hence are designed to mimic fluid turbulence in two-dimensions (2D). The main result is that the observed state is well described as a formal statistical equilibrium, closely analogous to the approach to two-dimensional ideal hydrodynamics of Onsager [Nuovo Cimento Suppl. 6, 279 (1949)], Hopf [J. Rat. Mech. Anal. 1, 87 (1952)], and Lee [Q. Appl. Math. 10, 69 (1952)]. In the presence of forcing and dissipation we observe a forward flux of enstrophy and a backward flux of energy. These fluxes can be understood as mean diffusive drifts from a source to two sinks in a system which is close to local equilibrium with Lagrange multipliers (``shell temperatures'') changing slowly with scale. This is clear evidence that the simplest shell models are not adequate to reproduce the main features of two-dimensional turbulence. The dimensional predictions on the power spectra from a supposed forward cascade of enstrophy and from one branch of the formal statistical equilibrium coincide in these shell models in contrast to the corresponding predictions for the Navier-Stokes and Euler equations in 2D. This coincidence has previously led to the mistaken conclusion that shell models exhibit a forward cascade of enstrophy. We also study the dynamical properties of the models and the growth of perturbations.

Modelling Detailed-Chemistry Effects on Turbulent Diffusion Flames using a Parallel Solution-Adaptive Scheme

NASA Astrophysics Data System (ADS)

Jha, Pradeep Kumar

Capturing the effects of detailed-chemistry on turbulent combustion processes is a central challenge faced by the numerical combustion community. However, the inherent complexity and non-linear nature of both turbulence and chemistry require that combustion models rely heavily on engineering approximations to remain computationally tractable. This thesis proposes a computationally efficient algorithm for modelling detailed-chemistry effects in turbulent diffusion flames and numerically predicting the associated flame properties. The cornerstone of this combustion modelling tool is the use of parallel Adaptive Mesh Refinement (AMR) scheme with the recently proposed Flame Prolongation of Intrinsic low-dimensional manifold (FPI) tabulated-chemistry approach for modelling complex chemistry. The effect of turbulence on the mean chemistry is incorporated using a Presumed Conditional Moment (PCM) approach based on a beta-probability density function (PDF). The two-equation k-w turbulence model is used for modelling the effects of the unresolved turbulence on the mean flow field. The finite-rate of methane-air combustion is represented here by using the GRI-Mech 3.0 scheme. This detailed mechanism is used to build the FPI tables. A state of the art numerical scheme based on a parallel block-based solution-adaptive algorithm has been developed to solve the Favre-averaged Navier-Stokes (FANS) and other governing partial-differential equations using a second-order accurate, fully-coupled finite-volume formulation on body-fitted, multi-block, quadrilateral/hexahedral mesh for two-dimensional and three-dimensional flow geometries, respectively. A standard fourth-order Runge-Kutta time-marching scheme is used for time-accurate temporal discretizations. Numerical predictions of three different diffusion flames configurations are considered in the present work: a laminar counter-flow flame; a laminar co-flow diffusion flame; and a Sydney bluff-body turbulent reacting flow. Comparisons are made between the predicted results of the present FPI scheme and Steady Laminar Flamelet Model (SLFM) approach for diffusion flames. The effects of grid resolution on the predicted overall flame solutions are also assessed. Other non-reacting flows have also been considered to further validate other aspects of the numerical scheme. The present schemes predict results which are in good agreement with published experimental results and reduces the computational cost involved in modelling turbulent diffusion flames significantly, both in terms of storage and processing time.

Application of Central Upwind Scheme for Solving Special Relativistic Hydrodynamic Equations

PubMed Central

Yousaf, Muhammad; Ghaffar, Tayabia; Qamar, Shamsul

2015-01-01

The accurate modeling of various features in high energy astrophysical scenarios requires the solution of the Einstein equations together with those of special relativistic hydrodynamics (SRHD). Such models are more complicated than the non-relativistic ones due to the nonlinear relations between the conserved and state variables. A high-resolution shock-capturing central upwind scheme is implemented to solve the given set of equations. The proposed technique uses the precise information of local propagation speeds to avoid the excessive numerical diffusion. The second order accuracy of the scheme is obtained with the use of MUSCL-type initial reconstruction and Runge-Kutta time stepping method. After a discussion of the equations solved and of the techniques employed, a series of one and two-dimensional test problems are carried out. To validate the method and assess its accuracy, the staggered central and the kinetic flux-vector splitting schemes are also applied to the same model. The scheme is robust and efficient. Its results are comparable to those obtained from the sophisticated algorithms, even in the case of highly relativistic two-dimensional test problems. PMID:26070067

High-order scheme for the source-sink term in a one-dimensional water temperature model

PubMed Central

Jing, Zheng; Kang, Ling

2017-01-01

The source-sink term in water temperature models represents the net heat absorbed or released by a water system. This term is very important because it accounts for solar radiation that can significantly affect water temperature, especially in lakes. However, existing numerical methods for discretizing the source-sink term are very simplistic, causing significant deviations between simulation results and measured data. To address this problem, we present a numerical method specific to the source-sink term. A vertical one-dimensional heat conduction equation was chosen to describe water temperature changes. A two-step operator-splitting method was adopted as the numerical solution. In the first step, using the undetermined coefficient method, a high-order scheme was adopted for discretizing the source-sink term. In the second step, the diffusion term was discretized using the Crank-Nicolson scheme. The effectiveness and capability of the numerical method was assessed by performing numerical tests. Then, the proposed numerical method was applied to a simulation of Guozheng Lake (located in central China). The modeling results were in an excellent agreement with measured data. PMID:28264005

High-order scheme for the source-sink term in a one-dimensional water temperature model.

PubMed

Jing, Zheng; Kang, Ling

2017-01-01

The source-sink term in water temperature models represents the net heat absorbed or released by a water system. This term is very important because it accounts for solar radiation that can significantly affect water temperature, especially in lakes. However, existing numerical methods for discretizing the source-sink term are very simplistic, causing significant deviations between simulation results and measured data. To address this problem, we present a numerical method specific to the source-sink term. A vertical one-dimensional heat conduction equation was chosen to describe water temperature changes. A two-step operator-splitting method was adopted as the numerical solution. In the first step, using the undetermined coefficient method, a high-order scheme was adopted for discretizing the source-sink term. In the second step, the diffusion term was discretized using the Crank-Nicolson scheme. The effectiveness and capability of the numerical method was assessed by performing numerical tests. Then, the proposed numerical method was applied to a simulation of Guozheng Lake (located in central China). The modeling results were in an excellent agreement with measured data.

Thermal transport in the Fermi-Pasta-Ulam model with long-range interactions

NASA Astrophysics Data System (ADS)

Bagchi, Debarshee

2017-03-01

We study the thermal transport properties of the one-dimensional Fermi-Pasta-Ulam model (β type) with long-range interactions. The strength of the long-range interaction decreases with the (shortest) distance between the lattice sites as distance-δ, where δ ≥0 . Two Langevin heat baths at unequal temperatures are connected to the ends of the one-dimensional lattice via short-range harmonic interactions that drive the system away from thermal equilibrium. In the nonequilibrium steady state the heat current, thermal conductivity, and temperature profiles are computed by solving the equations of motion numerically. It is found that the conductivity κ has an interesting nonmonotonic dependence with δ with a maximum at δ =2.0 for this model. Moreover, at δ =2.0 ,κ diverges almost linearly with system size N and the temperature profile has a negligible slope, as one expects in ballistic transport for an integrable system. We demonstrate that the nonmonotonic behavior of the conductivity and the nearly ballistic thermal transport at δ =2.0 obtained under nonequilibrium conditions can be explained consistently by studying the variation of largest Lyapunov exponent λmax with δ , and excess energy diffusion in the equilibrium microcanonical system.

Particle Interactions Mediated by Dynamical Networks: Assessment of Macroscopic Descriptions

NASA Astrophysics Data System (ADS)

Barré, J.; Carrillo, J. A.; Degond, P.; Peurichard, D.; Zatorska, E.

2018-02-01

We provide a numerical study of the macroscopic model of Barré et al. (Multiscale Model Simul, 2017, to appear) derived from an agent-based model for a system of particles interacting through a dynamical network of links. Assuming that the network remodeling process is very fast, the macroscopic model takes the form of a single aggregation-diffusion equation for the density of particles. The theoretical study of the macroscopic model gives precise criteria for the phase transitions of the steady states, and in the one-dimensional case, we show numerically that the stationary solutions of the microscopic model undergo the same phase transitions and bifurcation types as the macroscopic model. In the two-dimensional case, we show that the numerical simulations of the macroscopic model are in excellent agreement with the predicted theoretical values. This study provides a partial validation of the formal derivation of the macroscopic model from a microscopic formulation and shows that the former is a consistent approximation of an underlying particle dynamics, making it a powerful tool for the modeling of dynamical networks at a large scale.

Particle Interactions Mediated by Dynamical Networks: Assessment of Macroscopic Descriptions.

PubMed

Barré, J; Carrillo, J A; Degond, P; Peurichard, D; Zatorska, E

2018-01-01

We provide a numerical study of the macroscopic model of Barré et al. (Multiscale Model Simul, 2017, to appear) derived from an agent-based model for a system of particles interacting through a dynamical network of links. Assuming that the network remodeling process is very fast, the macroscopic model takes the form of a single aggregation-diffusion equation for the density of particles. The theoretical study of the macroscopic model gives precise criteria for the phase transitions of the steady states, and in the one-dimensional case, we show numerically that the stationary solutions of the microscopic model undergo the same phase transitions and bifurcation types as the macroscopic model. In the two-dimensional case, we show that the numerical simulations of the macroscopic model are in excellent agreement with the predicted theoretical values. This study provides a partial validation of the formal derivation of the macroscopic model from a microscopic formulation and shows that the former is a consistent approximation of an underlying particle dynamics, making it a powerful tool for the modeling of dynamical networks at a large scale.

Study on formation of step bunching on 6H-SiC (0001) surface by kinetic Monte Carlo method

NASA Astrophysics Data System (ADS)

Li, Yuan; Chen, Xuejiang; Su, Juan

2016-05-01

The formation and evolution of step bunching during step-flow growth of 6H-SiC (0001) surfaces were studied by three-dimensional kinetic Monte Carlo (KMC) method and compared with the analytic model based on the theory of Burton-Cabera-Frank (BCF). In the KMC model the crystal lattice was represented by a structured mesh which fixed the position of atoms and interatomic bonding. The events considered in the model were adatoms adsorption and diffusion on the terrace, and adatoms attachment, detachment and interlayer transport at the step edges. In addition, effects of Ehrlich-Schwoebel (ES) barriers at downward step edges and incorporation barriers at upwards step edges were also considered. In order to obtain more elaborate information for the behavior of atoms in the crystal surface, silicon and carbon atoms were treated as the minimal diffusing species. KMC simulation results showed that multiple-height steps were formed on the vicinal surface oriented toward [ 1 1 bar 00 ] or [ 11 2 bar 0 ] directions. And then the formation mechanism of the step bunching was analyzed. Finally, to further analyze the formation processes of step bunching, a one-dimensional BCF analytic model with ES and incorporation barriers was used, and then it was solved numerically. In the BCF model, the periodic boundary conditions (PBC) were applied, and the parameters were corresponded to those used in the KMC model. The evolution character of step bunching was consistent with the results obtained by KMC simulation.

Calculations of thermal radiation transfer of C2H2 and C2H4 together with H2O, CO2, and CO in a one-dimensional enclosure using LBL and SNB models

NASA Astrophysics Data System (ADS)

Qi, Chaobo; Zheng, Shu; Zhou, Huaichun

2017-08-01

Generally, the involvement of hydrocarbons such as C2H4 and its derivative C2H2 in thermal radiation has not been accounted in the numerical simulation of their flames, which may cause serious error for estimation of temperature in the early stage of combustion. At the first, the Statistical Narrow-Band (SNB) model parameters for C2H2 and C2H4 are generated from line by line (LBL) calculations. The distributions of the concentrations of radiating gases such as H2O, CO2, CO, C2H2 and C2H4, and the temperature along the centerline of a laminar ethylene/air diffusion flame were chosen to form a one-dimensional, planar enclosure to be tested in this study. Thermal radiation transfer in such an enclosure was calculated using the LBL approach and the SNB model, most of the relative errors are less than 8% and the results of these two models shows an excellent agreement. Below the height of 20 mm, which is the early stage of the flame, the average fraction contributed by C2H2 and C2H4 in the radiative heat source is 33.8%, while that by CO is only 5.8%. This result indicates that the involvement of C2H2 and C2H4 in radiation heat transfer needs to be taken into account in the numerical modeling of the ethylene/air diffusion flame, especially in the early stage of combustion.

A one dimensional moving bed biofilm reactor model for nitrification of municipal wastewaters.

PubMed

Barry, Ugo; Choubert, Jean-Marc; Canler, Jean-Pierre; Pétrimaux, Olivier; Héduit, Alain; Lessard, Paul

2017-08-01

This work presents a one-dimensional model of a moving bed bioreactor (MBBR) process designed for the removal of nitrogen from raw wastewaters. A comprehensive experimental strategy was deployed at a semi-industrial pilot-scale plant fed with a municipal wastewater operated at 10-12 °C, and surface loading rates of 1-2 g filtered COD/m 2 d and 0.4-0.55 g NH 4 -N/m 2 d. Data were collected on influent/effluent composition, and on measurement of key variables or parameters (biofilm mass and maximal thickness, thickness of the limit liquid layer, maximal nitrification rate, oxygen mass transfer coefficient). Based on time-course variations in these variables, the MBBR model was calibrated at two time-scales and magnitudes of dynamic conditions, i.e., short-term (4 days) calibration under dynamic conditions and long-term (33 days) calibration, and for three types of carriers. A set of parameters suitable for the conditions was proposed, and the calibrated parameter set is able to simulate the time-course change of nitrogen forms in the effluent of the MBBR tanks, under the tested operated conditions. Parameters linked to diffusion had a strong influence on how robustly the model is able to accurately reproduce time-course changes in effluent quality. Then the model was used to optimize the operations of MBBR layout. It was shown that the main optimization track consists of the limitation of the aeration supply without changing the overall performance of the process. Further work would investigate the influence of the hydrodynamic conditions onto the thickness of the limit liquid layer and the "apparent" diffusion coefficient in the biofilm parameters.

A 3D model for rain-induced landslides based on molecular dynamics with fractal and fractional water diffusion

NASA Astrophysics Data System (ADS)

Martelloni, Gianluca; Bagnoli, Franco; Guarino, Alessio

2017-09-01

We present a three-dimensional model of rain-induced landslides, based on cohesive spherical particles. The rainwater infiltration into the soil follows either the fractional or the fractal diffusion equations. We analytically solve the fractal partial differential equation (PDE) for diffusion with particular boundary conditions to simulate a rainfall event. We developed a numerical integration scheme for the PDE, compared with the analytical solution. We adapt the fractal diffusion equation obtaining the gravimetric water content that we use as input of a triggering scheme based on Mohr-Coulomb limit-equilibrium criterion. This triggering is then complemented by a standard molecular dynamics algorithm, with an interaction force inspired by the Lennard-Jones potential, to update the positions and velocities of particles. We present our results for homogeneous and heterogeneous systems, i.e., systems composed by particles with same or different radius, respectively. Interestingly, in the heterogeneous case, we observe segregation effects due to the different volume of the particles. Finally, we analyze the parameter sensibility both for the triggering and the propagation phases. Our simulations confirm the results of a previous two-dimensional model and therefore the feasible applicability to real cases.

Void Formation during Diffusion - Two-Dimensional Approach

NASA Astrophysics Data System (ADS)

Wierzba, Bartek

2016-06-01

The final set of equations defining the interdiffusion process in solid state is presented. The model is supplemented by vacancy evolution equation. The competition between the Kirkendall shift, backstress effect and vacancy migration is considered. The proper diffusion flux based on the Nernst-Planck formula is proposed. As a result, the comparison of the experimental and calculated evolution of the void formation in the Fe-Pd diffusion couple is shown.

3D DOSY-TROSY to determine the translational diffusion coefficient of large protein complexes.

PubMed

Didenko, Tatiana; Boelens, Rolf; Rüdiger, Stefan G D

2011-01-01

The translational diffusion coefficient is a sensitive parameter to probe conformational changes in proteins and protein-protein interactions. Pulsed-field gradient NMR spectroscopy allows one to measure the translational diffusion with high accuracy. Two-dimensional (2D) heteronuclear NMR spectroscopy combined with diffusion-ordered spectroscopy (DOSY) provides improved resolution and therefore selectivity when compared with a conventional 1D readout. Here, we show that a combination of selective isotope labelling, 2D ¹H-¹³C methyl-TROSY (transverse relaxation-optimised spectroscopy) and DOSY allows one to study diffusion properties of large protein complexes. We propose that a 3D DOSY-heteronuclear multiple quantum coherence (HMQC) pulse sequence, that uses the TROSY effect of the HMQC sequence for ¹³C methyl-labelled proteins, is highly suitable for measuring the diffusion coefficient of large proteins. We used the 20 kDa co-chaperone p23 as model system to test this 3D DOSY-TROSY technique under various conditions. We determined the diffusion coefficient of p23 in viscous solutions, mimicking large complexes of up to 200 kDa. We found the experimental data to be in excellent agreement with theoretical predictions. To demonstrate the use for complex formation, we applied this technique to record the formation of a complex of p23 with the molecular chaperone Hsp90, which is around 200 kDa. We anticipate that 3D DOSY-TROSY will be a useful tool to study conformational changes in large protein complexes.

One-dimensional error-diffusion technique adapted for binarization of rotationally symmetric pupil filters

NASA Astrophysics Data System (ADS)

Kowalczyk, Marek; Martínez-Corral, Manuel; Cichocki, Tomasz; Andrés, Pedro

1995-02-01

Two novel algorithms for the binarization of continuous rotationally symmetric real and positive pupil filters are presented. Both algorithms are based on the one-dimensional error diffusion concept. In our numerical experiment an original gray-tone apodizer is substituted by a set of transparent and opaque concentric annular zones. Depending on the algorithm the resulting binary mask consists of either equal width or equal area zones. The diffractive behavior of binary filters is evaluated. It is shown that the filter with equal width zones gives Fraunhofer diffraction pattern more similar to that of the original gray-tone apodizer than that with equal area zones, assuming in both cases the same resolution limit of device used to print both filters.

One-Dimensional Fast Transient Simulator for Modeling Cadmium Sulfide/Cadmium Telluride Solar Cells

NASA Astrophysics Data System (ADS)

Guo, Da

Solar energy, including solar heating, solar architecture, solar thermal electricity and solar photovoltaics, is one of the primary alternative energy sources to fossil fuel. Being one of the most important techniques, significant research has been conducted in solar cell efficiency improvement. Simulation of various structures and materials of solar cells provides a deeper understanding of device operation and ways to improve their efficiency. Over the last two decades, polycrystalline thin-film Cadmium-Sulfide and Cadmium-Telluride (CdS/CdTe) solar cells fabricated on glass substrates have been considered as one of the most promising candidate in the photovoltaic technologies, for their similar efficiency and low costs when compared to traditional silicon-based solar cells. In this work a fast one dimensional time-dependent/steady-state drift-diffusion simulator, accelerated by adaptive non-uniform mesh and automatic time-step control, for modeling solar cells has been developed and has been used to simulate a CdS/CdTe solar cell. These models are used to reproduce transients of carrier transport in response to step-function signals of different bias and varied light intensity. The time-step control models are also used to help convergence in steady-state simulations where constrained material constants, such as carrier lifetimes in the order of nanosecond and carrier mobility in the order of 100 cm2/Vs, must be applied.

Wave Augmented Diffusers for Centrifugal Compressors

NASA Technical Reports Server (NTRS)

Paxson, Daniel E.; Skoch, Gary J.

1998-01-01

A conceptual device is introduced which would utilize unsteady wave motion to slow and turn flows in the diffuser section of a centrifugal compressor. The envisioned device would substantially reduce the size of conventional centrifugal diffusers by eliminating the relatively large ninety degree bend needed to turn the flow from the radial/tangential to the axial direction. The bend would be replaced by a wall and the flow would instead exit through a series of rotating ports located on a disk, adjacent to the diffuser hub, and fixed to the impeller shaft. The ports would generate both expansion and compression waves which would rapidly transition from the hub/shroud (axial) direction to the radial/tangential direction. The waves would in turn induce radial/tangential and axial flow. This paper presents a detailed description of the device. Simplified cycle analysis and performance results are presented which were obtained using a time accurate, quasi-one-dimensional CFD code with models for turning, port flow conditions, and losses due to wall shear stress. The results indicate that a periodic wave system can be established which yields diffuser performance comparable to a conventional diffuser. Discussion concerning feasibility, accuracy, and integration follow.

An experimental investigation of compressible three-dimensional boundary layer flow in annular diffusers

NASA Technical Reports Server (NTRS)

Om, Deepak; Childs, Morris E.

1987-01-01

An experimental study is described in which detailed wall pressure measurements have been obtained for compressible three-dimensional unseparated boundary layer flow in annular diffusers with and without normal shock waves. Detailed mean flow-field data were also obtained for the diffuser flow without a shock wave. Two diffuser flows with shock waves were investigated. In one case, the normal shock existed over the complete annulus whereas in the second case, the shock existed over a part of the annulus. The data obtained can be used to validate computational codes for predicting such flow fields. The details of the flow field without the shock wave show flow reversal in the circumferential direction on both inner and outer surfaces. However, there is a lag in the flow reversal between the inner nad the outer surfaces. This is an interesting feature of this flow and should be a good test for the computational codes.

One-Dimensional Singlet Exciton Diffusion in Poly(3-hexylthiophene) Crystalline Domains.

PubMed

Tamai, Yasunari; Matsuura, Yuu; Ohkita, Hideo; Benten, Hiroaki; Ito, Shinzaburo

2014-01-16

Singlet exciton dynamics in crystalline domains of regioregular poly(3-hexylthiophene) (P3HT) films was studied by transient absorption spectroscopy. Upon the selective excitation of crystalline P3HT at the absorption edge, no red shift of the singlet exciton band was observed with an elapse of time, suggesting singlet exciton dynamics in relatively homogeneous P3HT crystalline domains without downhill relaxation in the energetic disorder. Even under such selective excitation conditions, the annihilation rate coefficient γ(t) was still dependent on time, γ(t) ∝ t(-1/2), which is attributed to anisotropic exciton diffusion in P3HT crystalline domains. From the annihilation rate coefficient, the singlet exciton diffusion coefficient D and exciton diffusion length LD in the crystalline domains were evaluated to be 7.9 × 10(-3) cm(2) s(-1) and 20 nm, respectively. The origin of the time-dependent exciton dynamics is discussed in terms of dimensionality.

Phase-field modeling of two-dimensional crystal growth with anisotropic diffusion.

PubMed

Meca, Esteban; Shenoy, Vivek B; Lowengrub, John

2013-11-01

In the present article, we introduce a phase-field model for thin-film growth with anisotropic step energy, attachment kinetics, and diffusion, with second-order (thin-interface) corrections. We are mainly interested in the limit in which kinetic anisotropy dominates, and hence we study how the expected shape of a crystallite, which in the long-time limit is the kinetic Wulff shape, is modified by anisotropic diffusion. We present results that prove that anisotropic diffusion plays an important, counterintuitive role in the evolving crystal shape, and we add second-order corrections to the model that provide a significant increase in accuracy for small supersaturations. We also study the effect of different crystal symmetries and discuss the influence of the deposition rate.

The development and preliminary application of an invariant coupled diffusion and chemistry model

NASA Technical Reports Server (NTRS)

Hilst, G. R.; Donaldson, C. DUP.; Teske, M.; Contiliano, R.; Freiberg, J.

1973-01-01

In many real-world pollution chemical reaction problems, the rate of reaction problems, the rate of reaction may be greatly affected by unmixedness. An approximate closure scheme for a chemical kinetic submodel which conforms to the principles of invariant modeling and which accounts for the effects of inhomogeneous mixing over a wide range of conditions has been developed. This submodel has been coupled successfully with invariant turbulence and diffusion models, permitting calculation of two-dimensional diffusion of two reacting (isothermally) chemical species. The initial calculations indicate the ozone reactions in the wake of stratospheric aircraft will be substantially affected by the rate of diffusion of ozone into the wake, and in the early wake, by unmixedness.

Slow-fast stochastic diffusion dynamics and quasi-stationarity for diploid populations with varying size.

PubMed

Coron, Camille

2016-01-01

We are interested in the long-time behavior of a diploid population with sexual reproduction and randomly varying population size, characterized by its genotype composition at one bi-allelic locus. The population is modeled by a 3-dimensional birth-and-death process with competition, weak cooperation and Mendelian reproduction. This stochastic process is indexed by a scaling parameter K that goes to infinity, following a large population assumption. When the individual birth and natural death rates are of order K, the sequence of stochastic processes indexed by K converges toward a new slow-fast dynamics with variable population size. We indeed prove the convergence toward 0 of a fast variable giving the deviation of the population from quasi Hardy-Weinberg equilibrium, while the sequence of slow variables giving the respective numbers of occurrences of each allele converges toward a 2-dimensional diffusion process that reaches (0,0) almost surely in finite time. The population size and the proportion of a given allele converge toward a Wright-Fisher diffusion with stochastically varying population size and diploid selection. We insist on differences between haploid and diploid populations due to population size stochastic variability. Using a non trivial change of variables, we study the absorption of this diffusion and its long time behavior conditioned on non-extinction. In particular we prove that this diffusion starting from any non-trivial state and conditioned on not hitting (0,0) admits a unique quasi-stationary distribution. We give numerical approximations of this quasi-stationary behavior in three biologically relevant cases: neutrality, overdominance, and separate niches.

Research on sudden environmental pollution public service platform construction based on WebGIS

NASA Astrophysics Data System (ADS)

Bi, T. P.; Gao, D. Y.; Zhong, X. Y.

2016-08-01

In order to actualize the social sharing and service of the emergency-response information for sudden pollution accidents, the public can share the risk source information service, dangerous goods control technology service and so on, The SQL Server and ArcSDE software are used to establish a spatial database to restore all kinds of information including risk sources, hazardous chemicals and handling methods in case of accidents. Combined with Chinese atmospheric environmental assessment standards, the SCREEN3 atmospheric dispersion model and one-dimensional liquid diffusion model are established to realize the query of related information and the display of the diffusion effect under B/S structure. Based on the WebGIS technology, C#.Net language is used to develop the sudden environmental pollution public service platform. As a result, the public service platform can make risk assessments and provide the best emergency processing services.

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.

Microstructural Analysis and Transport Properties of Thermally Sprayed Multiple-Layer Ceramic Coatings

NASA Astrophysics Data System (ADS)

Wang, Hsin; Muralidharan, Govindarajan; Leonard, Donovan N.; Haynes, J. Allen; Porter, Wallace D.; England, Roger D.; Hays, Michael; Dwivedi, Gopal; Sampath, Sanjay

2018-02-01

Multilayer, graded ceramic/metal coatings were prepared by an air plasma spray method on Ti-6Al-4V, 4140 steel and graphite substrates. The coatings were designed to provide thermal barriers for diesel engine pistons to operate at higher temperatures with improved thermal efficiency and cleaner emissions. A systematic, progressive variation in the mixture of yttria-stabilized zirconia and bondcoat alloys (NiCoCrAlYHfSi) was designed to provide better thermal expansion match with the substrate and to improve thermal shock resistance and cycle life. Heat transfer through the layers was evaluated by a flash diffusivity technique based on a model of one-dimensional heat flow. The aging effect of the as-sprayed coatings was captured during diffusivity measurements, which included one heating and cooling cycle. The hysteresis of thermal diffusivity due to aging was not observed after 100-h annealing at 800 °C. The measurements of coatings on substrate and freestanding coatings allowed the influence of interface resistance to be evaluated. The microstructure of the multilayer coating was examined using scanning electron microscope and electron probe microanalysis.

Isotopic dependence of fusion enhancement of various heavy ion systems using energy dependent Woods-Saxon potential

NASA Astrophysics Data System (ADS)

Gautam, Manjeet Singh

2015-01-01

In the present work, the fusion of symmetric and asymmetric projectile-target combinations are deeply analyzed within the framework of energy dependent Woods-Saxon potential model (EDWSP model) in conjunction with one dimensional Wong formula and the coupled channel code CCFULL. The neutron transfer channels and the inelastic surface excitations of collision partners are dominating mode of couplings and the coupling of relative motion of colliding nuclei to such relevant internal degrees of freedom produces a significant fusion enhancement at sub-barrier energies. It is quite interesting that the effects of dominant intrinsic degrees of freedom such as multi-phonon vibrational states, neutron transfer channels and proton transfer channels can be simulated by introducing the energy dependence in the nucleus-nucleus potential (EDWSP model). In the EDWSP model calculations, a wide range of diffuseness parameter ranging from a = 0.85 fm to a = 0.97 fm, which is much larger than a value (a = 0.65 fm) extracted from the elastic scattering data, is needed to reproduce sub-barrier fusion data. However, such diffuseness anomaly, which might be an artifact of some dynamical effects, has been resolved by trajectory fluctuation dissipation (TFD) model wherein the resulting nucleus-nucleus potential possesses normal diffuseness parameter.

VALDRIFT 1.0: A valley atmospheric dispersion model with deposition

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

Allwine, K.J.; Bian, X.; Whiteman, C.D.

1995-05-01

VALDRIFT version 1.0 is an atmospheric transport and diffusion model for use in well-defined mountain valleys. It is designed to determine the extent of ddft from aedal pesticide spraying activities, but can also be applied to estimate the transport and diffusion of various air pollutants in valleys. The model is phenomenological -- that is, the dominant meteorological processes goveming the behavior of the valley atmosphere are formulated explicitly in the model, albeit in a highly parameterized fashion. The key meteorological processes treated are: (1) nonsteady and nonhomogeneous along-valley winds and turbulent diffusivities, (2) convective boundary layer growth, (3) inversion descent,more » (4) noctumal temperature inversion breakup, and (5) subsidence. The model is applicable under relatively cloud-free, undisturbed synoptic conditions and is configured to operate through one diumal cycle for a single valley. The inputs required are the valley topographical characteristics, pesticide release rate as a function of time and space, along-valley wind speed as a function of time and space, temperature inversion characteristics at sunrise, and sensible heat flux as a function of time following sunrise. Default values are provided for certain inputs in the absence of detailed observations. The outputs are three-dimensional air concentration and ground-level deposition fields as a function of time.« less

The implementation and validation of improved landsurface hydrology in an atmospheric general circulation model

NASA Technical Reports Server (NTRS)

Johnson, Kevin D.; Entekhabi, Dara; Eagleson, Peter S.

1991-01-01

Landsurface hydrological parameterizations are implemented in the NASA Goddard Institute for Space Studies (GISS) General Circulation Model (GCM). These parameterizations are: (1) runoff and evapotranspiration functions that include the effects of subgrid scale spatial variability and use physically based equations of hydrologic flux at the soil surface, and (2) a realistic soil moisture diffusion scheme for the movement of water in the soil column. A one dimensional climate model with a complete hydrologic cycle is used to screen the basic sensitivities of the hydrological parameterizations before implementation into the full three dimensional GCM. Results of the final simulation with the GISS GCM and the new landsurface hydrology indicate that the runoff rate, especially in the tropics is significantly improved. As a result, the remaining components of the heat and moisture balance show comparable improvements when compared to observations. The validation of model results is carried from the large global (ocean and landsurface) scale, to the zonal, continental, and finally the finer river basin scales.

Galactic Cosmic-ray Transport in the Global Heliosphere: A Four-Dimensional Stochastic Model

NASA Astrophysics Data System (ADS)

Florinski, V.

2009-04-01

We study galactic cosmic-ray transport in the outer heliosphere and heliosheath using a newly developed transport model based on stochastic integration of the phase-space trajectories of Parker's equation. The model employs backward integration of the diffusion-convection transport equation using Ito calculus and is four-dimensional in space+momentum. We apply the model to the problem of galactic proton transport in the heliosphere during a negative solar minimum. Model results are compared with the Voyager measurements of galactic proton radial gradients and spectra in the heliosheath. We show that the heliosheath is not as efficient in diverting cosmic rays during solar minima as predicted by earlier two-dimensional models.

Tritium permeation model for plasma facing components

NASA Astrophysics Data System (ADS)

Longhurst, G. R.

1992-12-01

This report documents the development of a simplified one-dimensional tritium permeation and retention model. The model makes use of the same physical mechanisms as more sophisticated, time-transient codes such as implantation, recombination, diffusion, trapping and thermal gradient effects. It takes advantage of a number of simplifications and approximations to solve the steady-state problem and then provides interpolating functions to make estimates of intermediate states based on the steady-state solution. The model is developed for solution using commercial spread-sheet software such as Lotus 123. Comparison calculations are provided with the verified and validated TMAP4 transient code with good agreement. Results of calculations for the ITER CDA diverter are also included.

Dynamic coupling between coordinates in a model for biomolecular isomerization

NASA Astrophysics Data System (ADS)

Ma, Ao; Nag, Ambarish; Dinner, Aaron R.

2006-04-01

To understand a complex reaction, it is necessary to project the dynamics of the system onto a low-dimensional subspace of physically meaningful coordinates. We recently introduced an automatic method for identifying coordinates that relate closely to stable-state commitment probabilities and successfully applied it to a model for biomolecular isomerization, the C7eq→αR transition of the alanine dipeptide [A. Ma and A. R. Dinner, J. Phys. Chem. B 109, 6769 (2005)]. Here, we explore approximate means for estimating diffusion tensors for systems subject to restraints in one and two dimensions and then use the results together with an extension of Kramers theory for unimolecular reaction rates [A. Berezhkovskii and A. Szabo, J. Chem. Phys. 122, 014503 (2005)] to show explicitly that both the potential of mean force and the diffusion tensor are essential for describing the dynamics of the alanine dipeptide quantitatively. In particular, the signficance of off-diagonal elements of the diffusion tensor suggests that the coordinates of interest are coupled by the hydrodynamic-like response of the bath of remaining degrees of freedom.

Critical spreading dynamics of parity conserving annihilating random walks with power-law branching

NASA Astrophysics Data System (ADS)

Laise, T.; dos Anjos, F. C.; Argolo, C.; Lyra, M. L.

2018-09-01

We investigate the critical spreading of the parity conserving annihilating random walks model with Lévy-like branching. The random walks are considered to perform normal diffusion with probability p on the sites of a one-dimensional lattice, annihilating in pairs by contact. With probability 1 - p, each particle can also produce two offspring which are placed at a distance r from the original site following a power-law Lévy-like distribution P(r) ∝ 1 /rα. We perform numerical simulations starting from a single particle. A finite-time scaling analysis is employed to locate the critical diffusion probability pc below which a finite density of particles is developed in the long-time limit. Further, we estimate the spreading dynamical exponents related to the increase of the average number of particles at the critical point and its respective fluctuations. The critical exponents deviate from those of the counterpart model with short-range branching for small values of α. The numerical data suggest that continuously varying spreading exponents sets up while the branching process still results in a diffusive-like spreading.

Multi-Dimensional, Mesoscopic Monte Carlo Simulations of Inhomogeneous Reaction-Drift-Diffusion Systems on Graphics-Processing Units

PubMed Central

Vigelius, Matthias; Meyer, Bernd

2012-01-01

For many biological applications, a macroscopic (deterministic) treatment of reaction-drift-diffusion systems is insufficient. Instead, one has to properly handle the stochastic nature of the problem and generate true sample paths of the underlying probability distribution. Unfortunately, stochastic algorithms are computationally expensive and, in most cases, the large number of participating particles renders the relevant parameter regimes inaccessible. In an attempt to address this problem we present a genuine stochastic, multi-dimensional algorithm that solves the inhomogeneous, non-linear, drift-diffusion problem on a mesoscopic level. Our method improves on existing implementations in being multi-dimensional and handling inhomogeneous drift and diffusion. The algorithm is well suited for an implementation on data-parallel hardware architectures such as general-purpose graphics processing units (GPUs). We integrate the method into an operator-splitting approach that decouples chemical reactions from the spatial evolution. We demonstrate the validity and applicability of our algorithm with a comprehensive suite of standard test problems that also serve to quantify the numerical accuracy of the method. We provide a freely available, fully functional GPU implementation. Integration into Inchman, a user-friendly web service, that allows researchers to perform parallel simulations of reaction-drift-diffusion systems on GPU clusters is underway. PMID:22506001

On the cross-field diffusion of ions in one- and two-dimensional hybrid simulations of collisionless shocks

NASA Technical Reports Server (NTRS)

Giacalone, Joe

1994-01-01

It can be demonstrated analytically that under certain geometries used in numerical simulations of collisionless shocks in which there is at least one ignorable spatial coordinate, the transport of particles across the magnetic field is essentially zero. This notion is tested using one- and two-dimensional hybrid simulations (kinetic ions/fluid electrons). We find, as the theorem predicts, the particles treated kinetically are tied to the same field line on which they start.

A GENERALIZED TWO-COMPONENT MODEL OF SOLAR WIND TURBULENCE AND AB INITIO DIFFUSION MEAN-FREE PATHS AND DRIFT LENGTHSCALES OF COSMIC RAYS

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

Wiengarten, T.; Fichtner, H.; Kleimann, J.

2016-12-10

We extend a two-component model for the evolution of fluctuations in the solar wind plasma so that it is fully three-dimensional (3D) and also coupled self-consistently to the large-scale magnetohydrodynamic equations describing the background solar wind. The two classes of fluctuations considered are a high-frequency parallel-propagating wave-like piece and a low-frequency quasi-two-dimensional component. For both components, the nonlinear dynamics is dominanted by quasi-perpendicular spectral cascades of energy. Driving of the fluctuations by, for example, velocity shear and pickup ions is included. Numerical solutions to the new model are obtained using the Cronos framework, and validated against previous simpler models. Comparing results frommore » the new model with spacecraft measurements, we find improved agreement relative to earlier models that employ prescribed background solar wind fields. Finally, the new results for the wave-like and quasi-two-dimensional fluctuations are used to calculate ab initio diffusion mean-free paths and drift lengthscales for the transport of cosmic rays in the turbulent solar wind.« less

Particle model for nonlocal heat transport in fusion plasmas.

PubMed

Bufferand, H; Ciraolo, G; Ghendrih, Ph; Lepri, S; Livi, R

2013-02-01

We present a simple stochastic, one-dimensional model for heat transfer in weakly collisional media as fusion plasmas. Energies of plasma particles are treated as lattice random variables interacting with a rate inversely proportional to their energy schematizing a screened Coulomb interaction. We consider both the equilibrium (microcanonical) and nonequilibrium case in which the system is in contact with heat baths at different temperatures. The model exhibits a characteristic length of thermalization that can be associated with an interaction mean free path and one observes a transition from ballistic to diffusive regime depending on the average energy of the system. A mean-field expression for heat flux is deduced from system heat transport properties. Finally, it is shown that the nonequilibrium steady state is characterized by long-range correlations.

A first principles kinetic Monte Carlo investigation of the adsorption and mobility of gadolinium on the (100) surface of tungsten

NASA Astrophysics Data System (ADS)

Samin, Adib J.; Zhang, Jinsuo

2017-05-01

An accurate characterization of lanthanide adsorption and mobility on tungsten surfaces is important for pyroprocessing. In the present study, the adsorption and diffusion of gadolinium on the (100) surface of tungsten was investigated. It was found that the hollow sites were the most energetically favorable for the adsorption. It was further observed that a magnetic moment was induced following the adsorption of gadolinium on the tungsten surface and that the system with adsorbed hollow sites had the largest magnetization. A pathway for the surface diffusion of gadolinium was determined to occur by hopping between the nearest neighbor hollow sites via the bridge site and the activation energy for the hop was calculated to be 0.75 eV. The surface diffusion process was further assessed using two distinct kinetic Monte Carlo models; one that accounted for lateral adsorbate interactions up to the second nearest neighbor and one that did not account for such interatomic interactions in the adlayer. When the lateral interactions were included in the simulations, the diffusivity was observed to have a strong dependence on coverage (for the coverage values being studied). The effects of lateral interactions were further observed in a one-dimensional simulation of the diffusion equation where the asymmetry in the surface coverage profile upon its approach to a steady state distribution was clear in comparison with the simulations which did not account for those interactions.

Three-dimensional structure of Erwinia carotovora L-asparaginase

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

Kislitsyn, Yu. A.; Kravchenko, O. V.; Nikonov, S. V.

2006-10-15

Three-dimensional structure of Erwinia carotovora L-asparaginase, which has antitumor activity and is used for the treatment of acute lymphoblastic leukemia, was solved at 3 A resolution and refined to R{sub cryst} = 20% and R{sub free} = 28%. Crystals of recombinant Erwinia carotovora L-asparaginase were grown by the hanging-drop vapor-diffusion method from protein solutions in a HEPES buffer (pH 6.5) and PEG MME 5000 solutions in a cacodylate buffer (pH 6.5) as the precipitant. Three-dimensional X-ray diffraction data were collected up to 3 A resolution from one crystal at room temperature. The structure was solved by the molecular replacement methodmore » using the coordinates of Erwinia chrysanthemi L-asparaginase as the starting model. The coordinates refined with the use of the CNS program package were deposited in the Protein Data Bank (PDB code 1ZCF)« less

Numerical solution of a multi-ion one-potential model for electroosmotic flow in two-dimensional rectangular microchannels.

PubMed

Van Theemsche, Achim; Deconinck, Johan; Van den Bossche, Bart; Bortels, Leslie

2002-10-01

A new more general numerical model for the simulation of electrokinetic flow in rectangular microchannels is presented. The model is based on the dilute solution model and the Navier-Stokes equations and has been implemented in a finite-element-based C++ code. The model includes the ion distribution in the Helmholtz double layer and considers only one single electrical' potential field variable throughout the domain. On a charged surface(s) the surface charge density, which is proportional to the local electrical field, is imposed. The zeta potential results, then, from this boundary condition and depends on concentrations, temperature, ion valence, molecular diffusion coefficients, and geometric conditions. Validation cases show that the model predicts accurately known analytical results, also for geometries having dimensions comparable to the Debye length. As a final study, the electro-osmotic flow in a controlled cross channel is investigated.

In Situ Three-Dimensional Reciprocal-Space Mapping of Diffuse Scattering Intensity Distribution and Data Analysis for Precursor Phenomenon in Shape-Memory Alloy

NASA Astrophysics Data System (ADS)

Cheng, Tian-Le; Ma, Fengde D.; Zhou, Jie E.; Jennings, Guy; Ren, Yang; Jin, Yongmei M.; Wang, Yu U.

2012-01-01

Diffuse scattering contains rich information on various structural disorders, thus providing a useful means to study the nanoscale structural deviations from the average crystal structures determined by Bragg peak analysis. Extraction of maximal information from diffuse scattering requires concerted efforts in high-quality three-dimensional (3D) data measurement, quantitative data analysis and visualization, theoretical interpretation, and computer simulations. Such an endeavor is undertaken to study the correlated dynamic atomic position fluctuations caused by thermal vibrations (phonons) in precursor state of shape-memory alloys. High-quality 3D diffuse scattering intensity data around representative Bragg peaks are collected by using in situ high-energy synchrotron x-ray diffraction and two-dimensional digital x-ray detector (image plate). Computational algorithms and codes are developed to construct the 3D reciprocal-space map of diffuse scattering intensity distribution from the measured data, which are further visualized and quantitatively analyzed to reveal in situ physical behaviors. Diffuse scattering intensity distribution is explicitly formulated in terms of atomic position fluctuations to interpret the experimental observations and identify the most relevant physical mechanisms, which help set up reduced structural models with minimal parameters to be efficiently determined by computer simulations. Such combined procedures are demonstrated by a study of phonon softening phenomenon in precursor state and premartensitic transformation of Ni-Mn-Ga shape-memory alloy.

Two-dimensional atmospheric transport and chemistry model - Numerical experiments with a new advection algorithm

NASA Technical Reports Server (NTRS)

Shia, Run-Lie; Ha, Yuk Lung; Wen, Jun-Shan; Yung, Yuk L.

1990-01-01

Extensive testing of the advective scheme proposed by Prather (1986) has been carried out in support of the California Institute of Technology-Jet Propulsion Laboratory two-dimensional model of the middle atmosphere. The original scheme is generalized to include higher-order moments. In addition, it is shown how well the scheme works in the presence of chemistry as well as eddy diffusion. Six types of numerical experiments including simple clock motion and pure advection in two dimensions have been investigated in detail. By comparison with analytic solutions, it is shown that the new algorithm can faithfully preserve concentration profiles, has essentially no numerical diffusion, and is superior to a typical fourth-order finite difference scheme.

A sensitivity analysis of low salinity habitats simulated by a hydrodynamic model in the Manatee River estuary in Florida, USA

NASA Astrophysics Data System (ADS)

Chen, XinJian

2012-06-01

This paper presents a sensitivity study of simulated availability of low salinity habitats by a hydrodynamic model for the Manatee River estuary located in the southwest portion of the Florida peninsula. The purpose of the modeling study was to establish a regulatory minimum freshwater flow rate required to prevent the estuarine ecosystem from significant harm. The model used in the study was a multi-block model that dynamically couples a three-dimensional (3D) hydrodynamic model with a laterally averaged (2DV) hydrodynamic model. The model was calibrated and verified against measured real-time data of surface elevation and salinity at five stations during March 2005-July 2006. The calibrated model was then used to conduct a series of scenario runs to investigate effects of the flow reduction on salinity distributions in the Manatee River estuary. Based on simulated salinity distribution in the estuary, water volumes, bottom areas and shoreline lengths for salinity less than certain predefined values were calculated and analyzed to help establish the minimum freshwater flow rate for the estuarine system. The sensitivity analysis conducted during the modeling study for the Manatee River estuary examined effects of the bottom roughness, ambient vertical eddy viscosity/diffusivity, horizontal eddy viscosity/diffusivity, and ungauged flow on the model results and identified the relative importance of these model parameters (input data) to the outcome of the availability of low salinity habitats. It is found that the ambient vertical eddy viscosity/diffusivity is the most influential factor controlling the model outcome, while the horizontal eddy viscosity/diffusivity is the least influential one.

Heat transfer to and from vegetated surfaces - An analytical method for the bulk exchange coefficients

NASA Technical Reports Server (NTRS)

Massman, William J.

1987-01-01

The semianalytical model outlined in a previous study (Massman, 1987) to describe momentum exchange between the atmosphere and vegetated surfaces is extended to include the exchange of heat. The methods employed are based on one-dimensional turbulent diffusivities, and use analytical solutions to the steady-state diffusion equation. The model is used to assess the influence that the canopy foliage structure and density, the wind profile structure within the canopy, and the shelter factor can have upon the inverse surface Stanton number (kB exp -1), as well as to explore the consequences of introducing a scalar displacement height which can be different from the momentum displacement height. In general, the triangular foliage area density function gives results which agree more closely with observations than that for constant foliage area density. The intended application of this work is for parameterizing the bulk aerodynamic resistances for heat and momentum exchange for use within large-scale models of plant-atmosphere exchanges.

The structure of mass-loading shocks. [interaction of solar wind with cometary coma or local interstellar medium using two-fluid model

NASA Technical Reports Server (NTRS)

Zank, G. P.; Khabibrakhmanov, I. KH.; Story, T.

1993-01-01

A new two-fluid model which describes mass loading in the solar wind (e.g., the interaction of the solar wind with a cometary coma or the local interstellar medium) is presented. The self-consistent back-reaction of the mass-loaded ions is included through their effective scattering in low-frequency MHD turbulence and the invocation of a diffusive approximation. Such an approximation has the advantage of introducing self-consistent dissipation coefficients into the governing equations, thereby facilitating the investigation of the internal structure of shocks in mass-loading environments. To illustrate the utility of the new model, we consider the structure of cometary shocks in the hypersonic one-dimensional limit, finding that the incoming solar wind is slowed by both mass loading and the development of a large cometary ion pressure gradient. The shock is broadened and smoothed by the cometary ions with a thickness of the order of the cometary ion diffusion scale.

Molecular sled is an eleven-amino acid vehicle facilitating biochemical interactions via sliding components along DNA

DOE PAGES

Mangel, Walter F.; McGrath, William J.; Xiong, Kan; ...

2016-02-02

Recently, we showed the adenovirus proteinase interacts productively with its protein substrates in vitro and in vivo in nascent virus particles via one-dimensional diffusion along the viral DNA. The mechanism by which this occurs has heretofore been unknown. We show sliding of these proteins along DNA occurs on a new vehicle in molecular biology, a ‘molecular sled’ named pVIc. This 11-amino acid viral peptide binds to DNA independent of sequence. pVIc slides on DNA, exhibiting the fastest one-dimensional diffusion constant, 26±1.8 × 10 6 (bp) 2 s −1. pVIc is a ‘molecular sled,’ because it can slide heterologous cargos along DNA,more » for example, a streptavidin tetramer. Similar peptides, for example, from the C terminus of β-actin or NLSIII of the p53 protein, slide along DNA. Finally, characteristics of the ‘molecular sled’ in its milieu (virion, nucleus) have implications for how proteins in the nucleus of cells interact and imply a new form of biochemistry, one-dimensional biochemistry.« less

Cellular automaton formulation of passive scalar dynamics

NASA Technical Reports Server (NTRS)

Chen, Hudong; Matthaeus, William H.

1987-01-01

Cellular automata modeling of the advection of a passive scalar in a two-dimensional flow is examined in the context of discrete lattice kinetic theory. It is shown that if the passive scalar is represented by tagging or 'coloring' automation particles a passive advection-diffusion equation emerges without use of perturbation expansions. For the specific case of the hydrodynamic lattice gas model of Frisch et al. (1986), the diffusion coefficient is calculated by perturbation.

Investigation of Sorption Mass Transfer Models Using Synthetic Soils

DTIC Science & Technology

1996-12-01

Goltz for his useful comments regarding my review of the literature. His comments served to enhance the readability of my review as well as the...versions. Researchers ( Goltz , 1986; Wu and Gschwend, 1986; Ball and Roberts, 1991b; Young and Ball, 1995) have applied Fick’s second law of diffusion...Values," Environmental Science and Technology, Vol. 21, pp. 243-248, 1987. Goltz , M.N., Three-Dimensional Analytical Modeling of Diffusion-limited

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

Kim, Sang Beom; Dsilva, Carmeline J.; Debenedetti, Pablo G., E-mail: pdebene@princeton.edu

Understanding the mechanisms by which proteins fold from disordered amino-acid chains to spatially ordered structures remains an area of active inquiry. Molecular simulations can provide atomistic details of the folding dynamics which complement experimental findings. Conventional order parameters, such as root-mean-square deviation and radius of gyration, provide structural information but fail to capture the underlying dynamics of the protein folding process. It is therefore advantageous to adopt a method that can systematically analyze simulation data to extract relevant structural as well as dynamical information. The nonlinear dimensionality reduction technique known as diffusion maps automatically embeds the high-dimensional folding trajectories inmore » a lower-dimensional space from which one can more easily visualize folding pathways, assuming the data lie approximately on a lower-dimensional manifold. The eigenvectors that parametrize the low-dimensional space, furthermore, are determined systematically, rather than chosen heuristically, as is done with phenomenological order parameters. We demonstrate that diffusion maps can effectively characterize the folding process of a Trp-cage miniprotein. By embedding molecular dynamics simulation trajectories of Trp-cage folding in diffusion maps space, we identify two folding pathways and intermediate structures that are consistent with the previous studies, demonstrating that this technique can be employed as an effective way of analyzing and constructing protein folding pathways from molecular simulations.« less

Models of MOS and SOS devices

NASA Technical Reports Server (NTRS)

Gassaway, J. D.; Mahmood, Q.; Trotter, J. D.

1980-01-01

Quarterly report describes progress in three programs: dc sputtering machine for aluminum and aluminum alloys; two dimensional computer modeling of MOS transistors; and development of computer techniques for calculating redistribution diffusion of dopants in silicon on sapphire films.

Rectification of depth measurement using pulsed thermography with logarithmic peak second derivative method

NASA Astrophysics Data System (ADS)

Li, Xiaoli; Zeng, Zhi; Shen, Jingling; Zhang, Cunlin; Zhao, Yuejin

2018-03-01

Logarithmic peak second derivative (LPSD) method is the most popular method for depth prediction in pulsed thermography. It is widely accepted that this method is independent of defect size. The theoretical model for LPSD method is based on the one-dimensional solution of heat conduction without considering the effect of defect size. When a decay term considering defect aspect ratio is introduced into the solution to correct the three-dimensional thermal diffusion effect, we found that LPSD method is affected by defect size by analytical model. Furthermore, we constructed the relation between the characteristic time of LPSD method and defect aspect ratio, which was verified with the experimental results of stainless steel and glass fiber reinforced plate (GFRP) samples. We also proposed an improved LPSD method for depth prediction when the effect of defect size was considered, and the rectification results of stainless steel and GFRP samples were presented and discussed.

USER'S MANUAL FOR THE INSTREAM SEDIMENT-CONTAMINANT TRANSPORT MODEL SERATRA

EPA Science Inventory

This manual guides the user in applying the sediment-contaminant transport model SERATRA. SERATRA is an unsteady, two-dimensional code that uses the finite element computation method with the Galerkin weighted residual technique. The model has general convection-diffusion equatio...

One-dimensional pore pressure diffusion of different grain-fluid mixtures

NASA Astrophysics Data System (ADS)

von der Thannen, Magdalena; Kaitna, Roland

2015-04-01

During the release and the flow of fully saturated debris, non-hydrostatic fluid pressure can build up and probably dissipate during the event. This excess fluid pressure has a strong influence on the flow and deposition behaviour of debris flows. Therefore, we investigate the influence of mixture composition on the dissipation of non-hydrostatic fluid pressures. For this we use a cylindrical pipe of acrylic glass with installed pore water pressure sensors in different heights and measure the evolution of the pore water pressure over time. Several mixtures with variable content of fine sediment (silt and clay) and variable content of coarse sediment (with fixed relative fractions of grains between 2 and 32 mm) are tested. For the fines two types of clay (smectite and kaolinite) and loam (Stoober Lehm) are used. The analysis is based on the one-dimensional consolidation theory which uses a diffusion coefficient D to model the decay of excess fluid pressure over time. Starting from artificially induced super-hydrostatic fluid pressures, we find dissipation coefficients ranging from 10-5 m²/s for liquid mixtures to 10-8 m²/s for viscous mixtures. The results for kaolinite and smectite are quite similar. For our limited number of mixtures the effect of fines content is more pronounced than the effect of different amounts of coarse particles.

Bursting Regimes in a Reaction-Diffusion System with Action Potential-Dependent Equilibrium

PubMed Central

Meier, Stephen R.; Lancaster, Jarrett L.; Starobin, Joseph M.

2015-01-01

The equilibrium Nernst potential plays a critical role in neural cell dynamics. A common approximation used in studying electrical dynamics of excitable cells is that the ionic concentrations inside and outside the cell membranes act as charge reservoirs and remain effectively constant during excitation events. Research into brain electrical activity suggests that relaxing this assumption may provide a better understanding of normal and pathophysiological functioning of the brain. In this paper we explore time-dependent ionic concentrations by allowing the ion-specific Nernst potentials to vary with developing transmembrane potential. As a specific implementation, we incorporate the potential-dependent Nernst shift into a one-dimensional Morris-Lecar reaction-diffusion model. Our main findings result from a region in parameter space where self-sustaining oscillations occur without external forcing. Studying the system close to the bifurcation boundary, we explore the vulnerability of the system with respect to external stimulations which disrupt these oscillations and send the system to a stable equilibrium. We also present results for an extended, one-dimensional cable of excitable tissue tuned to this parameter regime and stimulated, giving rise to complex spatiotemporal pattern formation. Potential applications to the emergence of neuronal bursting in similar two-variable systems and to pathophysiological seizure-like activity are discussed. PMID:25823018

3-D Modeling of Double-Diffusive Convection During Directional Solidification of a Non-Dilute Alloy with Application to the HgCdTe Growth Under Microgravity Conditions

NASA Technical Reports Server (NTRS)

Bune, Andris V.; Gillies, Donald C.; Lehoczky, Sandor L.

1998-01-01

A numerical calculation for a non-dilute alloy solidification was performed using the FIDAP finite element code. For low growth velocities plane front solidification occurs. The location and the shape of the interface was determined using melting temperatures from the HgCdTe liquidus curve. The low thermal conductivity of the solid HgCdTe causes thermal short circuit through the ampoule walls, resulting in curved isotherms in the vicinity of the interface. Double-diffusive convection in the melt is caused by radial temperature gradients and by material density inversion with temperature. Cooling from below and the rejection at the solid-melt interface of the heavier HgTe-rich solute each tend to reduce convection. Because of these complicating factors dimensional rather then non-dimensional modeling was performed. Estimates of convection contributions for various gravity conditions was performed parametrically. For gravity levels higher then 1 0 -7 of earth's gravity it was found that the maximum convection velocity is extremely sensitive to gravity vector orientation and can be reduced at least by factor of 50% for precise orientation of the ampoule in the microgravity environment. The predicted interface shape is in agreement with one obtained experimentally by quenching. The results of 3-D modeling are compared with previous 2-D finding. A video film featuring melt convection will be presented.

A new methodology to determine kinetic parameters for one- and two-step chemical models

NASA Technical Reports Server (NTRS)

Mantel, T.; Egolfopoulos, F. N.; Bowman, C. T.

1996-01-01

In this paper, a new methodology to determine kinetic parameters for simple chemical models and simple transport properties classically used in DNS of premixed combustion is presented. First, a one-dimensional code is utilized to performed steady unstrained laminar methane-air flame in order to verify intrinsic features of laminar flames such as burning velocity and temperature and concentration profiles. Second, the flame response to steady and unsteady strain in the opposed jet configuration is numerically investigated. It appears that for a well determined set of parameters, one- and two-step mechanisms reproduce the extinction limit of a laminar flame submitted to a steady strain. Computations with the GRI-mech mechanism (177 reactions, 39 species) and multicomponent transport properties are used to validate these simplified models. A sensitivity analysis of the preferential diffusion of heat and reactants when the Lewis number is close to unity indicates that the response of the flame to an oscillating strain is very sensitive to this number. As an application of this methodology, the interaction between a two-dimensional vortex pair and a premixed laminar flame is performed by Direct Numerical Simulation (DNS) using the one- and two-step mechanisms. Comparison with the experimental results of Samaniego et al. (1994) shows a significant improvement in the description of the interaction when the two-step model is used.

Three dimensional flow field inside compressor rotor, including blade boundary layers

NASA Technical Reports Server (NTRS)

Galmes, J. M.; Pouagere, M.; Lakshminarayana, B.

1982-01-01

The Reynolds stress equation, pressure strain correlation, and dissipative terms and diffusion are discussed in relation to turbulence modelling using the Reynolds stress model. Algebraic modeling of Reynolds stresses and calculation of the boundary layer over an axial cylinder are examined with regards to the kinetic energy model for turbulence modelling. The numerical analysis of blade and hub wall boundary layers, and an experimental study of rotor blade boundary layer in an axial flow compressor rotor are discussed. The Patankar-Spalding numerical method for two dimensional boundary layers is included.

Turing mechanism for homeostatic control of synaptic density during C. elegans growth

NASA Astrophysics Data System (ADS)

Brooks, Heather A.; Bressloff, Paul C.

2017-07-01

We propose a mechanism for the homeostatic control of synapses along the ventral cord of Caenorhabditis elegans during development, based on a form of Turing pattern formation on a growing domain. C. elegans is an important animal model for understanding cellular mechanisms underlying learning and memory. Our mathematical model consists of two interacting chemical species, where one is passively diffusing and the other is actively trafficked by molecular motors, which switch between forward and backward moving states (bidirectional transport). This differs significantly from the standard mechanism for Turing pattern formation based on the interaction between fast and slow diffusing species. We derive evolution equations for the chemical concentrations on a slowly growing one-dimensional domain, and use numerical simulations to demonstrate the insertion of new concentration peaks as the length increases. Taking the passive component to be the protein kinase CaMKII and the active component to be the glutamate receptor GLR-1, we interpret the concentration peaks as sites of new synapses along the length of C. elegans, and thus show how the density of synaptic sites can be maintained.

MODELED MESOSCALE METEOROLOGICAL FIELDS WITH FOUR-DIMENSIONAL DATA ASSIMILATION IN REGIONAL SCALE AIR QUALITY MODELS

EPA Science Inventory

This paper addresses the need to increase the temporal and spatial resolution of meteorological data currently used in air quality simulation models, AQSMs. ransport and diffusion parameters including mixing heights and stability used in regulatory air quality dispersion models a...

Investigation of Three-Dimensional Unsteady Flow Characteristics in Transonic Diffusers

NASA Astrophysics Data System (ADS)

Proshchanka, Dzianis; Yonezawa, Koichi; Tsujimoto, Yoshinobu

Three-dimensional characteristics of unsteady flow in supercritical transonic diffuser are investigated. For various pressure ratios three-dimensional flow containing a normal shock/turbulent boundary layer interaction regions with shockwave and pseudo-shockwaves fluctuating in longitudinal and spanwise directions is observed. Experimental and numerical investigations show details of the flowfield in the vicinity of terminal shock, interaction regions and downstream turbulent unsteady flow. Spectral analysis of pressure fluctuations reveals existence of two characteristic frequencies attributed to the shockwave fluctuation in longitudinal direction for the lower frequency case and acoustic resonance in spanwise direction for the higher one. Vortices appear at each corner in transversal sections modifying the core flow. As a result, size and depth of longitudinal and vertical penetration of separation regions impelled by the terminal shock is either increased or decreased.

Semi-implicit integration factor methods on sparse grids for high-dimensional systems

NASA Astrophysics Data System (ADS)

Wang, Dongyong; Chen, Weitao; Nie, Qing

2015-07-01

Numerical methods for partial differential equations in high-dimensional spaces are often limited by the curse of dimensionality. Though the sparse grid technique, based on a one-dimensional hierarchical basis through tensor products, is popular for handling challenges such as those associated with spatial discretization, the stability conditions on time step size due to temporal discretization, such as those associated with high-order derivatives in space and stiff reactions, remain. Here, we incorporate the sparse grids with the implicit integration factor method (IIF) that is advantageous in terms of stability conditions for systems containing stiff reactions and diffusions. We combine IIF, in which the reaction is treated implicitly and the diffusion is treated explicitly and exactly, with various sparse grid techniques based on the finite element and finite difference methods and a multi-level combination approach. The overall method is found to be efficient in terms of both storage and computational time for solving a wide range of PDEs in high dimensions. In particular, the IIF with the sparse grid combination technique is flexible and effective in solving systems that may include cross-derivatives and non-constant diffusion coefficients. Extensive numerical simulations in both linear and nonlinear systems in high dimensions, along with applications of diffusive logistic equations and Fokker-Planck equations, demonstrate the accuracy, efficiency, and robustness of the new methods, indicating potential broad applications of the sparse grid-based integration factor method.

Stochastic simulation of reaction-diffusion systems: A fluctuating-hydrodynamics approach

NASA Astrophysics Data System (ADS)

Kim, Changho; Nonaka, Andy; Bell, John B.; Garcia, Alejandro L.; Donev, Aleksandar

2017-03-01

We develop numerical methods for stochastic reaction-diffusion systems based on approaches used for fluctuating hydrodynamics (FHD). For hydrodynamic systems, the FHD formulation is formally described by stochastic partial differential equations (SPDEs). In the reaction-diffusion systems we consider, our model becomes similar to the reaction-diffusion master equation (RDME) description when our SPDEs are spatially discretized and reactions are modeled as a source term having Poisson fluctuations. However, unlike the RDME, which becomes prohibitively expensive for an increasing number of molecules, our FHD-based description naturally extends from the regime where fluctuations are strong, i.e., each mesoscopic cell has few (reactive) molecules, to regimes with moderate or weak fluctuations, and ultimately to the deterministic limit. By treating diffusion implicitly, we avoid the severe restriction on time step size that limits all methods based on explicit treatments of diffusion and construct numerical methods that are more efficient than RDME methods, without compromising accuracy. Guided by an analysis of the accuracy of the distribution of steady-state fluctuations for the linearized reaction-diffusion model, we construct several two-stage (predictor-corrector) schemes, where diffusion is treated using a stochastic Crank-Nicolson method, and reactions are handled by the stochastic simulation algorithm of Gillespie or a weakly second-order tau leaping method. We find that an implicit midpoint tau leaping scheme attains second-order weak accuracy in the linearized setting and gives an accurate and stable structure factor for a time step size of an order of magnitude larger than the hopping time scale of diffusing molecules. We study the numerical accuracy of our methods for the Schlögl reaction-diffusion model both in and out of thermodynamic equilibrium. We demonstrate and quantify the importance of thermodynamic fluctuations to the formation of a two-dimensional Turing-like pattern and examine the effect of fluctuations on three-dimensional chemical front propagation. By comparing stochastic simulations to deterministic reaction-diffusion simulations, we show that fluctuations accelerate pattern formation in spatially homogeneous systems and lead to a qualitatively different disordered pattern behind a traveling wave.

Stochastic simulation of reaction-diffusion systems: A fluctuating-hydrodynamics approach

DOE PAGES

Kim, Changho; Nonaka, Andy; Bell, John B.; ...

2017-03-24

Here, we develop numerical methods for stochastic reaction-diffusion systems based on approaches used for fluctuating hydrodynamics (FHD). For hydrodynamic systems, the FHD formulation is formally described by stochastic partial differential equations (SPDEs). In the reaction-diffusion systems we consider, our model becomes similar to the reaction-diffusion master equation (RDME) description when our SPDEs are spatially discretized and reactions are modeled as a source term having Poisson fluctuations. However, unlike the RDME, which becomes prohibitively expensive for an increasing number of molecules, our FHD-based description naturally extends from the regime where fluctuations are strong, i.e., each mesoscopic cell has few (reactive) molecules,more » to regimes with moderate or weak fluctuations, and ultimately to the deterministic limit. By treating diffusion implicitly, we avoid the severe restriction on time step size that limits all methods based on explicit treatments of diffusion and construct numerical methods that are more efficient than RDME methods, without compromising accuracy. Guided by an analysis of the accuracy of the distribution of steady-state fluctuations for the linearized reaction-diffusion model, we construct several two-stage (predictor-corrector) schemes, where diffusion is treated using a stochastic Crank-Nicolson method, and reactions are handled by the stochastic simulation algorithm of Gillespie or a weakly second-order tau leaping method. We find that an implicit midpoint tau leaping scheme attains second-order weak accuracy in the linearized setting and gives an accurate and stable structure factor for a time step size of an order of magnitude larger than the hopping time scale of diffusing molecules. We study the numerical accuracy of our methods for the Schlögl reaction-diffusion model both in and out of thermodynamic equilibrium. We demonstrate and quantify the importance of thermodynamic fluctuations to the formation of a two-dimensional Turing-like pattern and examine the effect of fluctuations on three-dimensional chemical front propagation. Furthermore, by comparing stochastic simulations to deterministic reaction-diffusion simulations, we show that fluctuations accelerate pattern formation in spatially homogeneous systems and lead to a qualitatively different disordered pattern behind a traveling wave.« less

Boundary Layer Model for Air Pollutant Concentrations Due to Highway Traffic

ERIC Educational Resources Information Center

Ragland, Kenneth W.; Peirce, J. Jeffrey

1975-01-01

A numerical solution of the three-dimensional steady-state diffusion equation for a finite width line source is presented. The wind speed and eddy diffusivity as a function of height above the roadway are obtained. Normalized ground level and elevated concentrations near a highway are obtained for winds perpendicular, parallel, and at 45 degrees.…

FLOW STRUCTURE AND TURBULENT DIFFUSION AROUND A THREE-DIMENSIONAL HILL. FLUID MODELING STUDY ON EFFECTS OF STRATIFICATION. PART I. FLOW STRUCTURE

EPA Science Inventory

This research program was initiated with the overall objective of gaining understanding of the flow and diffusion of pollutants in complex terrain under both neutral and stably stratified conditions. This report covers the first phase of the project; it describes the flow structu...

Further Studies on Oceanic Biogeochemistry and Carbon Cycling

NASA Technical Reports Server (NTRS)

Signorini, S. R.; McClain, C. R.

2003-01-01

This TM consists of two chapters. Chapter I describes the development of a coupled, one-dimensional biogeochemical model using turbulence closure mixed layer (TCMLM) dynamics. The model is applied to the Sargasso Sea at the BATS (Bermuda Atlantic Time Series) site and the results are compared with a previous model study in the same region described in NASNTP-2001-209991. The use of the TCMLM contributed to some improvements in the model simulation of chlorophyll, PAR, nitrate, phosphate, and oxygen, but most importantly, the current model achieved good agreement with the data with much more realistic background eddy diffusivity. However, off-line calculations of horizontal transport of biogeochemical properties revealed that one-dimensional dynamics can only provide a limited assessment of the nutrient and carbon balances at BATS. Future studies in the BATS region will require comprehensive three-dimensional field studies, combined with three-dimensional eddy resolving numerical experiments, to adequately quantify the impact of the local and remote forcing on ecosystem dynamics and carbon cycling. Chapter II addresses the sensitivity of global sea-air CO, flux estimates to wind speed, temperature, and salinity. Sensitivity analyses of sea-air CO, flux to wind speed climatologies, gas transfer algorithms, SSS and SST were conducted for the global oceans and regional domains. Large uncertainties in the global sea-air flux are identified, primarily due to the different gas transfer algorithms used. The sensitivity of the sea-air flux to SST and SSS is similar in magnitude to the effect of using different wind climatologies. Globally, the mean ocean uptake of CO, changes by 5 to 16%, depending upon the combination of SST and SSS used.

Modelling coupled turbulence - dissolved oxygen dynamics near the sediment-water interface under wind waves and sea swell.

PubMed

Chatelain, Mathieu; Guizien, Katell

2010-03-01

A one-dimensional vertical unsteady numerical model for diffusion-consumption of dissolved oxygen (DO) above and below the sediment-water interface was developed to investigate DO profile dynamics under wind waves and sea swell (high-frequency oscillatory flows with periods ranging from 2 to 30s). We tested a new approach to modelling DO profiles that coupled an oscillatory turbulent bottom boundary layer model with a Michaelis-Menten based consumption model. The flow regime controls both the mean value and the fluctuations of the oxygen mass transfer efficiency during a wave cycle, as expressed by the non-dimensional Sherwood number defined with the maximum shear velocity (Sh). The Sherwood number was found to be non-dependent on the sediment biogeochemical activity (mu). In the laminar regime, both cycle-averaged and variance of the Sherwood number are very low (Sh <0.05, VAR(Sh)<0.1%). In the turbulent regime, the cycle-averaged Sherwood number is larger (Sh approximately 0.2). The Sherwood number also has intra-wave cycle fluctuations that increase with the wave Reynolds number (VAR(Sh) up to 30%). Our computations show that DO mass transfer efficiency under high-frequency oscillatory flows in the turbulent regime are water-side controlled by: (a) the diffusion time across the diffusive boundary layer and (b) diffusive boundary layer dynamics during a wave cycle. As a result of these two processes, when the wave period decreases, the Sh minimum increases and the Sh maximum decreases. Sh values vary little, ranging from 0.17 to 0.23. For periods up to 30s, oxygen penetration depth into the sediment did not show any intra-wave fluctuations. Values for the laminar regime are small (

Using spatially detailed water-quality data and solute-transport modeling to improve support total maximum daily load development

USGS Publications Warehouse

Walton-Day, Katherine; Runkel, Robert L.; Kimball, Briant A.

2012-01-01

Spatially detailed mass-loading studies and solute-transport modeling using OTIS (One-dimensional Transport with Inflow and Storage) demonstrate how natural attenuation and loading from distinct and diffuse sources control stream water quality and affect load reductions predicted in total maximum daily loads (TMDLs). Mass-loading data collected during low-flow from Cement Creek (a low-pH, metal-rich stream because of natural and mining sources, and subject to TMDL requirements) were used to calibrate OTIS and showed spatially variable effects of natural attenuation (instream reactions) and loading from diffuse (groundwater) and distinct sources. OTIS simulations of the possible effects of TMDL-recommended remediation of mine sites showed less improvement to dissolved zinc load and concentration (14% decrease) than did the TMDL (53-63% decrease). The TMDL (1) assumed conservative transport, (2) accounted for loads removed by remediation by subtracting them from total load at the stream mouth, and (3) did not include diffuse-source loads. In OTIS, loads were reduced near their source; the resulting concentration was decreased by natural attenuation and increased by diffuse-source loads during downstream transport. Thus, by not including natural attenuation and loading from diffuse sources, the TMDL overestimated remediation effects at low flow. Use of the techniques presented herein could improve TMDLs by incorporating these processes during TMDL development.

A Diffusion Approximation Based on Renewal Processes with Applications to Strongly Biased Run-Tumble Motion.

PubMed

Thygesen, Uffe Høgsbro

2016-03-01

We consider organisms which use a renewal strategy such as run-tumble when moving in space, for example to perform chemotaxis in chemical gradients. We derive a diffusion approximation for the motion, applying a central limit theorem due to Anscombe for renewal-reward processes; this theorem has not previously been applied in this context. Our results extend previous work, which has established the mean drift but not the diffusivity. For a classical model of tumble rates applied to chemotaxis, we find that the resulting chemotactic drift saturates to the swimming velocity of the organism when the chemical gradients grow increasingly steep. The dispersal becomes anisotropic in steep gradients, with larger dispersal across the gradient than along the gradient. In contrast to one-dimensional settings, strong bias increases dispersal. We next include Brownian rotation in the model and find that, in limit of high chemotactic sensitivity, the chemotactic drift is 64% of the swimming velocity, independent of the magnitude of the Brownian rotation. We finally derive characteristic timescales of the motion that can be used to assess whether the diffusion limit is justified in a given situation. The proposed technique for obtaining diffusion approximations is conceptually and computationally simple, and applicable also when statistics of the motion is obtained empirically or through Monte Carlo simulation of the motion.

Theory and simulation of ion conduction in the pentameric GLIC channel.

PubMed

Zhu, Fangqiang; Hummer, Gerhard

2012-10-09

GLIC is a bacterial member of the large family of pentameric ligand-gated ion channels. To study ion conduction through GLIC and other membrane channels, we combine the one-dimensional potential of mean force for ion passage with a Smoluchowski diffusion model, making it possible to calculate single-channel conductance in the regime of low ion concentrations from all-atom molecular dynamics (MD) simulations. We then perform MD simulations to examine sodium ion conduction through the GLIC transmembrane pore in two systems with different bulk ion concentrations. The ion potentials of mean force, calculated from umbrella sampling simulations with Hamiltonian replica exchange, reveal a major barrier at the hydrophobic constriction of the pore. The relevance of this barrier for ion transport is confirmed by a committor function that rises sharply in the barrier region. From the free evolution of Na(+) ions starting at the barrier top, we estimate the effective diffusion coefficient in the barrier region, and subsequently calculate the conductance of the pore. The resulting diffusivity compares well with the position-dependent ion diffusion coefficient obtained from restrained simulations. The ion conductance obtained from the diffusion model agrees with the value determined via a reactive-flux rate calculation. Our results show that the conformation in the GLIC crystal structure, with an estimated conductance of ~1 picosiemens at 140 mM ion concentration, is consistent with a physiologically open state of the channel.

Modeling the effect of glutamate diffusion and uptake on NMDA and non-NMDA receptor saturation.

PubMed Central

Holmes, W R

1995-01-01

One- and two-dimensional models of glutamate diffusion, uptake, and binding in the synaptic cleft were developed to determine if the release of single vesicles of glutamate would saturate NMDA and non-NMDA receptors. Ranges of parameter values were used in the simulations to determine the conditions when saturation could occur. Single vesicles of glutamate did not saturate NMDA receptors unless diffusion was very slow and the number of glutamate molecules in a vesicle was large. However, the release of eight vesicles at 400 Hz caused NMDA receptor saturation for all parameter values tested. Glutamate uptake was found to reduce NMDA receptor saturation, but the effect was smaller than that of changes in the diffusion coefficient or in the number of glutamate molecules in a vesicle. Non-NMDA receptors were not saturated unless diffusion was very slow and the number of glutamate molecules in a vesicle was large. The release of eight vesicles at 400 Hz caused significant non-NMDA receptor desensitization. The results suggest that NMDA and non-NMDA receptors are not saturated by single vesicles of glutamate under usual conditions, and that tetanic input, of the type typically used to induce long-term potentiation, will increase calcium influx by increasing receptor binding as well as by reducing voltage-dependent block of NMDA receptors. Images FIGURE 1 PMID:8580317

Vertical profile of tritium concentration in air during a chronic atmospheric HT release.

PubMed

Noguchi, Hiroshi; Yokoyama, Sumi

2003-03-01

The vertical profiles of tritium gas and tritiated water concentrations in air, which would have an influence on the assessment of tritium doses as well as on the environmental monitoring of tritium, were measured in a chronic tritium gas release experiment performed in Canada in 1994. While both of the profiles were rather uniform during the day because of atmospheric mixing, large gradients of the profiles were observed at night. The gradient coefficients of the profiles were derived from the measurements. Correlations were analyzed between the gradient coefficients and meteorological conditions: solar radiation, wind speed, and turbulent diffusivity. It was found that the solar radiation was highly correlated with the gradient coefficients of tritium gas and tritiated water profiles and that the wind speed and turbulent diffusivity showed weaker correlations with those of tritiated water profiles. A one-dimensional tritium transport model was developed to analyze the vertical diffusion of tritiated water re-emitted from the ground into the atmosphere. The model consists of processes of tritium gas deposition to soil including oxidation into tritiated water, reemission of tritiated water, dilution of tritiated water in soil by rain, and vertical diffusion of tritiated water in the atmosphere. The model accurately represents the accumulation of tritiated water in soil water and the time variations and vertical profiles of tritiated water concentrations in air.

A non-orthogonal decomposition of flows into discrete events

NASA Astrophysics Data System (ADS)

Boxx, Isaac; Lewalle, Jacques

1998-11-01

This work is based on the formula for the inverse Hermitian wavelet transform. A signal can be interpreted as a (non-unique) superposition of near-singular, partially overlapping events arising from Dirac functions and/or its derivatives combined with diffusion.( No dynamics implied: dimensionless diffusion is related to the definition of the analyzing wavelets.) These events correspond to local maxima of spectral energy density. We successfully fitted model events of various orders on a succession of fields, ranging from elementary signals to one-dimensional hot-wire traces. We document edge effects, event overlap and its implications on the algorithm. The interpretation of the discrete singularities as flow events (such as coherent structures) and the fundamental non-uniqueness of the decomposition are discussed. The dynamics of these events will be examined in the companion paper.

Ultrafast Spectral Diffusion of the First Subband Exciton in Single-Wall Carbon Nanotubes

NASA Astrophysics Data System (ADS)

Schilling, Daniel; Hertel, Tobias

2013-03-01

The width of optical transitions in semiconductors is determined by homogeneous and inhomogeneous contributions. Here, we report on the determination of homogeneous linewidths for the first exciton subband transition and the dynamics of spectral diffusion in single-wall carbon nanotubes (SWNTs) using one- and two-dimensional time resolved spectral hole burning spectroscopy. Our investigation of highly purified semiconducting (6,5)-SWNTs suggests that room temperature homogeneous linewidths are on the order of 4 meV and are rapidly broadened by an ultrafast sub-ps spectral diffusion process. These findings are supported by our off-resonant excitation experiments where we observe sub-ps population transfer reflecting the thermal distribution of energy levels around the first subband exciton transition. The results of temperature-dependent spectral hole burning experiments between 17 K and 293 K suggest that homogeneous linewidths are due to exciton interaction with low energy optical phonons, most likely of the radial breathing mode type. In contrast, we find that inhomogeneous broadening is determined by an electronic degree of freedom such as ultrafast intra-tube exciton diffusion which is characteristic and unique for excitons in these one-dimensional semiconductors.

Thermal motion of a nonlinear localized pattern in a quasi-one-dimensional system.

PubMed

Dessup, Tommy; Coste, Christophe; Saint Jean, Michel

2016-07-01

We study the dynamics of localized nonlinear patterns in a quasi-one-dimensional many-particle system near a subcritical pitchfork bifurcation. The normal form at the bifurcation is given and we show that these patterns can be described as solitary-wave envelopes. They are stable in a large temperature range and can diffuse along the chain of interacting particles. During their displacements the particles are continually redistributed on the envelope. This change of particle location induces a small modulation of the potential energy of the system, with an amplitude that depends on the transverse confinement. At high temperature, this modulation is irrelevant and the thermal motion of the localized patterns displays all the characteristics of a free quasiparticle diffusion with a diffusion coefficient that may be deduced from the normal form. At low temperature, significant physical effects are induced by the modulated potential. In particular, the localized pattern may be trapped at very low temperature. We also exhibit a series of confinement values for which the modulation amplitudes vanishes. For these peculiar confinements, the mean-square displacement of the localized patterns also evidences free-diffusion behavior at low temperature.

A porous media theory for characterization of membrane blood oxygenation devices

NASA Astrophysics Data System (ADS)

Sano, Yoshihiko; Adachi, Jun; Nakayama, Akira

2013-07-01

A porous media theory has been proposed to characterize oxygen transport processes associated with membrane blood oxygenation devices. For the first time, a rigorous mathematical procedure based a volume averaging procedure has been presented to derive a complete set of the governing equations for the blood flow field and oxygen concentration field. As a first step towards a complete three-dimensional numerical analysis, one-dimensional steady case is considered to model typical membrane blood oxygenator scenarios, and to validate the derived equations. The relative magnitudes of oxygen transport terms are made clear, introducing a dimensionless parameter which measures the distance the oxygen gas travels to dissolve in the blood as compared with the blood dispersion length. This dimensionless number is found so large that the oxygen diffusion term can be neglected in most cases. A simple linear relationship between the blood flow rate and total oxygen transfer rate is found for oxygenators with sufficiently large membrane surface areas. Comparison of the one-dimensional analytic results and available experimental data reveals the soundness of the present analysis.

Three-Dimensional Printed Modeling of Diffuse Low-Grade Gliomas and Associated White Matter Tract Anatomy.

PubMed

Thawani, Jayesh P; Singh, Nickpreet; Pisapia, Jared M; Abdullah, Kalil G; Parker, Drew; Pukenas, Bryan A; Zager, Eric L; Verma, Ragini; Brem, Steven

2017-04-01

Diffuse low-grade gliomas (DLGGs) represent several pathological entities that infiltrate and invade cortical and subcortical structures in the brain. To describe methods for rapid prototyping of DLGGs and surgically relevant anatomy. Using high-definition imaging data and rapid prototyping technologies, we were able to generate 3 patient DLGGs to scale and represent the associated white matter tracts in 3 dimensions using advanced diffusion tensor imaging techniques. This report represents a novel application of 3-dimensional (3-D) printing in neurosurgery and a means to model individualized tumors in 3-D space with respect to subcortical white matter tract anatomy. Faculty and resident evaluations of this technology were favorable at our institution. Developing an understanding of the anatomic relationships existing within individuals is fundamental to successful neurosurgical therapy. Imaging-based rapid prototyping may improve on our ability to plan for and treat complex neuro-oncologic pathology. Copyright © 2017 by the Congress of Neurological Surgeons

Influence investigation of a void region on modeling light propagation in a heterogeneous medium.

PubMed

Yang, Defu; Chen, Xueli; Ren, Shenghan; Qu, Xiaochao; Tian, Jie; Liang, Jimin

2013-01-20

A void region exists in some biological tissues, and previous studies have shown that inaccurate images would be obtained if it were not processed. A hybrid radiosity-diffusion method (HRDM) that couples the radiosity theory and the diffusion equation has been proposed to deal with the void problem and has been well demonstrated in two-dimensional and three-dimensional (3D) simple models. However, the extent of the impact of the void region on the accuracy of modeling light propagation has not been investigated. In this paper, we first implemented and verified the HRDM in 3D models, including both the regular geometries and a digital mouse model, and then investigated the influences of the void region on modeling light propagation in a heterogeneous medium. Our investigation results show that the influence of the region can be neglected when the size of the void is less than a certain range, and other cases must be taken into account.

The {sech}( {\\hat{ξ }} ) -Type Profiles: A Swiss-Army Knife for Exact Analytical Modeling of Thermal Diffusion and Wave Propagation in Graded Media

NASA Astrophysics Data System (ADS)

Krapez, J.-C.

2018-07-01

This work deals with the exact analytical modeling of transfer phenomena in heterogeneous materials exhibiting one-dimensional continuous variations of their properties. Regarding heat transfer, it has recently been shown that by applying a Liouville transformation and multiple Darboux transformations, infinite sequences of solvable profiles of thermal effusivity can be constructed together with the associated temperature (exact) solutions, all in closed-form expressions (vs. the diffusion-time variable and with a growing number of parameters). In addition, a particular class of profiles, the so-called {sech}( {\\hat{ξ }} ) -type profiles, exhibit high agility and at the same time parsimony. In this paper we delve further into the description of these solvable profiles and their properties. Most importantly, their quadrupole formulation is provided, enabling smooth synthetic profiles of effusivity of arbitrary complexity to be built, and allowing the corresponding temperature dynamic response to be obtained very easily thereafter. Examples are given with increasing variability of the effusivity and an increasing number of elementary profiles. These highly flexible profiles are equally relevant to providing an exact analytical solution to wave propagation problems in 1D graded media (i.e., Maxwell's equations, the acoustic equation, the telegraph equation, etc.). From now on, whether it be for diffusion-like or wave-like problems, when the leading properties present (possibly piecewise-) continuously heterogeneous profiles, the classical staircase model can be advantageously replaced by a "high-level" quadrupole model consisting of one or more {sech}( {\\hat{ξ }} ) -type profiles, which makes the latter a true Swiss-Army knife for analytical modeling.

Intermode light diffusion in multimode optical waveguides with rough surfaces.

PubMed

Stepanov, S; Chaikina, E I; Leskova, T A; Méndez, E R

2005-06-01

A theoretical analysis of incoherent intermode light power diffusion in multimode dielectric waveguides with rough (corrugated) surfaces is presented. The correlation length a of the surface-profile variations is assumed to be sufficiently large (a less less than lambda/2pi) to permit light scattering into the outer space only from the modes close to the critical angles of propagation and yet sufficiently small (a less less than d, where d is the average width of the waveguide) to permit direct interaction between a given mode and a large number of neighboring ones. The cases of a one-dimensional (1D) slab waveguide and a two-dimensional cylindrical waveguide (optical fiber) are analyzed, and we find that in both cases the partial differential equations that govern the evolution of the angular light power profile propagating along the waveguide are 1D and of the diffusion type. However, whereas in the former case the effective conductivity coefficient proves to be linearly dependent on the transverse-mode wave number, in the latter one the linear dependence is for the effective diffusion coefficient. The theoretical predictions are in reasonable agreement with experimental results for the intermode power diffusion in multimode (700 x 700) optical fibers with etched surfaces. The characteristic length of dispersion of a narrow angular power profile evaluated from the correlation length and standard deviation of heights of the surface profile proved to be in good agreement with the experimentally observed changes in the output angular power profiles.

Scrambling and thermalization in a diffusive quantum many-body system

DOE PAGES

Bohrdt, A.; Mendl, C. B.; Endres, M.; ...

2017-06-02

Out-of-time ordered (OTO) correlation functions describe scrambling of information in correlated quantum matter. They are of particular interest in incoherent quantum systems lacking well defined quasi-particles. Thus far, it is largely elusive how OTO correlators spread in incoherent systems with diffusive transport governed by a few globally conserved quantities. Here, we study the dynamical response of such a system using high-performance matrix-product-operator techniques. Specifically, we consider the non-integrable, one-dimensional Bose–Hubbard model in the incoherent high-temperature regime. Our system exhibits diffusive dynamics in time-ordered correlators of globally conserved quantities, whereas OTO correlators display a ballistic, light-cone spreading of quantum information. Themore » slowest process in the global thermalization of the system is thus diffusive, yet information spreading is not inhibited by such slow dynamics. We furthermore develop an experimentally feasible protocol to overcome some challenges faced by existing proposals and to probe time-ordered and OTO correlation functions. As a result, our study opens new avenues for both the theoretical and experimental exploration of thermalization and information scrambling dynamics.« less

Scrambling and thermalization in a diffusive quantum many-body system

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

Bohrdt, A.; Mendl, C. B.; Endres, M.

Out-of-time ordered (OTO) correlation functions describe scrambling of information in correlated quantum matter. They are of particular interest in incoherent quantum systems lacking well defined quasi-particles. Thus far, it is largely elusive how OTO correlators spread in incoherent systems with diffusive transport governed by a few globally conserved quantities. Here, we study the dynamical response of such a system using high-performance matrix-product-operator techniques. Specifically, we consider the non-integrable, one-dimensional Bose–Hubbard model in the incoherent high-temperature regime. Our system exhibits diffusive dynamics in time-ordered correlators of globally conserved quantities, whereas OTO correlators display a ballistic, light-cone spreading of quantum information. Themore » slowest process in the global thermalization of the system is thus diffusive, yet information spreading is not inhibited by such slow dynamics. We furthermore develop an experimentally feasible protocol to overcome some challenges faced by existing proposals and to probe time-ordered and OTO correlation functions. As a result, our study opens new avenues for both the theoretical and experimental exploration of thermalization and information scrambling dynamics.« less

Isochronal Ice Sheet Model: a New Approach to Tracer Transport by Explicitly Tracing Accumulation Layers

NASA Astrophysics Data System (ADS)

Born, A.; Stocker, T. F.

2014-12-01

The long, high-resolution and largely undisturbed depositional record of polar ice sheets is one of the greatest resources in paleoclimate research. The vertical profile of isotopic and other geochemical tracers provides a full history of depositional and dynamical variations. Numerical simulations of this archive could afford great advances both in the interpretation of these tracers as well as to help improve ice sheet models themselves, as show successful implementations in oceanography and atmospheric dynamics. However, due to the slow advection velocities, tracer modeling in ice sheets is particularly prone to numerical diffusion, thwarting efforts that employ straightforward solutions. Previous attemps to circumvent this issue follow conceptually and computationally extensive approaches that augment traditional Eulerian models of ice flow with a semi-Lagrangian tracer scheme (e.g. Clarke et al., QSR, 2005). Here, we propose a new vertical discretization for ice sheet models that eliminates numerical diffusion entirely. Vertical motion through the model mesh is avoided by mimicking the real-world ice flow as a thinning of underlying layers (see figure). A new layer is added to the surface at equidistant time intervals (isochronally). Therefore, each layer is uniquely identified with an age. Horizontal motion follows the shallow ice approximation using an implicit numerical scheme. Vertical diffusion of heat which is physically desirable is also solved implicitly. A simulation of a two-dimensional section through the Greenland ice sheet will be discussed.

Collisional transport across the magnetic field in drift-fluid models

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

Madsen, J., E-mail: jmad@fysik.dtu.dk; Naulin, V.; Nielsen, A. H.

2016-03-15

Drift ordered fluid models are widely applied in studies of low-frequency turbulence in the edge and scrape-off layer regions of magnetically confined plasmas. Here, we show how collisional transport across the magnetic field is self-consistently incorporated into drift-fluid models without altering the drift-fluid energy integral. We demonstrate that the inclusion of collisional transport in drift-fluid models gives rise to diffusion of particle density, momentum, and pressures in drift-fluid turbulence models and, thereby, obviates the customary use of artificial diffusion in turbulence simulations. We further derive a computationally efficient, two-dimensional model, which can be time integrated for several turbulence de-correlation timesmore » using only limited computational resources. The model describes interchange turbulence in a two-dimensional plane perpendicular to the magnetic field located at the outboard midplane of a tokamak. The model domain has two regions modeling open and closed field lines. The model employs a computational expedient model for collisional transport. Numerical simulations show good agreement between the full and the simplified model for collisional transport.« less

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

NASA Astrophysics Data System (ADS)

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

2009-04-01

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

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

USGS Publications Warehouse

Shapiro, Allen M.

2001-01-01

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

Dynamic density functional theory with hydrodynamic interactions: theoretical development and application in the study of phase separation in gas-liquid systems.

PubMed

Kikkinides, E S; Monson, P A

2015-03-07

Building on recent developments in dynamic density functional theory, we have developed a version of the theory that includes hydrodynamic interactions. This is achieved by combining the continuity and momentum equations eliminating velocity fields, so the resulting model equation contains only terms related to the fluid density and its time and spatial derivatives. The new model satisfies simultaneously continuity and momentum equations under the assumptions of constant dynamic or kinematic viscosity and small velocities and/or density gradients. We present applications of the theory to spinodal decomposition of subcritical temperatures for one-dimensional and three-dimensional density perturbations for both a van der Waals fluid and for a lattice gas model in mean field theory. In the latter case, the theory provides a hydrodynamic extension to the recently studied dynamic mean field theory. We find that the theory correctly describes the transition from diffusive phase separation at short times to hydrodynamic behaviour at long times.

Dynamic density functional theory with hydrodynamic interactions: Theoretical development and application in the study of phase separation in gas-liquid systems

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

Kikkinides, E. S.; Monson, P. A.

Building on recent developments in dynamic density functional theory, we have developed a version of the theory that includes hydrodynamic interactions. This is achieved by combining the continuity and momentum equations eliminating velocity fields, so the resulting model equation contains only terms related to the fluid density and its time and spatial derivatives. The new model satisfies simultaneously continuity and momentum equations under the assumptions of constant dynamic or kinematic viscosity and small velocities and/or density gradients. We present applications of the theory to spinodal decomposition of subcritical temperatures for one-dimensional and three-dimensional density perturbations for both a van dermore » Waals fluid and for a lattice gas model in mean field theory. In the latter case, the theory provides a hydrodynamic extension to the recently studied dynamic mean field theory. We find that the theory correctly describes the transition from diffusive phase separation at short times to hydrodynamic behaviour at long times.« less

Orbital Transfer Vehicle Engine Technology High Velocity Ratio Diffusing Crossover

NASA Technical Reports Server (NTRS)

Lariviere, Brian W.

1992-01-01

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

Bounded fractional diffusion in geological media: Definition and Lagrangian approximation

NASA Astrophysics Data System (ADS)

Zhang, Yong; Green, Christopher T.; LaBolle, Eric M.; Neupauer, Roseanna M.; Sun, HongGuang

2016-11-01

Spatiotemporal fractional-derivative models (FDMs) have been increasingly used to simulate non-Fickian diffusion, but methods have not been available to define boundary conditions for FDMs in bounded domains. This study defines boundary conditions and then develops a Lagrangian solver to approximate bounded, one-dimensional fractional diffusion. Both the zero-value and nonzero-value Dirichlet, Neumann, and mixed Robin boundary conditions are defined, where the sign of Riemann-Liouville fractional derivative (capturing nonzero-value spatial-nonlocal boundary conditions with directional superdiffusion) remains consistent with the sign of the fractional-diffusive flux term in the FDMs. New Lagrangian schemes are then proposed to track solute particles moving in bounded domains, where the solutions are checked against analytical or Eulerian solutions available for simplified FDMs. Numerical experiments show that the particle-tracking algorithm for non-Fickian diffusion differs from Fickian diffusion in relocating the particle position around the reflective boundary, likely due to the nonlocal and nonsymmetric fractional diffusion. For a nonzero-value Neumann or Robin boundary, a source cell with a reflective face can be applied to define the release rate of random-walking particles at the specified flux boundary. Mathematical definitions of physically meaningful nonlocal boundaries combined with bounded Lagrangian solvers in this study may provide the only viable techniques at present to quantify the impact of boundaries on anomalous diffusion, expanding the applicability of FDMs from infinite domains to those with any size and boundary conditions.

Three Dimensional Compressible Turbulent Flow Computations for a Diffusing S-Duct With/Without Vortex Generators

NASA Technical Reports Server (NTRS)

Cho, Soo-Yong; Greber, Isaac

1994-01-01

Numerical investigations on a diffusing S-duct with/without vortex generators and a straight duct with vortex generators are presented. The investigation consists of solving the full three-dimensional unsteady compressible mass averaged Navier-Stokes equations. An implicit finite volume lower-upper time marching code (RPLUS3D) has been employed and modified. A three-dimensional Baldwin-Lomax turbulence model has been modified in conjunction with the flow physics. A model for the analysis of vortex generators in a fully viscous subsonic internal flow is evaluated. A vortical structure for modeling the shed vortex is used as a source term in the computation domain. The injected vortex paths in the straight duct are compared with the analysis by two kinds of prediction models. The flow structure by the vortex generators are investigated along the duct. Computed results of the flow in a circular diffusing S-duct provide an understanding of the flow structure within a typical engine inlet system. These are compared with the experimental wall static-pressure, static- and total-pressure field, and secondary velocity profiles. Additionally, boundary layer thickness, skin friction values, and velocity profiles in wall coordinates are presented. In order to investigate the effect of vortex generators, various vortex strengths are examined in this study. The total-pressure recovery and distortion coefficients are obtained at the exit of the S-duct. The numerical results clearly depict the interaction between the low velocity flow by the flow separation and the injected vortices.

Performance Characteristics of Plane-Wall Two-Dimensional Diffusers

NASA Technical Reports Server (NTRS)

Reid, Elliott G

1953-01-01

Experiments have been made at Stanford University to determine the performance characteristics of plane-wall, two-dimensional diffusers which were so proportioned as to insure reasonable approximation of two-dimensional flow. All of the diffusers had identical entrance cross sections and discharged directly into a large plenum chamber; the test program included wide variations of divergence angle and length. During all tests a dynamic pressure of 60 pounds per square foOt was maintained at the diffuser entrance and the boundary layer there was thin and fully turbulent. The most interesting flow characteristics observed were the occasional appearance of steady, unseparated, asymmetric flow - which was correlated with the boundary-layer coalescence - and the rapid deterioration of flow steadiness - which occurred as soon as the divergence angle for maximum static pressure recovery was exceeded. Pressure efficiency was found to be controlled almost exclusively by divergence angle, whereas static pressure recovery was markedly influenced by area ratio (or length) as well as divergence angle. Volumetric efficiency. diminished as area ratio increased, and at a greater rate with small lengths than with large ones. Large values of the static-pressure-recovery coefficient were attained only with long diffusers of large area ratio; under these conditions pressure efficiency was high and. volumetric efficiency low. Auxiliary tests with asymmetric diffusers demonstrated that longitudinal pressure gradient, rather than wall divergence angle, controlled flow separation. Others showed that the addition of even a short exit duct of uniform section augmented pressure recovery. Finally, it was found that the installation of a thin, central, longitudinal partition suppressed flow separation in short diffusers and thereby improved pressure recovery

Diffusion maps, clustering and fuzzy Markov modeling in peptide folding transitions

NASA Astrophysics Data System (ADS)

Nedialkova, Lilia V.; Amat, Miguel A.; Kevrekidis, Ioannis G.; Hummer, Gerhard

2014-09-01

Using the helix-coil transitions of alanine pentapeptide as an illustrative example, we demonstrate the use of diffusion maps in the analysis of molecular dynamics simulation trajectories. Diffusion maps and other nonlinear data-mining techniques provide powerful tools to visualize the distribution of structures in conformation space. The resulting low-dimensional representations help in partitioning conformation space, and in constructing Markov state models that capture the conformational dynamics. In an initial step, we use diffusion maps to reduce the dimensionality of the conformational dynamics of Ala5. The resulting pretreated data are then used in a clustering step. The identified clusters show excellent overlap with clusters obtained previously by using the backbone dihedral angles as input, with small—but nontrivial—differences reflecting torsional degrees of freedom ignored in the earlier approach. We then construct a Markov state model describing the conformational dynamics in terms of a discrete-time random walk between the clusters. We show that by combining fuzzy C-means clustering with a transition-based assignment of states, we can construct robust Markov state models. This state-assignment procedure suppresses short-time memory effects that result from the non-Markovianity of the dynamics projected onto the space of clusters. In a comparison with previous work, we demonstrate how manifold learning techniques may complement and enhance informed intuition commonly used to construct reduced descriptions of the dynamics in molecular conformation space.

Diffusion maps, clustering and fuzzy Markov modeling in peptide folding transitions

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

Nedialkova, Lilia V.; Amat, Miguel A.; Kevrekidis, Ioannis G., E-mail: yannis@princeton.edu, E-mail: gerhard.hummer@biophys.mpg.de

Using the helix-coil transitions of alanine pentapeptide as an illustrative example, we demonstrate the use of diffusion maps in the analysis of molecular dynamics simulation trajectories. Diffusion maps and other nonlinear data-mining techniques provide powerful tools to visualize the distribution of structures in conformation space. The resulting low-dimensional representations help in partitioning conformation space, and in constructing Markov state models that capture the conformational dynamics. In an initial step, we use diffusion maps to reduce the dimensionality of the conformational dynamics of Ala5. The resulting pretreated data are then used in a clustering step. The identified clusters show excellent overlapmore » with clusters obtained previously by using the backbone dihedral angles as input, with small—but nontrivial—differences reflecting torsional degrees of freedom ignored in the earlier approach. We then construct a Markov state model describing the conformational dynamics in terms of a discrete-time random walk between the clusters. We show that by combining fuzzy C-means clustering with a transition-based assignment of states, we can construct robust Markov state models. This state-assignment procedure suppresses short-time memory effects that result from the non-Markovianity of the dynamics projected onto the space of clusters. In a comparison with previous work, we demonstrate how manifold learning techniques may complement and enhance informed intuition commonly used to construct reduced descriptions of the dynamics in molecular conformation space.« less

Diffusion maps, clustering and fuzzy Markov modeling in peptide folding transitions

PubMed Central

Nedialkova, Lilia V.; Amat, Miguel A.; Kevrekidis, Ioannis G.; Hummer, Gerhard

2014-01-01

Using the helix-coil transitions of alanine pentapeptide as an illustrative example, we demonstrate the use of diffusion maps in the analysis of molecular dynamics simulation trajectories. Diffusion maps and other nonlinear data-mining techniques provide powerful tools to visualize the distribution of structures in conformation space. The resulting low-dimensional representations help in partitioning conformation space, and in constructing Markov state models that capture the conformational dynamics. In an initial step, we use diffusion maps to reduce the dimensionality of the conformational dynamics of Ala5. The resulting pretreated data are then used in a clustering step. The identified clusters show excellent overlap with clusters obtained previously by using the backbone dihedral angles as input, with small—but nontrivial—differences reflecting torsional degrees of freedom ignored in the earlier approach. We then construct a Markov state model describing the conformational dynamics in terms of a discrete-time random walk between the clusters. We show that by combining fuzzy C-means clustering with a transition-based assignment of states, we can construct robust Markov state models. This state-assignment procedure suppresses short-time memory effects that result from the non-Markovianity of the dynamics projected onto the space of clusters. In a comparison with previous work, we demonstrate how manifold learning techniques may complement and enhance informed intuition commonly used to construct reduced descriptions of the dynamics in molecular conformation space. PMID:25240340

Quantitative model of price diffusion and market friction based on trading as a mechanistic random process.

PubMed

Daniels, Marcus G; Farmer, J Doyne; Gillemot, László; Iori, Giulia; Smith, Eric

2003-03-14

We model trading and price formation in a market under the assumption that order arrival and cancellations are Poisson random processes. This model makes testable predictions for the most basic properties of markets, such as the diffusion rate of prices (which is the standard measure of financial risk) and the spread and price impact functions (which are the main determinants of transaction cost). Guided by dimensional analysis, simulation, and mean-field theory, we find scaling relations in terms of order flow rates. We show that even under completely random order flow the need to store supply and demand to facilitate trading induces anomalous diffusion and temporal structure in prices.

Quantitative Model of Price Diffusion and Market Friction Based on Trading as a Mechanistic Random Process

NASA Astrophysics Data System (ADS)

Daniels, Marcus G.; Farmer, J. Doyne; Gillemot, László; Iori, Giulia; Smith, Eric

2003-03-01

We model trading and price formation in a market under the assumption that order arrival and cancellations are Poisson random processes. This model makes testable predictions for the most basic properties of markets, such as the diffusion rate of prices (which is the standard measure of financial risk) and the spread and price impact functions (which are the main determinants of transaction cost). Guided by dimensional analysis, simulation, and mean-field theory, we find scaling relations in terms of order flow rates. We show that even under completely random order flow the need to store supply and demand to facilitate trading induces anomalous diffusion and temporal structure in prices.

Mathematical modeling of microbially induced crown corrosion in wastewater collection systems and laboratory investigation and modeling of sulfuric acid corrosion of concrete

NASA Astrophysics Data System (ADS)

Jahani, Fereidoun

In the model for microbially induced crown corrosion, the diffusion of sulfide inside the concrete pores, its biological conversion to sulfuric acid, and the corrosion of calcium carbonate aggregates are represented. The corrosion front is modeled as a moving boundary. The location of the interface between the corrosion layer and the concrete is determined as part of the solution to the model equations. This model consisted of a system of one dimensional reaction-diffusion equations coupled to an equation describing the movement of the corrosion front. The equations were solved numerically using finite element Galerkin approximation. The concentration profiles of sulfide in the air and the liquid phases, the pH as a function of concrete depth, and the position of the corrosion front. A new equation for the corrosion rate was also derived. A more specific model for the degradation of a concrete specimen exposed to a sulfuric acid solution was also studied. In this model, diffusion of hydrogen ions and their reaction with alkaline components of concrete were expressed using Fick's Law of diffusion. The model equations described the moving boundary, the dissolution rate of alkaline components in the concrete, volume increase of sulfuric acid solution over the concrete specimen, and the boundary conditions on the surface of the concrete. An apparatus was designed and experiments were performed to measure pH changes on the surface of concrete. The data were used to calculate the dissolution rate of the concrete and, with the model, to determine the diffusion rate of sulfuric acid in the corrosion layer and corrosion layer thickness. Electrochemical Impedance Spectroscopy (EIS) was used to study the corrosion rate of iron pins embedded in the concrete sample. The open circuit potential (OCP) determined the onset of corrosion on the surface of the pins. Visual observation of the corrosion layer thickness was in good agreement with the simulation results.

An enriched finite element method to fractional advection-diffusion equation

NASA Astrophysics Data System (ADS)

Luan, Shengzhi; Lian, Yanping; Ying, Yuping; Tang, Shaoqiang; Wagner, Gregory J.; Liu, Wing Kam

2017-08-01

In this paper, an enriched finite element method with fractional basis [ 1,x^{α }] for spatial fractional partial differential equations is proposed to obtain more stable and accurate numerical solutions. For pure fractional diffusion equation without advection, the enriched Galerkin finite element method formulation is demonstrated to simulate the exact solution successfully without any numerical oscillation, which is advantageous compared to the traditional Galerkin finite element method with integer basis [ 1,x] . For fractional advection-diffusion equation, the oscillatory behavior becomes complex due to the introduction of the advection term which can be characterized by a fractional element Peclet number. For the purpose of addressing the more complex numerical oscillation, an enriched Petrov-Galerkin finite element method is developed by using a dimensionless fractional stabilization parameter, which is formulated through a minimization of the residual of the nodal solution. The effectiveness and accuracy of the enriched finite element method are demonstrated by a series of numerical examples of fractional diffusion equation and fractional advection-diffusion equation, including both one-dimensional and two-dimensional, steady-state and time-dependent cases.

Spin injection and transport in semiconductor and metal nanostructures

NASA Astrophysics Data System (ADS)

Zhu, Lei

In this thesis we investigate spin injection and transport in semiconductor and metal nanostructures. To overcome the limitation imposed by the low efficiency of spin injection and extraction and strict requirements for retention of spin polarization within the semiconductor, novel device structures with additional logic functionality and optimized device performance have been developed. Weak localization/antilocalization measurements and analysis are used to assess the influence of surface treatments on elastic, inelastic and spin-orbit scatterings during the electron transport within the two-dimensional electron layer at the InAs surface. Furthermore, we have used spin-valve and scanned probe microscopy measurements to investigate the influence of sulfur-based surface treatments and electrically insulating barrier layers on spin injection into, and spin transport within, the two-dimensional electron layer at the surface of p-type InAs. We also demonstrate and analyze a three-terminal, all-electrical spintronic switching device, combining charge current cancellation by appropriate device biasing and ballistic electron transport. The device yields a robust, electrically amplified spin-dependent current signal despite modest efficiency in electrical injection of spin-polarized electrons. Detailed analyses provide insight into the advantages of ballistic, as opposed to diffusive, transport in device operation, as well as scalability to smaller dimensions, and allow us to eliminate the possibility of phenomena unrelated to spin transport contributing to the observed device functionality. The influence of the device geometry on magnetoresistance of nanoscale spin-valve structures is also demonstrated and discussed. Shortcomings of the simplified one-dimensional spin diffusion model for spin valve are elucidated, with comparison of the thickness and the spin diffusion length in the nonmagnetic channel as the criterion for validity of the 1D model. Our work contributes directly to the realization of spin valve and spin transistor devices based on III-V semiconductors, and offers new opportunities to engineer the behavior of spintronic devices at the nanoscale.