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.

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.

Two-dimensional enzyme diffusion in laterally confined DNA monolayers.

PubMed

Castronovo, Matteo; Lucesoli, Agnese; Parisse, Pietro; Kurnikova, Anastasia; Malhotra, Aseem; Grassi, Mario; Grassi, Gabriele; Scaggiante, Bruna; Casalis, Loredana; Scoles, Giacinto

2011-01-01

Addressing the effects of confinement and crowding on biomolecular function may provide insight into molecular mechanisms within living organisms, and may promote the development of novel biotechnology tools. Here, using molecular manipulation methods, we investigate restriction enzyme reactions with double-stranded (ds)DNA oligomers confined in relatively large (and flat) brushy matrices of monolayer patches of controlled, variable density. We show that enzymes from the contacting solution cannot access the dsDNAs from the top-matrix interface, and instead enter at the matrix sides to diffuse two-dimensionally in the gap between top- and bottom-matrix interfaces. This is achieved by limiting lateral access with a barrier made of high-density molecules that arrest enzyme diffusion. We put forward, as a possible explanation, a simple and general model that relates these data to the steric hindrance in the matrix, and we briefly discuss the implications and applications of this strikingly new phenomenon.

Derivation of a closed form analytical expression for fluorescence recovery after photo bleaching in the case of continuous bleaching during read out

NASA Astrophysics Data System (ADS)

Endress, E.; Weigelt, S.; Reents, G.; Bayerl, T. M.

2005-01-01

Measurements of very slow diffusive processes in membranes, like the diffusion of integral membrane proteins, by fluorescence recovery after photo bleaching (FRAP) are hampered by bleaching of the probe during the read out of the fluorescence recovery. In the limit of long observation time (very slow diffusion as in the case of large membrane proteins), this bleaching may cause errors to the recovery function and thus provides error-prone diffusion coefficients. In this work we present a new approach to a two-dimensional closed form analytical solution of the reaction-diffusion equation, based on the addition of a dissipative term to the conventional diffusion equation. The calculation was done assuming (i) a Gaussian laser beam profile for bleaching the spot and (ii) that the fluorescence intensity profile emerging from the spot can be approximated by a two-dimensional Gaussian. The detection scheme derived from the analytical solution allows for diffusion measurements without the constraint of observation bleaching. Recovery curves of experimental FRAP data obtained under non-negligible read-out bleaching for native membranes (rabbit endoplasmic reticulum) on a planar solid support showed excellent agreement with the analytical solution and allowed the calculation of the lipid diffusion coefficient.

Theory of diffusion of active particles that move at constant speed in two dimensions.

PubMed

Sevilla, Francisco J; Gómez Nava, Luis A

2014-08-01

Starting from a Langevin description of active particles that move with constant speed in infinite two-dimensional space and its corresponding Fokker-Planck equation, we develop a systematic method that allows us to obtain the coarse-grained probability density of finding a particle at a given location and at a given time in arbitrary short-time regimes. By going beyond the diffusive limit, we derive a generalization of the telegrapher equation. Such generalization preserves the hyperbolic structure of the equation and incorporates memory effects in the diffusive term. While no difference is observed for the mean-square displacement computed from the two-dimensional telegrapher equation and from our generalization, the kurtosis results in a sensible parameter that discriminates between both approximations. We carry out a comparative analysis in Fourier space that sheds light on why the standard telegrapher equation is not an appropriate model to describe the propagation of particles with constant speed in dispersive media.

Extrapolation techniques applied to matrix methods in neutron diffusion problems

NASA Technical Reports Server (NTRS)

Mccready, Robert R

1956-01-01

A general matrix method is developed for the solution of characteristic-value problems of the type arising in many physical applications. The scheme employed is essentially that of Gauss and Seidel with appropriate modifications needed to make it applicable to characteristic-value problems. An iterative procedure produces a sequence of estimates to the answer; and extrapolation techniques, based upon previous behavior of iterants, are utilized in speeding convergence. Theoretically sound limits are placed on the magnitude of the extrapolation that may be tolerated. This matrix method is applied to the problem of finding criticality and neutron fluxes in a nuclear reactor with control rods. The two-dimensional finite-difference approximation to the two-group neutron fluxes in a nuclear reactor with control rods. The two-dimensional finite-difference approximation to the two-group neutron-diffusion equations is treated. Results for this example are indicated.

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.

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.

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

Impact of local diffusion on macroscopic dispersion in three-dimensional porous media

NASA Astrophysics Data System (ADS)

Dartois, Arthur; Beaudoin, Anthony; Huberson, Serge

2018-02-01

While macroscopic longitudinal and transverse dispersion in three-dimensional porous media has been simulated previously mostly under purely advective conditions, the impact of diffusion on macroscopic dispersion in 3D remains an open question. Furthermore, both in 2D and 3D, recurring difficulties have been encountered due to computer limitation or analytical approximation. In this work, we use the Lagrangian velocity covariance function and the temporal derivative of second-order moments to study the influence of diffusion on dispersion in highly heterogeneous 2D and 3D porous media. The first approach characterizes the correlation between the values of Eulerian velocity components sampled by particles undergoing diffusion at two times. The second approach allows the estimation of dispersion coefficients and the analysis of their behaviours as functions of diffusion. These two approaches allowed us to reach new results. The influence of diffusion on dispersion seems to be globally similar between highly heterogeneous 2D and 3D porous media. Diffusion induces a decrease in the dispersion in the direction parallel to the flow direction and an increase in the dispersion in the direction perpendicular to the flow direction. However, the amplification of these two effects with the permeability variance is clearly different between 2D and 3D. For the direction parallel to the flow direction, the amplification is more important in 3D than in 2D. It is reversed in the direction perpendicular to the flow direction.

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.

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.

Laser range profile of cones

NASA Astrophysics Data System (ADS)

Zhou, Wenzhen; Gong, Yanjun; Wang, Mingjun; Gong, Lei

2016-10-01

technology. Laser one-dimensional 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 about cone is given in this paper. This paper demonstrates the analytical model of laser one-dimensional range profile of cone based on the radar equation of the pulse laser. Simulations results of laser one-dimensional range profiles of some cones are given. Laser one-dimensional range profiles of cone, whose surface material with diffuse lambertian reflectance, is given in this paper. Laser one-dimensional range profiles of cone, whose surface mater with diffuse materials whose retroreflectance can be modeled closely with an exponential term that decays with increasing incidence angles, is given in this paper. Laser one-dimensional range profiles of different pulse width of cone is given in this paper. The influences of surface material, pulse width, attitude on the one-dimensional range are analyzed. The laser two-dimensional range profile is two-dimensional scattering imaging of pulse laser of target. The two-dimensional range profile of roughness target can provide range resolved information. An analytical model of two-dimensional laser range profile of cone is proposed. The simulations of two-dimensional laser range profiles of some cones are given. Laser two-dimensional range profiles of cone, whose surface mater with diffuse lambertian reflectance, is given in this paper. Laser two-dimensional range profiles of cone, whose surface mater with diffuse materials whose retroreflectance can be modeled closely with an exponential term that decays with increasing incidence angles, is given in this paper. The influence of pulse width, surface material on laser two-dimensional range profile is analyzed. Laser one-dimensional range profile and laser two-dimensional range profile are called as laser range profile (LRP).

A cubic spline approximation for problems in fluid mechanics

NASA Technical Reports Server (NTRS)

Rubin, S. G.; Graves, R. A., Jr.

1975-01-01

A cubic spline approximation is presented which is suited for many fluid-mechanics problems. This procedure provides a high degree of accuracy, even with a nonuniform mesh, and leads to an accurate treatment of derivative boundary conditions. The truncation errors and stability limitations of several implicit and explicit integration schemes are presented. For two-dimensional flows, a spline-alternating-direction-implicit method is evaluated. The spline procedure is assessed, and results are presented for the one-dimensional nonlinear Burgers' equation, as well as the two-dimensional diffusion equation and the vorticity-stream function system describing the viscous flow in a driven cavity. Comparisons are made with analytic solutions for the first two problems and with finite-difference calculations for the cavity flow.

Continuous Diffusion Flames and Flame Streets in Micro-Channels

NASA Astrophysics Data System (ADS)

Mohan, Shikhar; Matalon, Moshe

2015-11-01

Experiments of non-premixed combustion in micro-channels have shown different modes of burning. Normally, a flame is established along, or near the axis of a channel that spreads the entire mixing layer and separates a region of fuel but no oxidizer from a region with only oxidizer. Often, however, a periodic sequence of extinction and reignition events, termed collectively as ``flame streets'', are observed. They constitute a series of diffusion flames, each with a tribrachial leading edge stabilized along the channel. This work focuses on understanding the underlying mechanism responsible for these distinct observations. Numerical simulations were conducted in the thermo-diffusive limit in order to study the effects of confinement and heat loss on non-premixed flames in three-dimensional micro-channels with low aspect ratios. The three dimensionality of the channel was captured qualitatively through a systematic asymptotic analysis that led to a two dimensional problem with an effective parameter representing heat losses in the vertical direction. There exist three key flame regimes: (1) a stable continuous diffusion flame, (2) an unsteady flame, and (3) a stable ``flame street'' the transition between regimes demarcated primarily by Reynolds and Nusselt numbers.

Multigrid for hypersonic viscous two- and three-dimensional flows

NASA Technical Reports Server (NTRS)

Turkel, E.; Swanson, R. C.; Vatsa, V. N.; White, J. A.

1991-01-01

The use of a multigrid method with central differencing to solve the Navier-Stokes equations for hypersonic flows is considered. The time dependent form of the equations is integrated with an explicit Runge-Kutta scheme accelerated by local time stepping and implicit residual smoothing. Variable coefficients are developed for the implicit process that removes the diffusion limit on the time step, producing significant improvement in convergence. A numerical dissipation formulation that provides good shock capturing capability for hypersonic flows is presented. This formulation is shown to be a crucial aspect of the multigrid method. Solutions are given for two-dimensional viscous flow over a NACA 0012 airfoil and three-dimensional flow over a blunt biconic.

On the motion of viscous fluids in the presence of diffusion

NASA Astrophysics Data System (ADS)

Secchi, Paolo

1988-01-01

The flow of a viscous incompressible two-component fluid with Fick's-law diffusion is investigated analytically. The existence of a unique global solution for small values of the diffusion coefficient (lambda) is proved for two-dimensional flow. The two- and three-dimensional solutions are also shown to converge toward the solutions of the Navier-Stokes equations for inhomogeneous fluids as lambda approaches zero.

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.

Diffusion Monte Carlo study of strongly interacting two-dimensional Fermi gases

DOE PAGES

Galea, Alexander; Dawkins, Hillary; Gandolfi, Stefano; ...

2016-02-01

Ultracold atomic Fermi gases have been a popular topic of research, with attention being paid recently to two-dimensional (2D) gases. In this work, we perform T=0 ab initio diffusion Monte Carlo calculations for a strongly interacting two-component Fermi gas confined to two dimensions. We first go over finite-size systems and the connection to the thermodynamic limit. After that, we illustrate pertinent 2D scattering physics and properties of the wave function. We then show energy results for the strong-coupling crossover, in between the Bose-Einstein condensation (BEC) and Bardeen-Cooper-Schrieffer (BCS) regimes. Our energy results for the BEC-BCS crossover are parametrized to producemore » an equation of state, which is used to determine Tan's contact. We carry out a detailed comparison with other microscopic results. Lastly, we calculate the pairing gap for a range of interaction strengths in the strong coupling regime, following from variationally optimized many-body wave functions.« less

Transmission of isotropic light across a dielectric surface in two and three dimensions.

NASA Technical Reports Server (NTRS)

Allen, W. A.

1973-01-01

Average transmittance of polarized diffuse light across a dielectric surface is calculated in both two and three dimensions. The incident light in both cases is confined to an angular range measured from the surface normal. Limiting values in three dimensions correspond to known results for two cases, (1) normal incidence, and (2) diffuse light incident from a 180 deg cone. The two-dimensional formulation is solvable in terms of elliptic functions and incomplete elliptic integrals of the first, second, and third kinds. Results are displayed graphically for values of transmittances in excess of 0.9 associated with relative indices of refraction in the range m = 1.0 to m = 2.6.

Short-range, overpressure-driven methane migration in coarse-grained gas hydrate reservoirs

DOE PAGES

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

2016-08-31

Two methane migration mechanisms have been proposed for coarse-grained gas hydrate reservoirs: short-range diffusive gas migration and long-range advective fluid transport from depth. Herein we demonstrate that short-range fluid flow due to overpressure in marine sediments is a significant additional methane transport mechanism that allows hydrate to precipitate in large quantities in thick, coarse-grained hydrate reservoirs. Two-dimensional simulations demonstrate that this migration mechanism, short-range advective transport, can supply significant amounts of dissolved gas and is unencumbered by limitations of the other two end-member mechanisms. Here, short-range advective migration can increase the amount of methane delivered to sands as compared tomore » the slow process of diffusion, yet it is not necessarily limited by effective porosity reduction as is typical of updip advection from a deep source.« less

Short-range, overpressure-driven methane migration in coarse-grained gas hydrate reservoirs

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

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

Two methane migration mechanisms have been proposed for coarse-grained gas hydrate reservoirs: short-range diffusive gas migration and long-range advective fluid transport from depth. Herein we demonstrate that short-range fluid flow due to overpressure in marine sediments is a significant additional methane transport mechanism that allows hydrate to precipitate in large quantities in thick, coarse-grained hydrate reservoirs. Two-dimensional simulations demonstrate that this migration mechanism, short-range advective transport, can supply significant amounts of dissolved gas and is unencumbered by limitations of the other two end-member mechanisms. Here, short-range advective migration can increase the amount of methane delivered to sands as compared tomore » the slow process of diffusion, yet it is not necessarily limited by effective porosity reduction as is typical of updip advection from a deep source.« less

An analysis of curvature effects for the control of wall-bounded shear flows

NASA Technical Reports Server (NTRS)

Gatski, T. B.; Savill, A. M.

1989-01-01

The Reynolds stress transport equations are used to predict the effects of simultaneous and sequential combinations of distortions on turbulent boundary layers. The equations are written in general orthogonal curvilinear coordinates, with the curvature terms expressed in terms of the principal radii of curvature of the respective coordinate surfaces. Results are obtained for the cases of two-dimensional and three-dimensional flows in the limit where production and pressure-strain redistribution dominate over diffusion effects.

Core structure of two-dimensional Fermi gas vortices in the BEC-BCS crossover region

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

Madeira, Lucas; Gandolfi, Stefano; Schmidt, Kevin E.

2017-05-02

We report T = 0 diffusion Monte Carlo results for the ground-state and vortex excitation of unpolarized spin-1/2 fermions in a two-dimensional disk. We investigate how vortex core structure properties behave over the BEC-BCS crossover. We calculate the vortex excitation energy, density pro les, and vortex core properties related to the current. We nd a density suppression at the vortex core on the BCS side of the crossover and a depleted core on the BEC limit. Size-effect dependencies in the disk geometry were carefully studied.

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

NASA Astrophysics Data System (ADS)

Rajaram, Harihar; Arshadi, Masoud

2015-04-01

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

Border-crossing model for the diffusive coarsening of two-dimensional and quasi-two-dimensional wet foams

NASA Astrophysics Data System (ADS)

Schimming, C. D.; Durian, D. J.

2017-09-01

For dry foams, the transport of gas from small high-pressure bubbles to large low-pressure bubbles is dominated by diffusion across the thin soap films separating neighboring bubbles. For wetter foams, the film areas become smaller as the Plateau borders and vertices inflate with liquid. So-called "border-blocking" models can explain some features of wet-foam coarsening based on the presumption that the inflated borders totally block the gas flux; however, this approximation dramatically fails in the wet or unjamming limit where the bubbles become close-packed spheres and coarsening proceeds even though there are no films. Here, we account for the ever-present border-crossing flux by a new length scale defined by the average gradient of gas concentration inside the borders. We compute that it is proportional to the geometric average of film and border thicknesses, and we verify this scaling by numerical solution of the diffusion equation. We similarly consider transport across inflated vertices and surface Plateau borders in quasi-two-dimensional foams. And we show how the d A /d t =K0(n -6 ) von Neumann law is modified by the appearance of terms that depend on bubble size and shape as well as the concentration gradient length scales. Finally, we use the modified von Neumann law to compute the growth rate of the average bubble area, which is not constant.

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.

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.

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.

Two-dimensional lithium diffusion behavior and probable hybrid phase transformation kinetics in olivine lithium iron phosphate

DOE PAGES

Hong, Liang; Li, Linsen; Chen-Wiegart, Yuchen-Karen; ...

2017-10-30

Olivine lithium iron phosphate is a technologically important electrode material for lithium-ion batteries and a model system for studying electrochemically driven phase transformations. Despite extensive studies, many aspects of the phase transformation and lithium transport in this material are still not well understood. Here we combine operando hard X-ray spectroscopic imaging and phase-field modeling to elucidate the delithiation dynamics of single-crystal lithium iron phosphate microrods with long-axis along the [010] direction. Lithium diffusivity is found to be two-dimensional in microsized particles containing ~3%lithium-iron anti-site defects. Our study provides direct evidence for the previously predicted surface reaction-limited phase-boundary migration mechanism andmore » the potential operation of a hybrid mode of phase growth, in which phase-boundary movement is controlled by surface reaction or lithium diffusion in different crystallographic directions. These findings uncover the rich phase-transformation behaviors in lithium iron phosphate and intercalation com-pounds in general and can help guide the design of better electrodes.« less

Two-dimensional lithium diffusion behavior and probable hybrid phase transformation kinetics in olivine lithium iron phosphate

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

Hong, Liang; Li, Linsen; Chen-Wiegart, Yuchen-Karen

Olivine lithium iron phosphate is a technologically important electrode material for lithium-ion batteries and a model system for studying electrochemically driven phase transformations. Despite extensive studies, many aspects of the phase transformation and lithium transport in this material are still not well understood. Here we combine operando hard X-ray spectroscopic imaging and phase-field modeling to elucidate the delithiation dynamics of single-crystal lithium iron phosphate microrods with long-axis along the [010] direction. Lithium diffusivity is found to be two-dimensional in microsized particles containing ~3%lithium-iron anti-site defects. Our study provides direct evidence for the previously predicted surface reaction-limited phase-boundary migration mechanism andmore » the potential operation of a hybrid mode of phase growth, in which phase-boundary movement is controlled by surface reaction or lithium diffusion in different crystallographic directions. These findings uncover the rich phase-transformation behaviors in lithium iron phosphate and intercalation com-pounds in general and can help guide the design of better electrodes.« less

Two-dimensional lithium diffusion behavior and probable hybrid phase transformation kinetics in olivine lithium iron phosphate

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

Hong, Liang; Chen-Wiegart, Yu-Chen K.

2017-10-30

Olivine lithium iron phosphate is a technologically important electrode material for lithium-ion batteries and a model system for studying electrochemically driven phase transformations. Despite extensive studies, many aspects of the phase transformation and lithium transport in this material are still not well understood. Here we combine operando hard X-ray spectroscopic imaging and phase-field modeling to elucidate the delithiation dynamics of single-crystal lithium iron phosphate microrods with long-axis along the [010] direction. Lithium diffusivity is found to be two-dimensional in microsized particles containing ~3%lithium-iron anti-site defects. Our study provides direct evidence for the previously predicted surface reaction-limited phase-boundary migration mechanism andmore » the potential operation of a hybrid mode of phase growth, in which phase-boundary movement is controlled by surface reaction or lithium diffusion in different crystallographic directions. These findings uncover the rich phase-transformation behaviors in lithium iron phosphate and intercalation com-pounds in general and can help guide the design of better electrodes.« less

Self-diffusion in a stochastically heated two-dimensional dusty plasma

NASA Astrophysics Data System (ADS)

Sheridan, T. E.

2016-09-01

Diffusion in a two-dimensional dusty plasma liquid (i.e., a Yukawa liquid) is studied experimentally. The dusty plasma liquid is heated stochastically by a surrounding three-dimensional toroidal dusty plasma gas which acts as a thermal reservoir. The measured dust velocity distribution functions are isotropic Maxwellians, giving a well-defined kinetic temperature. The mean-square displacement for dust particles is found to increase linearly with time, indicating normal diffusion. The measured diffusion coefficients increase approximately linearly with temperature. The effective collision rate is dominated by collective dust-dust interactions rather than neutral gas drag, and is comparable to the dusty-plasma frequency.

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

Abnormal growth kinetics of h-BN epitaxial monolayer on Ru(0001) enhanced by subsurface Ar species

NASA Astrophysics Data System (ADS)

Wei, Wei; Meng, Jie; Meng, Caixia; Ning, Yanxiao; Li, Qunxiang; Fu, Qiang; Bao, Xinhe

2018-04-01

Growth kinetics of epitaxial films often follows the diffusion-limited aggregation mechanism, which shows a "fractal-to-compact" morphological transition with increasing growth temperature or decreasing deposition flux. Here, we observe an abnormal "compact-to-fractal" morphological transition with increasing growth temperature for hexagonal boron nitride growth on the Ru(0001) surface. The unusual growth process can be explained by a reaction-limited aggregation (RLA) mechanism. Moreover, introduction of the subsurface Ar atoms has enhanced this RLA growth behavior by decreasing both reaction and diffusion barriers. Our work may shed light on the epitaxial growth of two-dimensional atomic crystals and help to control their morphology.

Theory of Stochastic Laplacian Growth

NASA Astrophysics Data System (ADS)

Alekseev, Oleg; Mineev-Weinstein, Mark

2017-07-01

We generalize the diffusion-limited aggregation by issuing many randomly-walking particles, which stick to a cluster at the discrete time unit providing its growth. Using simple combinatorial arguments we determine probabilities of different growth scenarios and prove that the most probable evolution is governed by the deterministic Laplacian growth equation. A potential-theoretical analysis of the growth probabilities reveals connections with the tau-function of the integrable dispersionless limit of the two-dimensional Toda hierarchy, normal matrix ensembles, and the two-dimensional Dyson gas confined in a non-uniform magnetic field. We introduce the time-dependent Hamiltonian, which generates transitions between different classes of equivalence of closed curves, and prove the Hamiltonian structure of the interface dynamics. Finally, we propose a relation between probabilities of growth scenarios and the semi-classical limit of certain correlation functions of "light" exponential operators in the Liouville conformal field theory on a pseudosphere.

Hybrid finite element and Brownian dynamics method for charged particles

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

Huber, Gary A., E-mail: ghuber@ucsd.edu; Miao, Yinglong; Zhou, Shenggao

2016-04-28

Diffusion is often the rate-determining step in many biological processes. Currently, the two main computational methods for studying diffusion are stochastic methods, such as Brownian dynamics, and continuum methods, such as the finite element method. A previous study introduced a new hybrid diffusion method that couples the strengths of each of these two methods, but was limited by the lack of interactions among the particles; the force on each particle had to be from an external field. This study further develops the method to allow charged particles. The method is derived for a general multidimensional system and is presented usingmore » a basic test case for a one-dimensional linear system with one charged species and a radially symmetric system with three charged species.« less

Characteristic power spectrum of diffusive interface dynamics in the two-dimensional Ising model

NASA Astrophysics Data System (ADS)

Masumoto, Yusuke; Takesue, Shinji

2018-05-01

We investigate properties of the diffusive motion of an interface in the two-dimensional Ising model in equilibrium or nonequilibrium situations. We focused on the relation between the power spectrum of a time sequence of spins and diffusive motion of an interface which was already clarified in one-dimensional systems with a nonequilibrium phase transition like the asymmetric simple exclusion process. It is clarified that the interface motion is a diffusion process with a drift force toward the higher-temperature side when the system is in contact with heat reservoirs at different temperatures and heat transfers through the system. Effects of the width of the interface are also discussed.

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.

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

Steady motion of skyrmions and domains walls under diffusive spin torques

NASA Astrophysics Data System (ADS)

Elías, Ricardo Gabriel; Vidal-Silva, Nicolas; Manchon, Aurélien

2017-03-01

We explore the role of the spin diffusion of conducting electrons in two-dimensional magnetic textures (domain walls and skyrmions) with spatial variation of the order of the spin precession length λex. The effect of diffusion reflects in four additional torques that are third order in spatial derivatives of magnetization and bilinear in λex and in the nonadiabatic parameter β'. In order to study the dynamics of the solitons when these diffusive torques are present, we derive the Thiele equation in the limit of steady motion and we compare the results with the nondiffusive limit. When considering a homogenous current these torques increase the longitudinal velocity of transverse domain walls of width Δ by a factor (λex/Δ)2(α/3), α being the magnetic damping constant. In the case of single skyrmions with core radius r0these new contributions tend to increase the Magnus effect in an amount proportional to (λex/r0) 2(1 +2 α β') .

Experimental dynamic response of a two-dimensional, Mach 2.7, mixed compression inlet

NASA Technical Reports Server (NTRS)

Baumbick, R. J.; Neiner, G. H.; Cole, G. L.

1972-01-01

A test program was conducted on a two-dimensional supersonic inlet. Internal disturbances in diffuser exit mass flow were produced by oscillating overboard bypass doors. Open-loop dynamic responses of shock position, throat exit and diffuser exit static pressures are presented. The steady-state and dynamic coupling between ducts were also obtained. The experimental results from the two-dimensional inlet are compared to results from a similar size axisymmetric inlet and also to a transfer function synthesis program.

Dimensional control of defect dynamics in perovskite oxide superlattices

NASA Astrophysics Data System (ADS)

Bredeson, Isaac; Zhang, Lipeng; Kent, P. R. C.; Cooper, Valentino R.; Xu, Haixuan

2018-03-01

Point defects play a critical role in the structural, physical, and interfacial properties of perovskite oxide superlattices. However, understanding of the fundamental properties of point defects in superlattices, especially their transport properties, is rather limited. Here, we report predictions of the stability and dynamics of oxygen vacancies in SrTi O3/PbTi O3 oxide superlattices using first-principles calculations in combination with the kinetic Monte Carlo method. By varying the stacking period, i.e., changing of n in n STO /n PTO , we discover a crossover from three-dimensional diffusion to primarily two-dimensional planar diffusion. Such planar diffusion may lead to novel designs of ionic conductors. We show that the dominant vacancy position may vary in the superlattices, depending on the superlattice structure and stacking period, contradicting the common assumption that point defects reside at interfaces. Moreover, we predict a significant increase in room-temperature ionic conductivity for 3STO/3PTO relative to the bulk phases. Considering the variety of cations that can be accommodated in perovskite superlattices and the potential mismatch of spin, charge, and orbitals at the interfaces, this paper identifies a pathway to control defect dynamics for technological applications.

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.

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.

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

NASA Astrophysics Data System (ADS)

Seki, Kazuhiko; Bagchi, Kaushik; Bagchi, Biman

2016-05-01

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

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

PubMed

Seki, Kazuhiko; Bagchi, Kaushik; Bagchi, Biman

2016-05-21

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

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.

Confinement effects on dipolar relaxation by translational dynamics of liquids in porous silica glasses

NASA Astrophysics Data System (ADS)

Korb, J.-P.; Xu, Shu; Jonas, J.

1993-02-01

A theory of dipolar relaxation by translational diffusion of a nonwetting liquid confined in model porous media is presented. We obtain expressions of the rates of spin-lattice relaxation 1/T1, spin-spin relaxation 1/T2, and spin-lattice relaxation in the rotating frame 1/T1ρ, which depend on the average pore size d. The frequency variations of these rates are intermediate between the two-dimensional and three-dimensional results. At small frequency they vary logarithmically for small d and tend progressively to a constant with increasing d. For small pore sizes we obtain quadratic confinement dependences of these rates (∝1/d2), at variance with the linear (∝1/d) relation coming from the biphasic fast exchange model usually applied for a wetting liquid in porous media. We apply such a theory to the 1H NMR relaxation of methylcyclohexane liquid in sol-gel porous silica glasses with a narrow pore-size distribution. The experiments confirm the theoretical predictions for very weak interacting solvent in porous silica glasses of pore sizes varying in the range of 18.4-87.2 Å and in the bulk. At the limit of small pores, the logarithmic frequency dependencies of 1/T1ρ and 1/T1 observed over several decades of frequency are interpreted with a model of unbounded two-dimensional diffusion in a layered geometry. The leveling off of the 1/T1ρ low-frequency dependence is interpreted in terms of the bounded two-dimensional diffusion due to the finite length L of the pores. An estimate of a finite size of L=100 Å is in excellent agreement with the experimental results of the transmission electron microscopy study of platinium-carbon replicated xerogels.

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.

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

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.

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.

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.

Comparison of analytical and experimental performance of a wind-tunnel diffuser section

NASA Technical Reports Server (NTRS)

Shyne, R. J.; Moore, R. D.; Boldman, D. R.

1986-01-01

Wind tunnel diffuser performance is evaluated by comparing experimental data with analytical results predicted by an one-dimensional integration procedure with skin friction coefficient, a two-dimensional interactive boundary layer procedure for analyzing conical diffusers, and a two-dimensional, integral, compressible laminar and turbulent boundary layer code. Pressure, temperature, and velocity data for a 3.25 deg equivalent cone half-angle diffuser (37.3 in., 94.742 cm outlet diameter) was obtained from the one-tenth scale Altitude Wind Tunnel modeling program at the NASA Lewis Research Center. The comparison is performed at Mach numbers of 0.162 (Re = 3.097x19(6)), 0.326 (Re = 6.2737x19(6)), and 0.363 (Re = 7.0129x10(6)). The Reynolds numbers are all based on an inlet diffuser diameter of 32.4 in., 82.296 cm, and reasonable quantitative agreement was obtained between the experimental data and computational codes.

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

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.

Hot-electron thermocouple and the diffusion thermopower of two-dimensional electrons in GaAs.

PubMed

Chickering, W E; Eisenstein, J P; Reno, J L

2009-07-24

A simple hot-electron thermocouple is realized in a two-dimensional electron system (2DES) and used to measure the diffusion thermopower of the 2DES at zero magnetic field. This hot-electron technique, which requires no micron-scale patterning of the 2DES, is much less sensitive than conventional methods to phonon-drag effects. Our thermopower results are in good agreement with the Mott formula for diffusion thermopower for temperatures up to T approximately 2 K.

Normal versus anomalous self-diffusion in two-dimensional fluids: memory function approach and generalized asymptotic Einstein relation.

PubMed

Shin, Hyun Kyung; Choi, Bongsik; Talkner, Peter; Lee, Eok Kyun

2014-12-07

Based on the generalized Langevin equation for the momentum of a Brownian particle a generalized asymptotic Einstein relation is derived. It agrees with the well-known Einstein relation in the case of normal diffusion but continues to hold for sub- and super-diffusive spreading of the Brownian particle's mean square displacement. The generalized asymptotic Einstein relation is used to analyze data obtained from molecular dynamics simulations of a two-dimensional soft disk fluid. We mainly concentrated on medium densities for which we found super-diffusive behavior of a tagged fluid particle. At higher densities a range of normal diffusion can be identified. The motion presumably changes to sub-diffusion for even higher densities.

Normal versus anomalous self-diffusion in two-dimensional fluids: Memory function approach and generalized asymptotic Einstein relation

NASA Astrophysics Data System (ADS)

Shin, Hyun Kyung; Choi, Bongsik; Talkner, Peter; Lee, Eok Kyun

2014-12-01

Based on the generalized Langevin equation for the momentum of a Brownian particle a generalized asymptotic Einstein relation is derived. It agrees with the well-known Einstein relation in the case of normal diffusion but continues to hold for sub- and super-diffusive spreading of the Brownian particle's mean square displacement. The generalized asymptotic Einstein relation is used to analyze data obtained from molecular dynamics simulations of a two-dimensional soft disk fluid. We mainly concentrated on medium densities for which we found super-diffusive behavior of a tagged fluid particle. At higher densities a range of normal diffusion can be identified. The motion presumably changes to sub-diffusion for even higher densities.

On the modeling of the bottom particles segregation with non-linear diffusion equations: application to the marine sand ripples

NASA Astrophysics Data System (ADS)

Tiguercha, Djlalli; Bennis, Anne-claire; Ezersky, Alexander

2015-04-01

The elliptical motion in surface waves causes an oscillating motion of the sand grains leading to the formation of ripple patterns on the bottom. Investigation how the grains with different properties are distributed inside the ripples is a difficult task because of the segration of particle. The work of Fernandez et al. (2003) was extended from one-dimensional to two-dimensional case. A new numerical model, based on these non-linear diffusion equations, was developed to simulate the grain distribution inside the marine sand ripples. The one and two-dimensional models are validated on several test cases where segregation appears. Starting from an homogeneous mixture of grains, the two-dimensional simulations demonstrate different segregation patterns: a) formation of zones with high concentration of light and heavy particles, b) formation of «cat's eye» patterns, c) appearance of inverse Brazil nut effect. Comparisons of numerical results with the new set of field data and wave flume experiments show that the two-dimensional non-linear diffusion equations allow us to reproduce qualitatively experimental results on particles segregation.

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.

THE IMPLICIT CONTRIBUTION OF SLAB MODES TO THE PERPENDICULAR DIFFUSION COEFFICIENT OF PARTICLES INTERACTING WITH TWO-COMPONENT TURBULENCE

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

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

2016-10-20

We explore the transport of energetic particles in two-component turbulence in which the stochastic magnetic field is assumed to be a superposition of slab and two-dimensional modes. It is known that in magnetostatic slab turbulence, the motion of particles across the mean magnetic field is subdiffusive. If a two-dimensional component is added, diffusion is recovered. It was also shown before that in two-component turbulence, the slab modes do not explicitly contribute to the perpendicular diffusion coefficient. In the current paper, the implicit contribution of slab modes is explored and it is shown that this contribution leads to a reduction ofmore » the perpendicular diffusion coefficient. This effect improves the agreement between simulations and analytical theory. Furthermore, the obtained results are relevant for investigations of diffusive shock acceleration.« less

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.

Reaction-diffusion systems and external morphogen gradients: the two-dimensional case, with an application to skeletal pattern formation.

PubMed

Glimm, Tilmann; Zhang, Jianying; Shen, Yun-Qiu; Newman, Stuart A

2012-03-01

We investigate a reaction-diffusion system consisting of an activator and an inhibitor in a two-dimensional domain. There is a morphogen gradient in the domain. The production of the activator depends on the concentration of the morphogen. Mathematically, this leads to reaction-diffusion equations with explicitly space-dependent terms. It is well known that in the absence of an external morphogen, the system can produce either spots or stripes via the Turing bifurcation. We derive first-order expansions for the possible patterns in the presence of an external morphogen and show how both stripes and spots are affected. This work generalizes previous one-dimensional results to two dimensions. Specifically, we consider the quasi-one-dimensional case of a thin rectangular domain and the case of a square domain. We apply the results to a model of skeletal pattern formation in vertebrate limbs. In the framework of reaction-diffusion models, our results suggest a simple explanation for some recent experimental findings in the mouse limb which are much harder to explain in positional-information-type models.

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.

Small particle transport across turbulent nonisothermal boundary layers

NASA Technical Reports Server (NTRS)

Rosner, D. E.; Fernandez De La Mora, J.

1982-01-01

The interaction between turbulent diffusion, Brownian diffusion, and particle thermophoresis in the limit of vanishing particle inertial effects is quantitatively modeled for applications in gas turbines. The model is initiated with consideration of the particle phase mass conservation equation for a two-dimensional boundary layer, including the thermophoretic flux term directed toward the cold wall. A formalism of a turbulent flow near a flat plate in a heat transfer problem is adopted, and variable property effects are neglected. Attention is given to the limit of very large Schmidt numbers and the particle concentration depletion outside of the Brownian sublayer. It is concluded that, in the parameter range of interest, thermophoresis augments the high Schmidt number mass-transfer coefficient by a factor equal to the product of the outer sink and the thermophoretic suction.

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.

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.

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.

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.

Diffusion in higher dimensional SYK model with complex fermions

NASA Astrophysics Data System (ADS)

Cai, Wenhe; Ge, Xian-Hui; Yang, Guo-Hong

2018-01-01

We construct a new higher dimensional SYK model with complex fermions on bipartite lattices. As an extension of the original zero-dimensional SYK model, we focus on the one-dimension case, and similar Hamiltonian can be obtained in higher dimensions. This model has a conserved U(1) fermion number Q and a conjugate chemical potential μ. We evaluate the thermal and charge diffusion constants via large q expansion at low temperature limit. The results show that the diffusivity depends on the ratio of free Majorana fermions to Majorana fermions with SYK interactions. The transport properties and the butterfly velocity are accordingly calculated at low temperature. The specific heat and the thermal conductivity are proportional to the temperature. The electrical resistivity also has a linear temperature dependence term.

Flow effects in a vertical CVD reactor

NASA Technical Reports Server (NTRS)

Young, G. W.; Hariharan, S. I.; Carnahan, R.

1992-01-01

A model is presented to simulate the non-Boussinesq flow in a vertical, two-dimensional, chemical vapor deposition reactor under atmospheric pressure. Temperature-dependent conductivity, mass diffusivity, viscosity models, and reactive species mass transfer to the substrate are incorporated. In the limits of small Mach number and small aspect ratio, asymptotic expressions for the flow, temperature, and species fields are developed. Soret diffusion effects are also investigated. Analytical solutions predict an inverse relationship between temperature field and concentration field due to Soret effects. This finding is consistent with numerical simulations, assisting in the understanding of the complex interactions amongst the flow, thermal, and species fields in a chemically reacting system.

Binarization of apodizers by adapted one-dimensional error diffusion method

NASA Astrophysics Data System (ADS)

Kowalczyk, Marek; Cichocki, Tomasz; Martinez-Corral, Manuel; Andres, Pedro

1994-10-01

Two novel algorithms for the binarization of continuous rotationally symmetric real positive pupil filters are presented. Both algorithms are based on 1-D error diffusion concept. The 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 pupils with equal width zones give Fraunhofer diffraction pattern more similar to that of the original continuous-tone pupil than those with equal area zones, assuming in both cases the same resolution limit of printing device.

Nonequilibrium fluctuations during diffusion in liquid layers

NASA Astrophysics Data System (ADS)

Brogioli, Doriano; Vailati, Alberto

2017-07-01

Theoretical analysis and experiments have provided compelling evidence of the presence of long-range nonequilibrium concentration fluctuations during diffusion processes in fluids. In this paper, we investigate the dependence of the features of the fluctuations from the dimensionality of the system. In three-dimensional fluids the amplitude of nonequilibrium fluctuations can become several orders of magnitude larger than that of equilibrium fluctuations. Notwithstanding that, the amplitude of nonequilibrium fluctuations remains small with respect to the concentration difference driving the diffusion process. By extending the theory to two-dimensional systems, such as liquid monolayers and bilayers, we show that the amplitude of the fluctuations becomes much stronger than in three-dimensional systems. We investigate the properties of the fronts of diffusion and show that they have a self-affine structure characterized by a Hurst exponent H =1 . We discuss the implications of these results for diffusion in liquid crystals and in cellular membranes of living organisms.

Nonequilibrium fluctuations during diffusion in liquid layers.

PubMed

Brogioli, Doriano; Vailati, Alberto

2017-07-01

Theoretical analysis and experiments have provided compelling evidence of the presence of long-range nonequilibrium concentration fluctuations during diffusion processes in fluids. In this paper, we investigate the dependence of the features of the fluctuations from the dimensionality of the system. In three-dimensional fluids the amplitude of nonequilibrium fluctuations can become several orders of magnitude larger than that of equilibrium fluctuations. Notwithstanding that, the amplitude of nonequilibrium fluctuations remains small with respect to the concentration difference driving the diffusion process. By extending the theory to two-dimensional systems, such as liquid monolayers and bilayers, we show that the amplitude of the fluctuations becomes much stronger than in three-dimensional systems. We investigate the properties of the fronts of diffusion and show that they have a self-affine structure characterized by a Hurst exponent H=1. We discuss the implications of these results for diffusion in liquid crystals and in cellular membranes of living organisms.

Limit Properties of One Dimensional Periodic Hopping Model

NASA Astrophysics Data System (ADS)

Zhang, Yun-xin

2010-02-01

One dimensional periodic hopping model is useful to understand the motion of microscopic particles in thermal noise environment. In this research, by formal calculation and based on detailed balance, the explicit expressions of the limits of mean velocity and diffusion constant of this model as the number of internal mechanochemical sates tend to infinity are obtained. These results will be helpful to understand the limit of the one dimensional hopping model. At the same time, the work can be used to get more useful results in continuous form from the corresponding ones obtained by discrete models.

Spintronics: spin accumulation in mesoscopic systems.

PubMed

Johnson, Mark

2002-04-25

In spintronics, in which use is made of the spin degree of freedom of the electron, issues concerning electrical spin injection and detection of electron spin diffusion are fundamentally important. Jedema et al. describe a magneto-resistance study in which they claim to have observed spin accumulation in a mesoscopic copper wire, but their one-dimensional model ignores two-dimensional spin-diffusion effects, which casts doubt on their analysis. A two-dimensional vector formalism of spin transport is called for to model spin-injection experiments, and the identification of spurious background resistance effects is crucial.

Effects of Channel Modification on Detection and Dating of Fault Scarps

NASA Astrophysics Data System (ADS)

Sare, R.; Hilley, G. E.

2016-12-01

Template matching of scarp-like features could potentially generate morphologic age estimates for individual scarps over entire regions, but data noise and scarp modification limits detection of fault scarps by this method. Template functions based on diffusion in the cross-scarp direction may fail to accurately date scarps near channel boundaries. Where channels reduce scarp amplitudes, or where cross-scarp noise is significant, signal-to-noise ratios decrease and the scarp may be poorly resolved. In this contribution, we explore the bias in morphologic age of a complex scarp produced by systematic changes in fault scarp curvature. For example, fault scarps may be modified by encroaching channel banks and mass failure, lateral diffusion of material into a channel, or undercutting parallel to the base of a scarp. We quantify such biases on morphologic age estimates using a block offset model subject to two-dimensional linear diffusion. We carry out a synthetic study of the effects of two-dimensional transport on morphologic age calculated using a profile model, and compare these results to a well- studied and constrained site along the San Andreas Fault at Wallace Creek, CA. This study serves as a first step towards defining regions of high confidence in template matching results based on scarp length, channel geometry, and near-scarp topography.

Asymptotic analysis of discrete schemes for non-equilibrium radiation diffusion

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

Cui, Xia, E-mail: cui_xia@iapcm.ac.cn; Yuan, Guang-wei; Shen, Zhi-jun

Motivated by providing well-behaved fully discrete schemes in practice, this paper extends the asymptotic analysis on time integration methods for non-equilibrium radiation diffusion in [2] to space discretizations. Therein studies were carried out on a two-temperature model with Larsen's flux-limited diffusion operator, both the implicitly balanced (IB) and linearly implicit (LI) methods were shown asymptotic-preserving. In this paper, we focus on asymptotic analysis for space discrete schemes in dimensions one and two. First, in construction of the schemes, in contrast to traditional first-order approximations, asymmetric second-order accurate spatial approximations are devised for flux-limiters on boundary, and discrete schemes with second-ordermore » accuracy on global spatial domain are acquired consequently. Then by employing formal asymptotic analysis, the first-order asymptotic-preserving property for these schemes and furthermore for the fully discrete schemes is shown. Finally, with the help of manufactured solutions, numerical tests are performed, which demonstrate quantitatively the fully discrete schemes with IB time evolution indeed have the accuracy and asymptotic convergence as theory predicts, hence are well qualified for both non-equilibrium and equilibrium radiation diffusion. - Highlights: • Provide AP fully discrete schemes for non-equilibrium radiation diffusion. • Propose second order accurate schemes by asymmetric approach for boundary flux-limiter. • Show first order AP property of spatially and fully discrete schemes with IB evolution. • Devise subtle artificial solutions; verify accuracy and AP property quantitatively. • Ideas can be generalized to 3-dimensional problems and higher order implicit schemes.« less

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.

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.

Kinetics of Surface-Mediated Fibrillization of Amyloid-β (12-28) Peptides.

PubMed

Lin, Yi-Chih; Li, Chen; Fakhraai, Zahra

2018-04-17

Surfaces or interfaces are considered to be key factors in facilitating the formation of amyloid fibrils under physiological conditions. In this report, we study the kinetics of the surface-mediated fibrillization (SMF) of an amyloid-β fragment (Aβ 12-28 ) on mica. We employ a spin-coating-based drying procedure to control the exposure time of the substrate to a low-concentration peptide solution and then monitor the fibril growth as a function of time via atomic force microscopy (AFM). The evolution of surface-mediated fibril growth is quantitatively characterized in terms of the length histogram of imaged fibrils and their surface concentration. A two-dimensional (2D) kinetic model is proposed to numerically simulate the length evolution of surface-mediated fibrils by assuming a diffusion-limited aggregation (DLA) process along with size-dependent rate constants. We find that both monomer and fibril diffusion on the surface are required to obtain length histograms as a function of time that resemble those observed in experiments. The best-fit simulated data can accurately describe the key features of experimental length histograms and suggests that the mobility of loosely bound amyloid species is crucial in regulating the kinetics of SMF. We determine that the mobility exponent for the size dependence of the DLA rate constants is α = 0.55 ± 0.05, which suggests that the diffusion of loosely bound surface fibrils roughly depends on the inverse of the square root of their size. These studies elucidate the influence of deposition rate and surface diffusion on the formation of amyloid fibrils through SMF. The method used here can be broadly adopted to study the diffusion and aggregation of peptides or proteins on various surfaces to investigate the role of chemical interactions in two-dimensional fibril formation and diffusion.

Comparisons between thermodynamic and one-dimensional combustion models of spark-ignition engines

NASA Technical Reports Server (NTRS)

Ramos, J. I.

1986-01-01

Results from a one-dimensional combustion model employing a constant eddy diffusivity and a one-step chemical reaction are compared with those of one-zone and two-zone thermodynamic models to study the flame propagation in a spark-ignition engine. One-dimensional model predictions are found to be very sensitive to the eddy diffusivity and reaction rate data. The average mixing temperature found using the one-zone thermodynamic model is higher than those of the two-zone and one-dimensional models during the compression stroke, and that of the one-dimensional model is higher than those predicted by both thermodynamic models during the expansion stroke. The one-dimensional model is shown to predict an accelerating flame even when the front approaches the cold cylinder wall.

Pursuing two-dimensional nanomaterials for flexible lithium-ion batteries

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

Liu, Bin; Zhang, Ji-Guang; Shen, Guozhen

2016-02-01

Stretchable/flexible electronics provide a foundation for various emerging applications that beyond the scope of conventional wafer/circuit board technologies due to their unique features that can satisfy a broad range of applications such as wearable devices. Stretchable electronic and optoelectronics devices require the bendable/wearable rechargeable Li-ion batteries, thus these devices can operate without limitation of external powers. Various two-dimensional (2D) nanomaterials are of great interest in flexible energy storage devices, especially Li-ion batteries. This is because 2D materials exhibit much more exposed surface area supplying abundant Li-insertion channels and shortened paths for fast lithium ion diffusion. Here, we will review themore » recent developments on the flexible Li-ion batteries based on two dimensional nanomaterials. These researches demonstrated advancements in flexible electronics by incorporating various 2D nanomaterials into bendable batteries to achieve high electrochemical performance, excellent mechanical flexibility as well as electrical stability under stretching/bending conditions.« less

Fast Fourier single-pixel imaging via binary illumination.

PubMed

Zhang, Zibang; Wang, Xueying; Zheng, Guoan; Zhong, Jingang

2017-09-20

Fourier single-pixel imaging (FSI) employs Fourier basis patterns for encoding spatial information and is capable of reconstructing high-quality two-dimensional and three-dimensional images. Fourier-domain sparsity in natural scenes allows FSI to recover sharp images from undersampled data. The original FSI demonstration, however, requires grayscale Fourier basis patterns for illumination. This requirement imposes a limitation on the imaging speed as digital micro-mirror devices (DMDs) generate grayscale patterns at a low refreshing rate. In this paper, we report a new strategy to increase the speed of FSI by two orders of magnitude. In this strategy, we binarize the Fourier basis patterns based on upsampling and error diffusion dithering. We demonstrate a 20,000 Hz projection rate using a DMD and capture 256-by-256-pixel dynamic scenes at a speed of 10 frames per second. The reported technique substantially accelerates image acquisition speed of FSI. It may find broad imaging applications at wavebands that are not accessible using conventional two-dimensional image sensors.

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

NASA Astrophysics Data System (ADS)

Lin, Guoxing

2018-05-01

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

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.

Controlled Self-Assembly of Low-Dimensional Alq3 Nanostructures from 1D Nanowires to 2D Plates via Intermolecular Interactions

NASA Astrophysics Data System (ADS)

Gu, Jianmin; Yin, Baipeng; Fu, Shaoyan; Jin, Cuihong; Liu, Xin; Bian, Zhenpan; Li, Jianjun; Wang, Lu; Li, Xiaoyu

2018-03-01

Due to the intense influence of the shape and size of the photon building blocks on the limitation and guidance of optical waves, an important strategy is the fabrication of different structures. Herein, organic semiconductor tris-(8-hydroxyquinoline)aluminium (Alq3) nanostructures with controllable morphology, ranging from one-dimensional nanowires to two-dimensional plates, have been prepared through altering intermolecular interactions with employing the anti-solvent diffusion cooperate with solvent-volatilization induced self-assembly method. The morphologies of the formed nanostructures, which are closely related to the stacking modes of the molecules, can be exactly controlled by altering the polarity of anti-solvents that can influence various intermolecular interactions. The synthesis strategy reported here can potentially be extended to other functional organic nanomaterials.

A third-order computational method for numerical fluxes to guarantee nonnegative difference coefficients for advection-diffusion equations in a semi-conservative form

NASA Astrophysics Data System (ADS)

Sakai, K.; Watabe, D.; Minamidani, T.; Zhang, G. S.

2012-10-01

According to Godunov theorem for numerical calculations of advection equations, there exist no higher-order schemes with constant positive difference coefficients in a family of polynomial schemes with an accuracy exceeding the first-order. We propose a third-order computational scheme for numerical fluxes to guarantee the non-negative difference coefficients of resulting finite difference equations for advection-diffusion equations in a semi-conservative form, in which there exist two kinds of numerical fluxes at a cell surface and these two fluxes are not always coincident in non-uniform velocity fields. The present scheme is optimized so as to minimize truncation errors for the numerical fluxes while fulfilling the positivity condition of the difference coefficients which are variable depending on the local Courant number and diffusion number. The feature of the present optimized scheme consists in keeping the third-order accuracy anywhere without any numerical flux limiter. We extend the present method into multi-dimensional equations. Numerical experiments for advection-diffusion equations showed nonoscillatory solutions.

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

Optimal approximation of harmonic growth clusters by orthogonal polynomials

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

Teodorescu, Razvan

2008-01-01

Interface dynamics in two-dimensional systems with a maximal number of conservation laws gives an accurate theoreticaI model for many physical processes, from the hydrodynamics of immiscible, viscous flows (zero surface-tension limit of Hele-Shaw flows), to the granular dynamics of hard spheres, and even diffusion-limited aggregation. Although a complete solution for the continuum case exists, efficient approximations of the boundary evolution are very useful due to their practical applications. In this article, the approximation scheme based on orthogonal polynomials with a deformed Gaussian kernel is discussed, as well as relations to potential theory.

Diffusive wave in the low Mach limit for non-viscous and heat-conductive gas

NASA Astrophysics Data System (ADS)

Liu, Yechi

2018-06-01

The low Mach number limit for one-dimensional non-isentropic compressible Navier-Stokes system without viscosity is investigated, where the density and temperature have different asymptotic states at far fields. It is proved that the solution of the system converges to a nonlinear diffusion wave globally in time as Mach number goes to zero. It is remarked that the velocity of diffusion wave is proportional with the variation of temperature. Furthermore, it is shown that the solution of compressible Navier-Stokes system also has the same phenomenon when Mach number is suitably small.

Flow measurements in two cambered vane diffusers with different passage widths

NASA Astrophysics Data System (ADS)

Stein, W.; Rautenberg, M.

1985-03-01

To investigate the influence of the vaneless space between impeller exit and the diffuser vanes, detailed flow measurements in two diffusers with the same vane geometry but different passage width are compared. The three-dimensional character of the flow changes between impeller exit and the entry to the two dimensional vanes depending on the shape of the shroud. After initial measurements with a constant area vaneless space, the width of the vaned diffuser was later on reduced by 10 percent. The compressor maps show increases in overall pressure rise and efficiency with the width reduction. To get further details of the flow field, measurements of the static pressure distribution at hub and shroud have been performed at several operation points for both diffusers. At the same points, the flow angle and total pressure distribution between hub and shroud upstream and downstream of the vanes have been measured with probes. The maximum efficiency of the narrow diffuser is nearly 2 percent higher than for the wide diffuser. The measurements give further details to explain this improvement.

Thermal analysis of a growing crystal in an aqueous solution

NASA Astrophysics Data System (ADS)

Shiomi, Yuji; Kuroda, Toshio; Ogawa, Tomoya

1980-10-01

The temperature profiles around growing crystals in aqueous solutions of Rochelle salt were measured with accuracy of 0.005°C in a two-dimensional cell which was used for elimination of thermal convection current in the cell. The temperature distribution became stationary after 2 h from injection of the mother liquid, but the concentration distribution did not become stationary because the diffusion constant of solute in the solution was much smaller than the thermal diffusivity of the solution. The growth rate was linearly proportional to the temperature gradient at every growing interface. Since crystal growth is a typical interaction process between thermal and material flow, the experimental results were analysed by such an interaction model. The analysis confirms that the material flow is limited by diffusion within a layer width of about a few hundreds micrometers on the growing interface.

Pattern formation in superdiffusion Oregonator model

NASA Astrophysics Data System (ADS)

Feng, Fan; Yan, Jia; Liu, Fu-Cheng; He, Ya-Feng

2016-10-01

Pattern formations in an Oregonator model with superdiffusion are studied in two-dimensional (2D) numerical simulations. Stability analyses are performed by applying Fourier and Laplace transforms to the space fractional reaction-diffusion systems. Antispiral, stable turing patterns, and travelling patterns are observed by changing the diffusion index of the activator. Analyses of Floquet multipliers show that the limit cycle solution loses stability at the wave number of the primitive vector of the travelling hexagonal pattern. We also observed a transition between antispiral and spiral by changing the diffusion index of the inhibitor. Project supported by the National Natural Science Foundation of China (Grant Nos. 11205044 and 11405042), the Research Foundation of Education Bureau of Hebei Province, China (Grant Nos. Y2012009 and ZD2015025), the Program for Young Principal Investigators of Hebei Province, China, and the Midwest Universities Comprehensive Strength Promotion Project.

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.

Dynamic colloidal assembly pathways via low dimensional models

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

Yang, Yuguang; Bevan, Michael A., E-mail: mabevan@jhu.edu; Thyagarajan, Raghuram

2016-05-28

Here we construct a low-dimensional Smoluchowski model for electric field mediated colloidal crystallization using Brownian dynamic simulations, which were previously matched to experiments. Diffusion mapping is used to infer dimensionality and confirm the use of two order parameters, one for degree of condensation and one for global crystallinity. Free energy and diffusivity landscapes are obtained as the coefficients of a low-dimensional Smoluchowski equation to capture the thermodynamics and kinetics of microstructure evolution. The resulting low-dimensional model quantitatively captures the dynamics of different assembly pathways between fluid, polycrystal, and single crystals states, in agreement with the full N-dimensional data as characterizedmore » by first passage time distributions. Numerical solution of the low-dimensional Smoluchowski equation reveals statistical properties of the dynamic evolution of states vs. applied field amplitude and system size. The low-dimensional Smoluchowski equation and associated landscapes calculated here can serve as models for predictive control of electric field mediated assembly of colloidal ensembles into two-dimensional crystalline objects.« less

Two-Dimensional Animal-Like Fractals in Thin Films

NASA Astrophysics Data System (ADS)

Gao, Hong-jun; Xue, Zeng-quan; Wu, Quan-de; Pang, Shi-jin

1996-02-01

We present a few unique animal-like fractal patterns in ionized-cluster-beam deposited fullerene-tetracyanoquinodimethane thin films. The fractal patterns consisting of animal-like aggregates such as "fishes" and "quasi-seahorses" have been characterized by transmission electron microscopy. The results indicate that the small aggregates of the animal-like body are composed of many single crystals whose crystalline directions are generally different. The formation of the fractal patterns can be attributed to the cluster-diffusion-limited aggregation.

Solutions of the two-dimensional Hubbard model: Benchmarks and results from a wide range of numerical algorithms

DOE PAGES

LeBlanc, J. P. F.; Antipov, Andrey E.; Becca, Federico; ...

2015-12-14

Numerical results for ground-state and excited-state properties (energies, double occupancies, and Matsubara-axis self-energies) of the single-orbital Hubbard model on a two-dimensional square lattice are presented, in order to provide an assessment of our ability to compute accurate results in the thermodynamic limit. Many methods are employed, including auxiliary-field quantum Monte Carlo, bare and bold-line diagrammatic Monte Carlo, method of dual fermions, density matrix embedding theory, density matrix renormalization group, dynamical cluster approximation, diffusion Monte Carlo within a fixed-node approximation, unrestricted coupled cluster theory, and multireference projected Hartree-Fock methods. Comparison of results obtained by different methods allows for the identification ofmore » uncertainties and systematic errors. The importance of extrapolation to converged thermodynamic-limit values is emphasized. Furthermore, cases where agreement between different methods is obtained establish benchmark results that may be useful in the validation of new approaches and the improvement of existing methods.« less

Kinetics of CO2 diffusion in human carbonic anhydrase: a study using molecular dynamics simulations and the Markov-state model.

PubMed

Chen, Gong; Kong, Xian; Lu, Diannan; Wu, Jianzhong; Liu, Zheng

2017-05-10

Molecular dynamics (MD) simulations, in combination with the Markov-state model (MSM), were applied to probe CO 2 diffusion from an aqueous solution into the active site of human carbonic anhydrase II (hCA-II), an enzyme useful for enhanced CO 2 capture and utilization. The diffusion process in the hydrophobic pocket of hCA-II was illustrated in terms of a two-dimensional free-energy landscape. We found that CO 2 diffusion in hCA-II is a rate-limiting step in the CO 2 diffusion-binding-reaction process. The equilibrium distribution of CO 2 shows its preferential accumulation within a hydrophobic domain in the protein core region. An analysis of the committors and reactive fluxes indicates that the main pathway for CO 2 diffusion into the active site of hCA-II is through a binding pocket where residue Gln 136 contributes to the maximal flux. The simulation results offer a new perspective on the CO 2 hydration kinetics and useful insights toward the development of novel biochemical processes for more efficient CO 2 sequestration and utilization.

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.

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.

Room-temperature ballistic energy transport in molecules with repeating units

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

Rubtsova, Natalia I.; Nyby, Clara M.; Zhang, Hong

2015-06-07

In materials, energy can propagate by means of two limiting regimes: diffusive and ballistic. Ballistic energy transport can be fast and efficient and often occurs with a constant speed. Using two-dimensional infrared spectroscopy methods, we discovered ballistic energy transport via individual polyethylene chains with a remarkably high speed of 1440 m/s and the mean free path length of 14.6 Å in solution at room temperature. Whereas the transport via the chains occurs ballistically, the mechanism switches to diffusive with the effective transport speed of 130 m/s at the end-groups attached to the chains. A unifying model of the transport inmore » molecules is presented with clear time separation and additivity among the transport along oligomeric fragments, which occurs ballistically, and the transport within the disordered fragments, occurring diffusively. The results open new avenues for making novel elements for molecular electronics, including ultrafast energy transporters, controlled chemical reactors, and sub-wavelength quantum nanoseparators.« less

Analysis and design of numerical schemes for gas dynamics 1: Artificial diffusion, upwind biasing, limiters and their effect on accuracy and multigrid convergence

NASA Technical Reports Server (NTRS)

Jameson, Antony

1994-01-01

The theory of non-oscillatory scalar schemes is developed in this paper in terms of the local extremum diminishing (LED) principle that maxima should not increase and minima should not decrease. This principle can be used for multi-dimensional problems on both structured and unstructured meshes, while it is equivalent to the total variation diminishing (TVD) principle for one-dimensional problems. A new formulation of symmetric limited positive (SLIP) schemes is presented, which can be generalized to produce schemes with arbitrary high order of accuracy in regions where the solution contains no extrema, and which can also be implemented on multi-dimensional unstructured meshes. Systems of equations lead to waves traveling with distinct speeds and possibly in opposite directions. Alternative treatments using characteristic splitting and scalar diffusive fluxes are examined, together with modification of the scalar diffusion through the addition of pressure differences to the momentum equations to produce full upwinding in supersonic flow. This convective upwind and split pressure (CUSP) scheme exhibits very rapid convergence in multigrid calculations of transonic flow, and provides excellent shock resolution at very high Mach numbers.

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.

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.

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.

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.

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.

Application of laser ranging and VLBI data to a study of plate tectonic driving forces. [finite element method

NASA Technical Reports Server (NTRS)

Solomon, S. C.

1980-01-01

The measurability of changes in plate driving or resistive forces associated with plate boundary earthquakes by laser rangefinding or VLBI is considered with emphasis on those aspects of plate forces that can be characterized by such measurements. Topics covered include: (1) analytic solutions for two dimensional stress diffusion in a plate following earthquake faulting on a finite fault; (2) two dimensional finite-element solutions for the global state of stress at the Earth's surface for possible plate driving forces; and (3) finite-element solutions for three dimensional stress diffusion in a viscoelastic Earth following earthquake faulting.

Computation for Electromigration in Interconnects of Microelectronic Devices

NASA Astrophysics Data System (ADS)

Averbuch, Amir; Israeli, Moshe; Ravve, Igor; Yavneh, Irad

2001-03-01

Reliability and performance of microelectronic devices depend to a large extent on the resistance of interconnect lines. Voids and cracks may occur in the interconnects, causing a severe increase in the total resistance and even open circuits. In this work we analyze void motion and evolution due to surface diffusion effects and applied external voltage. The interconnects under consideration are three-dimensional (sandwich) constructs made of a very thin metal film of possibly variable thickness attached to a substrate of nonvanishing conductance. A two-dimensional level set approach was applied to study the dynamics of the moving (assumed one-dimensional) boundary of a void in the metal film. The level set formulation of an electromigration and diffusion model results in a fourth-order nonlinear (two-dimensional) time-dependent PDE. This equation was discretized by finite differences on a regular grid in space and a Runge-Kutta integration scheme in time, and solved simultaneously with a second-order static elliptic PDE describing the electric potential distribution throughout the interconnect line. The well-posed three-dimensional problem for the potential was approximated via singular perturbations, in the limit of small aspect ratio, by a two-dimensional elliptic equation with variable coefficients describing the combined local conductivity of metal and substrate (which is allowed to vary in time and space). The difference scheme for the elliptic PDE was solved by a multigrid technique at each time step. Motion of voids in both weak and strong electric fields was examined, and different initial void configurations were considered, including circles, ellipses, polygons with rounded corners, a butterfly, and long grooves. Analysis of the void behavior and its influence on the resistance gives the circuit designer a tool for choosing the proper parameters of an interconnect (width-to-length ratio, properties of the line material, conductivity of the underlayer, etc.).

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.

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

Renormalized charge in a two-dimensional model of colloidal suspension from hypernetted chain approach.

PubMed

Camargo, Manuel; Téllez, Gabriel

2008-04-07

The renormalized charge of a simple two-dimensional model of colloidal suspension was determined by solving the hypernetted chain approximation and Ornstein-Zernike equations. At the infinite dilution limit, the asymptotic behavior of the correlation functions is used to define the effective interactions between the components of the system and these effective interactions were compared to those derived from the Poisson-Boltzmann theory. The results we obtained show that, in contrast to the mean-field theory, the renormalized charge does not saturate, but exhibits a maximum value and then decays monotonically as the bare charge increases. The results also suggest that beyond the counterion layer near to the macroion surface, the ionic cloud is not a diffuse layer which can be handled by means of the linearized theory, as the two-state model claims, but a more complex structure is settled by the correlations between microions.

Projecting diffusion along the normal bundle of a plane curve

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

Valero-Valdés, Carlos; Herrera-Guzmán, Rafael

2014-05-15

The purpose of this paper is to provide new formulas for the effective diffusion coefficient of a generalized Fick-Jacob's equation obtained by projecting the two-dimensional diffusion equation along the normal directions of an arbitrary curve on the plane.

Selection theory of free dendritic growth in a potential flow.

PubMed

von Kurnatowski, Martin; Grillenbeck, Thomas; Kassner, Klaus

2013-04-01

The Kruskal-Segur approach to selection theory in diffusion-limited or Laplacian growth is extended via combination with the Zauderer decomposition scheme. This way nonlinear bulk equations become tractable. To demonstrate the method, we apply it to two-dimensional crystal growth in a potential flow. We omit the simplifying approximations used in a preliminary calculation for the same system [Fischaleck, Kassner, Europhys. Lett. 81, 54004 (2008)], thus exhibiting the capability of the method to extend mathematical rigor to more complex problems than hitherto accessible.

Causal electric charge diffusion and balance functions in relativistic heavy-ion collisions

NASA Astrophysics Data System (ADS)

Kapusta, Joseph I.; Plumberg, Christopher

2018-01-01

We study the propagation and diffusion of electric charge fluctuations in high-energy heavy-ion collisions using the Cattaneo form for the dissipative part of the electric current. As opposed to the ordinary diffusion equation this form limits the speed at which charge can propagate. Including the noise term in the current, which arises uniquely from the fluctuation-dissipation theorem, we calculate the balance functions for charged hadrons in a simple 1+1-dimensional Bjorken hydrodynamical model. Limiting the speed of propagation of charge fluctuations increases the height and reduces the width of these balance functions when plotted versus rapidity. We also estimate the numerical value of the associated diffusion time constant from anti-de Sitter-space/conformal-field theory.

Solution of a cauchy problem for a diffusion equation in a Hilbert space by a Feynman formula

NASA Astrophysics Data System (ADS)

Remizov, I. D.

2012-07-01

The Cauchy problem for a class of diffusion equations in a Hilbert space is studied. It is proved that the Cauchy problem in well posed in the class of uniform limits of infinitely smooth bounded cylindrical functions on the Hilbert space, and the solution is presented in the form of the so-called Feynman formula, i.e., a limit of multiple integrals against a gaussian measure as the multiplicity tends to infinity. It is also proved that the solution of the Cauchy problem depends continuously on the diffusion coefficient. A process reducing an approximate solution of an infinite-dimensional diffusion equation to finding a multiple integral of a real function of finitely many real variables is indicated.

Structure-correlated diffusion anisotropy in nanoporous channel networks by Monte Carlo simulations and percolation theory

NASA Astrophysics Data System (ADS)

Kondrashova, Daria; Valiullin, Rustem; Kärger, Jörg; Bunde, Armin

2017-07-01

Nanoporous silicon consisting of tubular pores imbedded in a silicon matrix has found many technological applications and provides a useful model system for studying phase transitions under confinement. Recently, a model for mass transfer in these materials has been elaborated [Kondrashova et al., Sci. Rep. 7, 40207 (2017)], which assumes that adjacent channels can be connected by "bridges" (with probability pbridge) which allows diffusion perpendicular to the channels. Along the channels, diffusion can be slowed down by "necks" which occur with probability pneck. In this paper we use Monte-Carlo simulations to study diffusion along the channels and perpendicular to them, as a function of pbridge and pneck, and find remarkable correlations between the diffusivities in longitudinal and radial directions. For clarifying the diffusivity in radial direction, which is governed by the concentration of bridges, we applied percolation theory. We determine analytically how the critical concentration of bridges depends on the size of the system and show that it approaches zero in the thermodynamic limit. Our analysis suggests that the critical properties of the model, including the diffusivity in radial direction, are in the universality class of two-dimensional lattice percolation, which is confirmed by our numerical study.

Scanning tunneling spectroscopy study of the proximity effect in a disordered two-dimensional metal.

PubMed

Serrier-Garcia, L; Cuevas, J C; Cren, T; Brun, C; Cherkez, V; Debontridder, F; Fokin, D; Bergeret, F S; Roditchev, D

2013-04-12

The proximity effect between a superconductor and a highly diffusive two-dimensional metal is revealed in a scanning tunneling spectroscopy experiment. The in situ elaborated samples consist of superconducting single crystalline Pb islands interconnected by a nonsuperconducting atomically thin disordered Pb wetting layer. In the vicinity of each superconducting island the wetting layer acquires specific tunneling characteristics which reflect the interplay between the proximity-induced superconductivity and the inherent electron correlations of this ultimate diffusive two-dimensional metal. The observed spatial evolution of the tunneling spectra is accounted for theoretically by combining the Usadel equations with the theory of dynamical Coulomb blockade; the relevant length and energy scales are extracted and found in agreement with available experimental data.

Optical second-harmonic diffraction study of anisotropic surface diffusion: CO on Ni(110)

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

Xiao, X.; Zhu, X.D.; Daum, W.

We describe in detail a technique using optical second-harmonic (SH) diffraction from a one-dimensional laser-induced monolayer grating to probe surface diffusion of adsorbates and its anisotropy on a solid surface. The case of CO on Ni(110) is used as a demonstration. The two orthogonal and independent diffusion tensor components along (1{bar 1}0) and (001) are measured, exhibiting a strong anisotropy in both the activation energy {ital E}{sub diff} and the preexponential factor {ital D}{sub 0} in the diffusion coefficients. A compensation effect between {ital E}{sub diff} and {ital D}{sub 0} is observed. In comparison with CO/Ni(111) and CO/Ni(100), our resultmore » suggests that the Ni(110) surface seen by CO is much smoother than Ni(111) and Ni(100). Both advantages and limitations of the present technique are mentioned and possible complications in the data analysis are discussed.« less

Transverse single-file diffusion and enhanced longitudinal diffusion near a subcritical bifurcation

NASA Astrophysics Data System (ADS)

Dessup, Tommy; Coste, Christophe; Saint Jean, Michel

2018-05-01

A quasi-one-dimensional system of repelling particles undergoes a configurational phase transition when the transverse confining potential decreases. Below a threshold, it becomes energetically favorable for the system to adopt one of two staggered raw patterns, symmetric with respect to the system axis. This transition is a subcritical pitchfork bifurcation for short range interactions. As a consequence, the homogeneous zigzag pattern is unstable in a finite zigzag amplitude range [hC 1,hC 2] . We exhibit strong qualitative effects of the subcriticality on the thermal motions of the particles. When the zigzag amplitude is close enough to the limits hC 1 and hC 2, a transverse vibrational soft mode occurs which induces a strongly subdiffusive behavior of the transverse fluctuations, similar to single-file diffusion. On the contrary, the longitudinal fluctuations are enhanced, with a diffusion coefficient which is more than doubled. Conversely, a simple measurement of the thermal fluctuations allows a precise determination of the bifurcation thresholds.

Effective diffusion of confined active Brownian swimmers.

PubMed

Sandoval, Mario; Dagdug, Leornardo

2014-12-01

We theoretically find the effect of confinement and thermal fluctuations on the diffusivity of a spherical active swimmer moving inside a two-dimensional narrow cavity of general shape. The explicit formulas for the effective diffusion coefficient of a swimmer moving inside two particular cavities are presented. We also compare our analytical results with Brownian dynamics simulations and we obtain excellent agreement.

Fokker-Planck description for the queue dynamics of large tick stocks.

PubMed

Garèche, A; Disdier, G; Kockelkoren, J; Bouchaud, J-P

2013-09-01

Motivated by empirical data, we develop a statistical description of the queue dynamics for large tick assets based on a two-dimensional Fokker-Planck (diffusion) equation. Our description explicitly includes state dependence, i.e., the fact that the drift and diffusion depend on the volume present on both sides of the spread. "Jump" events, corresponding to sudden changes of the best limit price, must also be included as birth-death terms in the Fokker-Planck equation. All quantities involved in the equation can be calibrated using high-frequency data on the best quotes. One of our central findings is that the dynamical process is approximately scale invariant, i.e., the only relevant variable is the ratio of the current volume in the queue to its average value. While the latter shows intraday seasonalities and strong variability across stocks and time periods, the dynamics of the rescaled volumes is universal. In terms of rescaled volumes, we found that the drift has a complex two-dimensional structure, which is a sum of a gradient contribution and a rotational contribution, both stable across stocks and time. This drift term is entirely responsible for the dynamical correlations between the ask queue and the bid queue.

Fokker-Planck description for the queue dynamics of large tick stocks

NASA Astrophysics Data System (ADS)

Garèche, A.; Disdier, G.; Kockelkoren, J.; Bouchaud, J.-P.

2013-09-01

Motivated by empirical data, we develop a statistical description of the queue dynamics for large tick assets based on a two-dimensional Fokker-Planck (diffusion) equation. Our description explicitly includes state dependence, i.e., the fact that the drift and diffusion depend on the volume present on both sides of the spread. “Jump” events, corresponding to sudden changes of the best limit price, must also be included as birth-death terms in the Fokker-Planck equation. All quantities involved in the equation can be calibrated using high-frequency data on the best quotes. One of our central findings is that the dynamical process is approximately scale invariant, i.e., the only relevant variable is the ratio of the current volume in the queue to its average value. While the latter shows intraday seasonalities and strong variability across stocks and time periods, the dynamics of the rescaled volumes is universal. In terms of rescaled volumes, we found that the drift has a complex two-dimensional structure, which is a sum of a gradient contribution and a rotational contribution, both stable across stocks and time. This drift term is entirely responsible for the dynamical correlations between the ask queue and the bid queue.

Electrical detection of spin transport in Si two-dimensional electron gas systems

NASA Astrophysics Data System (ADS)

Chang, Li-Te; Fischer, Inga Anita; Tang, Jianshi; Wang, Chiu-Yen; Yu, Guoqiang; Fan, Yabin; Murata, Koichi; Nie, Tianxiao; Oehme, Michael; Schulze, Jörg; Wang, Kang L.

2016-09-01

Spin transport in a semiconductor-based two-dimensional electron gas (2DEG) system has been attractive in spintronics for more than ten years. The inherent advantages of high-mobility channel and enhanced spin-orbital interaction promise a long spin diffusion length and efficient spin manipulation, which are essential for the application of spintronics devices. However, the difficulty of making high-quality ferromagnetic (FM) contacts to the buried 2DEG channel in the heterostructure systems limits the potential developments in functional devices. In this paper, we experimentally demonstrate electrical detection of spin transport in a high-mobility 2DEG system using FM Mn-germanosilicide (Mn(Si0.7Ge0.3)x) end contacts, which is the first report of spin injection and detection in a 2DEG confined in a Si/SiGe modulation doped quantum well structure (MODQW). The extracted spin diffusion length and lifetime are l sf = 4.5 μm and {τ }{{s}}=16 {{ns}} at 1.9 K respectively. Our results provide a promising approach for spin injection into 2DEG system in the Si-based MODQW, which may lead to innovative spintronic applications such as spin-based transistor, logic, and memory devices.

An asymptotic preserving unified gas kinetic scheme for gray radiative transfer equations

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

Sun, Wenjun, E-mail: sun_wenjun@iapcm.ac.cn; Jiang, Song, E-mail: jiang@iapcm.ac.cn; Xu, Kun, E-mail: makxu@ust.hk

The solutions of radiative transport equations can cover both optical thin and optical thick regimes due to the large variation of photon's mean-free path and its interaction with the material. In the small mean free path limit, the nonlinear time-dependent radiative transfer equations can converge to an equilibrium diffusion equation due to the intensive interaction between radiation and material. In the optical thin limit, the photon free transport mechanism will emerge. In this paper, we are going to develop an accurate and robust asymptotic preserving unified gas kinetic scheme (AP-UGKS) for the gray radiative transfer equations, where the radiation transportmore » equation is coupled with the material thermal energy equation. The current work is based on the UGKS framework for the rarefied gas dynamics [14], and is an extension of a recent work [12] from a one-dimensional linear radiation transport equation to a nonlinear two-dimensional gray radiative system. The newly developed scheme has the asymptotic preserving (AP) property in the optically thick regime in the capturing of diffusive solution without using a cell size being smaller than the photon's mean free path and time step being less than the photon collision time. Besides the diffusion limit, the scheme can capture the exact solution in the optical thin regime as well. The current scheme is a finite volume method. Due to the direct modeling for the time evolution solution of the interface radiative intensity, a smooth transition of the transport physics from optical thin to optical thick can be accurately recovered. Many numerical examples are included to validate the current approach.« less

Joint estimation of phase and phase diffusion for quantum metrology.

PubMed

Vidrighin, Mihai D; Donati, Gaia; Genoni, Marco G; Jin, Xian-Min; Kolthammer, W Steven; Kim, M S; Datta, Animesh; Barbieri, Marco; Walmsley, Ian A

2014-04-14

Phase estimation, at the heart of many quantum metrology and communication schemes, can be strongly affected by noise, whose amplitude may not be known, or might be subject to drift. Here we investigate the joint estimation of a phase shift and the amplitude of phase diffusion at the quantum limit. For several relevant instances, this multiparameter estimation problem can be effectively reshaped as a two-dimensional Hilbert space model, encompassing the description of an interferometer phase probed with relevant quantum states--split single-photons, coherent states or N00N states. For these cases, we obtain a trade-off bound on the statistical variances for the joint estimation of phase and phase diffusion, as well as optimum measurement schemes. We use this bound to quantify the effectiveness of an actual experimental set-up for joint parameter estimation for polarimetry. We conclude by discussing the form of the trade-off relations for more general states and measurements.

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.

Theoretical description of spin-selective reactions of radical pairs diffusing in spherical 2D and 3D microreactors

NASA Astrophysics Data System (ADS)

Ivanov, Konstantin L.; Sadovsky, Vladimir M.; Lukzen, Nikita N.

2015-08-01

In this work, we treat spin-selective recombination of a geminate radical pair (RP) in a spherical "microreactor," i.e., of a RP confined in a micelle, vesicle, or liposome. We consider the microreactor model proposed earlier, in which one of the radicals is located at the center of the micelle and the other one undergoes three-dimensional diffusion inside the micelle. In addition, we suggest a two-dimensional model, in which one of the radicals is located at the "pole" of the sphere, while the other one diffuses on the spherical surface. For this model, we have obtained a general analytical expression for the RP recombination yield in terms of the free Green function of two-dimensional diffusion motion. In turn, this Green function is expressed via the Legendre functions and thus takes account of diffusion over a restricted spherical surface and its curvature. The obtained expression allows one to calculate the RP recombination efficiency at an arbitrary magnetic field strength. We performed a comparison of the two models taking the same geometric parameters (i.e., the microreactor radius and the closest approach distance of the radicals), chemical reactivity, magnetic interactions in the RP and diffusion coefficient. Significant difference between the predictions of the two models is found, which is thus originating solely from the dimensionality effect: for different dimensionality of space, the statistics of diffusional contacts of radicals becomes different altering the reaction yield. We have calculated the magnetic field dependence of the RP reaction yield and chemically induced dynamic nuclear polarization of the reaction products at different sizes of the microreactor, exchange interaction, and spin relaxation rates. Interestingly, due to the intricate interplay of diffusional contacts of reactants and spin dynamics, the dependence of the reaction yield on the microreactor radius is non-monotonous. Our results are of importance for (i) interpreting experimental data for magnetic field effects on RP recombination in confined space and (ii) for describing kinetics of chemical reactions, which occur predominantly on the surfaces of biomembranes, i.e., lipid peroxidation reactions.

Theoretical description of spin-selective reactions of radical pairs diffusing in spherical 2D and 3D microreactors

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

Ivanov, Konstantin L., E-mail: ivanov@tomo.nsc.ru; Lukzen, Nikita N.; Novosibirsk State University, Pirogova St. 2, Novosibirsk 630090

2015-08-28

In this work, we treat spin-selective recombination of a geminate radical pair (RP) in a spherical “microreactor,” i.e., of a RP confined in a micelle, vesicle, or liposome. We consider the microreactor model proposed earlier, in which one of the radicals is located at the center of the micelle and the other one undergoes three-dimensional diffusion inside the micelle. In addition, we suggest a two-dimensional model, in which one of the radicals is located at the “pole” of the sphere, while the other one diffuses on the spherical surface. For this model, we have obtained a general analytical expression formore » the RP recombination yield in terms of the free Green function of two-dimensional diffusion motion. In turn, this Green function is expressed via the Legendre functions and thus takes account of diffusion over a restricted spherical surface and its curvature. The obtained expression allows one to calculate the RP recombination efficiency at an arbitrary magnetic field strength. We performed a comparison of the two models taking the same geometric parameters (i.e., the microreactor radius and the closest approach distance of the radicals), chemical reactivity, magnetic interactions in the RP and diffusion coefficient. Significant difference between the predictions of the two models is found, which is thus originating solely from the dimensionality effect: for different dimensionality of space, the statistics of diffusional contacts of radicals becomes different altering the reaction yield. We have calculated the magnetic field dependence of the RP reaction yield and chemically induced dynamic nuclear polarization of the reaction products at different sizes of the microreactor, exchange interaction, and spin relaxation rates. Interestingly, due to the intricate interplay of diffusional contacts of reactants and spin dynamics, the dependence of the reaction yield on the microreactor radius is non-monotonous. Our results are of importance for (i) interpreting experimental data for magnetic field effects on RP recombination in confined space and (ii) for describing kinetics of chemical reactions, which occur predominantly on the surfaces of biomembranes, i.e., lipid peroxidation reactions.« 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.

Solute-solvent complex switching dynamics of chloroform between acetone and dimethylsulfoxide-two-dimensional IR chemical exchange spectroscopy.

PubMed

Kwak, Kyungwon; Rosenfeld, Daniel E; Chung, Jean K; Fayer, Michael D

2008-11-06

Hydrogen bonds formed between C-H and various hydrogen bond acceptors play important roles in the structure of proteins and organic crystals, and the mechanisms of C-H bond cleavage reactions. Chloroform, a C-H hydrogen bond donor, can form weak hydrogen-bonded complexes with acetone and with dimethylsulfoxide (DMSO). When chloroform is dissolved in a mixed solvent consisting of acetone and DMSO, both types of hydrogen-bonded complexes exist. The two complexes, chloroform-acetone and chloroform-DMSO, are in equilibrium, and they rapidly interconvert by chloroform exchanging hydrogen bond acceptors. This fast hydrogen bond acceptor substitution reaction is probed using ultrafast two-dimensional infrared (2D-IR) vibrational echo chemical exchange spectroscopy. Deuterated chloroform is used in the experiments, and the 2D-IR spectrum of the C-D stretching mode is measured. The chemical exchange of the chloroform hydrogen bonding partners is tracked by observing the time-dependent growth of off-diagonal peaks in the 2D-IR spectra. The measured substitution rate is 1/30 ps for an acetone molecule to replace a DMSO molecule in a chloroform-DMSO complex and 1/45 ps for a DMSO molecule to replace an acetone molecule in a chloroform-acetone complex. Free chloroform exists in the mixed solvent, and it acts as a reactive intermediate in the substitution reaction, analogous to a SN1 type reaction. From the measured rates and the equilibrium concentrations of acetone and DMSO, the dissociation rates for the chloroform-DMSO and chloroform-acetone complexes are found to be 1/24 ps and 1/5.5 ps, respectively. The difference between the measured rate for the complete substitution reaction and the rate for complex dissociation corresponds to the diffusion limited rate. The estimated diffusion limited rate agrees well with the result from a Smoluchowski treatment of diffusive reactions.

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

Calibration of a thin metal foil for infrared imaging video bolometer to estimate the spatial variation of thermal diffusivity using a photo-thermal technique.

PubMed

Pandya, Shwetang N; Peterson, Byron J; Sano, Ryuichi; Mukai, Kiyofumi; Drapiko, Evgeny A; Alekseyev, Andrey G; Akiyama, Tsuyoshi; Itomi, Muneji; Watanabe, Takashi

2014-05-01

A thin metal foil is used as a broad band radiation absorber for the InfraRed imaging Video Bolometer (IRVB), which is a vital diagnostic for studying three-dimensional radiation structures from high temperature plasmas in the Large Helical Device. The two-dimensional (2D) heat diffusion equation of the foil needs to be solved numerically to estimate the radiation falling on the foil through a pinhole geometry. The thermal, physical, and optical properties of the metal foil are among the inputs to the code besides the spatiotemporal variation of temperature, for reliable estimation of the exhaust power from the plasma illuminating the foil. The foil being very thin and of considerable size, non-uniformities in these properties need to be determined by suitable calibration procedures. The graphite spray used for increasing the surface emissivity also contributes to a change in the thermal properties. This paper discusses the application of the thermographic technique for determining the spatial variation of the effective in-plane thermal diffusivity of the thin metal foil and graphite composite. The paper also discusses the advantages of this technique in the light of limitations and drawbacks presented by other calibration techniques being practiced currently. The technique is initially applied to a material of known thickness and thermal properties for validation and finally to thin foils of gold and platinum both with two different thicknesses. It is observed that the effect of the graphite layer on the estimation of the thermal diffusivity becomes more pronounced for thinner foils and the measured values are approximately 2.5-3 times lower than the literature values. It is also observed that the percentage reduction in thermal diffusivity due to the coating is lower for high thermal diffusivity materials such as gold. This fact may also explain, albeit partially, the higher sensitivity of the platinum foil as compared to gold.

Calibration of a thin metal foil for infrared imaging video bolometer to estimate the spatial variation of thermal diffusivity using a photo-thermal technique

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

Pandya, Shwetang N., E-mail: pandya.shwetang@LHD.nifs.ac.jp; Sano, Ryuichi; Peterson, Byron J.

A thin metal foil is used as a broad band radiation absorber for the InfraRed imaging Video Bolometer (IRVB), which is a vital diagnostic for studying three-dimensional radiation structures from high temperature plasmas in the Large Helical Device. The two-dimensional (2D) heat diffusion equation of the foil needs to be solved numerically to estimate the radiation falling on the foil through a pinhole geometry. The thermal, physical, and optical properties of the metal foil are among the inputs to the code besides the spatiotemporal variation of temperature, for reliable estimation of the exhaust power from the plasma illuminating the foil.more » The foil being very thin and of considerable size, non-uniformities in these properties need to be determined by suitable calibration procedures. The graphite spray used for increasing the surface emissivity also contributes to a change in the thermal properties. This paper discusses the application of the thermographic technique for determining the spatial variation of the effective in-plane thermal diffusivity of the thin metal foil and graphite composite. The paper also discusses the advantages of this technique in the light of limitations and drawbacks presented by other calibration techniques being practiced currently. The technique is initially applied to a material of known thickness and thermal properties for validation and finally to thin foils of gold and platinum both with two different thicknesses. It is observed that the effect of the graphite layer on the estimation of the thermal diffusivity becomes more pronounced for thinner foils and the measured values are approximately 2.5–3 times lower than the literature values. It is also observed that the percentage reduction in thermal diffusivity due to the coating is lower for high thermal diffusivity materials such as gold. This fact may also explain, albeit partially, the higher sensitivity of the platinum foil as compared to gold.« less

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

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

PubMed

Wu, Wen; Wu, Zhouhu; Song, Zhiwen

2017-07-01

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

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

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.

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).

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.

Three-dimensional analysis of flow and segregation in vertical Bridgman crystal growth under axial and transversal magnetic fields

NASA Astrophysics Data System (ADS)

Lan, C. W.; Lee, I. F.; Yeh, B. C.

2003-07-01

Three-dimensional simulation, both pseudo-steady and time-dependent states, is carried out to illustrate the effects of magnetic fields on the flow and segregation in a vertical Bridgman crystal growth. With an axial magnetic field in a perfectly vertical growth, the calculated results are in good agreement with those obtained by a two-dimensional axisymmetric model. The asymptotic scaling of flow damping is also consistent with the boundary layer approximation regardless to the magnetic orientation. Radial and axial segregations are further discussed concluding that radial segregation could be severe if the flow damping is not adequate. Moreover, there is a regime of enhanced global dopant mixing due to the flow stretching by the axial field. Accordingly, the transversal field is more effective in pushing the growth to the diffusion-controlled limit and suppressing the asymmetric global flow due to ampule tilting.

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.

Three-dimensional thermographic imaging using a virtual wave concept

NASA Astrophysics Data System (ADS)

Burgholzer, Peter; Thor, Michael; Gruber, Jürgen; Mayr, Günther

2017-03-01

In this work, it is shown that image reconstruction methods from ultrasonic imaging can be employed for thermographic signals. Before using these imaging methods, a virtual signal is calculated by applying a local transformation to the temperature evolution measured on a sample surface. The introduced transformation describes all the irreversibility of the heat diffusion process and can be used for every sample shape. To date, one-dimensional methods have been primarily used in thermographic imaging. The proposed two-stage algorithm enables reconstruction in two and three dimensions. The feasibility of this approach is demonstrated through simulations and experiments. For the latter, small steel beads embedded in an epoxy resin are imaged. The resolution limit is found to be proportional to the depth of the structures and to be inversely proportional to the logarithm of the signal-to-noise ratio. Limited-view artefacts can arise if the measurement is performed on a single planar detection surface. These artifacts can be reduced by measuring the thermographic signals from multiple planes, which is demonstrated by numerical simulations and by experiments performed on an epoxy cube.

Validation of a mixture-averaged thermal diffusion model for premixed lean hydrogen flames

NASA Astrophysics Data System (ADS)

Schlup, Jason; Blanquart, Guillaume

2018-03-01

The mixture-averaged thermal diffusion model originally proposed by Chapman and Cowling is validated using multiple flame configurations. Simulations using detailed hydrogen chemistry are done on one-, two-, and three-dimensional flames. The analysis spans flat and stretched, steady and unsteady, and laminar and turbulent flames. Quantitative and qualitative results using the thermal diffusion model compare very well with the more complex multicomponent diffusion model. Comparisons are made using flame speeds, surface areas, species profiles, and chemical source terms. Once validated, this model is applied to three-dimensional laminar and turbulent flames. For these cases, thermal diffusion causes an increase in the propagation speed of the flames as well as increased product chemical source terms in regions of high positive curvature. The results illustrate the necessity for including thermal diffusion, and the accuracy and computational efficiency of the mixture-averaged thermal diffusion model.

Diffusion in phospholipid bilayer membranes: dual-leaflet dynamics and the roles of tracer–leaflet and inter-leaflet coupling

PubMed Central

Hill, Reghan J.; Wang, Chih-Ying

2014-01-01

A variety of observations—sometimes controversial—have been made in recent decades when attempting to elucidate the roles of interfacial slip on tracer diffusion in phospholipid membranes. Evans–Sackmann theory (1988) has furnished membrane viscosities and lubrication-film thicknesses for supported membranes from experimentally measured lateral diffusion coefficients. Similar to the Saffman and Delbrück model, which is the well-known counterpart for freely supported membranes, the bilayer is modelled as a single two-dimensional fluid. However, the Evans–Sackman model cannot interpret the mobilities of monotopic tracers, such as individual lipids or rigidly bound lipid assemblies; neither does it account for tracer–leaflet and inter-leaflet slip. To address these limitations, we solve the model of Wang and Hill, in which two leaflets of a bilayer membrane, a circular tracer and supports are coupled by interfacial friction, using phenomenological friction/slip coefficients. This furnishes an exact solution that can be readily adopted to interpret the mobilities of a variety of mosaic elements—including lipids, integral monotopic and polytopic proteins, and lipid rafts—in supported bilayer membranes. PMID:25002822

Stable dissipative optical vortex clusters by inhomogeneous effective diffusion.

PubMed

Li, Huishan; Lai, Shiquan; Qui, Yunli; Zhu, Xing; Xie, Jianing; Mihalache, Dumitru; He, Yingji

2017-10-30

We numerically show the generation of robust vortex clusters embedded in a two-dimensional beam propagating in a dissipative medium described by the generic cubic-quintic complex Ginzburg-Landau equation with an inhomogeneous effective diffusion term, which is asymmetrical in the two transverse directions and periodically modulated in the longitudinal direction. We show the generation of stable optical vortex clusters for different values of the winding number (topological charge) of the input optical beam. We have found that the number of individual vortex solitons that form the robust vortex cluster is equal to the winding number of the input beam. We have obtained the relationships between the amplitudes and oscillation periods of the inhomogeneous effective diffusion and the cubic gain and diffusion (viscosity) parameters, which depict the regions of existence and stability of vortex clusters. The obtained results offer a method to form robust vortex clusters embedded in two-dimensional optical beams, and we envisage potential applications in the area of structured light.

MR diffusion histology and micro-tractography reveal mesoscale features of the human cerebellum.

PubMed

Dell'Acqua, Flavio; Bodi, Istvan; Slater, David; Catani, Marco; Modo, Michel

2013-12-01

After 140 years from the discovery of Golgi's black reaction, the study of connectivity of the cerebellum remains a fascinating yet challenging task. Current histological techniques provide powerful methods for unravelling local axonal architecture, but the relatively low volume of data that can be acquired in a reasonable amount of time limits their application to small samples. State-of-the-art in vivo magnetic resonance imaging (MRI) methods, such as diffusion tractography techniques, can reveal trajectories of the major white matter pathways, but their correspondence with underlying anatomy is yet to be established. Hence, a significant gap exists between these two approaches as neither of them can adequately describe the three-dimensional complexity of fibre architecture at the level of the mesoscale (from a few millimetres to micrometres). In this study, we report the application of MR diffusion histology and micro-tractography methods to reveal the combined cytoarchitectural organisation and connectivity of the human cerebellum at a resolution of 100-μm (2 nl/voxel volume). Results show that the diffusion characteristics for each layer of the cerebellar cortex correctly reflect the known cellular composition and its architectural pattern. Micro-tractography also reveals details of the axonal connectivity of individual cerebellar folia and the intra-cortical organisation of the different cerebellar layers. The direct correspondence between MR diffusion histology and micro-tractography with immunohistochemistry indicates that these approaches have the potential to complement traditional histology techniques by providing a non-destructive, quantitative and three-dimensional description of the microstructural organisation of the healthy and pathological tissue.

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.

Strain-engineered diffusive atomic switching in two-dimensional crystals

PubMed Central

Kalikka, Janne; Zhou, Xilin; Dilcher, Eric; Wall, Simon; Li, Ju; Simpson, Robert E.

2016-01-01

Strain engineering is an emerging route for tuning the bandgap, carrier mobility, chemical reactivity and diffusivity of materials. Here we show how strain can be used to control atomic diffusion in van der Waals heterostructures of two-dimensional (2D) crystals. We use strain to increase the diffusivity of Ge and Te atoms that are confined to 5 Å thick 2D planes within an Sb2Te3–GeTe van der Waals superlattice. The number of quintuple Sb2Te3 2D crystal layers dictates the strain in the GeTe layers and consequently its diffusive atomic disordering. By identifying four critical rules for the superlattice configuration we lay the foundation for a generalizable approach to the design of switchable van der Waals heterostructures. As Sb2Te3–GeTe is a topological insulator, we envision these rules enabling methods to control spin and topological properties of materials in reversible and energy efficient ways. PMID:27329563

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

Results of Tests Performed on the Acoustic Quiet Flow Facility Three-Dimensional Model Tunnel

NASA Technical Reports Server (NTRS)

Barna, P. S.

1995-01-01

The test results briefly described in this report were obtained on the three-dimensional 1:48 scale tunnel modeled on the design proposed by Messrs. D.S.M.A. Corporation. More particularly, while the test chamber dimensions were indeed scaled down in the ration of 1:48, including the contraction and the collector as well, the duct system itself leading to and from the chamber was adapted to suit laboratory conditions and space limitations. Earlier tests with the two-dimensional model showed that blowing mode was preferred as against the suction mode, hence all tests were performed with blowing only. At the exit of the contraction the maximum airspeed attained with the 1 HP blower unit was about 200 ft/sec. This airspeed may be increased in future if desired. The test results show that pressure recovery in the diffuser was about 34 percent due to the large blockage at its entrance. Velocity traverses taken across the diffuser entrance explain the reason for this blockage. Recirculation, studied with both, hot-wire anemometry and flow-visualization techniques, was largely affected by the design of the test chamber itself and the amount of vent-air admitted to the chamber. Vent-air helped to decrease the level of turbulence.

An Excel®-based visualization tool of 2-D soil gas concentration profiles in petroleum vapor intrusion

PubMed Central

Verginelli, Iason; Yao, Yijun; Suuberg, Eric M.

2017-01-01

In this study we present a petroleum vapor intrusion tool implemented in Microsoft® Excel® using Visual Basic for Applications (VBA) and integrated within a graphical interface. The latter helps users easily visualize two-dimensional soil gas concentration profiles and indoor concentrations as a function of site-specific conditions such as source strength and depth, biodegradation reaction rate constant, soil characteristics and building features. This tool is based on a two-dimensional explicit analytical model that combines steady-state diffusion-dominated vapor transport in a homogeneous soil with a piecewise first-order aerobic biodegradation model, in which rate is limited by oxygen availability. As recommended in the recently released United States Environmental Protection Agency's final Petroleum Vapor Intrusion guidance, a sensitivity analysis and a simplified Monte Carlo uncertainty analysis are also included in the spreadsheet. PMID:28163564

An Excel®-based visualization tool of 2-D soil gas concentration profiles in petroleum vapor intrusion.

PubMed

Verginelli, Iason; Yao, Yijun; Suuberg, Eric M

2016-01-01

In this study we present a petroleum vapor intrusion tool implemented in Microsoft ® Excel ® using Visual Basic for Applications (VBA) and integrated within a graphical interface. The latter helps users easily visualize two-dimensional soil gas concentration profiles and indoor concentrations as a function of site-specific conditions such as source strength and depth, biodegradation reaction rate constant, soil characteristics and building features. This tool is based on a two-dimensional explicit analytical model that combines steady-state diffusion-dominated vapor transport in a homogeneous soil with a piecewise first-order aerobic biodegradation model, in which rate is limited by oxygen availability. As recommended in the recently released United States Environmental Protection Agency's final Petroleum Vapor Intrusion guidance, a sensitivity analysis and a simplified Monte Carlo uncertainty analysis are also included in the spreadsheet.

Two-dimensional nanoscale correlations in the strong negative thermal expansion material ScF 3

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

Handunkanda, Sahan U.; Occhialini, Connor A.; Said, Ayman H.

We present diffuse x-ray scattering data on the strong negative thermal expansion (NTE) material ScF3 and find that two-dimensional nanoscale correlations exist at momentum-space regions associated with possibly rigid rotations of the perovskite octahedra. We address the extent to which rigid octahedral motion describes the dynamical fluctuations behind NTE by generalizing a simple model supporting a single floppy mode that is often used to heuristically describe instances of NTE. We find this model has tendencies toward dynamic inhomogeneities and its application to recent and existing experimental data suggest an intricate link between the nanometer correlation length scale, the energy scalemore » for octahedral tilt fluctuations, and the coefficient of thermal expansion in ScF3. We then investigate the breakdown of the rigid limit and propose a resolution to an outstanding debate concerning the role of molecular rigidity in strong NTE materials.« less

Long-range two-dimensional superstructure in the superconducting electron-doped cuprate Pr 0.88 LaCe 0.12 CuO 4

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

Campbell, B. J.; Rosenkranz, S.; Kang, H. J.

2015-07-01

Utilizing single-crystal synchrotron x-ray scattering, we observe distorted CuO 2 planes in the electron- doped superconductor Pr 1-xLaCe xCuO 4+δ , x =0.12. Resolution-limited rods of scattering are indicative of a long-range two-dimensional 2√2 × 2√2 superstructure in the a-b plane, adhering to planar space-group symmetry p4gm, which is subject to stacking disorder perpendicular to the planes. This superstructure is present only in annealed, superconducting samples, but not in the as-grown, nonsuperconducting samples. These long-range distortions of the CuO 2 planes, which are generally considered to be detrimental to superconductivity, have avoided detection to date due to the challenges ofmore » observing and interpreting subtle diffuse-scattering features.« less

Diffusion in biased turbulence

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

Vlad, M.; Spineanu, F.; Misguich, J. H.

2001-06-01

Particle transport in two-dimensional divergence-free stochastic velocity fields with constant average is studied. Analytical expressions for the Lagrangian velocity correlation and for the time-dependent diffusion coefficients are obtained. They apply to stationary and homogeneous Gaussian velocity fields.

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.

On the local well-posedness and a Prodi-Serrin-type regularity criterion of the three-dimensional MHD-Boussinesq system without thermal diffusion

NASA Astrophysics Data System (ADS)

Larios, Adam; Pei, Yuan

2017-07-01

We prove a Prodi-Serrin-type global regularity condition for the three-dimensional Magnetohydrodynamic-Boussinesq system (3D MHD-Boussinesq) without thermal diffusion, in terms of only two velocity and two magnetic components. To the best of our knowledge, this is the first Prodi-Serrin-type criterion for such a 3D hydrodynamic system which is not fully dissipative, and indicates that such an approach may be successful on other systems. In addition, we provide a constructive proof of the local well-posedness of solutions to the fully dissipative 3D MHD-Boussinesq system, and also the fully inviscid, irresistive, non-diffusive MHD-Boussinesq equations. We note that, as a special case, these results include the 3D non-diffusive Boussinesq system and the 3D MHD equations. Moreover, they can be extended without difficulty to include the case of a Coriolis rotational term.

Transport of volatile organic compounds across the capillary fringe

USGS Publications Warehouse

McCarthy, Kathleen A.; Johnson, Richard L.

1993-01-01

Physical experiments were conducted to investigate the transport of a dissolved volatile organic compound (trichloroethylene, TCE) from shallow groundwater to the unsaturated zone under a variety of conditions including changes in the soil moisture profile and water table position. Experimental data indicated that at moderate groundwater velocities (0.1 m/d), vertical mechanical dispersion was negligible and molecular diffusion was the dominant vertical transport mechanism. Under these conditions, TCE concentrations decreased nearly 3 orders of magnitude across the capillary fringe and soil gas concentrations remained low relative to those of underlying groundwater. Data collected during a water table drop showed a short-term increase in concentrations throughout most of the unsaturated zone, but these concentrations quickly declined and approached initial values after the water table was returned to its original level. In the deep part of the unsaturated zone, the water table drop resulted in a long-term decrease in concentrations, illustrating the effects of hysteresis in the soil moisture profile. A two-dimensional random walk advection-diffusion model was developed to simulate the experimental conditions, and numerical simulations agreed well with experimental data. A simpler, one-dimensional finite-difference diffusion-dispersion model was also developed. One-dimensional simulations based on molecular diffusion also agreed well with experimental data. Simulations which incorporated mechanical dispersion tended to overestimate flux across the capillary fringe. Good agreement between the one- and two-dimensional models suggested that a simple, one-dimensional approximation of vertical transport across the capillary fringe can be useful when conditions are appropriate.

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 accessibility as a method for visualizing macromolecular surface geometry.

PubMed

Tsai, Yingssu; Holton, Thomas; Yeates, Todd O

2015-10-01

Important three-dimensional spatial features such as depth and surface concavity can be difficult to convey clearly in the context of two-dimensional images. In the area of macromolecular visualization, the computer graphics technique of ray-tracing can be helpful, but further techniques for emphasizing surface concavity can give clearer perceptions of depth. The notion of diffusion accessibility is well-suited for emphasizing such features of macromolecular surfaces, but a method for calculating diffusion accessibility has not been made widely available. Here we make available a web-based platform that performs the necessary calculation by solving the Laplace equation for steady state diffusion, and produces scripts for visualization that emphasize surface depth by coloring according to diffusion accessibility. The URL is http://services.mbi.ucla.edu/DiffAcc/. © 2015 The Protein Society.

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.

Random walk on a leash: a simple single-molecule diffusion model for surface-tethered redox molecules with flexible linkers.

PubMed

Huang, Kuan-Chun; White, Ryan J

2013-08-28

We develop a random walk model to simulate the Brownian motion and the electrochemical response of a single molecule confined to an electrode surface via a flexible molecular tether. We use our simple model, which requires no prior knowledge of the physics of the molecular tether, to predict and better understand the voltammetric response of surface-confined redox molecules when motion of the redox molecule becomes important. The single molecule is confined to a hemispherical volume with a maximum radius determined by the flexible molecular tether (5-20 nm) and is allowed to undergo true three-dimensional diffusion. Distance- and potential-dependent electron transfer probabilities are evaluated throughout the simulations to generate cyclic voltammograms of the model system. We find that at sufficiently slow cyclic voltammetric scan rates the electrochemical reaction behaves like an adsorbed redox molecule with no mass transfer limitation; thus, the peak current is proportional to the scan rate. Conversely, at faster scan rates the diffusional motion of the molecule limits the simulated peak current, which exhibits a linear dependence on the square root of the scan rate. The switch between these two limiting regimes occurs when the diffusion layer thickness, (2Dt)(1/2), is ~10 times the tether length. Finally, we find that our model predicts the voltammetric behavior of a redox-active methylene blue tethered to an electrode surface via short flexible single-stranded, polythymine DNAs, allowing the estimation of diffusion coefficients for the end-tethered molecule.

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.

Formation and structure of stable aggregates in binary diffusion-limited cluster-cluster aggregation processes

NASA Astrophysics Data System (ADS)

López-López, J. M.; Moncho-Jordá, A.; Schmitt, A.; Hidalgo-Álvarez, R.

2005-09-01

Binary diffusion-limited cluster-cluster aggregation processes are studied as a function of the relative concentration of the two species. Both, short and long time behaviors are investigated by means of three-dimensional off-lattice Brownian Dynamics simulations. At short aggregation times, the validity of the Hogg-Healy-Fuerstenau approximation is shown. At long times, a single large cluster containing all initial particles is found to be formed when the relative concentration of the minority particles lies above a critical value. Below that value, stable aggregates remain in the system. These stable aggregates are composed by a few minority particles that are highly covered by majority ones. Our off-lattice simulations reveal a value of approximately 0.15 for the critical relative concentration. A qualitative explanation scheme for the formation and growth of the stable aggregates is developed. The simulations also explain the phenomenon of monomer discrimination that was observed recently in single cluster light scattering experiments.

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.

Diffusive growth of a single droplet with three different boundary conditions

NASA Astrophysics Data System (ADS)

Tavassoli, Z.; Rodgers, G. J.

2000-02-01

We study a single, motionless three-dimensional droplet growing by adsorption of diffusing monomers on a 2D substrate. The diffusing monomers are adsorbed at the aggregate perimeter of the droplet with different boundary conditions. Models with both an adsorption boundary condition and a radiation boundary condition, as well as a phenomenological model, are considered and solved in a quasistatic approximation. The latter two models allow particle detachment. In the short time limit, the droplet radius grows as a power of the time with exponents of 1/4, 1/2 and 3/4 for the models with adsorption, radiation and phenomenological boundary conditions, respectively. In the long time limit a universal growth rate as $[t/\\ln(t)]^{1/3}$ is observed for the radius of the droplet for all models independent of the boundary conditions. This asymptotic behaviour was obtained by Krapivsky \\cite{krapquasi} where a similarity variable approach was used to treat the growth of a droplet with an adsorption boundary condition based on a quasistatic approximation. Another boundary condition with a constant flux of monomers at the aggregate perimeter is also examined. The results exhibit a power law growth rate with an exponent of 1/3 for all times.

Applications of Laser Scattering Probes to Turbulent Diffusion Flames

DTIC Science & Technology

1983-11-01

APPLICATIONS OF LASER SCATTERING PROBES TO TURBULENT DIFFUSION FLAMES u ^ j FINAL REPORT Contract N00014-80-C-0882 Submitted to Office of...Include Security Classification) Applications of Laser Scattering Probes to Turbulent Diffusion Flames PROJECT NO. TASK NO. WORK UNIT NO. 12...for a co-flowing jet turbulent diffusion flame, and planar laser-induced fluorescence to provide two- dimensional instantaneous images of the flame

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.

Chinks in Solar Dynamo Theory: Turbulent Diffusion, Dynamo Waves and Magnetic Helicity

NASA Technical Reports Server (NTRS)

DeLuca, E. E.; Wagner, William J. (Technical Monitor)

2001-01-01

We have investigated the generation of magnetic fields in the Sun using two-dimensional and three-dimensional numerical simulations. The results of our investigations have been presented at scientific meetings and published.

Symmetry of the gradient profile as second experimental dimension in the short-time expansion of the apparent diffusion coefficient as measured with NMR diffusometry.

PubMed

Laun, Frederik Bernd; Kuder, Tristan Anselm; Zong, Fangrong; Hertel, Stefan; Galvosas, Petrik

2015-10-01

The time-dependent apparent diffusion coefficient as measured by pulsed gradient NMR can be used to estimate parameters of porous structures including the surface-to-volume ratio and the mean curvature of pores. In this work, the short-time diffusion limit and in particular the influence of the temporal profile of diffusion gradients on the expansion as proposed by Mitra et al. (1993) is investigated. It is shown that flow-compensated waveforms, i.e. those whose first moment is zero, are blind to the term linear in observation time, which is the term that is proportional to mean curvature and surface permeability. A gradient waveform that smoothly interpolates between flow-compensated and bipolar waveform is proposed and the degree of flow-compensation is used as a second experimental dimension. This two-dimensional ansatz is shown to yield an improved precision when characterizing the confining domain. This technique is demonstrated with simulations and in experiments performed with cylindrical capillaries of 100 μm radius. Copyright © 2015 Elsevier Inc. All rights reserved.

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.

Kubo conductivity of a strongly magnetized two-dimensional plasma.

NASA Technical Reports Server (NTRS)

Montgomery, D.; Tappert, F.

1971-01-01

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

Magnetic properties of tapiolite (FeTa2O6); a quasi two-dimensional (2D) antiferromagnet

NASA Astrophysics Data System (ADS)

Chung, E. M. L.; Lees, M. R.; McIntyre, G. J.; Wilkinson, C.; Balakrishnan, G.; Hague, J. P.; Visser, D.; McK Paul, D.

2004-11-01

The possibilities of two-dimensional (2D) short-range magnetic correlations and frustration effects in the mineral tapiolite are investigated using bulk-property measurements and neutron Laue diffraction. In this study of the magnetic properties of synthetic single-crystals of tapiolite, we find that single crystals of FeTa2O6 order antiferromagnetically at TN = 7.95 ± 0.05 K, with extensive two-dimensional correlations existing up to at least 40 K. Although we find no evidence that FeTa2O6 is magnetically frustrated, hallmarks of two-dimensional magnetism observed in our single-crystal data include: (i) broadening of the susceptibility maximum due to short-range correlations, (ii) a spin-flop transition and (iii) lambda anomalies in the heat capacity and d(χT)/dT. Complementary neutron Laue diffraction measurements reveal 1D magnetic diffuse scattering extending along the c* direction perpendicular to the magnetic planes. This magnetic diffuse scattering, observed for the first time using the neutron Laue technique by VIVALDI, arises directly as a result of 2D short-range spin correlations.

Thickness-independent capacitance of vertically aligned liquid-crystalline MXenes

DOE PAGES

Xia, Yu; Mathis, Tyler S.; Zhao, Meng -Qiang; ...

2018-05-16

The scalable and sustainable manufacture of thick electrode films with high energy and power densities is critical for the large-scale storage of electrochemical energy for application in transportation and stationary electric grids. Two-dimensional nanomaterials have become the predominant choice of electrode material in the pursuit of high energy and power densities owing to their large surface-area-to-volume ratios and lack of solid-state diffusion. However, traditional electrode fabrication methods often lead to restacking of two-dimensional nanomaterials, which limits ion transport in thick films and results in systems in which the electrochemical performance is highly dependent on the thickness of the film. Strategiesmore » for facilitating ion transport—such as increasing the interlayer spacing by intercalation or introducing film porosity by designing nanoarchitectures—result in materials with low volumetric energy storage as well as complex and lengthy ion transport paths that impede performance at high charge–discharge rates. Vertical alignment of two-dimensional flakes enables directional ion transport that can lead to thickness-independent electrochemical performances in thick films. However, so far only limited success has been reported, and the mitigation of performance losses remains a major challenge when working with films of two-dimensional nanomaterials with thicknesses that are near to or exceed the industrial standard of 100 micrometres. Here we demonstrate electrochemical energy storage that is independent of film thickness for vertically aligned two-dimensional titanium carbide (Ti 3C 2T x), a material from the MXene family (two-dimensional carbides and nitrides of transition metals (M), where X stands for carbon or nitrogen). The vertical alignment was achieved by mechanical shearing of a discotic lamellar liquid-crystal phase of Ti 3C 2T x. The resulting electrode films show excellent performance that is nearly independent of film thickness up to 200 micrometres, which makes them highly attractive for energy storage applications. In conclusion, the self-assembly approach presented here is scalable and can be extended to other systems that involve directional transport, such as catalysis and filtration.« less

Thickness-independent capacitance of vertically aligned liquid-crystalline MXenes

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

Xia, Yu; Mathis, Tyler S.; Zhao, Meng -Qiang

The scalable and sustainable manufacture of thick electrode films with high energy and power densities is critical for the large-scale storage of electrochemical energy for application in transportation and stationary electric grids. Two-dimensional nanomaterials have become the predominant choice of electrode material in the pursuit of high energy and power densities owing to their large surface-area-to-volume ratios and lack of solid-state diffusion. However, traditional electrode fabrication methods often lead to restacking of two-dimensional nanomaterials, which limits ion transport in thick films and results in systems in which the electrochemical performance is highly dependent on the thickness of the film. Strategiesmore » for facilitating ion transport—such as increasing the interlayer spacing by intercalation or introducing film porosity by designing nanoarchitectures—result in materials with low volumetric energy storage as well as complex and lengthy ion transport paths that impede performance at high charge–discharge rates. Vertical alignment of two-dimensional flakes enables directional ion transport that can lead to thickness-independent electrochemical performances in thick films. However, so far only limited success has been reported, and the mitigation of performance losses remains a major challenge when working with films of two-dimensional nanomaterials with thicknesses that are near to or exceed the industrial standard of 100 micrometres. Here we demonstrate electrochemical energy storage that is independent of film thickness for vertically aligned two-dimensional titanium carbide (Ti 3C 2T x), a material from the MXene family (two-dimensional carbides and nitrides of transition metals (M), where X stands for carbon or nitrogen). The vertical alignment was achieved by mechanical shearing of a discotic lamellar liquid-crystal phase of Ti 3C 2T x. The resulting electrode films show excellent performance that is nearly independent of film thickness up to 200 micrometres, which makes them highly attractive for energy storage applications. In conclusion, the self-assembly approach presented here is scalable and can be extended to other systems that involve directional transport, such as catalysis and filtration.« 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.

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.

Universal scaling laws of diffusion in two-dimensional granular liquids.

PubMed

Wang, Chen-Hung; Yu, Szu-Hsuan; Chen, Peilong

2015-06-01

We find, in a two-dimensional air table granular system, that the reduced diffusion constant D* and excess entropy S(2) follow two distinct scaling laws: D*∼e(S(2)*) for dense liquids and D∼e(3S(2)*) for dilute ones. The scaling for dense liquids is very similar to that for three-dimensional liquids proposed previously [M. Dzugutov, Nature (London) 381, 137 (1996); A. Samanta et al., Phys. Rev. Lett. 92, 145901 (2004)]. In the dilute regime, a power law [Y. Rosenfeld, J. Phys.: Condens. Matter 11, 5415 (1999)] also fits our data reasonably well. In our system, particles experience low air drag dissipation and interact with each others through embedded magnets. These near-conservative many-body interactions are responsible for the measured Gaussian velocity distribution functions and the scaling laws. The dominance of cage relaxations in dense liquids leads to the different scaling laws for dense and dilute regimes.

Flow regimes for fluid injection into a confined porous medium

DOE PAGES

Zheng, Zhong; Guo, Bo; Christov, Ivan C.; ...

2015-02-24

We report theoretical and numerical studies of the flow behaviour when a fluid is injected into a confined porous medium saturated with another fluid of different density and viscosity. For a two-dimensional configuration with point source injection, a nonlinear convection–diffusion equation is derived to describe the time evolution of the fluid–fluid interface. In the early time period, the fluid motion is mainly driven by the buoyancy force and the governing equation is reduced to a nonlinear diffusion equation with a well-known self-similar solution. In the late time period, the fluid flow is mainly driven by the injection, and the governingmore » equation is approximated by a nonlinear hyperbolic equation that determines the global spreading rate; a shock solution is obtained when the injected fluid is more viscous than the displaced fluid, whereas a rarefaction wave solution is found when the injected fluid is less viscous. In the late time period, we also obtain analytical solutions including the diffusive term associated with the buoyancy effects (for an injected fluid with a viscosity higher than or equal to that of the displaced fluid), which provide the structure of the moving front. Numerical simulations of the convection–diffusion equation are performed; the various analytical solutions are verified as appropriate asymptotic limits, and the transition processes between the individual limits are demonstrated.« less

Direct observation of two-step crystallization in nanoparticle superlattice formation

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

Park, Jungwon; Zheng, Haimei; Lee, Won Chul

2011-10-06

Direct imaging of nanoparticle solutions by liquid phase transmission electron microscopy has enabled unique in-situ studies of nanoparticle motion and growth. In the present work, we report on real-time formation of two-dimensional nanoparticle arrays in the very low diffusive limit, where nanoparticles are mainly driven by capillary forces and solvent fluctuations. We find that superlattice formation appears to be segregated into multiple regimes. Initially, the solvent front drags the nanoparticles, condensing them into an amorphous agglomerate. Subsequently, the nanoparticle crystallization into an array is driven by local fluctuations. Following the crystallization event, superlattice growth can also occur via the additionmore » of individual nanoparticles drawn from outlying regions by different solvent fronts. The dragging mechanism is consistent with simulations based on a coarse-grained lattice gas model at the same limit.« less

Transformed Fourier and Fick equations for the control of heat and mass diffusion

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

Guenneau, S.; Petiteau, D.; Zerrad, M.

We review recent advances in the control of diffusion processes in thermodynamics and life sciences through geometric transforms in the Fourier and Fick equations, which govern heat and mass diffusion, respectively. We propose to further encompass transport properties in the transformed equations, whereby the temperature is governed by a three-dimensional, time-dependent, anisotropic heterogeneous convection-diffusion equation, which is a parabolic partial differential equation combining the diffusion equation and the advection equation. We perform two dimensional finite element computations for cloaks, concentrators and rotators of a complex shape in the transient regime. We precise that in contrast to invisibility cloaks for waves,more » the temperature (or mass concentration) inside a diffusion cloak crucially depends upon time, its distance from the source, and the diffusivity of the invisibility region. However, heat (or mass) diffusion outside cloaks, concentrators and rotators is unaffected by their presence, whatever their shape or position. Finally, we propose simplified designs of layered cylindrical and spherical diffusion cloaks that might foster experimental efforts in thermal and biochemical metamaterials.« less

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

Oxidation of Carbon Fibers in a Cracked Ceramic Matrix Composite Modeled as a Function of Temperature

NASA Technical Reports Server (NTRS)

Halbig, Michael C.; Cawley, James D.; Eckel, Andrew J.

2003-01-01

The oxidation model simulates the oxidation of the reinforcing carbon fibers within a ceramic matrix composite material containing as-fabricated microcracks. The physics-based oxidation model uses theoretically and experimentally determined variables as input for the model. The model simulates the ingress of oxygen through microcracks into a two-dimensional plane within the composite material. Model input includes temperature, oxygen concentration, the reaction rate constant, the diffusion coefficient, and the crack opening width as a function of the mechanical and thermal loads. The model is run in an iterative process for a two-dimensional grid system in which oxygen diffuses through the porous and cracked regions of the material and reacts with carbon in short time steps. The model allows the local oxygen concentrations and carbon volumes from the edge to the interior of the composite to be determined over time. Oxidation damage predicted by the model was compared with that observed from microstructural analysis of experimentally tested composite material to validate the model for two temperatures of interest. When the model is run for low-temperature conditions, the kinetics are reaction controlled. Carbon and oxygen reactions occur relatively slowly. Therefore, oxygen can bypass the carbon near the outer edge and diffuse into the interior so that it saturates the entire composite at relatively high concentrations. The kinetics are limited by the reaction rate between carbon and oxygen. This results in an interior that has high local concentrations of oxygen and a similar amount of consumed carbon throughout the cross section. When the model is run for high-temperature conditions, the kinetics are diffusion controlled. Carbon and oxygen reactions occur very quickly. The carbon consumes oxygen as soon as it is supplied. The kinetics are limited by the relatively slow rate at which oxygen is supplied in comparison to the relatively fast rate at which carbon and oxygen reactions occur. This results in a sharp gradient in oxygen concentration from the edge where it is supplied to the nearest source of carbon, which is where the oxygen is quickly consumed. A moving reaction front is seen in which the outlaying carbon is consumed before the next inner layer of carbon begins to react.

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.

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.

Dynamical properties and transport coefficients of one-dimensional Lennard-Jones fluids: A molecular dynamics study

NASA Astrophysics Data System (ADS)

Bazhenov, Alexiev M.; Heyes, David M.

1990-01-01

The thermodynamics, structure, and transport coefficients, as defined by the Green-Kubo integrals, of the one-dimensional Lennard-Jones fluid are evaluated for a wide range of state points by molecular dynamics computer simulation. These calculations are performed for the first time for thermal conductivity and the viscosity. We observe a transition from hard-rod behavior at low number density to harmonic-spring fluid behavior in the close-packed limit. The self-diffusion coefficient decays with increasing density to a finite limiting value. The thermal conductivity increases with density, tending to ∞ in the close-packed limit. The viscosity in contrast maximizes at intermediate density, tending to zero in the zero density and close-packed limits.

Group iterative methods for the solution of two-dimensional time-fractional diffusion equation

NASA Astrophysics Data System (ADS)

Balasim, Alla Tareq; Ali, Norhashidah Hj. Mohd.

2016-06-01

Variety of problems in science and engineering may be described by fractional partial differential equations (FPDE) in relation to space and/or time fractional derivatives. The difference between time fractional diffusion equations and standard diffusion equations lies primarily in the time derivative. Over the last few years, iterative schemes derived from the rotated finite difference approximation have been proven to work well in solving standard diffusion equations. However, its application on time fractional diffusion counterpart is still yet to be investigated. In this paper, we will present a preliminary study on the formulation and analysis of new explicit group iterative methods in solving a two-dimensional time fractional diffusion equation. These methods were derived from the standard and rotated Crank-Nicolson difference approximation formula. Several numerical experiments were conducted to show the efficiency of the developed schemes in terms of CPU time and iteration number. At the request of all authors of the paper an updated version of this article was published on 7 July 2016. The original version supplied to AIP Publishing contained an error in Table 1 and References 15 and 16 were incomplete. These errors have been corrected in the updated and republished article.

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

PubMed

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

2015-12-31

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

The Kirkendall and Frenkel effects during 2D diffusion process

NASA Astrophysics Data System (ADS)

Wierzba, Bartek

2014-11-01

The two-dimensional approach for inter-diffusion and voids generation is presented. The voids evolution and growth is discussed. This approach is based on the bi-velocity (Darken) method which combines the Darken and Brenner concepts that the volume velocity is essential in defining the local material velocity in multi-component mixture at non-equilibrium. The model is formulated for arbitrary multi-component two-dimensional systems. It is shown that the voids growth is due to the drift velocity and vacancy migration. The radius of the void can be easily estimated. The distributions of (1) components, (2) vacancy and (3) voids radius over the distance is presented.

A Novel Color Image Encryption Algorithm Based on Quantum Chaos Sequence

NASA Astrophysics Data System (ADS)

Liu, Hui; Jin, Cong

2017-03-01

In this paper, a novel algorithm of image encryption based on quantum chaotic is proposed. The keystreams are generated by the two-dimensional logistic map as initial conditions and parameters. And then general Arnold scrambling algorithm with keys is exploited to permute the pixels of color components. In diffusion process, a novel encryption algorithm, folding algorithm, is proposed to modify the value of diffused pixels. In order to get the high randomness and complexity, the two-dimensional logistic map and quantum chaotic map are coupled with nearest-neighboring coupled-map lattices. Theoretical analyses and computer simulations confirm that the proposed algorithm has high level of security.

Two-dimensional dynamics of a trapped active Brownian particle in a shear flow

NASA Astrophysics Data System (ADS)

Li, Yunyun; Marchesoni, Fabio; Debnath, Tanwi; Ghosh, Pulak K.

2017-12-01

We model the two-dimensional dynamics of a pointlike artificial microswimmer diffusing in a harmonic trap subject to the shear flow of a highly viscous medium. The particle is driven simultaneously by the linear restoring force of the trap, the drag force exerted by the flow, and the torque due to the shear gradient. For a Couette flow, elliptical orbits in the noiseless regime, and the correlation functions between the particle's displacements parallel and orthogonal to the flow are computed analytically. The effects of thermal fluctuations (translational) and self-propulsion fluctuations (angular) are treated separately. Finally, we discuss how to extend our approach to the diffusion of a microswimmer in a Poiseuille flow. These results provide an accurate reference solution to investigate, both numerically and experimentally, hydrodynamics corrections to the diffusion of active matter in confined geometries.

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.

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.

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.

Diffusion of flexible random-coil dextran polymers measured in anisotropic brain extracellular space by integrative optical imaging.

PubMed

Xiao, Fanrong; Nicholson, Charles; Hrabe, Jan; Hrabetová, Sabina

2008-08-01

There are a limited number of methods available to quantify the extracellular diffusion of macromolecules in an anisotropic brain region, e.g., an area containing numerous aligned fibers where diffusion is faster along the fibers than across. We applied the integrative optical imaging method to measure diffusion of the fluorophore Alexa Fluor 488 (molecular weight (MW) 547) and fluorophore-labeled flexible random-coil dextran polymers (dex3, MW 3000; dex75, MW 75,000; dex282, MW 282,000; dex525, MW 525,000) in the extracellular space (ECS) of the anisotropic molecular layer of the isolated turtle cerebellum. For all molecules, two-dimensional images acquired an elliptical shape with major and minor axes oriented along and across, respectively, the unmyelinated parallel fibers. The effective diffusion coefficients, D*(major) and D*(minor), decreased with molecular size. The diffusion anisotropy ratio (DAR = D*(major)/D*(minor)) increased for Alexa Fluor 488 through dex75 but then unexpectedly reached a plateau. We argue that dex282 and dex525 approach the ECS width and deform to diffuse. In support of this concept, scaling theory shows the diffusion behavior of dex282 and dex525 to be consistent with transition to a reptation regime, and estimates the average ECS width at approximately 31 nm. These findings have implications for the interstitial transport of molecules and drugs, and for modeling neurotransmitter diffusion during ectopic release and spillover.

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.

First-Passage Times in d -Dimensional Heterogeneous Media

NASA Astrophysics Data System (ADS)

Vaccario, G.; Antoine, C.; Talbot, J.

2015-12-01

Although there are many theoretical studies of the mean first-passage time (MFPT), most neglect the diffusive heterogeneity of real systems. We present exact analytical expressions for the MFPT and residence times of a pointlike particle diffusing in a spherically symmetric d -dimensional heterogeneous system composed of two concentric media with different diffusion coefficients with an absorbing inner boundary (target) and a reflecting outer boundary. By varying the convention, e.g., Itō, Stratonovich, or isothermal, chosen to interpret the overdamped Langevin equation with multiplicative noise describing the diffusion process, we find different predictions and counterintuitive results for the residence time in the outer region and hence for the MFPT, while the residence time in the inner region is independent of the convention. This convention dependence of residence times and the MFPT could provide insights about the heterogeneous diffusion in a cell or in a tumor, or for animal and insect searches inside their home range.

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.

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.

Advanced carbon materials/olivine LiFePO4 composites cathode for lithium ion batteries

NASA Astrophysics Data System (ADS)

Gong, Chunli; Xue, Zhigang; Wen, Sheng; Ye, Yunsheng; Xie, Xiaolin

2016-06-01

In the past two decades, LiFePO4 has undoubtly become a competitive candidate for the cathode material of the next-generation LIBs due to its abundant resources, low toxicity and excellent thermal stability, etc. However, the poor electronic conductivity as well as low lithium ion diffusion rate are the two major drawbacks for the commercial applications of LiFePO4 especially in the power energy field. The introduction of highly graphitized advanced carbon materials, which also possess high electronic conductivity, superior specific surface area and excellent structural stability, into LiFePO4 offers a better way to resolve the issue of limited rate performance caused by the two obstacles when compared with traditional carbon materials. In this review, we focus on advanced carbon materials such as one-dimensional (1D) carbon (carbon nanotubes and carbon fibers), two-dimensional (2D) carbon (graphene, graphene oxide and reduced graphene oxide) and three-dimensional (3D) carbon (carbon nanotubes array and 3D graphene skeleton), modified LiFePO4 for high power lithium ion batteries. The preparation strategies, structure, and electrochemical performance of advanced carbon/LiFePO4 composite are summarized and discussed in detail. The problems encountered in its application and the future development of this composite are also discussed.

Shot noise at high temperatures

NASA Astrophysics Data System (ADS)

Gutman, D. B.; Gefen, Yuval

2003-07-01

We consider the possibility of measuring nonequilibrium properties of the current correlation functions at high temperatures (and small bias). Through the example of the third cumulant of the current (S3) we demonstrate that odd-order correlation functions represent nonequilibrium physics even at small external bias and high temperatures. We calculate S3=y(eV/T)e2I for a quasi-one-dimensional diffusive constriction. We calculate the scaling function y in two regimes: when the scattering processes are purely elastic and when the inelastic electron-electron scattering is strong. In both cases we find that y interpolates between two constants. In the low- (high-) temperature limit y is strongly (weakly) enhanced (suppressed) by the electron-electron scattering.

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.

Design of a Two Dimensional Planer Pressurized Air Labyrinth Seal Test Rig

DTIC Science & Technology

1993-12-01

identity by block number) Dump Diffuser, Flow Modification, Laser Doppler Velocimeter, Labyrinth Seal , Leakage Prediction, Press --ized air 19 Abstract...reducing this high to low pressure leakage . Figure 1.1 is a two dimensional representation of a 3 dimensional annular labyrinth seal . The object of this... Labyrinth Seal literature, Sneck [2] credits C.A. Parsons with development of the labyrinth seal in concert with Parson’s [31 development of the steam

Cooperative simulation of lithography and topography for three-dimensional high-aspect-ratio etching

NASA Astrophysics Data System (ADS)

Ichikawa, Takashi; Yagisawa, Takashi; Furukawa, Shinichi; Taguchi, Takafumi; Nojima, Shigeki; Murakami, Sadatoshi; Tamaoki, Naoki

2018-06-01

A topography simulation of high-aspect-ratio etching considering transports of ions and neutrals is performed, and the mechanism of reactive ion etching (RIE) residues in three-dimensional corner patterns is revealed. Limited ion flux and CF2 diffusion from the wide space of the corner is found to have an effect on the RIE residues. Cooperative simulation of lithography and topography is used to solve the RIE residue problem.

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.

Two-Dimensional Diffusion Theory Analysis of Reactivity Effects of a Fuel-Plate-Removal Experiment

NASA Technical Reports Server (NTRS)

Gotsky, Edward R.; Cusick, James P.; Bogart, Donald

1959-01-01

Two-dimensional two-group diffusion calculations were performed on the NASA reactor simulator in order to evaluate the reactivity effects of fuel plates removed successively from the center experimental fuel element of a seven- by three-element core loading at the Oak Ridge Bulk Shielding Facility. The reactivity calculations were performed by two methods: In the first, the slowing-down properties of the experimental fuel element were represented by its infinite media parameters; and, in the second, the finite size of the experimental fuel element was recognized, and the slowing-down properties of the surrounding core were attributed to this small region. The latter calculation method agreed very well with the experimented reactivity effects; the former method underestimated the experimental reactivity effects.

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.

Wanted: Scalable Tracers for Diffusion Measurements

PubMed Central

2015-01-01

Scalable tracers are potentially a useful tool to examine diffusion mechanisms and to predict diffusion coefficients, particularly for hindered diffusion in complex, heterogeneous, or crowded systems. Scalable tracers are defined as a series of tracers varying in size but with the same shape, structure, surface chemistry, deformability, and diffusion mechanism. Both chemical homology and constant dynamics are required. In particular, branching must not vary with size, and there must be no transition between ordinary diffusion and reptation. Measurements using scalable tracers yield the mean diffusion coefficient as a function of size alone; measurements using nonscalable tracers yield the variation due to differences in the other properties. Candidate scalable tracers are discussed for two-dimensional (2D) diffusion in membranes and three-dimensional diffusion in aqueous solutions. Correlations to predict the mean diffusion coefficient of globular biomolecules from molecular mass are reviewed briefly. Specific suggestions for the 3D case include the use of synthetic dendrimers or random hyperbranched polymers instead of dextran and the use of core–shell quantum dots. Another useful tool would be a series of scalable tracers varying in deformability alone, prepared by varying the density of crosslinking in a polymer to make say “reinforced Ficoll” or “reinforced hyperbranched polyglycerol.” PMID:25319586

Multitopic ligand directed assembly of low-dimensional metal-chalcogenide organic frameworks.

PubMed

Liu, Yi; Ye, Kaiqi; Wang, Yue; Zhang, Qichun; Bu, Xianhui; Feng, Pingyun

2017-01-31

Despite tremendous progress in metal-organic frameworks, only limited success has been achieved with metal-chalcogenide organic frameworks. Metal-chalcogenide organic frameworks are desirable because they offer a promising route towards tunable semiconducting porous frameworks. Here, four novel semiconducting chalcogenide-organic hybrid compounds have been synthesized through a solvothermal method. Multitopic organic molecules, i.e., 1,2-di-(4-pyridyl)ethylene (L 1 ), 1,3,5-tris(4-pyridyl-trans-ethenyl)benzene (L 2 ) and tetrakis(4-pyridyloxymethylene)methane (L 3 ), have been used as linkers to assemble Zn(SAr) 2 or Zn 2 (SAr) 4 units to generate different patterns of spatial organizations. Single-crystal structural analyses indicate that compounds NTU-2, NTU-3 and NTU-4 possess two-dimensional layer structures, while compound NTU-1 adopts a one-dimensional coordination framework (NTU-n, where n is the number related to a specific structure). The diffuse-reflectance spectra demonstrate that these four compounds possess indirect bandgaps and their tunable bandgaps are correlated with their compositions and crystal structures.

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.

Lattice Light Sheet Microscopy: Imaging Molecules to Embryos at High Spatiotemporal Resolution

PubMed Central

Chen, Bi-Chang; Legant, Wesley R.; Wang, Kai; Shao, Lin; Milkie, Daniel E.; Davidson, Michael W.; Janetopoulos, Chris; Wu, Xufeng S.; Hammer, John A.; Liu, Zhe; English, Brian P.; Mimori-Kiyosue, Yuko; Romero, Daniel P.; Ritter, Alex T.; Lippincott-Schwartz, Jennifer; Fritz-Laylin, Lillian; Mullins, R. Dyche; Mitchell, Diana M.; Bembenek, Joshua N.; Reymann, Anne-Cecile; Böhme, Ralph; Grill, Stephan W.; Wang, Jennifer T.; Seydoux, Geraldine; Tulu, U. Serdar; Kiehart, Daniel P.; Betzig, Eric

2015-01-01

Although fluorescence microscopy provides a crucial window into the physiology of living specimens, many biological processes are too fragile, too small, or occur too rapidly to see clearly with existing tools. We crafted ultra-thin light sheets from two-dimensional optical lattices that allowed us to image three-dimensional (3D) dynamics for hundreds of volumes, often at sub-second intervals, at the diffraction limit and beyond. We applied this to systems spanning four orders of magnitude in space and time, including the diffusion of single transcription factor molecules in stem cell spheroids, the dynamic instability of mitotic microtubules, the immunological synapse, neutrophil motility in a 3D matrix, and embryogenesis in Caenorhabditis elegans and Drosophila melanogaster. The results provide a visceral reminder of the beauty and complexity of living systems. PMID:25342811

Hindered diffusion of high molecular weight compounds in brain extracellular microenvironment measured with integrative optical imaging.

PubMed

Nicholson, C; Tao, L

1993-12-01

This paper describes the theory of an integrative optical imaging system and its application to the analysis of the diffusion of 3-, 10-, 40-, and 70-kDa fluorescent dextran molecules in agarose gel and brain extracellular microenvironment. The method uses a precisely defined source of fluorescent molecules pressure ejected from a micropipette, and a detailed theory of the intensity contributions from out-of-focus molecules in a three-dimensional medium to a two-dimensional image. Dextrans tagged with either tetramethylrhodamine or Texas Red were ejected into 0.3% agarose gel or rat cortical slices maintained in a perfused chamber at 34 degrees C and imaged using a compound epifluorescent microscope with a 10 x water-immersion objective. About 20 images were taken at 2-10-s intervals, recorded with a cooled CCD camera, then transferred to a 486 PC for quantitative analysis. The diffusion coefficient in agarose gel, D, and the apparent diffusion coefficient, D*, in brain tissue were determined by fitting an integral expression relating the measured two-dimensional image intensity to the theoretical three-dimensional dextran concentration. The measurements in dilute agarose gel provided a reference value of D and validated the method. Values of the tortuosity, lambda = (D/D*)1/2, for the 3- and 10-kDa dextrans were 1.70 and 1.63, respectively, which were consistent with previous values derived from tetramethylammonium measurements in cortex. Tortuosities for the 40- and 70-kDa dextrans had significantly larger values of 2.16 and 2.25, respectively. This suggests that the extracellular space may have local constrictions that hinder the diffusion of molecules above a critical size that lies in the range of many neurotrophic compounds.

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

Influence of two-dimensional hygrothermal gradients on interlaminar stresses near free edges

NASA Technical Reports Server (NTRS)

Farley, G. L.; Herakovich, C. T.

1977-01-01

Interlaminar stresses are determined for mechanical loading, uniform hygrothermal loading, and gradient moisture loading through implementation of a finite element computer code. Nonuniform two-dimensional hygroscopic gradients are obtained from a finite difference solution of the diffusion equation. It is shown that hygroscopic induced stresses can be larger than those resulting from mechanical and thermal loading, and that the distribution of the interlaminar normal stress may be changed significantly in the presence of a two-dimensional moisture gradient in the boundary layer of a composite laminate.

Interface- and discontinuity-aware numerical schemes for plasma 3-T radiation diffusion in two and three dimensions

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

Dai, William W., E-mail: dai@lanl.gov; Scannapieco, Anthony J.

2015-11-01

A set of numerical schemes is developed for two- and three-dimensional time-dependent 3-T radiation diffusion equations in systems involving multi-materials. To resolve sub-cell structure, interface reconstruction is implemented within any cell that has more than one material. Therefore, the system of 3-T radiation diffusion equations is solved on two- and three-dimensional polyhedral meshes. The focus of the development is on the fully coupling between radiation and material, the treatment of nonlinearity in the equations, i.e., in the diffusion terms and source terms, treatment of the discontinuity across cell interfaces in material properties, the formulations for both transient and steady states,more » the property for large time steps, and second order accuracy in both space and time. The discontinuity of material properties between different materials is correctly treated based on the governing physics principle for general polyhedral meshes and full nonlinearity. The treatment is exact for arbitrarily strong discontinuity. The scheme is fully nonlinear for the full nonlinearity in the 3-T diffusion equations. Three temperatures are fully coupled and are updated simultaneously. The scheme is general in two and three dimensions on general polyhedral meshes. The features of the scheme are demonstrated through numerical examples for transient problems and steady states. The effects of some simplifications of numerical schemes are also shown through numerical examples, such as linearization, simple average of diffusion coefficient, and approximate treatment for the coupling between radiation and material.« less

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.

A Critical Study of Agglomerated Multigrid Methods for Diffusion

NASA Technical Reports Server (NTRS)

Nishikawa, Hiroaki; Diskin, Boris; Thomas, James L.

2011-01-01

Agglomerated multigrid techniques used in unstructured-grid methods are studied critically for a model problem representative of laminar diffusion in the incompressible limit. The studied target-grid discretizations and discretizations used on agglomerated grids are typical of current node-centered formulations. Agglomerated multigrid convergence rates are presented using a range of two- and three-dimensional randomly perturbed unstructured grids for simple geometries with isotropic and stretched grids. Two agglomeration techniques are used within an overall topology-preserving agglomeration framework. The results show that multigrid with an inconsistent coarse-grid scheme using only the edge terms (also referred to in the literature as a thin-layer formulation) provides considerable speedup over single-grid methods but its convergence deteriorates on finer grids. Multigrid with a Galerkin coarse-grid discretization using piecewise-constant prolongation and a heuristic correction factor is slower and also grid-dependent. In contrast, grid-independent convergence rates are demonstrated for multigrid with consistent coarse-grid discretizations. Convergence rates of multigrid cycles are verified with quantitative analysis methods in which parts of the two-grid cycle are replaced by their idealized counterparts.

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

A Generalization of Theory for Two-Dimensional Fluorescence Recovery after Photobleaching Applicable to Confocal Laser Scanning Microscopes

PubMed Central

Kang, Minchul; Day, Charles A.; Drake, Kimberly; Kenworthy, Anne K.; DiBenedetto, Emmanuele

2009-01-01

Abstract Fluorescence recovery after photobleaching (FRAP) using confocal laser scanning microscopes (confocal FRAP) has become a valuable technique for studying the diffusion of biomolecules in cells. However, two-dimensional confocal FRAP sometimes yields results that vary with experimental setups, such as different bleaching protocols and bleaching spot sizes. In addition, when confocal FRAP is used to measure diffusion coefficients (D) for fast diffusing molecules, it often yields D-values that are one or two orders-of-magnitude smaller than that predicted theoretically or measured by alternative methods such as fluorescence correlation spectroscopy. Recently, it was demonstrated that this underestimation of D can be corrected by taking diffusion during photobleaching into consideration. However, there is currently no consensus on confocal FRAP theory, and no efforts have been made to unify theories on conventional and confocal FRAP. To this end, we generalized conventional FRAP theory to incorporate diffusion during photobleaching so that analysis by conventional FRAP theory for a circular region of interest is easily applicable to confocal FRAP. Finally, we demonstrate the accuracy of these new (to our knowledge) formulae by measuring D for soluble enhanced green fluorescent protein in aqueous glycerol solution and in the cytoplasm and nucleus of COS7 cells. PMID:19720039

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.

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.

An application of a two-equation model of turbulence to three-dimensional chemically reacting flows

NASA Technical Reports Server (NTRS)

Lee, J.

1994-01-01

A numerical study of three dimensional chemically reacting and non-reacting flowfields is conducted using a two-equation model of turbulence. A generalized flow solver using an implicit Lower-Upper (LU) diagonal decomposition numerical technique and finite-rate chemistry has been coupled with a low-Reynolds number two-equation model of turbulence. This flow solver is then used to study chemically reacting turbulent supersonic flows inside combustors with synergetic fuel injectors. The reacting and non-reacting turbulent combustor solutions obtained are compared with zero-equation turbulence model solutions and with available experimental data. The hydrogen-air chemistry is modeled using a nine-species/eighteen reaction model. A low-Reynolds number k-epsilon model was used to model the effect of turbulence because, in general, the low-Reynolds number k-epsilon models are easier to implement numerically and are far more general than algebraic models. However, low-Reynolds number k-epsilon models require a much finer near-wall grid resolution than high-Reynolds number models to resolve accurately the near-wall physics. This is especially true in complex flowfields, where the stiff nature of the near-wall turbulence must be resolved. Therefore, the limitations imposed by the near-wall characteristics and compressible model corrections need to be evaluated further. The gradient-diffusion hypothesis is used to model the effects of turbulence on the mass diffusion process. The influence of this low-Reynolds number turbulence model on the reacting flowfield predictions was studied parametrically.

Implementation and assessment of diffusion-weighted partial Fourier readout-segmented echo-planar imaging.

PubMed

Frost, Robert; Porter, David A; Miller, Karla L; Jezzard, Peter

2012-08-01

Single-shot echo-planar imaging has been used widely in diffusion magnetic resonance imaging due to the difficulties in correcting motion-induced phase corruption in multishot data. Readout-segmented EPI has addressed the multishot problem by introducing a two-dimensional nonlinear navigator correction with online reacquisition of uncorrectable data to enable acquisition of high-resolution diffusion data with reduced susceptibility artifact and T*(2) blurring. The primary shortcoming of readout-segmented EPI in its current form is its long acquisition time (longer than similar resolution single-shot echo-planar imaging protocols by approximately the number of readout segments), which limits the number of diffusion directions. By omitting readout segments at one side of k-space and using partial Fourier reconstruction, readout-segmented EPI imaging times could be reduced. In this study, the effects of homodyne and projection onto convex sets reconstructions on estimates of the fractional anisotropy, mean diffusivity, and diffusion orientation in fiber tracts and raw T(2)- and trace-weighted signal are compared, along with signal-to-noise ratio results. It is found that projections onto convex sets reconstruction with 3/5 segments in a 2 mm isotropic diffusion tensor image acquisition and 9/13 segments in a 0.9 × 0.9 × 4.0 mm(3) diffusion-weighted image acquisition provide good fidelity relative to the full k-space parameters. This allows application of readout-segmented EPI to tractography studies, and clinical stroke and oncology protocols. Copyright © 2011 Wiley-Liss, Inc.

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.

Role of boundary layer diffusion in vapor deposition growth of chalcogenide nanosheets: the case of GeS.

PubMed

Li, Chun; Huang, Liang; Snigdha, Gayatri Pongur; Yu, Yifei; Cao, Linyou

2012-10-23

We report a synthesis of single-crystalline two-dimensional GeS nanosheets using vapor deposition processes and show that the growth behavior of the nanosheet is substantially different from those of other nanomaterials and thin films grown by vapor depositions. The nanosheet growth is subject to strong influences of the diffusion of source materials through the boundary layer of gas flows. This boundary layer diffusion is found to be the rate-determining step of the growth under typical experimental conditions, evidenced by a substantial dependence of the nanosheet's size on diffusion fluxes. We also find that high-quality GeS nanosheets can grow only in the diffusion-limited regime, as the crystalline quality substantially deteriorates when the rate-determining step is changed away from the boundary layer diffusion. We establish a simple model to analyze the diffusion dynamics in experiments. Our analysis uncovers an intuitive correlation of diffusion flux with the partial pressure of source materials, the flow rate of carrier gas, and the total pressure in the synthetic setup. The observed significant role of boundary layer diffusions in the growth is unique for nanosheets. It may be correlated with the high growth rate of GeS nanosheets, ~3-5 μm/min, which is 1 order of magnitude higher than other nanomaterials (such as nanowires) and thin films. This fundamental understanding of the effect of boundary layer diffusions may generally apply to other chalcogenide nanosheets that can grow rapidly. It can provide useful guidance for the development of general paradigms to control the synthesis of nanosheets.

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

PubMed

Loskutov, V V; Sevriugin, V A

2013-05-01

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

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

PubMed

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

2012-04-04

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

Green-noise halftoning with dot diffusion

NASA Astrophysics Data System (ADS)

Lippens, Stefaan; Philips, Wilfried

2007-02-01

Dot diffusion is a halftoning technique that is based on the traditional error diffusion concept, but offers a high degree of parallel processing by its block based approach. Traditional dot diffusion however suffers from periodicity artifacts. To limit the visibility of these artifacts, we propose grid diffusion, which applies different class matrices for different blocks. Furthermore, in this paper we will discuss two approaches in the dot diffusion framework to generate green-noise halftone patterns. The first approach is based on output dependent feedback (hysteresis), analogous to the standard green-noise error diffusion techniques. We observe that the resulting halftones are rather coarse and highly dependent on the used dot diffusion class matrices. In the second approach we don't limit the diffusion to the nearest neighbors. This leads to less coarse halftones, compared to the first approach. The drawback is that it can only cope with rather limited cluster sizes. We can reduce these drawbacks by combining the two approaches.

Self-diffusion of polycrystalline ice Ih under confining pressure: Hydrogen isotope analysis using 2-D Raman imaging

NASA Astrophysics Data System (ADS)

Noguchi, Naoki; Kubo, Tomoaki; Durham, William B.; Kagi, Hiroyuki; Shimizu, Ichiko

2016-08-01

We have developed a high-resolution technique based on micro Raman spectroscopy to measure hydrogen isotope diffusion profiles in ice Ih. The calibration curve for quantitative analysis of deuterium in ice Ih was constructed using micro Raman spectroscopy. Diffusion experiments using diffusion couples composed of dense polycrystalline H2O and D2O ice were carried out under a gas confining pressure of 100 MPa (to suppress micro-fracturing and pore formation) at temperatures from 235 K to 245 K and diffusion times from 0.2 to 94 hours. Two-dimensional deuterium profiles across the diffusion couples were determined by Raman imaging. The location of small spots of frost from room air could be detected from the shapes of the Raman bands of OH and OD stretching modes, which change because of the effect of the molar ratio of deuterium on the molecular coupling interaction. We emphasize the validity for screening the impurities utilizing the coupling interaction. Some recrystallization and grain boundary migration occurred in recovered diffusion couples, but analysis of two-dimensional diffusion profiles of regions not affected by grain boundary migration allowed us to measure a volume diffusivity for ice at 100 MPa of (2.8 ± 0.4) ×10-3exp[ -57.0 ± 15.4kJ /mol RT ] m2 /s (R is the gas constant, T is temperature). Based on ambient pressure diffusivity measurements by others, this value indicates a high (negative) activation volume for volume diffusivity of -29.5 cm3/mol or more. We can also constrain the value of grain boundary diffusivity in ice at 100 MPa to be <104 that of volume diffusivity.

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.

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.

Numerical Tests and Properties of Waves in Radiating Fluids

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

Johnson, B M; Klein, R I

2009-09-03

We discuss the properties of an analytical solution for waves in radiating fluids, with a view towards its implementation as a quantitative test of radiation hydrodynamics codes. A homogeneous radiating fluid in local thermodynamic equilibrium is periodically driven at the boundary of a one-dimensional domain, and the solution describes the propagation of the waves thus excited. Two modes are excited for a given driving frequency, generally referred to as a radiative acoustic wave and a radiative diffusion wave. While the analytical solution is well known, several features are highlighted here that require care during its numerical implementation. We compare themore » solution in a wide range of parameter space to a numerical integration with a Lagrangian radiation hydrodynamics code. Our most significant observation is that flux-limited diffusion does not preserve causality for waves on a homogeneous background.« less

A self-organizing Lagrangian particle method for adaptive-resolution advection-diffusion simulations

NASA Astrophysics Data System (ADS)

Reboux, Sylvain; Schrader, Birte; Sbalzarini, Ivo F.

2012-05-01

We present a novel adaptive-resolution particle method for continuous parabolic problems. In this method, particles self-organize in order to adapt to local resolution requirements. This is achieved by pseudo forces that are designed so as to guarantee that the solution is always well sampled and that no holes or clusters develop in the particle distribution. The particle sizes are locally adapted to the length scale of the solution. Differential operators are consistently evaluated on the evolving set of irregularly distributed particles of varying sizes using discretization-corrected operators. The method does not rely on any global transforms or mapping functions. After presenting the method and its error analysis, we demonstrate its capabilities and limitations on a set of two- and three-dimensional benchmark problems. These include advection-diffusion, the Burgers equation, the Buckley-Leverett five-spot problem, and curvature-driven level-set surface refinement.

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

NASA Astrophysics Data System (ADS)

Kreer, Torsten; Meyer, Hendrik; Baschnagel, Joerg

2008-03-01

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

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.

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.

Application of ToFSIMS to Studying Surface Diffusion: Do cocaine and heroin form a two-dimensional gas on surfaces?

NASA Astrophysics Data System (ADS)

Avci, Recep; Maccagnano, Sara; Bohannan, Gary; Gresham, Gary; Groenewold, Gary

2001-03-01

Imaging time-of-flight secondary ion mass spectroscopy ( ToFSIMS) is a practical tool for studying the movement of molecules on material surfaces as a function of time. The high detection sensitivity, rapid data acquisition and reasonable spatial resolution present ideal conditions for such studies. An application of ToFSIMS is presented characterizing the diffusion of large molecules on gold-coated Si wafers. Polydimethylsiloxane (PDMS) was selected for study because it contaminates material surfaces and can be detected easily. Also, the temperature dependent diffusion properties of hydrochlorinated heroin and cocaine are presented as part of a forensic application. While the PDMS diffusion could be explained by a two-dimensional ( 2-D) Brownian motion with a Gaussian probability distribution function (pdf) with a diffusion coefficient of 1.6 μ m^2/sec, the cocaine and to a lesser extent heroin were observed to move nearly freely on the surfaces as though they were part of a 2-D gas evaporating in 2-D from a condensed phase. The results could be described reasonably well using an extreme Lévi pdf with an index of stability α<= 0.01.

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.

Determination of minority-carrier lifetime and surface recombination velocity with high spacial resolution

NASA Technical Reports Server (NTRS)

Watanabe, M.; Actor, G.; Gatos, H. C.

1977-01-01

Quantitative analysis of the electron beam induced current in conjunction with high-resolution scanning makes it possible to evaluate the minority-carrier lifetime three dimensionally in the bulk and the surface recombination velocity two dimensionally, with a high spacial resolution. The analysis is based on the concept of the effective excitation strength of the carriers which takes into consideration all possible recombination sources. Two-dimensional mapping of the surface recombination velocity of phosphorus-diffused silicon diodes is presented as well as a three-dimensional mapping of the changes in the minority-carrier lifetime in ion-implanted silicon.

Visibility graphs of random scalar fields and spatial data

NASA Astrophysics Data System (ADS)

Lacasa, Lucas; Iacovacci, Jacopo

2017-07-01

We extend the family of visibility algorithms to map scalar fields of arbitrary dimension into graphs, enabling the analysis of spatially extended data structures as networks. We introduce several possible extensions and provide analytical results on the topological properties of the graphs associated to different types of real-valued matrices, which can be understood as the high and low disorder limits of real-valued scalar fields. In particular, we find a closed expression for the degree distribution of these graphs associated to uncorrelated random fields of generic dimension. This result holds independently of the field's marginal distribution and it directly yields a statistical randomness test, applicable in any dimension. We showcase its usefulness by discriminating spatial snapshots of two-dimensional white noise from snapshots of a two-dimensional lattice of diffusively coupled chaotic maps, a system that generates high dimensional spatiotemporal chaos. The range of potential applications of this combinatorial framework includes image processing in engineering, the description of surface growth in material science, soft matter or medicine, and the characterization of potential energy surfaces in chemistry, disordered systems, and high energy physics. An illustration on the applicability of this method for the classification of the different stages involved in carcinogenesis is briefly discussed.

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.

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

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.

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.

Can phoretic particles swim in two dimensions?

NASA Astrophysics Data System (ADS)

Sondak, David; Hawley, Cory; Heng, Siyu; Vinsonhaler, Rebecca; Lauga, Eric; Thiffeault, Jean-Luc

2016-12-01

Artificial phoretic particles swim using self-generated gradients in chemical species (self-diffusiophoresis) or charges and currents (self-electrophoresis). These particles can be used to study the physics of collective motion in active matter and might have promising applications in bioengineering. In the case of self-diffusiophoresis, the classical physical model relies on a steady solution of the diffusion equation, from which chemical gradients, phoretic flows, and ultimately the swimming velocity may be derived. Motivated by disk-shaped particles in thin films and under confinement, we examine the extension to two dimensions. Because the two-dimensional diffusion equation lacks a steady state with the correct boundary conditions, Laplace transforms must be used to study the long-time behavior of the problem and determine the swimming velocity. For fixed chemical fluxes on the particle surface, we find that the swimming velocity ultimately always decays logarithmically in time. In the case of finite Péclet numbers, we solve the full advection-diffusion equation numerically and show that this decay can be avoided by the particle moving to regions of unconsumed reactant. Finite advection thus regularizes the two-dimensional phoretic problem.

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.

Boundary shape identification problems in two-dimensional domains related to thermal testing of materials

NASA Technical Reports Server (NTRS)

Banks, H. T.; Kojima, Fumio

1988-01-01

The identification of the geometrical structure of the system boundary for a two-dimensional diffusion system is reported. The domain identification problem treated here is converted into an optimization problem based on a fit-to-data criterion and theoretical convergence results for approximate identification techniques are discussed. Results of numerical experiments to demonstrate the efficacy of the theoretical ideas are reported.

Coarsening and persistence in a one-dimensional system of orienting arrowheads: Domain-wall kinetics with A +B →0

NASA Astrophysics Data System (ADS)

Khandkar, Mahendra D.; Stinchcombe, Robin; Barma, Mustansir

2017-01-01

We demonstrate the large-scale effects of the interplay between shape and hard-core interactions in a system with left- and right-pointing arrowheads <> on a line, with reorientation dynamics. This interplay leads to the formation of two types of domain walls, >< (A ) and <> (B ). The correlation length in the equilibrium state diverges exponentially with increasing arrowhead density, with an ordered state of like orientations arising in the limit. In this high-density limit, the A domain walls diffuse, while the B walls are static. In time, the approach to the ordered state is described by a coarsening process governed by the kinetics of domain-wall annihilation A +B →0 , quite different from the A +A →0 kinetics pertinent to the Glauber-Ising model. The survival probability of a finite set of walls is shown to decay exponentially with time, in contrast to the power-law decay known for A +A →0 . In the thermodynamic limit with a finite density of walls, coarsening as a function of time t is studied by simulation. While the number of walls falls as t-1/2, the fraction of persistent arrowheads decays as t-θ where θ is close to 1/4 , quite different from the Ising value. The global persistence too has θ =1/4 , as follows from a heuristic argument. In a generalization where the B walls diffuse slowly, θ varies continuously, increasing with increasing diffusion constant.

Coarsening and persistence in a one-dimensional system of orienting arrowheads: Domain-wall kinetics with A+B→0.

PubMed

Khandkar, Mahendra D; Stinchcombe, Robin; Barma, Mustansir

2017-01-01

We demonstrate the large-scale effects of the interplay between shape and hard-core interactions in a system with left- and right-pointing arrowheads <> on a line, with reorientation dynamics. This interplay leads to the formation of two types of domain walls, >< (A) and <> (B). The correlation length in the equilibrium state diverges exponentially with increasing arrowhead density, with an ordered state of like orientations arising in the limit. In this high-density limit, the A domain walls diffuse, while the B walls are static. In time, the approach to the ordered state is described by a coarsening process governed by the kinetics of domain-wall annihilation A+B→0, quite different from the A+A→0 kinetics pertinent to the Glauber-Ising model. The survival probability of a finite set of walls is shown to decay exponentially with time, in contrast to the power-law decay known for A+A→0. In the thermodynamic limit with a finite density of walls, coarsening as a function of time t is studied by simulation. While the number of walls falls as t^{-1/2}, the fraction of persistent arrowheads decays as t^{-θ} where θ is close to 1/4, quite different from the Ising value. The global persistence too has θ=1/4, as follows from a heuristic argument. In a generalization where the B walls diffuse slowly, θ varies continuously, increasing with increasing diffusion constant.

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

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.

Surface recombination velocity and diffusion length of minority carriers in heavily doped silicon layers

NASA Technical Reports Server (NTRS)

Gatos, H. C.; Watanabe, M.; Actor, G.

1977-01-01

Quantitative analysis of the electron beam-induced current and the dependence of the effective diffusion length of the minority carriers on the penetration depth of the electron beam were employed for the analysis of the carrier recombination characteristics in heavily doped silicon layers. The analysis is based on the concept of the effective excitation strength of the carriers which takes into consideration all possible recombination sources. Two dimensional mapping of the surface recombination velocity of P-diffused Si layers will be presented together with a three dimensional mapping of minority carrier lifetime in ion implanted Si. Layers heavily doped with As exhibit improved recombination characteristics as compared to those of the layers doped with P.

The mechanistic basis of internal conductance: a theoretical analysis of mesophyll cell photosynthesis and CO2 diffusion.

PubMed

Tholen, Danny; Zhu, Xin-Guang

2011-05-01

Photosynthesis is limited by the conductance of carbon dioxide (CO(2)) from intercellular spaces to the sites of carboxylation. Although the concept of internal conductance (g(i)) has been known for over 50 years, shortcomings in the theoretical description of this process may have resulted in a limited understanding of the underlying mechanisms. To tackle this issue, we developed a three-dimensional reaction-diffusion model of photosynthesis in a typical C(3) mesophyll cell that includes all major components of the CO(2) diffusion pathway and associated reactions. Using this novel systems model, we systematically and quantitatively examined the mechanisms underlying g(i). Our results identify the resistances of the cell wall and chloroplast envelope as the most significant limitations to photosynthesis. In addition, the concentration of carbonic anhydrase in the stroma may also be limiting for the photosynthetic rate. Our analysis demonstrated that higher levels of photorespiration increase the apparent resistance to CO(2) diffusion, an effect that has thus far been ignored when determining g(i). Finally, we show that outward bicarbonate leakage through the chloroplast envelope could contribute to the observed decrease in g(i) under elevated CO(2). Our analysis suggests that physiological and anatomical features associated with g(i) have been evolutionarily fine-tuned to benefit CO(2) diffusion and photosynthesis. The model presented here provides a novel theoretical framework to further analyze the mechanisms underlying diffusion processes in the mesophyll.

The Mechanistic Basis of Internal Conductance: A Theoretical Analysis of Mesophyll Cell Photosynthesis and CO2 Diffusion1[W][OA

PubMed Central

Tholen, Danny; Zhu, Xin-Guang

2011-01-01

Photosynthesis is limited by the conductance of carbon dioxide (CO2) from intercellular spaces to the sites of carboxylation. Although the concept of internal conductance (gi) has been known for over 50 years, shortcomings in the theoretical description of this process may have resulted in a limited understanding of the underlying mechanisms. To tackle this issue, we developed a three-dimensional reaction-diffusion model of photosynthesis in a typical C3 mesophyll cell that includes all major components of the CO2 diffusion pathway and associated reactions. Using this novel systems model, we systematically and quantitatively examined the mechanisms underlying gi. Our results identify the resistances of the cell wall and chloroplast envelope as the most significant limitations to photosynthesis. In addition, the concentration of carbonic anhydrase in the stroma may also be limiting for the photosynthetic rate. Our analysis demonstrated that higher levels of photorespiration increase the apparent resistance to CO2 diffusion, an effect that has thus far been ignored when determining gi. Finally, we show that outward bicarbonate leakage through the chloroplast envelope could contribute to the observed decrease in gi under elevated CO2. Our analysis suggests that physiological and anatomical features associated with gi have been evolutionarily fine-tuned to benefit CO2 diffusion and photosynthesis. The model presented here provides a novel theoretical framework to further analyze the mechanisms underlying diffusion processes in the mesophyll. PMID:21441385

Axi-symmetric generalized thermoelastic diffusion problem with two-temperature and initial stress under fractional order heat conduction

NASA Astrophysics Data System (ADS)

Deswal, Sunita; Kalkal, Kapil Kumar; Sheoran, Sandeep Singh

2016-09-01

A mathematical model of fractional order two-temperature generalized thermoelasticity with diffusion and initial stress is proposed to analyze the transient wave phenomenon in an infinite thermoelastic half-space. The governing equations are derived in cylindrical coordinates for a two dimensional axi-symmetric problem. The analytical solution is procured by employing the Laplace and Hankel transforms for time and space variables respectively. The solutions are investigated in detail for a time dependent heat source. By using numerical inversion method of integral transforms, we obtain the solutions for displacement, stress, temperature and diffusion fields in physical domain. Computations are carried out for copper material and displayed graphically. The effect of fractional order parameter, two-temperature parameter, diffusion, initial stress and time on the different thermoelastic and diffusion fields is analyzed on the basis of analytical and numerical results. Some special cases have also been deduced from the present investigation.

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.

Unity and diversity in mixing: Stretching, diffusion, breakup, and aggregation in chaotic flows

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

Ottino, J.M.

1991-05-01

Experiments and theory have produced a reasonably good qualitative understanding of the evolution of chaotic mixing of passive tracers, especially in two-dimensional time-periodic flow fields. Such an understanding forms a fabric for the evolution of breakup, aggregation, and diffusion-controlled reactions in more complex flows. These systems can be viewed as a population of microstructures'' whose behavior is dictated by iterations of a chaotic flow; microstructures break, diffuse, and aggregate, causing the population to evolve in space and time. This paper presents simple physical models for such processes. Self-similarity is common to all the problems; examples arise in the context ofmore » the distribution of stretchings within chaotic flows, in the asymptotic evolution of diffusion-reaction processes at striation thickness scales, in the equilibrium distribution of drop sizes generated upon mixing of immiscible fluids, in the equations describing mean-field kinetics of coagulation, in the sequence of actions necessary for the destruction of islands in two-dimensional flow, and in the fractal structure of clusters produced upon aggregation in chaotic flows.« less

3D Radiative Hydrodynamics Simulations of Protoplanetary Disks: A Comparison Between Two Radiative Cooling Algorithms

NASA Astrophysics Data System (ADS)

Lord, Jesse W.; Boley, A. C.; Durisen, R. H.

2006-12-01

We present a comparison between two three-dimensional radiative hydrodynamics simulations of a gravitationally unstable 0.07 Msun protoplanetary disk around a 0.5 Msun star. The first simulation is the radiatively cooled disk described in Boley et al. (2006, ApJ, 651). This simulation employed an algorithm that uses 3D flux-limited diffusion wherever the vertical Rosseland optical depth is greater than 2/3, which defines the optically thick region. The optically thin atmosphere of the disk, which cools according to its emissivity, is coupled to the optically thick region through an Eddington-like boundary condition. The second simulation employed an algorithm that uses a combination of solving the radiative transfer equation along rays in the z direction and flux limited diffusion in the r and phi directions on a cylindrical grid. We compare the following characteristics of the disk simulations: the mass transport and torques induced by gravitational instabilities, the effective temperature profiles of the disks, the gravitational and Reynolds stresses measured in the disk and those expected in an alpha-disk, and the amplitudes of the Fourier modes. This work has been supported by the National Science Foundation through grant AST-0452975 (astronomy REU program to Indiana University).

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.

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.

Three-Dimensional Analytical Modeling of Diffusion-Limited Solute Transport.

DTIC Science & Technology

1986-07-01

displace- ment through an aggregated oxisol , Soil Sci. Soc. Am. J., 46, 471-476. Nkedi-Kizza, P., J. W. Biggar, H. M. Selim, M. Th. van Genuchten, P. J...aggregated oxisol , Water Resources Research, 20(8), 1123-1130. National Research Council (NRC), 1984. Groundwater Contamination, Panel on Groundwater

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.

NUMERICAL ANALYSES FOR TREATING DIFFUSION IN SINGLE-, TWO-, AND THREE-PHASE BINARY ALLOY SYSTEMS

NASA Technical Reports Server (NTRS)

Tenney, D. R.

1994-01-01

This package consists of a series of three computer programs for treating one-dimensional transient diffusion problems in single and multiple phase binary alloy systems. An accurate understanding of the diffusion process is important in the development and production of binary alloys. Previous solutions of the diffusion equations were highly restricted in their scope and application. The finite-difference solutions developed for this package are applicable for planar, cylindrical, and spherical geometries with any diffusion-zone size and any continuous variation of the diffusion coefficient with concentration. Special techniques were included to account for differences in modal volumes, initiation and growth of an intermediate phase, disappearance of a phase, and the presence of an initial composition profile in the specimen. In each analysis, an effort was made to achieve good accuracy while minimizing computation time. The solutions to the diffusion equations for single-, two-, and threephase binary alloy systems are numerically calculated by the three programs NAD1, NAD2, and NAD3. NAD1 treats the diffusion between pure metals which belong to a single-phase system. Diffusion in this system is described by a one-dimensional Fick's second law and will result in a continuous composition variation. For computational purposes, Fick's second law is expressed as an explicit second-order finite difference equation. Finite difference calculations are made by choosing the grid spacing small enough to give convergent solutions of acceptable accuracy. NAD2 treats diffusion between pure metals which form a two-phase system. Diffusion in the twophase system is described by two partial differential equations (a Fick's second law for each phase) and an interface-flux-balance equation which describes the location of the interface. Actual interface motion is obtained by a mass conservation procedure. To account for changes in the thicknesses of the two phases as diffusion progresses, a variable grid technique developed by Murray and Landis is employed. These equations are expressed in finite difference form and solved numerically. Program NAD3 treats diffusion between pure metals which form a two-phase system with an intermediate third phase. Diffusion in the three-phase system is described by three partial differential expressions of Fick's second law and two interface-flux-balance equations. As with the two-phase case, a variable grid finite difference is used to numerically solve the diffusion equations. Computation time is minimized without sacrificing solution accuracy by treating the three-phase problem as a two-phase problem when the thickness of the intermediate phase is less than a preset value. Comparisons between these programs and other solutions have shown excellent agreement. The programs are written in FORTRAN IV for batch execution on the CDC 6600 with a central memory requirement of approximately 51K (octal) 60 bit words.

Extension of the dielectric breakdown model for simulation of viscous fingering at finite viscosity ratios.

PubMed

Doorwar, Shashvat; Mohanty, Kishore K

2014-07-01

Immiscible displacement of viscous oil by water in a petroleum reservoir is often hydrodynamically unstable. Due to similarities between the physics of dielectric breakdown and immiscible flow in porous media, we extend the existing dielectric breakdown model to simulate viscous fingering patterns for a wide range of viscosity ratios (μ(r)). At low values of power-law index η, the system behaves like a stable Eden growth model and as the value of η is increased to unity, diffusion limited aggregation-like fractals appear. This model is compared with our two-dimensional (2D) experiments to develop a correlation between the viscosity ratio and the power index, i.e., η = 10(-5)μ(r)(0.8775). The 2D and three-dimensional (3D) simulation data appear scalable. The fingering pattern in 3D simulations at finite viscosity ratios appear qualitatively similar to the few experimental results published in the literature.

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.

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)

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.

Effects of the approximations of light propagation on quantitative photoacoustic tomography using two-dimensional photon diffusion equation and linearization

NASA Astrophysics Data System (ADS)

Okawa, Shinpei; Hirasawa, Takeshi; Kushibiki, Toshihiro; Ishihara, Miya

2017-12-01

Quantitative photoacoustic tomography (QPAT) employing a light propagation model will play an important role in medical diagnoses by quantifying the concentration of hemoglobin or a contrast agent. However, QPAT by the light propagation model with the three-dimensional (3D) radiative transfer equation (RTE) requires a huge computational load in the iterative forward calculations involved in the updating process to reconstruct the absorption coefficient. The approximations of the light propagation improve the efficiency of the image reconstruction for the QPAT. In this study, we compared the 3D/two-dimensional (2D) photon diffusion equation (PDE) approximating 3D RTE with the Monte Carlo simulation based on 3D RTE. Then, the errors in a 2D PDE-based linearized image reconstruction caused by the approximations were quantitatively demonstrated and discussed in the numerical simulations. It was clearly observed that the approximations affected the reconstructed absorption coefficient. The 2D PDE-based linearized algorithm succeeded in the image reconstruction of the region with a large absorption coefficient in the 3D phantom. The value reconstructed in the phantom experiment agreed with that in the numerical simulation, so that it was validated that the numerical simulation of the image reconstruction predicted the relationship between the true absorption coefficient of the target in the 3D medium and the reconstructed value with the 2D PDE-based linearized algorithm. Moreover, the the true absorption coefficient in 3D medium was estimated from the 2D reconstructed image on the basis of the prediction by the numerical simulation. The estimation was successful in the phantom experiment, although some limitations were revealed.

Low-coverage surface diffusion in complex periodic energy landscapes: Analytical solution for systems with symmetric hops and application to intercalation in topological insulators

NASA Astrophysics Data System (ADS)

Gosálvez, Miguel A.; Otrokov, Mikhail M.; Ferrando, Nestor; Ryabishchenkova, Anastasia G.; Ayuela, Andres; Echenique, Pedro M.; Chulkov, Evgueni V.

2016-02-01

This is the first of two papers that introduce a general expression for the tracer diffusivity in complex, periodic energy landscapes with M distinct hop rates in one-, two-, and three-dimensional diluted systems (low-coverage, single-tracer limit). The present report focuses on the analysis of diffusion in systems where the end sites of the hops are located symmetrically with respect to the hop origins (symmetric hops), as encountered in many ideal surfaces and bulk materials. For diffusion in two dimensions, a number of formulas are presented for complex combinations of the different hops in systems with triangular, rectangular, and square symmetry. The formulas provide values in excellent agreement with kinetic Monte Carlo simulations, concluding that the diffusion coefficient can be directly determined from the proposed expressions without performing the simulations. Based on the diffusion barriers obtained from first-principles calculations and a physically meaningful estimate of the attempt frequencies, the proposed formulas are used to analyze the diffusion of Cu, Ag, and Rb adatoms on the surface and within the van der Waals (vdW) gap of a model topological insulator, Bi2Se3 . Considering the possibility of adsorbate intercalation from the terraces to the vdW gaps at morphological steps, we infer that, at low coverage and room temperature, (i) a majority of the Rb atoms bounce back at the steps and remain on the terraces, (ii) Cu atoms mostly intercalate into the vdW gap, the remaining fraction staying at the steps, and (iii) Ag atoms essentially accumulate at the steps and gradually intercalate into the vdW gap. These conclusions are in good qualitative agreement with previous experiments. The companion report (M. A. Gosálvez et al., Phys. Rev. B, submitted] extends the present study to the description of systems that contain asymmetric hops.

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.

STAN5: A program for numerical computation of two-dimensional internal and external boundary layer flows

NASA Technical Reports Server (NTRS)

Crawford, M. E.; Kays, W. M.

1976-01-01

A large variety of two dimensional flows can be accommodated by the program, including boundary layers on a flat plate, flow inside nozzles and diffusers (for a prescribed potential flow distribution), flow over axisymmetric bodies, and developing and fully developed flow inside circular pipes and flat ducts. The flows may be laminar or turbulent, and provision is made to handle transition.

Water dynamics in small reverse micelles in two solvents: two-dimensional infrared vibrational echoes with two-dimensional background subtraction.

PubMed

Fenn, Emily E; Wong, Daryl B; Fayer, M D

2011-02-07

Water dynamics as reflected by the spectral diffusion of the water hydroxyl stretch were measured in w(0) = 2 (1.7 nm diameter) Aerosol-OT (AOT)/water reverse micelles in carbon tetrachloride and in isooctane solvents using ultrafast 2D IR vibrational echo spectroscopy. Orientational relaxation and population relaxation are observed for w(0) = 2, 4, and 7.5 in both solvents using IR pump-probe measurements. It is found that the pump-probe observables are sensitive to w(0), but not to the solvent. However, initial analysis of the vibrational echo data from the water nanopool in the reverse micelles in the isooctane solvent seems to yield different dynamics than the CCl(4) system in spite of the fact that the spectra, vibrational lifetimes, and orientational relaxation are the same in the two systems. It is found that there are beat patterns in the interferograms with isooctane as the solvent. The beats are observed from a signal generated by the AOT/isooctane system even when there is no water in the system. A beat subtraction data processing procedure does a reasonable job of removing the distortions in the isooctane data, showing that the reverse micelle dynamics are the same within experimental error regardless of whether isooctane or carbon tetrachloride is used as the organic phase. Two time scales are observed in the vibrational echo data, ~1 and ~10 ps. The slower component contains a significant amount of the total inhomogeneous broadening. Physical arguments indicate that there is a much slower component of spectral diffusion that is too slow to observe within the experimental window, which is limited by the OD stretch vibrational lifetime.

Water dynamics in small reverse micelles in two solvents: Two-dimensional infrared vibrational echoes with two-dimensional background subtraction

NASA Astrophysics Data System (ADS)

Fenn, Emily E.; Wong, Daryl B.; Fayer, M. D.

2011-02-01

Water dynamics as reflected by the spectral diffusion of the water hydroxyl stretch were measured in w0 = 2 (1.7 nm diameter) Aerosol-OT (AOT)/water reverse micelles in carbon tetrachloride and in isooctane solvents using ultrafast 2D IR vibrational echo spectroscopy. Orientational relaxation and population relaxation are observed for w0 = 2, 4, and 7.5 in both solvents using IR pump-probe measurements. It is found that the pump-probe observables are sensitive to w0, but not to the solvent. However, initial analysis of the vibrational echo data from the water nanopool in the reverse micelles in the isooctane solvent seems to yield different dynamics than the CCl4 system in spite of the fact that the spectra, vibrational lifetimes, and orientational relaxation are the same in the two systems. It is found that there are beat patterns in the interferograms with isooctane as the solvent. The beats are observed from a signal generated by the AOT/isooctane system even when there is no water in the system. A beat subtraction data processing procedure does a reasonable job of removing the distortions in the isooctane data, showing that the reverse micelle dynamics are the same within experimental error regardless of whether isooctane or carbon tetrachloride is used as the organic phase. Two time scales are observed in the vibrational echo data, ~1 and ~10 ps. The slower component contains a significant amount of the total inhomogeneous broadening. Physical arguments indicate that there is a much slower component of spectral diffusion that is too slow to observe within the experimental window, which is limited by the OD stretch vibrational lifetime.

Application of advanced computational codes in the design of an experiment for a supersonic throughflow fan rotor

NASA Technical Reports Server (NTRS)

Wood, Jerry R.; Schmidt, James F.; Steinke, Ronald J.; Chima, Rodrick V.; Kunik, William G.

1987-01-01

Increased emphasis on sustained supersonic or hypersonic cruise has revived interest in the supersonic throughflow fan as a possible component in advanced propulsion systems. Use of a fan that can operate with a supersonic inlet axial Mach number is attractive from the standpoint of reducing the inlet losses incurred in diffusing the flow from a supersonic flight Mach number to a subsonic one at the fan face. The design of the experiment using advanced computational codes to calculate the components required is described. The rotor was designed using existing turbomachinery design and analysis codes modified to handle fully supersonic axial flow through the rotor. A two-dimensional axisymmetric throughflow design code plus a blade element code were used to generate fan rotor velocity diagrams and blade shapes. A quasi-three-dimensional, thin shear layer Navier-Stokes code was used to assess the performance of the fan rotor blade shapes. The final design was stacked and checked for three-dimensional effects using a three-dimensional Euler code interactively coupled with a two-dimensional boundary layer code. The nozzle design in the expansion region was analyzed with a three-dimensional parabolized viscous code which corroborated the results from the Euler code. A translating supersonic diffuser was designed using these same codes.

Scanning, non-contact, hybrid broadband diffuse optical spectroscopy and diffuse correlation spectroscopy system.

PubMed

Johansson, Johannes D; Mireles, Miguel; Morales-Dalmau, Jordi; Farzam, Parisa; Martínez-Lozano, Mar; Casanovas, Oriol; Durduran, Turgut

2016-02-01

A scanning system for small animal imaging using non-contact, hybrid broadband diffuse optical spectroscopy (ncDOS) and diffuse correlation spectroscopy (ncDCS) is presented. The ncDOS uses a two-dimensional spectrophotometer retrieving broadband (610-900 nm) spectral information from up to fifty-seven source-detector distances between 2 and 5 mm. The ncDCS data is simultaneously acquired from four source-detector pairs. The sample is scanned in two dimensions while tracking variations in height. The system has been validated with liquid phantoms, demonstrated in vivo on a human fingertip during an arm cuff occlusion and on a group of mice with xenoimplanted renal cell carcinoma.

On Multi-Dimensional Unstructured Mesh Adaption

NASA Technical Reports Server (NTRS)

Wood, William A.; Kleb, William L.

1999-01-01

Anisotropic unstructured mesh adaption is developed for a truly multi-dimensional upwind fluctuation splitting scheme, as applied to scalar advection-diffusion. The adaption is performed locally using edge swapping, point insertion/deletion, and nodal displacements. Comparisons are made versus the current state of the art for aggressive anisotropic unstructured adaption, which is based on a posteriori error estimates. Demonstration of both schemes to model problems, with features representative of compressible gas dynamics, show the present method to be superior to the a posteriori adaption for linear advection. The performance of the two methods is more similar when applied to nonlinear advection, with a difference in the treatment of shocks. The a posteriori adaption can excessively cluster points to a shock, while the present multi-dimensional scheme tends to merely align with a shock, using fewer nodes. As a consequence of this alignment tendency, an implementation of eigenvalue limiting for the suppression of expansion shocks is developed for the multi-dimensional distribution scheme. The differences in the treatment of shocks by the adaption schemes, along with the inherently low levels of artificial dissipation in the fluctuation splitting solver, suggest the present method is a strong candidate for applications to compressible gas dynamics.

Suppression of transient enhanced diffusion in sub-micron patterned silicon template by dislocation loops formation

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

Hu, Kuan-Kan; Woon, Wei Yen; Chang, Ruey-Dar

We investigate the evolution of two dimensional transient enhanced diffusion (TED) of phosphorus in sub-micron scale patterned silicon template. Samples doped with low dose phosphorus with and without high dose silicon self-implantation, were annealed for various durations. Dopant diffusion is probed with plane-view scanning capacitance microscopy. The measurement revealed two phases of TED. Significant suppression in the second phase TED is observed for samples with high dose self-implantation. Transmission electron microscopy suggests the suppressed TED is related to the evolution of end of range defect formed around ion implantation sidewalls.

Suppression of transient enhanced diffusion in sub-micron patterned silicon template by dislocation loops formation

NASA Astrophysics Data System (ADS)

Hu, Kuan-Kan; Chang, Ruey-Dar; Woon, Wei Yen

2015-10-01

We investigate the evolution of two dimensional transient enhanced diffusion (TED) of phosphorus in sub-micron scale patterned silicon template. Samples doped with low dose phosphorus with and without high dose silicon self-implantation, were annealed for various durations. Dopant diffusion is probed with plane-view scanning capacitance microscopy. The measurement revealed two phases of TED. Significant suppression in the second phase TED is observed for samples with high dose self-implantation. Transmission electron microscopy suggests the suppressed TED is related to the evolution of end of range defect formed around ion implantation sidewalls.

Effective diffusion of confined active Brownian swimmers

NASA Astrophysics Data System (ADS)

Sandoval, Mario; Dagdug, Leonardo

2014-11-01

We find theoretically the effect of confinement and thermal fluctuations, on the diffusivity of a spherical active swimmer moving inside a two-dimensional narrow cavity of general shape. The explicit formulas for the effective diffusion coefficient of a swimmer moving inside two particular cavities are presented. We also compare our analytical results with Brownian Dynamics simulations and we obtain excellent agreement. L.D. thanks Consejo Nacional de Ciencia y Tecnologia (CONACyT) Mexico, for partial support by Grant No. 176452. M. S. thanks CONACyT and Programa de Mejoramiento de Profesorado (PROMEP) for partially funding this work under Grant No. 103.5/13/6732.

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...

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

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

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 Critical Study of Agglomerated Multigrid Methods for Diffusion

NASA Technical Reports Server (NTRS)

Thomas, James L.; Nishikawa, Hiroaki; Diskin, Boris

2009-01-01

Agglomerated multigrid techniques used in unstructured-grid methods are studied critically for a model problem representative of laminar diffusion in the incompressible limit. The studied target-grid discretizations and discretizations used on agglomerated grids are typical of current node-centered formulations. Agglomerated multigrid convergence rates are presented using a range of two- and three-dimensional randomly perturbed unstructured grids for simple geometries with isotropic and highly stretched grids. Two agglomeration techniques are used within an overall topology-preserving agglomeration framework. The results show that multigrid with an inconsistent coarse-grid scheme using only the edge terms (also referred to in the literature as a thin-layer formulation) provides considerable speedup over single-grid methods but its convergence deteriorates on finer grids. Multigrid with a Galerkin coarse-grid discretization using piecewise-constant prolongation and a heuristic correction factor is slower and also grid-dependent. In contrast, grid-independent convergence rates are demonstrated for multigrid with consistent coarse-grid discretizations. Actual cycle results are verified using quantitative analysis methods in which parts of the cycle are replaced by their idealized counterparts.

Discontinuous Finite Element Quasidiffusion Methods

DOE PAGES

Anistratov, Dmitriy Yurievich; Warsa, James S.

2018-05-21

Here in this paper, two-level methods for solving transport problems in one-dimensional slab geometry based on the quasi-diffusion (QD) method are developed. A linear discontinuous finite element method (LDFEM) is derived for the spatial discretization of the low-order QD (LOQD) equations. It involves special interface conditions at the cell edges based on the idea of QD boundary conditions (BCs). We consider different kinds of QD BCs to formulate the necessary cell-interface conditions. We develop two-level methods with independent discretization of the high-order transport equation and LOQD equations, where the transport equation is discretized using the method of characteristics and themore » LDFEM is applied to the LOQD equations. We also formulate closures that lead to the discretization consistent with a LDFEM discretization of the transport equation. The proposed methods are studied by means of test problems formulated with the method of manufactured solutions. Numerical experiments are presented demonstrating the performance of the proposed methods. Lastly, we also show that the method with independent discretization has the asymptotic diffusion limit.« less

Discontinuous Finite Element Quasidiffusion Methods

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

Anistratov, Dmitriy Yurievich; Warsa, James S.

Here in this paper, two-level methods for solving transport problems in one-dimensional slab geometry based on the quasi-diffusion (QD) method are developed. A linear discontinuous finite element method (LDFEM) is derived for the spatial discretization of the low-order QD (LOQD) equations. It involves special interface conditions at the cell edges based on the idea of QD boundary conditions (BCs). We consider different kinds of QD BCs to formulate the necessary cell-interface conditions. We develop two-level methods with independent discretization of the high-order transport equation and LOQD equations, where the transport equation is discretized using the method of characteristics and themore » LDFEM is applied to the LOQD equations. We also formulate closures that lead to the discretization consistent with a LDFEM discretization of the transport equation. The proposed methods are studied by means of test problems formulated with the method of manufactured solutions. Numerical experiments are presented demonstrating the performance of the proposed methods. Lastly, we also show that the method with independent discretization has the asymptotic diffusion limit.« less

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.

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.

Glasses-free large size high-resolution three-dimensional display based on the projector array

NASA Astrophysics Data System (ADS)

Sang, Xinzhu; Wang, Peng; Yu, Xunbo; Zhao, Tianqi; Gao, Xing; Xing, Shujun; Yu, Chongxiu; Xu, Daxiong

2014-11-01

Normally, it requires a huge amount of spatial information to increase the number of views and to provide smooth motion parallax for natural three-dimensional (3D) display similar to real life. To realize natural 3D video display without eye-wears, a huge amount of 3D spatial information is normal required. However, minimum 3D information for eyes should be used to reduce the requirements for display devices and processing time. For the 3D display with smooth motion parallax similar to the holographic stereogram, the size the virtual viewing slit should be smaller than the pupil size of eye at the largest viewing distance. To increase the resolution, two glass-free 3D display systems rear and front projection are presented based on the space multiplexing with the micro-projector array and the special designed 3D diffuse screens with the size above 1.8 m× 1.2 m. The displayed clear depths are larger 1.5m. The flexibility in terms of digitized recording and reconstructed based on the 3D diffuse screen relieves the limitations of conventional 3D display technologies, which can realize fully continuous, natural 3-D display. In the display system, the aberration is well suppressed and the low crosstalk is achieved.

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

Three-dimensional visualization of morphology and ventilation procedure (air flow and diffusion) of a subdivision of the acinus using synchrotron radiation microtomography of the human lung specimens

NASA Astrophysics Data System (ADS)

Shimizu, Kenji; Ikura, Hirohiko; Ikezoe, Junpei; Nagareda, Tomofumi; Yagi, Naoto; Umetani, Keiji; Imai, Yutaka

2004-04-01

We have previously reported a synchrotron radiation (SR) microtomography system constructed at the bending magnet beamline at the SPring-8. This system has been applied to the lungs obtained at autopsy and inflated and fixed by Heitzman"s method. Normal lung and lung specimens with two different types of pathologic processes (fibrosis and emphysema) were included. Serial SR microtomographic images were stacked to yield the isotropic volumetric data with high-resolution (12 μm3 in voxel size). Within the air spaces of a subdivision of the acinus, each voxel is segmented three-dimensionally using a region growing algorithm ("rolling ball algorithm"). For each voxel within the segmented air spaces, two types of voxel coding have been performed: single-seeded (SS) coding and boundary-seeded (BS) coding, in which the minimum distance from an initial point as the only seed point and all object boundary voxels as a seed set were calculated and assigned as the code values to each voxel, respectively. With these two codes, combinations of surface rendering and volume rendering techniques were applied to visualize three-dimensional morphology of a subdivision of the acinus. Furthermore, sequentially filling process of air into a subdivision of the acinus was simulated under several conditions to visualize the ventilation procedure (air flow and diffusion). A subdivision of the acinus was reconstructed three-dimensionally, demonstrating the normal architecture of the human lung. Significant differences in appearance of ventilation procedure were observed between normal and two pathologic processes due to the alteration of the lung architecture. Three-dimensional reconstruction of the microstructure of a subdivision of the acinus and visualization of the ventilation procedure (air flow and diffusion) with SR microtomography would offer a new approach to study the morphology, physiology, and pathophysiology of the human respiratory system.

Cold spray nozzle mach number limitation

NASA Astrophysics Data System (ADS)

Jodoin, B.

2002-12-01

The classic one-dimensional isentropic flow approach is used along with a two-dimensional axisymmetric numerical model to show that the exit Mach number of a cold spray nozzle should be limited due to two factors. To show this, the two-dimensional model is validated with experimental data. Although both models show that the stagnation temperature is an important limiting factor, the one-dimensional approach fails to show how important the shock-particle interactions are at limiting the nozzle Mach number. It is concluded that for an air nozzle spraying solid powder particles, the nozzle Mach number should be set between 1.5 and 3 to limit the negative effects of the high stagnation temperature and of the shock-particle interactions.

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.

Reaction time for trimolecular reactions in compartment-based reaction-diffusion models

NASA Astrophysics Data System (ADS)

Li, Fei; Chen, Minghan; Erban, Radek; Cao, Yang

2018-05-01

Trimolecular reaction models are investigated in the compartment-based (lattice-based) framework for stochastic reaction-diffusion modeling. The formulae for the first collision time and the mean reaction time are derived for the case where three molecules are present in the solution under periodic boundary conditions. For the case of reflecting boundary conditions, similar formulae are obtained using a computer-assisted approach. The accuracy of these formulae is further verified through comparison with numerical results. The presented derivation is based on the first passage time analysis of Montroll [J. Math. Phys. 10, 753 (1969)]. Montroll's results for two-dimensional lattice-based random walks are adapted and applied to compartment-based models of trimolecular reactions, which are studied in one-dimensional or pseudo one-dimensional domains.

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.

OBJECT KINETIC MONTE CARLO SIMULATIONS OF RADIATION DAMAGE IN BULK TUNGSTEN

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

Nandipati, Giridhar; Setyawan, Wahyu; Heinisch, Howard L.

2015-09-22

We used our recently developed lattice based OKMC code; KSOME [1] to carryout simulations of radiation damage in bulk W. We study the effect of dimensionality of self interstitial atom (SIA) diffusion i.e. 1D versus 3D on the defect accumulation during irradiation with a primary knock-on atom (PKA) energy of 100 keV at 300 K for the dose rates of 10-5 and 10-6 dpa/s. As expected 3D SIA diffusion significantly reduces damage accumulation due to increased probability of recombination events. In addition, dose rate, over the limited range examined here, appears to have no effect in both cases of SIAmore » diffusion.« less

Transport, diffusion, and energy studies in the Arnold-Beltrami-Childress map

NASA Astrophysics Data System (ADS)

Das, Swetamber; Gupte, Neelima

2017-09-01

We study the transport and diffusion properties of passive inertial particles described by a six-dimensional dissipative bailout embedding map. The base map chosen for the study is the three-dimensional incompressible Arnold-Beltrami-Childress (ABC) map chosen as a representation of volume preserving flows. There are two distinct cases: the two-action and the one-action cases, depending on whether two or one of the parameters (A ,B ,C ) exceed 1. The embedded map dynamics is governed by two parameters (α ,γ ), which quantify the mass density ratio and dissipation, respectively. There are important differences between the aerosol (α <1 ) and the bubble (α >1 ) regimes. We have studied the diffusive behavior of the system and constructed the phase diagram in the parameter space by computing the diffusion exponents η . Three classes have been broadly classified—subdiffusive transport (η <1 ), normal diffusion (η ≈1 ), and superdiffusion (η >1 ) with η ≈2 referred to as the ballistic regime. Correlating the diffusive phase diagram with the phase diagram for dynamical regimes seen earlier, we find that the hyperchaotic bubble regime is largely correlated with normal and superdiffusive behavior. In contrast, in the aerosol regime, ballistic superdiffusion is seen in regions that largely show periodic dynamical behaviors, whereas subdiffusive behavior is seen in both periodic and chaotic regimes. The probability distributions of the diffusion exponents show power-law scaling for both aerosol and bubbles in the superdiffusive regimes. We further study the Poincáre recurrence times statistics of the system. Here, we find that recurrence time distributions show power law regimes due to the existence of partial barriers to transport in the phase space. Moreover, the plot of average particle kinetic energies versus the mass density ratio for the two-action case exhibits a devil's staircase-like structure for higher dissipation values. We explain these results and discuss their implications for realistic systems.

Bulk dynamics of Brownian hard disks: Dynamical density functional theory versus experiments on two-dimensional colloidal hard spheres

NASA Astrophysics Data System (ADS)

Stopper, Daniel; Thorneywork, Alice L.; Dullens, Roel P. A.; Roth, Roland

2018-03-01

Using dynamical density functional theory (DDFT), we theoretically study Brownian self-diffusion and structural relaxation of hard disks and compare to experimental results on quasi two-dimensional colloidal hard spheres. To this end, we calculate the self-van Hove correlation function and distinct van Hove correlation function by extending a recently proposed DDFT-approach for three-dimensional systems to two dimensions. We find that the theoretical results for both self-part and distinct part of the van Hove function are in very good quantitative agreement with the experiments up to relatively high fluid packing fractions of roughly 0.60. However, at even higher densities, deviations between the experiment and the theoretical approach become clearly visible. Upon increasing packing fraction, in experiments, the short-time self-diffusive behavior is strongly affected by hydrodynamic effects and leads to a significant decrease in the respective mean-squared displacement. By contrast, and in accordance with previous simulation studies, the present DDFT, which neglects hydrodynamic effects, shows no dependence on the particle density for this quantity.

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.

Spectral analysis and multigrid preconditioners for two-dimensional space-fractional diffusion equations

NASA Astrophysics Data System (ADS)

Moghaderi, Hamid; Dehghan, Mehdi; Donatelli, Marco; Mazza, Mariarosa

2017-12-01

Fractional diffusion equations (FDEs) are a mathematical tool used for describing some special diffusion phenomena arising in many different applications like porous media and computational finance. In this paper, we focus on a two-dimensional space-FDE problem discretized by means of a second order finite difference scheme obtained as combination of the Crank-Nicolson scheme and the so-called weighted and shifted Grünwald formula. By fully exploiting the Toeplitz-like structure of the resulting linear system, we provide a detailed spectral analysis of the coefficient matrix at each time step, both in the case of constant and variable diffusion coefficients. Such a spectral analysis has a very crucial role, since it can be used for designing fast and robust iterative solvers. In particular, we employ the obtained spectral information to define a Galerkin multigrid method based on the classical linear interpolation as grid transfer operator and damped-Jacobi as smoother, and to prove the linear convergence rate of the corresponding two-grid method. The theoretical analysis suggests that the proposed grid transfer operator is strong enough for working also with the V-cycle method and the geometric multigrid. On this basis, we introduce two computationally favourable variants of the proposed multigrid method and we use them as preconditioners for Krylov methods. Several numerical results confirm that the resulting preconditioning strategies still keep a linear convergence rate.

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.

Nucleation of rotating crystals by Thiovulum majus bacteria

NASA Astrophysics Data System (ADS)

Petroff, A. P.; Libchaber, A.

2018-01-01

Thiovulum majus self-organize on glass surfaces into active two-dimensional crystals of rotating cells. Unlike classical crystals, these bacterial crystallites continuously rotate and reorganize as the power of rotating cells is dissipated by the surrounding flow. In this article, we describe the earliest stage of crystallization, the attraction of two bacteria into a hydrodynamically-bound dimer. This process occurs in three steps. First a free-swimming cell collides with the wall and becomes hydrodynamically bound to the two-dimensional surface. We present a simple model to understand how viscous forces localize cells near the chamber walls. Next, the cell diffuses over the surface for an average of 63+/- 6 s before escaping to the bulk fluid. The diffusion coefficient {D}{{eff}}=7.98 +/- 0.1 μ {{{m}}}2 {{{s}}}-1 of these 8.5 μ {{m}} diameter cells corresponds to a temperature of (4.16+/- 0.05)× {10}4 K, and thus cannot be explained by equilibrium fluctuations. Finally, two cells coalesce into a rotating dimer when the convergent flow created by each cell overwhelms their active Brownian motion. This occurs when cells diffuse to within a distance of 13.3 ± 0.2 μm of each other.

Two-Dimensional Failure Waves and Ignition Fronts in Premixed Combustion

NASA Technical Reports Server (NTRS)

Vedarajan, T. G.; Buckmaster J.; Ronney, P.

1998-01-01

This paper is a continuation of our work on edge-flames in premixed combustion. An edge-flame is a two-dimensional structure constructed from a one-dimensional configuration that has two stable solutions (bistable equilibrium). Edge-flames can display wavelike behavior, advancing as ignition fronts or retreating as failure waves. Here we consider two one-dimensional configurations: twin deflagrations in a straining flow generated by the counterflow of fresh streams of mixture: and a single deflagration subject to radiation losses. The edge-flames constructed from the first configuration have positive or negative speeds, according to the value of the strain rate. But our numerical solutions strongly suggest that only positive speeds (corresponding to ignition fronts) can exist for the second configuration. We show that this phenomenon can also occur in diffusion flames when the Lewis numbers are small. And we discuss the asymptotics of the one-dimensional twin deflagration configuration. an overlooked problem from the 70s.

An improved large-field focusing schlieren system

NASA Technical Reports Server (NTRS)

Weinstein, Leonard M.

1991-01-01

The analysis and performance of a high-brightness large-field focusing schlieren system is described. The system can be used to examine complex two- and three-dimensional flows. Techniques are described to obtain focusing schlieren through distorting optical elements, to use multiple colors in a time multiplexing technique, and to use diffuse screen holography for three-dimensional photographs.

Deep-tissue temperature mapping by multi-illumination photoacoustic tomography aided by a diffusion optical model: a numerical study

NASA Astrophysics Data System (ADS)

Zhou, Yuan; Tang, Eric; Luo, Jianwen; Yao, Junjie

2018-01-01

Temperature mapping during thermotherapy can help precisely control the heating process, both temporally and spatially, to efficiently kill the tumor cells and prevent the healthy tissues from heating damage. Photoacoustic tomography (PAT) has been used for noninvasive temperature mapping with high sensitivity, based on the linear correlation between the tissue's Grüneisen parameter and temperature. However, limited by the tissue's unknown optical properties and thus the optical fluence at depths beyond the optical diffusion limit, the reported PAT thermometry usually takes a ratiometric measurement at different temperatures and thus cannot provide absolute measurements. Moreover, ratiometric measurement over time at different temperatures has to assume that the tissue's optical properties do not change with temperatures, which is usually not valid due to the temperature-induced hemodynamic changes. We propose an optical-diffusion-model-enhanced PAT temperature mapping that can obtain the absolute temperature distribution in deep tissue, without the need of multiple measurements at different temperatures. Based on the initial acoustic pressure reconstructed from multi-illumination photoacoustic signals, both the local optical fluence and the optical parameters including absorption and scattering coefficients are first estimated by the optical-diffusion model, then the temperature distribution is obtained from the reconstructed Grüneisen parameters. We have developed a mathematic model for the multi-illumination PAT of absolute temperatures, and our two-dimensional numerical simulations have shown the feasibility of this new method. The proposed absolute temperature mapping method may set the technical foundation for better temperature control in deep tissue in thermotherapy.

Two-dimensional single-shot diffusion-weighted stimulated EPI with reduced FOV for ultrahigh-b radial diffusion-weighted imaging of spinal cord.

PubMed

Sapkota, Nabraj; Shi, Xianfeng; Shah, Lubdha M; Bisson, Erica F; Rose, John W; Jeong, Eun-Kee

2017-06-01

High-resolution diffusion-weighted imaging (DWI) of the spinal cord (SC) is problematic because of the small cross-section of the SC and the large field inhomogeneity. Obtaining the ultrahigh-b DWI poses a further challenge. The purpose of the study was to design and validate two-dimensional (2D) single-shot diffusion-weighted stimulated echo planar imaging with reduced field of view (2D ss-DWSTEPI-rFOV) for ultrahigh-b radial DWI (UHB-rDWI) of the SC. A novel time-efficient 2D ss-DWSTEPI-rFOV sequence was developed based on the stimulated echo sequence. Reduced-phase field of view was obtained by using two slice-selective 90 ° radiofrequency pulses in the presence of the orthogonal slice selection gradients. The sequence was validated on a cylindrical phantom and demonstrated on SC imaging. Ultrahigh-b radial diffusion-weighted ( bmax = 7300 s/mm2) images of the SC with greatly reduced distortion were obtained. The exponential plus constant fitting of the diffusion-decay curve estimated the constant fraction (restricted water fraction) as 0.36 ± 0.05 in the SC white matter. A novel 2D ss-DWSTEPI-rFOV sequence has been designed and demonstrated for high-resolution UHB-rDWI of localized anatomic structures with significantly reduced distortion induced by nonlinear static field inhomogeneity. Magn Reson Med 77:2167-2173, 2017. © 2016 International Society for Magnetic Resonance in Medicine. © 2016 International Society for Magnetic Resonance in Medicine.

Low-energy ion acceleration at quasi-perpendicular shocks: Transverse diffusion

NASA Technical Reports Server (NTRS)

Giacalone, J.; Jokipii, J. R.

1995-01-01

The problem of ion injection and acceleration at quasi perpendicular shocks has been the subject of some debate over the past two decades. It is widely known that these shocks efficiently accelerate particles that are well in the high-energy tail of the distribution. However, the issue of injection, or the acceleration of low-energy ions, has yet to reach a consensus. The fundamental issue is whether there is enough diffusion normal to the magnetic field for the particles to remain near the shock. Since transverse diffusion is a physical process that is not well understood in space plasmas, this is an important, and difficult issue to address. In this report, we will investigate the ion injection problem by performing test particle orbit integrations using synthesized turbulent fields. These fields are fully three-dimensional so that transverse diffusion is possible (cross-field diffusion is not possible in geometries where the electromagnetic fields are less than three dimensional). The synthesized fields are produced by superimposing a three-dimensional wave field on a background field. For completeness, we will compare the results from this model with the more well-established theories, such as the diffusive approximation and scatter-free shock drift acceleration. We will also compare these results with other numerical simulation techniques such as the well known hybrid simulation, and other test-particle calculations in which the shock fields are specified to have less than three dimensions. We will also discuss some recent relevant observations and how these compare with our results.

Cellular structure of lean hydrogen flames in microgravity

NASA Technical Reports Server (NTRS)

Patnaik, G.; Kailasanath, K.

1990-01-01

Detailed, time-dependent, two-dimensional numerical simulations of premixed laminar flames have been used to study the initiation and subsequent development of cellular structures in lean hydrogen-air flames. The model includes detailed hydrogen-oxygen combustion with 24 elementary reactions of eight reactive species and a nitrogen diluent, molecular diffusion of all species, thermal conduction, viscosity, and convection. This model has been used to study the nonlinear evolution of cellular flame structure and shows that cell splitting, as observed in experiments, can be predicted numerically for sufficiently reactive mixtures. The structures that evolved also resembled the cellular structures observed in experiments. The present study shows that the 'cell-split limit' postulated from experimental observations is an intrinsic property of the mixture and that external factors such as heat losses are not necessary to cause this limit.

Recent development of a jet-diffuser ejector

NASA Technical Reports Server (NTRS)

Alperin, M.; Wu, J. J.

1980-01-01

The paper considers thrust augmenting ejectors in which the processes of mixing and diffusion are partly carried out downstream of the ejector solid surfaces. A jet sheet surrounding the periphery of a widely diverging diffuser prevents separation and forms a gaseous, curved surface to provide effective diffuser ratio and additional length for mixing of primary and induced flows. Three-dimensional potential flow methods achieved a large reduction in the length of the associated solid surface; primary nozzle design further reduced the volume required by the jet-diffuser ejectors, resulting in thrust augmentation in excess of two, and an overall length of about 2 1/2 times the throat width.

The Harrison Diffusion Kinetics Regimes in Solute Grain Boundary Diffusion

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

Belova, Irina; Fiedler, T; Kulkarni, Nagraj S

2012-01-01

Knowledge of the limits of the principal Harrison kinetics regimes (Type-A, B and C) for grain boundary diffusion is very important for the correct analysis of the depth profiles in a tracer diffusion experiment. These regimes for self-diffusion have been extensively studied in the past by making use of the phenomenological Lattice Monte Carlo (LMC) method with the result that the limits are now well established. The relationship of those self-diffusion limits to the corresponding ones for solute diffusion in the presence of solute segregation to the grain boundaries remains unclear. In the present study, the influence of solute segregationmore » on the limits is investigated with the LMC method for the well-known parallel grain boundary slab model by showing the equivalence of two diffusion models. It is shown which diffusion parameters are useful for identifying the limits of the Harrison kinetics regimes for solute grain boundary diffusion. It is also shown how the measured segregation factor from the diffusion experiment in the Harrison Type-B kinetics regime may differ from the global segregation factor.« less

Electro-convective versus electroosmotic instability in concentration polarization.

PubMed

Rubinstein, Isaak; Zaltzman, Boris

2007-10-31

Electro-convection is reviewed as a mechanism of mixing in the diffusion layer of a strong electrolyte adjacent to a charge-selective solid, such as an ion exchange (electrodialysis) membrane or an electrode. Two types of electro-convection in strong electrolytes may be distinguished: bulk electro-convection, due to the action of the electric field upon the residual space charge of a quasi-electro-neutral bulk solution, and convection induced by electroosmotic slip, due to electric forces acting in the thin electric double layer of either quasi-equilibrium or non-equilibrium type near the solid/liquid interface. According to recent studies, the latter appears to be the likely source of mixing in the diffusion layer, leading to 'over-limiting' conductance in electrodialysis. Electro-convection near a planar uniform charge selective solid/liquid interface sets on as a result of hydrodynamic instability of one-dimensional steady state electric conduction through such an interface. We compare the results of linear stability analysis obtained for instabilities of this kind appearing in the full electro-convective and limiting non-equilibrium electroosmotic formulations. The short- and long-wave aspects of these instabilities are discussed along with the wave number selection principles.

Diffusion-prepared stimulated-echo turbo spin echo (DPsti-TSE): An eddy current-insensitive sequence for three-dimensional high-resolution and undistorted diffusion-weighted imaging.

PubMed

Zhang, Qinwei; Coolen, Bram F; Versluis, Maarten J; Strijkers, Gustav J; Nederveen, Aart J

2017-07-01

In this study, we present a new three-dimensional (3D), diffusion-prepared turbo spin echo sequence based on a stimulated-echo read-out (DPsti-TSE) enabling high-resolution and undistorted diffusion-weighted imaging (DWI). A dephasing gradient in the diffusion preparation module and rephasing gradients in the turbo spin echo module create stimulated echoes, which prevent signal loss caused by eddy currents. Near to perfect agreement of apparent diffusion coefficient (ADC) values between DPsti-TSE and diffusion-weighted echo planar imaging (DW-EPI) was demonstrated in both phantom transient signal experiments and phantom imaging experiments. High-resolution and undistorted DPsti-TSE was demonstrated in vivo in prostate and carotid vessel wall. 3D whole-prostate DWI was achieved with four b values in only 6 min. Undistorted ADC maps of the prostate peripheral zone were obtained at low and high imaging resolutions with no change in mean ADC values [(1.60 ± 0.10) × 10 -3 versus (1.60 ± 0.02) × 10 -3  mm 2 /s]. High-resolution 3D DWI of the carotid vessel wall was achieved in 12 min, with consistent ADC values [(1.40 ± 0.23) × 10 -3  mm 2 /s] across different subjects, as well as slice locations through the imaging volume. This study shows that DPsti-TSE can serve as a robust 3D diffusion-weighted sequence and is an attractive alternative to the traditional two-dimensional DW-EPI approaches. Copyright © 2017 John Wiley & Sons, Ltd.

Diffusive and localization behavior of electromagnetic waves in a two-dimensional random medium

NASA Astrophysics Data System (ADS)

Wang, Ken Kang-Hsin; Ye, Zhen

2003-10-01

In this paper, we discuss the transport phenomena of electromagnetic waves in a two-dimensional random system which is composed of arrays of electrical dipoles, following the model presented earlier by Erdogan et al. [J. Opt. Soc. Am. B 10, 391 (1993)]. A set of self-consistent equations is presented, accounting for the multiple scattering in the system, and is then solved numerically. A strong localization regime is discovered in the frequency domain. The transport properties within, near the edge of, and nearly outside the localization regime are investigated for different parameters such as filling factor and system size. The results show that within the localization regime, waves are trapped near the transmitting source. Meanwhile, the diffusive waves follow an intuitive but expected picture. That is, they increase with traveling path as more and more random scattering incurs, followed by a saturation, then start to decay exponentially when the travelling path is large enough, signifying the localization effect. For the cases where the frequencies are near the boundary of or outside the localization regime, the results of diffusive waves are compared with the diffusion approximation, showing less encouraging agreement as in other systems [Asatryan et al., Phys. Rev. E 67, 036605 (2003)].

Three-Dimensional Upward Flame Spreading in Partial-Gravity Buoyant Flows

NASA Technical Reports Server (NTRS)

Sacksteder, Kurt R.; Feier, Ioan I.; Shih, Hsin-Yi; T'ien, James S.

2001-01-01

Reduced-gravity environments have been used to establish low-speed, purely forced flows for both opposed- and concurrent-flow flame spread studies. Altenkirch's group obtained spacebased experimental results and developed unsteady, two-dimensional numerical simulations of opposed-flow flame spread including gas-phase radiation, primarily away from the flammability limit for thin fuels, but including observations of thick fuel quenching in quiescent environments. T'ien's group contributed some early flame spreading results for thin fuels both in opposed flow and concurrent flow regimes, with more focus on near-limit conditions. T'ien's group also developed two- and three-dimensional numerical simulations of concurrent-flow flame spread incorporating gas-phase radiative models, including predictions of a radiatively-induced quenching limit reached in very low-speed air flows. Radiative quenching has been subsequently observed in other studies of combustion in very low-speed flows including other flame spread investigations, droplet combustion and homogeneous diffusion flames, and is the subject of several contemporary studies reported in this workshop. Using NASA aircraft flying partial-gravity "parabolic" trajectories, flame spreading in purely buoyant, opposed-flow (downward burning) has been studied. These results indicated increases in flame spread rates and enhanced flammability (lower limiting atmospheric oxygen content) as gravity levels were reduced from normal Earth gravity, and were consistent with earlier data obtained by Altenkirch using a centrifuge. In this work, experimental results and a three-dimensional numerical simulation of upward flame spreading in variable partial-gravity environments were obtained including some effects of reduced pressure and variable sample width. The simulation provides physical insight for interpreting the experimental results and shows the intrinsic 3-D nature of buoyant, upward flame spreading. This study is intended to link the evolving understanding of flame spreading in purely-forced flows to the purely-buoyant flow environment, particularly in the concurrent flow regime; provide additional insight into the existence of steady flame spread in concurrent flows; and stimulate direct comparisons between opposed- and concurrent-flow flame spread. Additionally, this effort is intended to provide direct practical understanding applicable to fire protection planning for the habitable facilities in partial gravity environments of anticipated Lunar and Martian explorations.

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.

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.

Application of Laser Ranging and VLBI Data to a Study of Plate Tectonic Driving Forces

NASA Technical Reports Server (NTRS)

Solomon, S. C.

1980-01-01

The conditions under which changes in plate driving or resistive forces associated with plate boundary earthquakes are measurable with laser ranging or very long base interferometry were investigated. Aspects of plate forces that can be characterized by such measurements were identified. Analytic solutions for two dimensional stress diffusion in a viscoelastic plate following earthquake faulting on a finite fault, finite element solutions for three dimensional stress diffusion in a viscoelastic Earth following earthquake faulting, and quantitative constraints from modeling of global intraplate stress on the magnitude of deviatoric stress in the lithosphere are among the topics discussed.

Waterlike anomalies in a two-dimensional core-softened potential

NASA Astrophysics Data System (ADS)

Bordin, José Rafael; Barbosa, Marcia C.

2018-02-01

We investigate the structural, thermodynamic, and dynamic behavior of a two-dimensional (2D) core-corona system using Langevin dynamics simulations. The particles are modeled by employing a core-softened potential which exhibits waterlike anomalies in three dimensions. In previous studies in a quasi-2D system a new region in the pressure versus temperature phase diagram of structural anomalies was observed. Here we show that for the two-dimensional case two regions in the pressure versus temperature phase diagram with structural, density, and diffusion anomalies are observed. Our findings indicate that, while the anomalous region at lower densities is due the competition between the two length scales in the potential at higher densities, the anomalous region is related to the reentrance of the melting line.

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<

Stabilization of a spatially uniform steady state in two systems exhibiting Turing patterns

NASA Astrophysics Data System (ADS)

Konishi, Keiji; Hara, Naoyuki

2018-05-01

This paper deals with the stabilization of a spatially uniform steady state in two coupled one-dimensional reaction-diffusion systems with Turing instability. This stabilization corresponds to amplitude death that occurs in a coupled system with Turing instability. Stability analysis of the steady state shows that stabilization does not occur if the two reaction-diffusion systems are identical. We derive a sufficient condition for the steady state to be stable for any length of system and any boundary conditions. Our analytical results are supported with numerical examples.

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.

Single-Molecule Resolution of Antimicrobial Peptide Interactions with Supported Lipid A Bilayers.

PubMed

Nelson, Nathaniel; Schwartz, Daniel K

2018-06-05

The molecular interactions between antimicrobial peptides (AMPs) and lipid A-containing supported lipid bilayers were probed using single-molecule total internal reflection fluorescence microscopy. Hybrid supported lipid bilayers with lipid A outer leaflets and phospholipid (1,2-dioleoyl-sn-glycero-3-phosphoethanolamine (DOPE)) inner leaflets were prepared and characterized, and the spatiotemporal trajectories of individual fluorescently labeled LL37 and Melittin AMPs were determined as they interacted with the bilayer surfaces comprising either monophosphoryl or diphosphoryl lipid A (from Escherichia coli) to determine the impact of electrostatic interactions. Large numbers of trajectories were obtained and analyzed to obtain the distributions of surface residence times and the statistics of the spatial trajectories. Interestingly, the AMP species were sensitive to subtle differences in the charge of the lipid, with both peptides diffusing more slowly and residing longer on the diphosphoryl lipid A. Furthermore, the single-molecule dynamics indicated a qualitative difference between the behavior of AMPs on hybrid Lipid A bilayers and on those composed entirely of DOPE. Whereas AMPs interacting with a DOPE bilayer exhibited two-dimensional Brownian diffusion with a diffusion coefficient of ∼1.7 μm 2 /s, AMPs adsorbed to the lipid A surface exhibited much slower apparent diffusion (on the order of ∼0.1 μm 2 /s) and executed intermittent trajectories that alternated between two-dimensional Brownian diffusion and desorption-mediated three-dimensional flights. Overall, these findings suggested that bilayers with lipid A in the outer leaflet, as it is in bacterial outer membranes, are valuable model systems for the study of the initial stage of AMP-bacterium interactions. Furthermore, single-molecule dynamics was sensitive to subtle differences in electrostatic interactions between cationic AMPs and monovalent or divalent anionic lipid A moieties. Copyright © 2018 Biophysical Society. All rights reserved.

A four-dimensional variational chemistry data assimilation scheme for Eulerian chemistry transport modeling

NASA Astrophysics Data System (ADS)

Eibern, Hendrik; Schmidt, Hauke

1999-08-01

The inverse problem of data assimilation of tropospheric trace gas observations into an Eulerian chemistry transport model has been solved by the four-dimensional variational technique including chemical reactions, transport, and diffusion. The University of Cologne European Air Pollution Dispersion Chemistry Transport Model 2 with the Regional Acid Deposition Model 2 gas phase mechanism is taken as the basis for developing a full four-dimensional variational data assimilation package, on the basis of the adjoint model version, which includes the adjoint operators of horizontal and vertical advection, implicit vertical diffusion, and the adjoint gas phase mechanism. To assess the potential and limitations of the technique without degrading the impact of nonperfect meteorological analyses and statistically not established error covariance estimates, artificial meteorological data and observations are used. The results are presented on the basis of a suite of experiments, where reduced records of artificial "observations" are provided to the assimilation procedure, while other "data" is retained for performance control of the analysis. The paper demonstrates that the four-dimensional variational technique is applicable for a comprehensive chemistry transport model in terms of computational and storage requirements on advanced parallel platforms. It is further shown that observed species can generally be analyzed, even if the "measurements" have unbiased random errors. More challenging experiments are presented, aiming to tax the skill of the method (1) by restricting available observations mostly to surface ozone observations for a limited assimilation interval of 6 hours and (2) by starting with poorly chosen first guess values. In this first such application to a three-dimensional chemistry transport model, success was also achieved in analyzing not only observed but also chemically closely related unobserved constituents.

Chaotic attractors of relaxation oscillators

NASA Astrophysics Data System (ADS)

Guckenheimer, John; Wechselberger, Martin; Young, Lai-Sang

2006-03-01

We develop a general technique for proving the existence of chaotic attractors for three-dimensional vector fields with two time scales. Our results connect two important areas of dynamical systems: the theory of chaotic attractors for discrete two-dimensional Henon-like maps and geometric singular perturbation theory. Two-dimensional Henon-like maps are diffeomorphisms that limit on non-invertible one-dimensional maps. Wang and Young formulated hypotheses that suffice to prove the existence of chaotic attractors in these families. Three-dimensional singularly perturbed vector fields have return maps that are also two-dimensional diffeomorphisms limiting on one-dimensional maps. We describe a generic mechanism that produces folds in these return maps and demonstrate that the Wang-Young hypotheses are satisfied. Our analysis requires a careful study of the convergence of the return maps to their singular limits in the Ck topology for k >= 3. The theoretical results are illustrated with a numerical study of a variant of the forced van der Pol oscillator.

Analytic Models of Oxygen and Nutrient Diffusion, Metabolism Dynamics, and Architecture Optimization in Three-Dimensional Tissue Constructs with Applications and Insights in Cerebral Organoids

PubMed Central

2016-01-01

Diffusion models are important in tissue engineering as they enable an understanding of gas, nutrient, and signaling molecule delivery to cells in cell cultures and tissue constructs. As three-dimensional (3D) tissue constructs become larger, more intricate, and more clinically applicable, it will be essential to understand internal dynamics and signaling molecule concentrations throughout the tissue and whether cells are receiving appropriate nutrient delivery. Diffusion characteristics present a significant limitation in many engineered tissues, particularly for avascular tissues and for cells whose viability, differentiation, or function are affected by concentrations of oxygen and nutrients. This article seeks to provide novel analytic solutions for certain cases of steady-state and nonsteady-state diffusion and metabolism in basic 3D construct designs (planar, cylindrical, and spherical forms), solutions that would otherwise require mathematical approximations achieved through numerical methods. This model is applied to cerebral organoids, where it is shown that limitations in diffusion and organoid size can be partially overcome by localizing metabolically active cells to an outer layer in a sphere, a regionalization process that is known to occur through neuroglial precursor migration both in organoids and in early brain development. The given prototypical solutions include a review of metabolic information for many cell types and can be broadly applied to many forms of tissue constructs. This work enables researchers to model oxygen and nutrient delivery to cells, predict cell viability, study dynamics of mass transport in 3D tissue constructs, design constructs with improved diffusion capabilities, and accurately control molecular concentrations in tissue constructs that may be used in studying models of development and disease or for conditioning cells to enhance survival after insults like ischemia or implantation into the body, thereby providing a framework for better understanding and exploring the characteristics and behaviors of engineered tissue constructs. PMID:26650970

A new two-Dimensional Physical Basis for the Complementary Relation Between Terrestrial and pan Evaporation

NASA Astrophysics Data System (ADS)

Pettijohn, J. C.; Salvucci, G. D.

2008-12-01

Archived global measurements of water loss from evaporation pans constitute an important indirect measure of evaporative flux. Historical data from evaporation pans shows a decreasing trend over the last half century, but the relationship between pan evaporation and moisture-limited terrestrial evaporation is complex, leading to ambiguities in the interpretation of this data. Under energy-limited conditions, pan evaporation (Epan) and moisture-limited terrestrial evaporation (E) increase or decrease together, while in moisture- limited conditions these fluxes form a complementary relation in which increases in one rate accompany decreases in the other. This has lead to debate about the meaning of the observed trends in the context of changing climate. Here a two-dimensional numerical model of a wet pan in a drying landscape is used to demonstrate that, over a wide range of realistic atmospheric and surface conditions, the influence that changes in E have on Epan (1) are complementary and linear, (2) do not depend upon surface wind speed, and (3) are strikingly asymmetrical, in that a unit decrease in E causes approximately a five-fold increase in Epan, as found in a recent analysis of daily evaporation from US grasslands (Kahler and Brutsaert, 2006). Previous attempts to explain the CR have been based on one dimensional diffusion and energy balance arguments, leading to analytic solutions based on Penman-type bulk difference equations. But without acknowledging the spatially complex multidimensional humidity and temperature field around the pan, and specifically how these fields change as the contrast between the wet pan and the drying land surface increases, such integrated bulk difference equations are a priori incomplete (they ignore important divergence terms), and thus these explanations must be considered physically incomplete. Results of the present study improve the theoretical foundation of the CR, thus increasing the reliability with which it can be applied to estimate water balance and to understand the pan evaporation record of climate change.

A coarse-grained Monte Carlo approach to diffusion processes in metallic nanoparticles

NASA Astrophysics Data System (ADS)

Hauser, Andreas W.; Schnedlitz, Martin; Ernst, Wolfgang E.

2017-06-01

A kinetic Monte Carlo approach on a coarse-grained lattice is developed for the simulation of surface diffusion processes of Ni, Pd and Au structures with diameters in the range of a few nanometers. Intensity information obtained via standard two-dimensional transmission electron microscopy imaging techniques is used to create three-dimensional structure models as input for a cellular automaton. A series of update rules based on reaction kinetics is defined to allow for a stepwise evolution in time with the aim to simulate surface diffusion phenomena such as Rayleigh breakup and surface wetting. The material flow, in our case represented by the hopping of discrete portions of metal on a given grid, is driven by the attempt to minimize the surface energy, which can be achieved by maximizing the number of filled neighbor cells.

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.

Downstream boundary effects on the frequency of self-excited oscillations in transonic diffuser flows

NASA Astrophysics Data System (ADS)

Hsieh, T.

1986-10-01

Investigation of downstream boundary effects on the frequency of self-excited oscillations in two-dimensional, separated transonic diffuser flows were conducted numerically by solving the compressible, Reynolds-averaged, thin-layer Navier-Stokes equation with two equation turbulence models. It was found that the flow fields are very sensitive to the location of the downstream boundary. Extension of the diffuser downstream boundary significantly reduces the frequency and amplitude of oscillations for pressure, velocity, and shock. The existence of a suction slot in the experimental setpup obscures the physical downstream boundary and therefore presents a difficulty for quantitative comparisons between computation and experiment.

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.

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.

The use of a selective saturation pulse to suppress t1 noise in two-dimensional 1H fast magic angle spinning solid-state NMR spectroscopy

NASA Astrophysics Data System (ADS)

Robertson, Aiden J.; Pandey, Manoj Kumar; Marsh, Andrew; Nishiyama, Yusuke; Brown, Steven P.

2015-11-01

A selective saturation pulse at fast magic angle spinning (MAS) frequencies (60+ kHz) suppresses t1 noise in the indirect dimension of two-dimensional 1H MAS NMR spectra. The method is applied to a synthetic nucleoside with an intense methyl 1H signal due to triisopropylsilyl (TIPS) protecting groups. Enhanced performance in terms of suppressing the methyl signal while minimising the loss of signal intensity of nearby resonances of interest relies on reducing spin diffusion - this is quantified by comparing two-dimensional 1H NOESY-like spin diffusion spectra recorded at 30-70 kHz MAS. For a saturation pulse centred at the methyl resonance, the effect of changing the nutation frequency at different MAS frequencies as well as the effect of changing the pulse duration is investigated. By applying a pulse of duration 30 ms and nutation frequency 725 Hz at 70 kHz MAS, a good compromise of significant suppression of the methyl resonance combined with the signal intensity of resonances greater than 5 ppm away from the methyl resonance being largely unaffected is achieved. The effectiveness of using a selective saturation pulse is demonstrated for both homonuclear 1H-1H double quantum (DQ)/single quantum (SQ) MAS and 14N-1H heteronuclear multiple quantum coherence (HMQC) two-dimensional solid-state NMR experiments.

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

VizieR Online Data Catalog: Diffuse ionized gas in the Antennae galaxy (Weilbacher+, 2018)

NASA Astrophysics Data System (ADS)

Weilbacher, P. M.; Monreal-Ibero, A.; Verhamme, A.; Sandin, C.; Steinmetz, M.; Kollatschny, W.; Krajnovic, D.; Kamann, S.; Roth, M. M.; Erroz-Ferrer, S.; Marino, R. A.; Maseda, M. V.; Wendt, M.; Bacon, R.; Dreizler, S.; Richard, J.; Wisotzki, L.

2017-11-01

We provide two-dimensional maps of two different ways to measure the diffuse ionized gas as traced by the Halpha emission line in the Antennae Galaxy, both for the central field and the field at the end of the southern tidal tail. We provide a velocity map derived from the Halpha emission line, binned to a S/N~30. Finally, we provide line measurements and derived properties for all HII regions discussed in the paper. (4 data files).

Multi-Dimensional, Non-Pyrolyzing Ablation Test Problems

NASA Technical Reports Server (NTRS)

Risch, Tim; Kostyk, Chris

2016-01-01

Non-pyrolyzingcarbonaceous materials represent a class of candidate material for hypersonic vehicle components providing both structural and thermal protection system capabilities. Two problems relevant to this technology are presented. The first considers the one-dimensional ablation of a carbon material subject to convective heating. The second considers two-dimensional conduction in a rectangular block subject to radiative heating. Surface thermochemistry for both problems includes finite-rate surface kinetics at low temperatures, diffusion limited ablation at intermediate temperatures, and vaporization at high temperatures. The first problem requires the solution of both the steady-state thermal profile with respect to the ablating surface and the transient thermal history for a one-dimensional ablating planar slab with temperature-dependent material properties. The slab front face is convectively heated and also reradiates to a room temperature environment. The back face is adiabatic. The steady-state temperature profile and steady-state mass loss rate should be predicted. Time-dependent front and back face temperature, surface recession and recession rate along with the final temperature profile should be predicted for the time-dependent solution. The second problem requires the solution for the transient temperature history for an ablating, two-dimensional rectangular solid with anisotropic, temperature-dependent thermal properties. The front face is radiatively heated, convectively cooled, and also reradiates to a room temperature environment. The back face and sidewalls are adiabatic. The solution should include the following 9 items: final surface recession profile, time-dependent temperature history of both the front face and back face at both the centerline and sidewall, as well as the time-dependent surface recession and recession rate on the front face at both the centerline and sidewall. The results of the problems from all submitters will be collected, summarized, and presented at a later conference.

Drift effect and "negative" mass transport in an inhomogeneous medium: limiting case of a two-component lattice gas.

PubMed

Lukyanets, Sergei P; Kliushnychenko, Oleksandr V

2010-11-01

The mass transport in an inhomogeneous medium is modeled as the limiting case of a two-component lattice gas with excluded volume constraint and one of the components fixed. In the long-wavelength approximation, the density relaxation of mobile particles is governed by diffusion and interaction with a medium inhomogeneity represented by the static component distribution. It is shown that the density relaxation can be locally accompanied by density distribution compression, i.e., the local mass transport directed from low-to high-density regions. The origin of such a "negative" mass transport is shown to be associated with the presence of a stationary drift flow defined by the medium inhomogeneity. In the quasi-one-dimensional case, the compression dynamics manifests itself in the hoppinglike motion of packet front position of diffusing substance due to staged passing through inhomogeneity barriers, and it leads to fragmentation of the packet and retardation of its spreading. The root-mean-square displacement reflects only the averaged packet front dynamics and becomes inappropriate as the transport characteristic in this regime. In the stationary case, the mass transport throughout the whole system may be directed from the boundary with lower concentration towards the boundary with higher concentration. Implications of the excluded volume constraint and particle distinguishability for these effects are discussed.

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.

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.

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

Strange kinetics of bulk-mediated diffusion on lipid bilayers

PubMed Central

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

2016-01-01

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

The bias of a 2D view: Comparing 2D and 3D mesophyll surface area estimates using non-invasive imaging

USDA-ARS?s Scientific Manuscript database

The surface area of the leaf mesophyll exposed to intercellular airspace per leaf area (Sm) is closely associated with CO2 diffusion and photosynthetic rates. Sm is typically estimated from two-dimensional (2D) leaf sections and corrected for the three-dimensional (3D) geometry of mesophyll cells, l...

Microscopic theory of topologically entangled fluids of rigid macromolecules

NASA Astrophysics Data System (ADS)

Sussman, Daniel M.; Schweizer, Kenneth S.

2011-06-01

We present a first-principles theory for the slow dynamics of a fluid of entangling rigid crosses of zero excluded volume based on a generalization of the dynamic mean-field approach of Szamel for infinitely thin nonrotating rods. The latter theory exactly includes topological constraints at the two-body collision level and self-consistently renormalizes an effective diffusion tensor to account for many-body effects. Remarkably, it predicts scaling laws consistent with the phenomenological reptation-tube predictions of Doi and Edwards for the long-time diffusion and the localization length in the heavily entangled limit. We generalize this approach to a different macromolecular architecture, infinitely thin three-dimensional crosses, and also extend the range of densities over which a dynamic localization length can be calculated for rods. Ideal gases of nonrotating crosses have recently received attention in computer simulations and are relevant as a simple model of both a strong-glass former and entangling star-branched polymers. Comparisons of our theory with these simulations reveal reasonable agreement for the magnitude and reduced density dependence of the localization length and also the self-diffusion constant if the consequences of local density fluctuations are taken into account.

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.

Thermal limitations in a rapid-fire multirail launcher powered by a pulsed magnetodhydrodynamic generator

NASA Astrophysics Data System (ADS)

Stankevich, S. V.; Shvetsov, G. A.; Butov, V. G.; Sinyaev, S. V.

2017-09-01

The operation of rapid burst firing multirail electromagnetic launchers of solids is numerically simulated using unsteady two-dimensional and three-dimensional models. In the calculations, the launchers are powered by a Sakhalin pulsed magnetohydrodynamic generator. Launchers with three and five pairs of parallel rails connected in a series electrical circuit are considered. Firing sequences of different numbers of solid projectiles of different masses is modeled. It is established that the heating of the rails is one of the main factors limiting the performance of launchers under such conditions. It is shown that the rate of heating of the rails is determined by the nonuniformity of the current density distribution over the rail cross-section due to the unsteady diffusion of the magnetic field into the rails. Calculations taking into account the unsteady current density distribution in the rails of a multirail launcher show that with an appropriate of the mass of the projectiles (up to 800 g), their number in the sequence, and the material of the rails, it is possible to attain launching velocities of 1.8-2.5 km/s with moderate heating of the rails.

Mechanism of nucleation and growth of catalyst-free self-organized GaN columns by MOVPE

NASA Astrophysics Data System (ADS)

Wang, Xue; Li, Shunfeng; Fündling, Sönke; Wehmann, Hergo-H.; Strassburg, Martin; Lugauer, Hans-Jürgen; Steegmüller, Ulrich; Waag, Andreas

2013-05-01

The growth mechanism of catalyst-free self-organized GaN nuclei and three-dimensional columns on sapphire by metal organic vapour phase epitaxy (MOVPE) is investigated. Temperature- and time-dependent growth is performed. The growth behaviour can be characterized by two different kinetic regimes: mass-transport-limited growth and thermodynamically limited growth. The sum of activation energies for thermodynamic barrier of nucleation and for surface diffusion/mass-transport limitation, i.e. Whet +Ed, is 0.57 eV in the ‘low’-temperature region and 2.43 eV in the ‘high’-temperature region. GaN columns grown under the same conditions have very comparable height, which is not dependent on their diameter or the distance to other columns. Therefore, the growth rate is presumably limited by the incorporation rate on the top surface of columns. The height and diameter at the top of the GaN columns increase linearly with time and no height limit is observed. The GaN columns can reach more than 40 µm in height. Moreover, the investigated GaN columns are Ga-polar.

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.

Monte-Carlo simulation of a stochastic differential equation

NASA Astrophysics Data System (ADS)

Arif, ULLAH; Majid, KHAN; M, KAMRAN; R, KHAN; Zhengmao, SHENG

2017-12-01

For solving higher dimensional diffusion equations with an inhomogeneous diffusion coefficient, Monte Carlo (MC) techniques are considered to be more effective than other algorithms, such as finite element method or finite difference method. The inhomogeneity of diffusion coefficient strongly limits the use of different numerical techniques. For better convergence, methods with higher orders have been kept forward to allow MC codes with large step size. The main focus of this work is to look for operators that can produce converging results for large step sizes. As a first step, our comparative analysis has been applied to a general stochastic problem. Subsequently, our formulization is applied to the problem of pitch angle scattering resulting from Coulomb collisions of charge particles in the toroidal devices.

MPI-AMRVAC 2.0 for Solar and Astrophysical Applications

NASA Astrophysics Data System (ADS)

Xia, C.; Teunissen, J.; El Mellah, I.; Chané, E.; Keppens, R.

2018-02-01

We report on the development of MPI-AMRVAC version 2.0, which is an open-source framework for parallel, grid-adaptive simulations of hydrodynamic and magnetohydrodynamic (MHD) astrophysical applications. The framework now supports radial grid stretching in combination with adaptive mesh refinement (AMR). The advantages of this combined approach are demonstrated with one-dimensional, two-dimensional, and three-dimensional examples of spherically symmetric Bondi accretion, steady planar Bondi–Hoyle–Lyttleton flows, and wind accretion in supergiant X-ray binaries. Another improvement is support for the generic splitting of any background magnetic field. We present several tests relevant for solar physics applications to demonstrate the advantages of field splitting on accuracy and robustness in extremely low-plasma β environments: a static magnetic flux rope, a magnetic null-point, and magnetic reconnection in a current sheet with either uniform or anomalous resistivity. Our implementation for treating anisotropic thermal conduction in multi-dimensional MHD applications is also described, which generalizes the original slope-limited symmetric scheme from two to three dimensions. We perform ring diffusion tests that demonstrate its accuracy and robustness, and show that it prevents the unphysical thermal flux present in traditional schemes. The improved parallel scaling of the code is demonstrated with three-dimensional AMR simulations of solar coronal rain, which show satisfactory strong scaling up to 2000 cores. Other framework improvements are also reported: the modernization and reorganization into a library, the handling of automatic regression tests, the use of inline/online Doxygen documentation, and a new future-proof data format for input/output.

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.

Random-walk approach to the d -dimensional disordered Lorentz gas

NASA Astrophysics Data System (ADS)

Adib, Artur B.

2008-02-01

A correlated random walk approach to diffusion is applied to the disordered nonoverlapping Lorentz gas. By invoking the Lu-Torquato theory for chord-length distributions in random media [J. Chem. Phys. 98, 6472 (1993)], an analytic expression for the diffusion constant in arbitrary number of dimensions d is obtained. The result corresponds to an Enskog-like correction to the Boltzmann prediction, being exact in the dilute limit, and better or nearly exact in comparison to renormalized kinetic theory predictions for all allowed densities in d=2,3 . Extensive numerical simulations were also performed to elucidate the role of the approximations involved.

Diffusion of small Cu islands on the Ni(111) surface: A self-learning kinetic Monte Carlo study

NASA Astrophysics Data System (ADS)

Acharya, Shree Ram; Shah, Syed Islamuddin; Rahman, Talat S.

2017-08-01

We elucidate the diffusion kinetics of a heteroepitaxial system consisting of two-dimensional small (1-8 atoms) Cu islands on the Ni(111) surface at (100-600) K using the Self-Learning Kinetic Monte Carlo (SLKMC-II) method. Study of the statics of the system shows that compact CuN (3≤N≤8) clusters made up of triangular units on fcc occupancy sites are the energetically most stable structures of those clusters. Interestingly, we find a correlation between the height of the activation energy barrier (Ea) and the location of the transition state (TS). The Ea of processes for Cu islands on the Ni(111) surface are in general smaller than those of their counterpart Ni islands on the same surface. We find this difference to correlate with the relative strength of the lateral interaction of the island atoms in the two systems. While our database consists of hundreds of possible processes, we identify and discuss the energetics of those that are the most dominant, or are rate-limiting, or most contributory to the diffusion of the islands. Since the Ea of single- and multi-atom processes that convert compact island shapes into non-compact ones are larger (with a significantly smaller Ea for their reverse processes) than that for the collective (concerted) motion of the island, the later dominate in the system kinetics - except for the cases of the dimer, pentamer and octamer. Short-jump involving one atom, long jump dimer-shearing, and long-jump corner shearing (via a single-atom) are, respectively, the dominating processes in the diffusion of the dimer, pentamer and octamer. Furthermore single-atom corner-rounding are the rate-limiting processes for the pentamer and octamer islands. Comparison of the energetics of selected processes and lateral interactions obtained from semi-empirical interatomic potentials with those from density functional theory show minor quantitative differences and overall qualitative 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.

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.

A meshless method for solving two-dimensional variable-order time fractional advection-diffusion equation

NASA Astrophysics Data System (ADS)

Tayebi, A.; Shekari, Y.; Heydari, M. H.

2017-07-01

Several physical phenomena such as transformation of pollutants, energy, particles and many others can be described by the well-known convection-diffusion equation which is a combination of the diffusion and advection equations. In this paper, this equation is generalized with the concept of variable-order fractional derivatives. The generalized equation is called variable-order time fractional advection-diffusion equation (V-OTFA-DE). An accurate and robust meshless method based on the moving least squares (MLS) approximation and the finite difference scheme is proposed for its numerical solution on two-dimensional (2-D) arbitrary domains. In the time domain, the finite difference technique with a θ-weighted scheme and in the space domain, the MLS approximation are employed to obtain appropriate semi-discrete solutions. Since the newly developed method is a meshless approach, it does not require any background mesh structure to obtain semi-discrete solutions of the problem under consideration, and the numerical solutions are constructed entirely based on a set of scattered nodes. The proposed method is validated in solving three different examples including two benchmark problems and an applied problem of pollutant distribution in the atmosphere. In all such cases, the obtained results show that the proposed method is very accurate and robust. Moreover, a remarkable property so-called positive scheme for the proposed method is observed in solving concentration transport phenomena.

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.

Reaction-diffusion on the fully-connected lattice: A+A\\rightarrow A

NASA Astrophysics Data System (ADS)

Turban, Loïc; Fortin, Jean-Yves

2018-04-01

Diffusion-coagulation can be simply described by a dynamic where particles perform a random walk on a lattice and coalesce with probability unity when meeting on the same site. Such processes display non-equilibrium properties with strong fluctuations in low dimensions. In this work we study this problem on the fully-connected lattice, an infinite-dimensional system in the thermodynamic limit, for which mean-field behaviour is expected. Exact expressions for the particle density distribution at a given time and survival time distribution for a given number of particles are obtained. In particular, we show that the time needed to reach a finite number of surviving particles (vanishing density in the scaling limit) displays strong fluctuations and extreme value statistics, characterized by a universal class of non-Gaussian distributions with singular behaviour.

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

Single-Nanoparticle Photoelectrochemistry at a Nanoparticulate TiO2 -Filmed Ultramicroelectrode.

PubMed

Peng, Yue-Yi; Ma, Hui; Ma, Wei; Long, Yi-Tao; Tian, He

2018-03-26

An ultrasensitive photoelectrochemical method for achieving real-time detection of single nanoparticle collision events is presented. Using a micrometer-thick nanoparticulate TiO 2 -filmed Au ultra-microelectrode (TiO 2 @Au UME), a sub-millisecond photocurrent transient was observed for an individual N719-tagged TiO 2 (N719@TiO 2 ) nanoparticle and is due to the instantaneous collision process. Owing to a trap-limited electron diffusion process as the rate-limiting step, a random three-dimensional diffusion model was developed to simulate electron transport dynamics in TiO 2 film. The combination of theoretical simulation and high-resolution photocurrent measurement allow electron-transfer information of a single N719@TiO 2 nanoparticle to be quantified at single-molecule accuracy and the electron diffusivity and the electron-collection efficiency of TiO 2 @Au UME to be estimated. This method provides a test for studies of photoinduced electron transfer at the single-nanoparticle level. © 2018 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

Revisiting Temporal Markov Chains for Continuum modeling of Transport in Porous Media

NASA Astrophysics Data System (ADS)

Delgoshaie, A. H.; Jenny, P.; Tchelepi, H.

2017-12-01

The transport of fluids in porous media is dominated by flow­-field heterogeneity resulting from the underlying permeability field. Due to the high uncertainty in the permeability field, many realizations of the reference geological model are used to describe the statistics of the transport phenomena in a Monte Carlo (MC) framework. There has been strong interest in working with stochastic formulations of the transport that are different from the standard MC approach. Several stochastic models based on a velocity process for tracer particle trajectories have been proposed. Previous studies have shown that for high variances of the log-conductivity, the stochastic models need to account for correlations between consecutive velocity transitions to predict dispersion accurately. The correlated velocity models proposed in the literature can be divided into two general classes of temporal and spatial Markov models. Temporal Markov models have been applied successfully to tracer transport in both the longitudinal and transverse directions. These temporal models are Stochastic Differential Equations (SDEs) with very specific drift and diffusion terms tailored for a specific permeability correlation structure. The drift and diffusion functions devised for a certain setup would not necessarily be suitable for a different scenario, (e.g., a different permeability correlation structure). The spatial Markov models are simple discrete Markov chains that do not require case specific assumptions. However, transverse spreading of contaminant plumes has not been successfully modeled with the available correlated spatial models. Here, we propose a temporal discrete Markov chain to model both the longitudinal and transverse dispersion in a two-dimensional domain. We demonstrate that these temporal Markov models are valid for different correlation structures without modification. Similar to the temporal SDEs, the proposed model respects the limited asymptotic transverse spreading of the plume in two-dimensional problems.

Three-dimensional Diffusive Strip Method

NASA Astrophysics Data System (ADS)

Martinez-Ruiz, Daniel; Meunier, Patrice; Duchemin, Laurent; Villermaux, Emmanuel

2016-11-01

The Diffusive Strip Method (DSM) is a near-exact numerical method developed for mixing computations at large Péclet number in two-dimensions. The method consists in following stretched material lines to compute a-posteriori the resulting scalar field is extended here to three-dimensional flows, following surfaces. We describe its 3D peculiarities, and show how it applies to a simple Taylor-Couette configuration with non-rotating boundary conditions at the top end, bottom and outer cylinder. This flow produces an elaborate, although controlled, steady 3D flow which relies on the Ekman pumping arising from the rotation of the inner cylinder is both studied experimentally, and numerically modeled. A recurrent two-cells structure appears formed by stream tubes shaped as nested tori. A scalar blob in the flow experiences a Lagrangian oscillating dynamics with stretchings and compressions, driving the mixing process, and yielding both rapidly-mixed and nearly pure-diffusive regions. A triangulated-surface method is developed to calculate the blob elongation and scalar concentration PDFs through a single variable computation along the advected blob surface, capturing the rich evolution observed in the experiments.

Numerical Test of Analytical Theories for Perpendicular Diffusion in Small Kubo Number Turbulence

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

Heusen, M.; Shalchi, A., E-mail: husseinm@myumanitoba.ca, E-mail: andreasm4@yahoo.com

In the literature, one can find various analytical theories for perpendicular diffusion of energetic particles interacting with magnetic turbulence. Besides quasi-linear theory, there are different versions of the nonlinear guiding center (NLGC) theory and the unified nonlinear transport (UNLT) theory. For turbulence with high Kubo numbers, such as two-dimensional turbulence or noisy reduced magnetohydrodynamic turbulence, the aforementioned nonlinear theories provide similar results. For slab and small Kubo number turbulence, however, this is not the case. In the current paper, we compare different linear and nonlinear theories with each other and test-particle simulations for a noisy slab model corresponding to smallmore » Kubo number turbulence. We show that UNLT theory agrees very well with all performed test-particle simulations. In the limit of long parallel mean free paths, the perpendicular mean free path approaches asymptotically the quasi-linear limit as predicted by the UNLT theory. For short parallel mean free paths we find a Rechester and Rosenbluth type of scaling as predicted by UNLT theory as well. The original NLGC theory disagrees with all performed simulations regardless what the parallel mean free path is. The random ballistic interpretation of the NLGC theory agrees much better with the simulations, but compared to UNLT theory the agreement is inferior. We conclude that for this type of small Kubo number turbulence, only the latter theory allows for an accurate description of perpendicular diffusion.« less

Characteristics of Superjunction Lateral-Double-Diffusion Metal Oxide Semiconductor Field Effect Transistor and Degradation after Electrical Stress

NASA Astrophysics Data System (ADS)

Lin, Jyh‑Ling; Lin, Ming‑Jang; Lin, Li‑Jheng

2006-04-01

The superjunction lateral double diffusion metal oxide semiconductor field effect has recently received considerable attention. Introducing heavily doped p-type strips to the n-type drift region increases the horizontal depletion capability. Consequently, the doping concentration of the drift region is higher and the conduction resistance is lower than those of conventional lateral-double-diffusion metal oxide semiconductor field effect transistors (LDMOSFETs). These characteristics may increase breakdown voltage (\\mathit{BV}) and reduce specific on-resistance (Ron,sp). In this study, we focus on the electrical characteristics of conventional LDMOSFETs on silicon bulk, silicon-on-insulator (SOI) LDMOSFETs and superjunction LDMOSFETs after bias stress. Additionally, the \\mathit{BV} and Ron,sp of superjunction LDMOSFETs with different N/P drift region widths and different dosages are discussed. Simulation tools, including two-dimensional (2-D) TSPREM-4/MEDICI and three-dimensional (3-D) DAVINCI, were employed to determine the device characteristics.

Numerical simulations of unsteady transonic flow in diffusers

NASA Technical Reports Server (NTRS)

Liou, M.-S.; Coakley, T. J.

1982-01-01

Forced and naturally occurring, self-sustaining oscillations of transonic flows in two-dimensional diffusers were computed using MacCormack's hybrid method. Depending upon the shock strengths and the area ratios, the flow was fully attached or separated by either the shock or the adverse pressure gradient associated with the enlarging diffuser area. In the case of forced oscillations, a sinusoidal plane pressure wave at frequency 300 Hz was prescribed at the exit. A sufficiently large amount of data were acquired and Fourier analyzed. The distrbutions of time-mean pressures, the power spectral density, and the amplitude with phase angle along the top wall and in the core region were determined. Comparison with experimental results for the forced oscillation generally gave very good agreement; some success was achieved for the case of self-sustaining oscillation despite substantial three-dimensionality in the test. An observation of the sequence of self-sustaining oscillations was given.

Classification of fMRI resting-state maps using machine learning techniques: A comparative study

NASA Astrophysics Data System (ADS)

Gallos, Ioannis; Siettos, Constantinos

2017-11-01

We compare the efficiency of Principal Component Analysis (PCA) and nonlinear learning manifold algorithms (ISOMAP and Diffusion maps) for classifying brain maps between groups of schizophrenia patients and healthy from fMRI scans during a resting-state experiment. After a standard pre-processing pipeline, we applied spatial Independent component analysis (ICA) to reduce (a) noise and (b) spatial-temporal dimensionality of fMRI maps. On the cross-correlation matrix of the ICA components, we applied PCA, ISOMAP and Diffusion Maps to find an embedded low-dimensional space. Finally, support-vector-machines (SVM) and k-NN algorithms were used to evaluate the performance of the algorithms in classifying between the two groups.

Surface ordering of (In,Ga)As quantum dots controlled by GaAs substrate indexes

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

Wang, Zh.M.; Seydmohamadi, Sh.; Lee, J.H.

Self-organized surface ordering of (In,Ga)As quantum dots in a GaAs matrix was investigated using stacked multiple quantum dot layers prepared by molecular-beam epitaxy. While one-dimensional chain-like ordering is formed on singular and slightly misorientated GaAs(100) surfaces, we report on two-dimensional square-like ordering that appears on GaAs(n11)B, where n is 7, 5, 4, and 3. Using a technique to control surface diffusion, the different ordering patterns are found to result from the competition between anisotropic surface diffusion and anisotropic elastic matrix, a similar mechanism suggested before by Solomon [Appl. Phys. Lett. 84, 2073 (2004)].

Role of back diffusion and biodegradation reactions in sustaining an MTBE/TBA plume in alluvial media.

PubMed

Rasa, Ehsan; Chapman, Steven W; Bekins, Barbara A; Fogg, Graham E; Scow, Kate M; Mackay, Douglas M

2011-11-01

A methyl tert-butyl ether (MTBE) / tert-butyl alcohol (TBA) plume originating from a gasoline spill in late 1994 at Vandenberg Air Force Base (VAFB) persisted for over 15 years within 200 feet of the original spill source. The plume persisted until 2010 despite excavation of the tanks and piping within months after the spill and excavations of additional contaminated sediments from the source area in 2007 and 2008. The probable history of MTBE concentrations along the plume centerline at its source was estimated using a wide variety of available information, including published details about the original spill, excavations and monitoring by VAFB consultants, and our own research data. Two-dimensional reactive transport simulations of MTBE along the plume centerline were conducted for a 20-year period following the spill. These analyses suggest that MTBE diffused from the thin anaerobic aquifer into the adjacent anaerobic silts and transformed to TBA in both aquifer and silt layers. The model reproduces the observation that after 2004 TBA was the dominant solute, diffusing back out of the silts into the aquifer and sustaining plume concentrations much longer than would have been the case in the absence of such diffusive exchange. Simulations also suggest that aerobic degradation of MTBE or TBA at the water table in the overlying silt layer significantly affected concentrations of MTBE and TBA by limiting the chemical mass available for back diffusion to the aquifer. Copyright © 2011 Elsevier B.V. All rights reserved.

Role of back diffusion and biodegradation reactions in sustaining an MTBE/TBA plume in alluvial media

NASA Astrophysics Data System (ADS)

Rasa, Ehsan; Chapman, Steven W.; Bekins, Barbara A.; Fogg, Graham E.; Scow, Kate M.; Mackay, Douglas M.

2011-11-01

A methyl tert-butyl ether (MTBE) / tert-butyl alcohol (TBA) plume originating from a gasoline spill in late 1994 at Vandenberg Air Force Base (VAFB) persisted for over 15 years within 200 feet of the original spill source. The plume persisted until 2010 despite excavation of the tanks and piping within months after the spill and excavations of additional contaminated sediments from the source area in 2007 and 2008. The probable history of MTBE concentrations along the plume centerline at its source was estimated using a wide variety of available information, including published details about the original spill, excavations and monitoring by VAFB consultants, and our own research data. Two-dimensional reactive transport simulations of MTBE along the plume centerline were conducted for a 20-year period following the spill. These analyses suggest that MTBE diffused from the thin anaerobic aquifer into the adjacent anaerobic silts and transformed to TBA in both aquifer and silt layers. The model reproduces the observation that after 2004 TBA was the dominant solute, diffusing back out of the silts into the aquifer and sustaining plume concentrations much longer than would have been the case in the absence of such diffusive exchange. Simulations also suggest that aerobic degradation of MTBE or TBA at the water table in the overlying silt layer significantly affected concentrations of MTBE and TBA by limiting the chemical mass available for back diffusion to the aquifer.

Role of back diffusion and biodegradation reactions in sustaining an MTBE/TBA plume in alluvial media

USGS Publications Warehouse

Rasa, Ehsan; Chapman, Steven W.; Bekins, Barbara A.; Fogg, Graham E.; Scow, Kate M.; Mackay, Douglas M.

2011-01-01

A methyl tert-butyl ether (MTBE) / tert-butyl alcohol (TBA) plume originating from a gasoline spill in late 1994 at Vandenberg Air Force Base (VAFB) persisted for over 15 years within 200 feet of the original spill source. The plume persisted until 2010 despite excavation of the tanks and piping within months after the spill and excavations of additional contaminated sediments from the source area in 2007 and 2008. The probable history of MTBE concentrations along the plume centerline at its source was estimated using a wide variety of available information, including published details about the original spill, excavations and monitoring by VAFB consultants, and our own research data. Two-dimensional reactive transport simulations of MTBE along the plume centerline were conducted for a 20-year period following the spill. These analyses suggest that MTBE diffused from the thin anaerobic aquifer into the adjacent anaerobic silts and transformed to TBA in both aquifer and silt layers. The model reproduces the observation that after 2004 TBA was the dominant solute, diffusing back out of the silts into the aquifer and sustaining plume concentrations much longer than would have been the case in the absence of such diffusive exchange. Simulations also suggest that aerobic degradation of MTBE or TBA at the water table in the overlying silt layer significantly affected concentrations of MTBE and TBA by limiting the chemical mass available for back diffusion to the aquifer.

Role of back diffusion and biodegradation reactions in sustaining an MTBE/TBA plume in alluvial media

PubMed Central

Rasa, Ehsan; Chapman, Steven W.; Bekins, Barbara A.; Fogg, Graham E.; Scow, Kate M.; Mackay, Douglas M.

2012-01-01

A methyl tert-butyl ether (MTBE) / tert-butyl alcohol (TBA) plume originating from a gasoline spill in late 1994 at Vandenberg Air Force Base (VAFB) persisted for over 15 years within 200 feet of the original spill source. The plume persisted until 2010 despite excavation of the tanks and piping within months after the spill and excavations of additional contaminated sediments from the source area in 2007 and 2008. The probable history of MTBE concentrations along the plume centerline at its source was estimated using a wide variety of available information, including published details about the original spill, excavations and monitoring by VAFB consultants, and our own research data. Two-dimensional reactive transport simulations of MTBE along the plume centerline were conducted for a 20-year period following the spill. These analyses suggest that MTBE diffused from the thin anaerobic aquifer into the adjacent anaerobic silts and transformed to TBA in both aquifer and silt layers. The model reproduces the observation that after 2004 TBA was the dominant solute, diffusing back out of the silts into the aquifer and sustaining plume concentrations much longer than would have been the case in the absence of such diffusive exchange. Simulations also suggest that aerobic degradation of MTBE or TBA at the water table in the overlying silt layer significantly affected concentrations of MTBE and TBA by limiting the chemical mass available for back diffusion to the aquifer. PMID:22115089

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.

A Semi-Implicit, Three-Dimensional Model for Estuarine Circulation

USGS Publications Warehouse

Smith, Peter E.

2006-01-01

A semi-implicit, finite-difference method for the numerical solution of the three-dimensional equations for circulation in estuaries is presented and tested. The method uses a three-time-level, leapfrog-trapezoidal scheme that is essentially second-order accurate in the spatial and temporal numerical approximations. The three-time-level scheme is shown to be preferred over a two-time-level scheme, especially for problems with strong nonlinearities. The stability of the semi-implicit scheme is free from any time-step limitation related to the terms describing vertical diffusion and the propagation of the surface gravity waves. The scheme does not rely on any form of vertical/horizontal mode-splitting to treat the vertical diffusion implicitly. At each time step, the numerical method uses a double-sweep method to transform a large number of small tridiagonal equation systems and then uses the preconditioned conjugate-gradient method to solve a single, large, five-diagonal equation system for the water surface elevation. The governing equations for the multi-level scheme are prepared in a conservative form by integrating them over the height of each horizontal layer. The layer-integrated volumetric transports replace velocities as the dependent variables so that the depth-integrated continuity equation that is used in the solution for the water surface elevation is linear. Volumetric transports are computed explicitly from the momentum equations. The resulting method is mass conservative, efficient, and numerically accurate.

Roles of back diffusion and biodegradation reactions in sustaining MTBE/TBA plumes in alluvial media

NASA Astrophysics Data System (ADS)

Mackay, D. M.; Rasa, E.

2011-12-01

A plume of methyl tert-butyl ether (MTBE) and tert-butyl alcohol (TBA) originating from a gasoline spill in late 1994 at Vandenberg Air Force Base (VAFB) persisted above regulatory concentration goals for over 15 years within 200 feet of the original spill source. The plume persisted until 2010 despite excavation of the tanks and piping within months after the spill and excavations of additional contaminated sediments from the source area in 2007 and 2008. Two-dimensional reactive transport simulations of MTBE and TBA along the plume centerline were conducted for a 20-year period following the spill. As previously reported by Rasa et al. (2011), these analyses suggest that MTBE diffused from the thin anaerobic aquifer into the adjacent anaerobic silts and transformed to TBA in both aquifer and silt layers. After 2004, TBA was the dominant solute, diffusing back out of the silts into the aquifer and sustaining plume concentrations. Simulations also suggest that aerobic degradation of MTBE or TBA at the water table in the overlying silt layer significantly reduced the time for MTBE and TBA concentrations to reach regulatory goals by limiting the chemical mass available for back diffusion to the aquifer. We have extended that prior work; using the same reaction and diffusion parameters, we explored the sensitivity of the results to thicknesses of the alluvial layers in order to determine under what sets of conditions a reaction zone accessed only by vertical diffusion through a silt from an underlying contaminated aquifer can significantly affect time to achievement of compliance goals within the aquifer.

Channel waveguides in glass via silver-sodium field-assisted ion exchange

NASA Technical Reports Server (NTRS)

Forrest, K.; Pagano, S. J.; Viehmann, W.

1986-01-01

Multimode channel waveguides have been formed in sodium aluminosilicate glass by field-assisted diffusion of Ag(+) ions from vacuum-evaporated Ag films. The two-dimensional refractive index profiles of the waveguides were controlled by varying the diffusion time, the diffusion temperature, and the electric field strength. Estimates of the diffusion rate through a strip aperture were obtained, assuming the electric field was strong 120-240 V/mm. The maximum change in refractive index in the sodium aluminosilicate glasses was estimated near 65 percent of the change in soda-lime silicate glass. The physical properties of the glasses are given in a table.

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.

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

Kinetic Monte Carlo simulations of electrodeposition: Crossover from continuous to instantaneous homogeneous nucleation within Avrami’s law

NASA Astrophysics Data System (ADS)

Frank, Stefan; Rikvold, Per Arne

2006-06-01

The influence of lateral adsorbate diffusion on the dynamics of the first-order phase transition in a two-dimensional Ising lattice gas with attractive nearest-neighbor interactions is investigated by means of kinetic Monte Carlo simulations. For example, electrochemical underpotential deposition proceeds by this mechanism. One major difference from adsorption in vacuum surface science is that under control of the electrode potential and in the absence of mass-transport limitations, local adsorption equilibrium is approximately established. We analyze our results using the theory of Kolmogorov, Johnson and Mehl, and Avrami (KJMA), which we extend to an exponentially decaying nucleation rate. Such a decay may occur due to a suppression of nucleation around existing clusters in the presence of lateral adsorbate diffusion. Correlation functions prove the existence of such exclusion zones. By comparison with microscopic results for the nucleation rate I and the interface velocity of the growing clusters v, we can show that the KJMA theory yields the correct order of magnitude for Iv2. This is true even though the spatial correlations mediated by diffusion are neglected. The decaying nucleation rate causes a gradual crossover from continuous to instantaneous nucleation, which is complete when the decay of the nucleation rate is very fast on the time scale of the phase transformation. Hence, instantaneous nucleation can be homogeneous, producing negative minima in the two-point correlation functions. We also present in this paper an n-fold way Monte Carlo algorithm for a square lattice gas with adsorption/desorption and lateral diffusion.

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

Multispectral breast imaging using a ten-wavelength, 64 x 64 source/detector channels silicon photodiode-based diffuse optical tomography system.

PubMed

Li, Changqing; Zhao, Hongzhi; Anderson, Bonnie; Jiang, Huabei

2006-03-01

We describe a compact diffuse optical tomography system specifically designed for breast imaging. The system consists of 64 silicon photodiode detectors, 64 excitation points, and 10 diode lasers in the near-infrared region, allowing multispectral, three-dimensional optical imaging of breast tissue. We also detail the system performance and optimization through a calibration procedure. The system is evaluated using tissue-like phantom experiments and an in vivo clinic experiment. Quantitative two-dimensional (2D) and three-dimensional (3D) images of absorption and reduced scattering coefficients are obtained from these experiments. The ten-wavelength spectra of the extracted reduced scattering coefficient enable quantitative morphological images to be reconstructed with this system. From the in vivo clinic experiment, functional images including deoxyhemoglobin, oxyhemoglobin, and water concentration are recovered and tumors are detected with correct size and position compared with the mammography.

Surface Mediated Self-Assembly of Amyloid Peptides

NASA Astrophysics Data System (ADS)

Fakhraai, Zahra

2015-03-01

Amyloid fibrils have been considered as causative agents in many neurodegenerative diseases, including Alzheimer's disease, Parkinson's disease, type II diabetes and amyloidosis. Amyloid fibrils form when proteins or peptides misfold into one dimensional crystals of stacked beta-sheets. In solution, amyloid fibrils form through a nucleation and growth mechanism. The rate limiting nucleation step requires a critical concentration much larger than those measured in physiological conditions. As such the exact origins of the seeds or oligomers that result in the formation of fully mature fibrils in the body remain topic intense studies. It has been suggested that surfaces and interfaces can enhance the fibrillization rate. However, studies of the mechanism and kinetics of the surface-mediated fibrillization are technologically challenging due to the small size of the oligomer and protofibril species. Using smart sample preparation technique to dry the samples after various incubation times we are able to study the kinetics of fibril formation both in solution and in the vicinity of various surfaces using high-resolution atomic force microscopy. These studies elucidate the role of surfaces in catalyzing amyloid peptide formation through a nucleation-free process. The nucleation free self-assembly is rapid and requires much smaller concentrations of peptides or proteins. We show that this process resembles diffusion limited aggregation and is governed by the peptide adhesion rate, two -dimensional diffusion of the peptides on the surface, and preferential interactions between the peptides. These studies suggest an alternative pathway for amyloid formation may exist, which could lead to new criteria for disease prevention and alternative therapies. Research was partially supported by a seed grant from the National Institute of Aging of the National Institutes of Health (NIH) under Award Number P30AG010124 (PI: John Trojanowski) and the University of Pennsylvania.

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.

Optimized Diffusion of Run-and-Tumble Particles in Crowded Environments

NASA Astrophysics Data System (ADS)

Bertrand, Thibault; Zhao, Yongfeng; Bénichou, Olivier; Tailleur, Julien; Voituriez, Raphaël

2018-05-01

We study the transport of self-propelled particles in dynamic complex environments. To obtain exact results, we introduce a model of run-and-tumble particles (RTPs) moving in discrete time on a d -dimensional cubic lattice in the presence of diffusing hard-core obstacles. We derive an explicit expression for the diffusivity of the RTP, which is exact in the limit of low density of fixed obstacles. To do so, we introduce a generalization of Kac's theorem on the mean return times of Markov processes, which we expect to be relevant for a large class of lattice gas problems. Our results show the diffusivity of RTPs to be nonmonotonic in the tumbling probability for low enough obstacle mobility. These results prove the potential for the optimization of the transport of RTPs in crowded and disordered environments with applications to motile artificial and biological systems.

The use of a selective saturation pulse to suppress t1 noise in two-dimensional (1)H fast magic angle spinning solid-state NMR spectroscopy.

PubMed

Robertson, Aiden J; Pandey, Manoj Kumar; Marsh, Andrew; Nishiyama, Yusuke; Brown, Steven P

2015-11-01

A selective saturation pulse at fast magic angle spinning (MAS) frequencies (60+kHz) suppresses t1 noise in the indirect dimension of two-dimensional (1)H MAS NMR spectra. The method is applied to a synthetic nucleoside with an intense methyl (1)H signal due to triisopropylsilyl (TIPS) protecting groups. Enhanced performance in terms of suppressing the methyl signal while minimising the loss of signal intensity of nearby resonances of interest relies on reducing spin diffusion--this is quantified by comparing two-dimensional (1)H NOESY-like spin diffusion spectra recorded at 30-70 kHz MAS. For a saturation pulse centred at the methyl resonance, the effect of changing the nutation frequency at different MAS frequencies as well as the effect of changing the pulse duration is investigated. By applying a pulse of duration 30 ms and nutation frequency 725 Hz at 70 kHz MAS, a good compromise of significant suppression of the methyl resonance combined with the signal intensity of resonances greater than 5 ppm away from the methyl resonance being largely unaffected is achieved. The effectiveness of using a selective saturation pulse is demonstrated for both homonuclear (1)H-(1)H double quantum (DQ)/single quantum (SQ) MAS and (14)N-(1)H heteronuclear multiple quantum coherence (HMQC) two-dimensional solid-state NMR experiments. Copyright © 2015 The Authors. Published by Elsevier Inc. All rights reserved.

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.

Codimension-Two Bifurcation, Chaos and Control in a Discrete-Time Information Diffusion Model

NASA Astrophysics Data System (ADS)

Ren, Jingli; Yu, Liping

2016-12-01

In this paper, we present a discrete model to illustrate how two pieces of information interact with online social networks and investigate the dynamics of discrete-time information diffusion model in three types: reverse type, intervention type and mutualistic type. It is found that the model has orbits with period 2, 4, 6, 8, 12, 16, 20, 30, quasiperiodic orbit, and undergoes heteroclinic bifurcation near 1:2 point, a homoclinic structure near 1:3 resonance point and an invariant cycle bifurcated by period 4 orbit near 1:4 resonance point. Moreover, in order to regulate information diffusion process and information security, we give two control strategies, the hybrid control method and the feedback controller of polynomial functions, to control chaos, flip bifurcation, 1:2, 1:3 and 1:4 resonances, respectively, in the two-dimensional discrete system.

I. Excitonic Phase Diagram in Silicon: Evidence for Two Condensed Phases. I. Motion of Photoexcited Carriers in GALLIUM-ARSENIDE/ALUMINUM(X)GALLIUM(1-X)ARSENIDE Multiple Quantum Wells-Anomalous Confinement at High Densities.

NASA Astrophysics Data System (ADS)

Smith, Leigh Morris

This thesis describes work on the thermodynamics and transport properties of photoexcited carriers in bulk and two-dimensional semiconductors. Two major topics are addressed. I. Photoluminescence experiments of excitons in unstressed silicon are presented which indicate the existence of a new non-degenerate condensed phase of plasma. This new liquid has a density one-tenth that of the ground state electron-hole liquid and is observed both above and below the liquid-gas critical point (~24.5K). A new phase diagram of excitons in silicon is presented which includes these two condensed plasmas. Consistent with the Gibbs phase rule, a triple point at 18.5 K is inferred from the luminescence data as the only temperature where the exciton gas, condensed plasma (CP) and electron-hole liquid (EHL) coexist. The low density condensed plasma persists up to a second critical point at 45 +/- 5K, above which the photoexcited carriers are observed to continuously decay into a partially ionized excitonic gas. II. We have measured the in-plane motion of photoexcited carriers in semiconductor quantum wells with 5 μm spatial and 10 ps temporal resolution and have discovered several surprising results. The effective diffusivity of the carriers at densities below n = 2 times 10^{11}cm ^{-2} is found to depend upon excitation level, possibly indicating defect-limited diffusion or phonon-wind effects. Above this density the spatial profiles exhibit two distinct components with widely differing diffusivities. This remarkable behavior may be understood with consideration of the interactions of non-equilibrium phonons with the photoexcited carriers. We postulate that the slowly diffusing component represents carriers which are "thermally confined" to a phonon hot spot, while the rapidly moving component is driven by the flux of non-equilibrium phonons away from the excitation region.

Two-dimensional fluorescence-detected coherent spectroscopy with absolute phasing by confocal imaging of a dynamic grating and 27-step phase-cycling

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

De, Arijit K., E-mail: akde@lbl.gov; Fleming, Graham R., E-mail: grfleming@lbl.gov; Department of Chemistry, University of California at Berkeley, Berkeley, California 94702

2014-05-21

We present a novel experimental scheme for two-dimensional fluorescence-detected coherent spectroscopy (2D-FDCS) using a non-collinear beam geometry with the aid of “confocal imaging” of dynamic (population) grating and 27-step phase-cycling to extract the signal. This arrangement obviates the need for distinct experimental designs for previously developed transmission detected non-collinear two-dimensional coherent spectroscopy (2D-CS) and collinear 2D-FDCS. We also describe a novel method for absolute phasing of the 2D spectrum. We apply this method to record 2D spectra of a fluorescent dye in solution at room temperature and observe “spectral diffusion.”.

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

PubMed

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

2005-03-01

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

Homogenization of Large-Scale Movement Models in Ecology

USGS Publications Warehouse

Garlick, M.J.; Powell, J.A.; Hooten, M.B.; McFarlane, L.R.

2011-01-01

A difficulty in using diffusion models to predict large scale animal population dispersal is that individuals move differently based on local information (as opposed to gradients) in differing habitat types. This can be accommodated by using ecological diffusion. However, real environments are often spatially complex, limiting application of a direct approach. Homogenization for partial differential equations has long been applied to Fickian diffusion (in which average individual movement is organized along gradients of habitat and population density). We derive a homogenization procedure for ecological diffusion and apply it to a simple model for chronic wasting disease in mule deer. Homogenization allows us to determine the impact of small scale (10-100 m) habitat variability on large scale (10-100 km) movement. The procedure generates asymptotic equations for solutions on the large scale with parameters defined by small-scale variation. The simplicity of this homogenization procedure is striking when compared to the multi-dimensional homogenization procedure for Fickian diffusion,and the method will be equally straightforward for more complex models. ?? 2010 Society for Mathematical Biology.

An easily fabricated three-dimensional threaded lemniscate-shaped micromixer for a wide range of flow rates

PubMed Central

Rafeie, Mehdi; Welleweerd, Marcel; Hassanzadeh-Barforoushi, Amin; Asadnia, Mohsen; Olthuis, Wouter; Ebrahimi Warkiani, Majid

2017-01-01

Mixing fluid samples or reactants is a paramount function in the fields of micro total analysis system (μTAS) and microchemical processing. However, rapid and efficient fluid mixing is difficult to achieve inside microchannels because of the difficulty of diffusive mass transfer in the laminar regime of the typical microfluidic flows. It has been well recorded that the mixing efficiency can be boosted by migrating from two-dimensional (2D) to three-dimensional (3D) geometries. Although several 3D chaotic mixers have been designed, most of them offer a high mixing efficiency only in a very limited range of Reynolds numbers (Re). In this work, we developed a 3D fine-threaded lemniscate-shaped micromixer whose maximum numerical and empirical efficiency is around 97% and 93%, respectively, and maintains its high performance (i.e., >90%) over a wide range of 1 < Re < 1000 which meets the requirements of both the μTAS and microchemical process applications. The 3D micromixer was designed based on two distinct mixing strategies, namely, the inducing of chaotic advection by the presence of Dean flow and diffusive mixing through thread-like grooves around the curved body of the mixers. First, a set of numerical simulations was performed to study the physics of the flow and to determine the essential geometrical parameters of the mixers. Second, a simple and cost-effective method was exploited to fabricate the convoluted structure of the micromixers through the removal of a 3D-printed wax structure from a block of cured polydimethylsiloxane. Finally, the fabricated mixers with different threads were tested using a fluorescent microscope demonstrating a good agreement with the results of the numerical simulation. We envisage that the strategy used in this work would expand the scope of the micromixer technology by broadening the range of efficient working flow rate and providing an easy way to the fabrication of 3D convoluted microstructures. PMID:28798843

An easily fabricated three-dimensional threaded lemniscate-shaped micromixer for a wide range of flow rates.

PubMed

Rafeie, Mehdi; Welleweerd, Marcel; Hassanzadeh-Barforoushi, Amin; Asadnia, Mohsen; Olthuis, Wouter; Ebrahimi Warkiani, Majid

2017-01-01

Mixing fluid samples or reactants is a paramount function in the fields of micro total analysis system (μTAS) and microchemical processing. However, rapid and efficient fluid mixing is difficult to achieve inside microchannels because of the difficulty of diffusive mass transfer in the laminar regime of the typical microfluidic flows. It has been well recorded that the mixing efficiency can be boosted by migrating from two-dimensional (2D) to three-dimensional (3D) geometries. Although several 3D chaotic mixers have been designed, most of them offer a high mixing efficiency only in a very limited range of Reynolds numbers ( Re ). In this work, we developed a 3D fine-threaded lemniscate-shaped micromixer whose maximum numerical and empirical efficiency is around 97% and 93%, respectively, and maintains its high performance (i.e., >90%) over a wide range of 1 <  Re  < 1000 which meets the requirements of both the μTAS and microchemical process applications. The 3D micromixer was designed based on two distinct mixing strategies, namely, the inducing of chaotic advection by the presence of Dean flow and diffusive mixing through thread-like grooves around the curved body of the mixers. First, a set of numerical simulations was performed to study the physics of the flow and to determine the essential geometrical parameters of the mixers. Second, a simple and cost-effective method was exploited to fabricate the convoluted structure of the micromixers through the removal of a 3D-printed wax structure from a block of cured polydimethylsiloxane. Finally, the fabricated mixers with different threads were tested using a fluorescent microscope demonstrating a good agreement with the results of the numerical simulation. We envisage that the strategy used in this work would expand the scope of the micromixer technology by broadening the range of efficient working flow rate and providing an easy way to the fabrication of 3D convoluted microstructures.

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.

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

PubMed

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

2017-11-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-11-01

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

Radiative transfer simulations of the two-dimensional ocean glint reflectance and determination of the sea surface roughness.

PubMed

Lin, Zhenyi; Li, Wei; Gatebe, Charles; Poudyal, Rajesh; Stamnes, Knut

2016-02-20

An optimized discrete-ordinate radiative transfer model (DISORT3) with a pseudo-two-dimensional bidirectional reflectance distribution function (BRDF) is used to simulate and validate ocean glint reflectances at an infrared wavelength (1036 nm) by matching model results with a complete set of BRDF measurements obtained from the NASA cloud absorption radiometer (CAR) deployed on an aircraft. The surface roughness is then obtained through a retrieval algorithm and is used to extend the simulation into the visible spectral range where diffuse reflectance becomes important. In general, the simulated reflectances and surface roughness information are in good agreement with the measurements, and the diffuse reflectance in the visible, ignored in current glint algorithms, is shown to be important. The successful implementation of this new treatment of ocean glint reflectance and surface roughness in DISORT3 will help improve glint correction algorithms in current and future ocean color remote sensing applications.

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.

Radiative Transfer Simulations of the Two-Dimensional Ocean Glint Reflectance and Determination of the Sea Surface Roughness

NASA Technical Reports Server (NTRS)

Lin, Zhenyi; Li, Wei; Gatebe, Charles; Poudyal, Rajesh; Stamnes, Knut

2016-01-01

An optimized discrete-ordinate radiative transfer model (DISORT3) with a pseudo-two-dimensional bidirectional reflectance distribution function (BRDF) is used to simulate and validate ocean glint reflectances at an infrared wavelength (1036 nm) by matching model results with a complete set of BRDF measurements obtained from the NASA cloud absorption radiometer (CAR) deployed on an aircraft. The surface roughness is then obtained through a retrieval algorithm and is used to extend the simulation into the visible spectral range where diffuse reflectance becomes important. In general, the simulated reflectances and surface roughness information are in good agreement with the measurements, and the diffuse reflectance in the visible, ignored in current glint algorithms, is shown to be important. The successful implementation of this new treatment of ocean glint reflectance and surface roughness in DISORT3 will help improve glint correction algorithms in current and future ocean color remote sensing applications.

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.

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.

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.

NMR-based diffusion lattice imaging

NASA Astrophysics Data System (ADS)

Laun, Frederik Bernd; Müller, Lars; Kuder, Tristan Anselm

2016-03-01

Nuclear magnetic resonance (NMR) diffusion experiments are widely employed as they yield information about structures hindering the diffusion process, e.g., about cell membranes. While it has been shown in recent articles that these experiments can be used to determine the shape of closed pores averaged over a volume of interest, it is still an open question how much information can be gained in open well-connected systems. In this theoretical work, it is shown that the full structure information of connected periodic systems is accessible. To this end, the so-called "SEquential Rephasing by Pulsed field-gradient Encoding N Time intervals" (SERPENT) sequence is used, which employs several diffusion encoding gradient pulses with different amplitudes. Two two-dimensional solid matrices that are surrounded by an NMR-visible medium are considered: a hexagonal lattice of cylinders and a rectangular lattice of isosceles triangles.

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.

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.

Topics in Diffusion Limited Reaction Processes

NASA Astrophysics Data System (ADS)

Lin, Jian-Cheng

We study, both theoretically and numerically, the macroscopic particle concentration in a class of simple diffusion-limited reactions: one species coagulation A + A to A, reversible coagulation A + A rightleftharpoons A, A + A to A with particle input, A + A rightleftharpoons A with particle input, single species annihilation A + A to inert, and two species annihilation A + B to inert. The main interest is in the asymptotic behavior of the particle concentration. We review the standard mean-field theory, mass-reaction kinetics and the associated nonlinear rate and diffusion-reaction equations. Theoretically we study the concentration using several closure schemes for truncating the infinite hierarchy of the kinetic equations for the joint density functions. Our goal is to evaluate the quality of some nonsystematic approximations by comparison with exact solutions. It is found that these approximations are very good at capturing the asymptotic behavior of the particle concentrations in the irreversible reactions, while they fail to predict the far-from-equilibrium dynamic phase transition in the one dimensional reversible coagulation reaction predicted by exact results. Numerically we use Monte Carlo simulation to study concentrations in the single species reversible coagulation process. In one dimension the numerical results are in excellent agreement with the exact analytic results. In two dimensions, our simulation data in the transient states suggest an interesting scaling for the deviation of the concentration from its equilibrium value, delta C(t) ~ exp( -beta(C_0)t^{alpha(C_0) }), where alpha(C_0) and beta(C_0) are functions of the initial concentration C_0. However, it seems unlikely to be able to answer the question of the existence of a dynamic phase transition in two dimensions by Monte Carlo simulation within a reasonable CPU time due to the long persistence of the transient states. In an appendix we solve exactly an annihilation-related percolation problem.

Extinguishment of a Diffusion Flame Over a PMMA Cylinder by Depressurization in Reduced-Gravity

NASA Technical Reports Server (NTRS)

Goldmeer, Jeffrey Scott

1996-01-01

Extinction of a diffusion flame burning over horizontal PMMA (Polymethyl methacrylate) cylinders in low-gravity was examined experimentally and via numerical simulations. Low-gravity conditions were obtained using the NASA Lewis Research Center's reduced-gravity aircraft. The effects of velocity and pressure on the visible flame were examined. The flammability of the burning solid was examined as a function of pressure and the solid-phase centerline temperature. As the solid temperature increased, the extinction pressure decreased, and with a centerline temperature of 525 K, the flame was sustained to 0.1 atmospheres before extinguishing. The numerical simulation iteratively coupled a two-dimensional quasi-steady, gas-phase model with a transient solid-phase model which included conductive heat transfer and surface regression. This model employed an energy balance at the gas/solid interface that included the energy conducted by the gas-phase to the gas/solid interface, Arrhenius pyrolysis kinetics, surface radiation, and the energy conducted into the solid. The ratio of the solid and gas-phase conductive fluxes Phi was a boundary condition for the gas-phase model at the solid-surface. Initial simulations modeled conditions similar to the low-gravity experiments and predicted low-pressure extinction limits consistent with the experimental limits. Other simulations examined the effects of velocity, depressurization rate and Phi on extinction.

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).

An improved design method and experimental performance of two dimensional curved wall diffusers

NASA Technical Reports Server (NTRS)

Yang, T.; Hudson, W. G.; El-Nashar, A. M.

1972-01-01

A computer design program was developed to incorporate the suction slots in solving the potential flow equations with prescribed boundary conditions. Using the contour generated from this program two Griffith diffusers were tested having area ratios AR = 3 and 4. The inlet Reynolds number ranged from 600,000 to 7 million. It was found that the slot suction required for metastable operation depends on the sidewall suction applied. Values of slot suction of 8% of the inlet flow rate was required for AR = 4 with metastable condition, provided that enough sidewall suction was applied. For AR = 3, the values of slot suction was about 25% lower than those required for AR = 4. For nearly all unseparated test runs, the effectiveness was 100% and the exit flow was uniform. In addition to the Griffith diffusers, dump and cusp diffusers of comparable area ratios were built and tested. The results obtained from these diffusers were compared with those of the Griffith diffusers. Flow separation occurred in all test runs with the dump and cusp diffusers.

Synchronization of hyperexcitable systems with phase-repulsive coupling

NASA Astrophysics Data System (ADS)

Balázsi, Gábor; Cornell-Bell, Ann; Neiman, Alexander B.; Moss, Frank

2001-10-01

We study two-dimensional arrays of FitzHugh-Nagumo elements with nearest-neighbor coupling from the viewpoint of synchronization. The elements are diffusively coupled. By varying the diffusion coefficient from positive to negative values, interesting synchronization patterns are observed. The results of the simulations resemble the intracellular oscillation patterns observed in cultured human epileptic astrocytes. Three measures are proposed to determine the degree of synchronization (or coupling) in both the simulated and the experimental system.

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.

An approximate analysis of the diffusing flow in a self-controlled heat pipe.

NASA Technical Reports Server (NTRS)

Somogyi, D.; Yen, H. H.

1973-01-01

Constant-density two-dimensional axisymmetric equations are presented for the diffusing flow of a class of self-controlled heat pipes. The analysis is restricted to the vapor space. Condensation of the vapor is related to its mass fraction at the wall by the gas kinetic formula. The Karman-Pohlhausen integral method is applied to obtain approximate solutions. Solutions are presented for a water heat pipe with neon control gas.

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.

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

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.

A novel multi-detection technique for three-dimensional reciprocal-space mapping in grazing-incidence X-ray diffraction.

PubMed

Schmidbauer, M; Schäfer, P; Besedin, S; Grigoriev, D; Köhler, R; Hanke, M

2008-11-01

A new scattering technique in grazing-incidence X-ray diffraction geometry is described which enables three-dimensional mapping of reciprocal space by a single rocking scan of the sample. This is achieved by using a two-dimensional detector. The new set-up is discussed in terms of angular resolution and dynamic range of scattered intensity. As an example the diffuse scattering from a strained multilayer of self-assembled (In,Ga)As quantum dots grown on GaAs substrate is presented.

Magnetoresistance in two-dimensional array of Ge/Si quantum dots

NASA Astrophysics Data System (ADS)

Stepina, N. P.; Koptev, E. S.; Pogosov, A. G.; Dvurechenskii, A. V.; Nikiforov, A. I.; Zhdanov, E. Yu

2012-07-01

Magnetoresistance in two-dimensional array of Ge/Si was studied for a wide range of the conductance, where the transport regime changes from hopping to diffusive one. The behavior of magnetoresistance is similar for all samples; it is negative in weak fields and becomes positive with increasing of magnetic field. Negative magnetoresistance can be described in the frame of weak localization approach with suggestion that quantum interference contribution to the conductance is restricted not only by the phase breaking length but also by the localization length.

Numerical simulations of thermal conductivity in dissipative two-dimensional Yukawa systems.

PubMed

Khrustalyov, Yu V; Vaulina, O S

2012-04-01

Numerical data on the heat transfer constants in two-dimensional Yukawa systems were obtained. Numerical study of the thermal conductivity and diffusivity was carried out for the equilibrium systems with parameters close to conditions of laboratory experiments with dusty plasma. For calculations of heat transfer constants the Green-Kubo formulas were used. The influence of dissipation (friction) on the heat transfer processes in nonideal systems was investigated. The approximation of the coefficient of thermal conductivity is proposed. Comparison of the obtained results to the existing experimental and numerical data is discussed.

Network patterns in exponentially growing two-dimensional biofilms

NASA Astrophysics Data System (ADS)

Zachreson, Cameron; Yap, Xinhui; Gloag, Erin S.; Shimoni, Raz; Whitchurch, Cynthia B.; Toth, Milos

2017-10-01

Anisotropic collective patterns occur frequently in the morphogenesis of two-dimensional biofilms. These patterns are often attributed to growth regulation mechanisms and differentiation based on gradients of diffusing nutrients and signaling molecules. Here, we employ a model of bacterial growth dynamics to show that even in the absence of growth regulation or differentiation, confinement by an enclosing medium such as agar can itself lead to stable pattern formation over time scales that are employed in experiments. The underlying mechanism relies on path formation through physical deformation of the enclosing environment.

Asymmetric skew Bessel processes and their applications to finance

NASA Astrophysics Data System (ADS)

Decamps, Marc; Goovaerts, Marc; Schoutens, Wim

2006-02-01

In this paper, we extend the Harrison and Shepp's construction of the skew Brownian motion (1981) and we obtain a diffusion similar to the two-dimensional Bessel process with speed and scale densities discontinuous at one point. Natural generalizations to multi-dimensional and fractional order Bessel processes are then discussed as well as invariance properties. We call this family of diffusions asymmetric skew Bessel processes in opposition to skew Bessel processes as defined in Barlow et al. [On Walsh's Brownian motions, Seminaire de Probabilities XXIII, Lecture Notes in Mathematics, vol. 1372, Springer, Berlin, New York, 1989, pp. 275-293]. We present factorizations involving (asymmetric skew) Bessel processes with random time. Finally, applications to the valuation of perpetuities and Asian options are proposed.

Fluctuation-controlled front propagation

NASA Astrophysics Data System (ADS)

Ridgway, Douglas Thacher

1997-09-01

A number of fundamental pattern-forming systems are controlled by fluctuations at the front. These problems involve the interaction of an infinite dimensional probability distribution with a strongly nonlinear, spatially extended pattern-forming system. We have examined fluctuation-controlled growth in the context of the specific problems of diffusion-limited growth and biological evolution. Mean field theory of diffusion-limited growth exhibits a finite time singularity. Near the leading edge of a diffusion-limited front, this leads to acceleration and blowup. This may be resolved, in an ad hoc manner, by introducing a cutoff below which growth is weakened or eliminated (8). This model, referred to as the BLT model, captures a number of qualitative features of global pattern formation in diffusion-limited aggregation: contours of the mean field match contours of averaged particle density in simulation, and the modified mean field theory can form dendritic features not possible in the naive mean field theory. The morphology transition between dendritic and non-dendritic global patterns requires that BLT fronts have a Mullins-Sekerka instability of the wavefront shape, in order to form concave patterns. We compute the stability of BLT fronts numerically, and compare the results to fronts without a cutoff. A significant morphological instability of the BLT fronts exists, with a dominant wavenumber on the scale of the front width. For standard mean field fronts, no instability is found. The naive and ad hoc mean field theories are continuum-deterministic models intended to capture the behavior of a discrete stochastic system. A transformation which maps discrete systems into a continuum model with a singular multiplicative noise is known, however numerical simulations of the continuum stochastic system often give mean field behavior instead of the critical behavior of the discrete system. We have found a new interpretation of the singular noise, based on maintaining the symmetry of the absorbing state, but which is unsuccessful at capturing the behavior of diffusion-limited growth. In an effort to find a simpler model system, we turned to modelling fitness increases in evolution. The work was motivated by an experiment on vesicular stomatitis virus, a short (˜9600bp) single-stranded RNA virus. A highly bottlenecked viral population increases in fitness rapidly until a certain point, after which the fitness increases at a slower rate. This is well modeled by a constant population reproducing and mutating on a smooth fitness landscape. Mean field theory of this system displays the same infinite propagation velocity blowup as mean field diffusion-limited aggregation. However, we have been able to make progress on a number of fronts. One is solving systems of moment equations, where a hierarchy of moments is truncated arbitrarily at some level. Good results for front propagation velocity are found with just two moments, corresponding to inclusion of the basic finite population clustering effect ignored by mean field theory. In addition, for small mutation rates, most of the population will be entirely on a single site or two adjacent sites, and the density of these cases can be described and solved. (Abstract shortened by UMI.)

Traditional Semiconductors in the Two-Dimensional Limit.

PubMed

Lucking, Michael C; Xie, Weiyu; Choe, Duk-Hyun; West, Damien; Lu, Toh-Ming; Zhang, S B

2018-02-23

Interest in two-dimensional materials has exploded in recent years. Not only are they studied due to their novel electronic properties, such as the emergent Dirac fermion in graphene, but also as a new paradigm in which stacking layers of distinct two-dimensional materials may enable different functionality or devices. Here, through first-principles theory, we reveal a large new class of two-dimensional materials which are derived from traditional III-V, II-VI, and I-VII semiconductors. It is found that in the ultrathin limit the great majority of traditional binary semiconductors studied (a series of 28 semiconductors) are not only kinetically stable in a two-dimensional double layer honeycomb structure, but more energetically stable than the truncated wurtzite or zinc-blende structures associated with three dimensional bulk. These findings both greatly increase the landscape of two-dimensional materials and also demonstrate that in the double layer honeycomb form, even ordinary semiconductors, such as GaAs, can exhibit exotic topological properties.

Sub-Fickean Diffusion in a One-Dimensional Plasma Ring

NASA Astrophysics Data System (ADS)

Theisen, W. L.

2013-12-01

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

A 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.

Possibilities and limitations of current stereo-endoscopy.

PubMed

Mueller-Richter, U D A; Limberger, A; Weber, P; Ruprecht, K W; Spitzer, W; Schilling, M

2004-06-01

Stereo-endoscopy has become a commonly used technology. In many comparative studies striking advantages of stereo-endoscopy over two-dimensional presentation could not be proven. To show the potential and fields for further improvement of this technology is the aim of this article. The physiological basis of three-dimensional vision limitations of current stereo-endoscopes is discussed and fields for further research are indicated. New developments in spatial picture acquisition and spatial picture presentation are discussed. Current limitations of stereo-endoscopy that prevent a better ranking in comparative studies with two-dimensional presentation are mainly based on insufficient picture acquisition. Devices for three-dimensional picture presentation are at a more advanced developmental stage than devices for three-dimensional picture acquisition. Further research should emphasize the development of new devices for three-dimensional picture acquisition.

Brownian Motion of Asymmetric Boomerang Colloidal Particles

NASA Astrophysics Data System (ADS)

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

2014-03-01

We used video microscopy and single particle tracking to study the diffusion and local behaviors of asymmetric boomerang particles in a quasi-two dimensional geometry. The motion is biased towards the center of hydrodynamic stress (CoH) and the mean square displacements of the particles are linear at short and long times with different diffusion coefficients and in the crossover regime it is sub-diffusive. Our model based on Langevin theory shows that these behaviors arise from the non-coincidence of the CoH with the center of the body. Since asymmetric boomerangs represent a class of rigid bodies of more generals shape, therefore our findings are generic and true for any non-skewed particle in two dimensions. Both experimental and theoretical results will be discussed.

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].

Growth Mechanism Studies of ZnO Nanowires: Experimental Observations and Short-Circuit Diffusion Analysis.

PubMed

Shih, Po-Hsun; Wu, Sheng Yun

2017-07-21

Plenty of studies have been performed to probe the diverse properties of ZnO nanowires, but only a few have focused on the physical properties of a single nanowire since analyzing the growth mechanism along a single nanowire is difficult. In this study, a single ZnO nanowire was synthesized using a Ti-assisted chemical vapor deposition (CVD) method to avoid the appearance of catalytic contamination. Two-dimensional energy dispersive spectroscopy (EDS) mapping with a diffusion model was used to obtain the diffusion length and the activation energy ratio. The ratio value is close to 0.3, revealing that the growth of ZnO nanowires was attributed to the short-circuit diffusion.

Image encryption using a synchronous permutation-diffusion technique

NASA Astrophysics Data System (ADS)

Enayatifar, Rasul; Abdullah, Abdul Hanan; Isnin, Ismail Fauzi; Altameem, Ayman; Lee, Malrey

2017-03-01

In the past decade, the interest on digital images security has been increased among scientists. A synchronous permutation and diffusion technique is designed in order to protect gray-level image content while sending it through internet. To implement the proposed method, two-dimensional plain-image is converted to one dimension. Afterward, in order to reduce the sending process time, permutation and diffusion steps for any pixel are performed in the same time. The permutation step uses chaotic map and deoxyribonucleic acid (DNA) to permute a pixel, while diffusion employs DNA sequence and DNA operator to encrypt the pixel. Experimental results and extensive security analyses have been conducted to demonstrate the feasibility and validity of this proposed image encryption method.

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

Subedi, P.; Matthaeus, W. H.; Chuychai, P.

The investigation of the diffusive transport of charged particles in a turbulent magnetic field remains a subject of considerable interest. Research has most frequently concentrated on determining the diffusion coefficient in the presence of a mean magnetic field. Here we consider the diffusion of charged particles in fully three-dimensional isotropic turbulent magnetic fields with no mean field, which may be pertinent to many astrophysical situations. We identify different ranges of particle energy depending upon the ratio of Larmor radius to the characteristic outer length scale of turbulence. Two different theoretical models are proposed to calculate the diffusion coefficient, each applicablemore » to a distinct range of particle energies. The theoretical results are compared to those from computer simulations, showing good agreement.« less

Generalized method calculating the effective diffusion coefficient in periodic channels.

PubMed

Kalinay, Pavol

2015-01-07

The method calculating the effective diffusion coefficient in an arbitrary periodic two-dimensional channel, presented in our previous paper [P. Kalinay, J. Chem. Phys. 141, 144101 (2014)], is generalized to 3D channels of cylindrical symmetry, as well as to 2D or 3D channels with particles driven by a constant longitudinal external driving force. The next possible extensions are also indicated. The former calculation was based on calculus in the complex plane, suitable for the stationary diffusion in 2D domains. The method is reformulated here using standard tools of functional analysis, enabling the generalization.

1D Resonance line Broadened Quasilinear (RBQ1D) code for fast ion Alfvenic relaxations and its validations

NASA Astrophysics Data System (ADS)

Gorelenkov, Nikolai; Duarte, Vinicius; Podesta, Mario

2017-10-01

The performance of the burning plasma can be limited by the requirements to confine the superalfvenic fusion products which are capable of resonating with the Alfvénic eigenmodes (AEs). The effect of AEs on fast ions is evaluated using the quasi-linear approach [Berk et al., Ph.Plasmas'96] generalized for this problem recently [Duarte et al., Ph.D.'17]. The generalization involves the resonance line broadened interaction regions with the diffusion coefficient prescribed to find the evolution of the velocity distribution function. The baseline eigenmode structures are found using the NOVA-K code perturbatively [Gorelenkov et al., Ph.Plasmas'99]. A RBQ1D code allowing the diffusion in radial direction is presented here. 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 RBQ1D is validated against recent DIIID results [Collins et al., PRL'16]. Supported by the US Department of Energy under DE-AC02-09CH11466.

The diffusive boundary layer of sediments: oxygen microgradients over a microbial mat

NASA Technical Reports Server (NTRS)

Jorgensen, B. B.; Des Marais, D. J.

1990-01-01

Oxygen microelectrodes were used to analyze the distribution of the diffusive boundary layer (DBL) at the sediment-water interface in relation to surface topography and flow velocity. The sediment, collected from saline ponds, was covered by a microbial mat that had high oxygen consumption rate and well-defined surface structure. Diffusion through the DBL constituted an important rate limitation to the oxygen uptake of the sediment. The mean effective DBL thickness decreased from 0.59 to 0.16 mm as the flow velocity of the overlying water was increased from 0.3 to 7.7 cm s-1 (measured 1 cm above the mat). The oxygen uptake rate concurrently increased from 3.9 to 9.4 nmol cm-2 min-1. The effects of surface roughness and topography on the thickness and distribution of the DBL were studied by three-dimensional mapping of the sediment-water interface and the upper DBL boundary at 0.1-mm spatial resolution. The DBL boundary followed mat structures that had characteristic dimensions > 1/2 DBL thickness but the DBL had a dampened relief relative to the mat. The effective surface area of the sediment-water interface and of the upper DBL boundary were 31 and 14% larger, respectively, than a flat plane. Surface topography thereby increased the oxygen flux across the sediment-water interface by 49% relative to a one-dimensional diffusion flux calculated from the vertical oxygen microgradients.

Oxygen diffusion and consumption in extracellular matrix gels: implications for designing three-dimensional cultures.

PubMed

Colom, Adai; Galgoczy, Roland; Almendros, Isaac; Xaubet, Antonio; Farré, Ramon; Alcaraz, Jordi

2014-08-01

Three-dimensional (3D) cultures are increasingly used as tissue surrogates to study many physiopathological processes. However, to what extent current 3D culture protocols provide physiologic oxygen tension conditions remains ill defined. To address this limitation, oxygen tension was measured in a panel of acellular or cellularized extracellular matrix (ECM) gels with A549 cells, and analyzed in terms of oxygen diffusion and consumption. Gels included reconstituted basement membrane, fibrin and collagen. Oxygen diffusivity in acellular gels was up to 40% smaller than that of water, and the lower values were observed in the denser gels. In 3D cultures, physiologic oxygen tension was achieved after 2 days in dense (≥3 mg/mL) but not sparse gels, revealing that the latter gels are not suitable tissue surrogates in terms of oxygen distribution. In dense gels, we observed a dominant effect of ECM composition over density in oxygen consumption. All diffusion and consumption data were used in a simple model to estimate ranges for gel thickness, seeding density and time-window that may support physiologic oxygen tension. Thus, we identified critical variables for oxygen tension in ECM gels, and introduced a model to assess initial values of these variables, which may short-cut the optimization step of 3D culture studies. © 2013 Wiley Periodicals, Inc.

Structural disorder in the decagonal Al-Co-Ni. I. Patterson analysis of diffuse x-ray scattering data

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

Kobas, Miroslav; Weber, Thomas; Steurer, Walter

The three-dimensional (3D) difference Patterson (autocorrelation) function of a disordered quasicrystal (Edagawa phase) has been analyzed. 3D diffuse x-ray diffraction data were collected in situ at 300, 1070, and 1120 K. A method, the punch-and-fill technique, has been developed for separating diffuse scattering and Bragg reflections. Its potential and limits are discussed in detail. The different Patterson maps are interpreted in terms of intercluster correlations as a function of temperature. Both at high and low temperatures, the clusters decorate the vertices of the same quasiperiodic covering. At low temperatures, for the disordered part of the structure, short-range intercluster correlations aremore » present, whereas at higher temperatures, medium-range intercluster correlations are formed. This indicates disorder mainly inside clusters at low temperatures, whereas at higher temperatures disorder takes place inside larger superclusters. Qualitatively, the Patterson maps may be interpreted by intercluster correlations mainly inside pentagonal superclusters below 1120 K, and inside the larger decagonal superclusters at 1120 K. The results of our diffraction study are published in two parts. Part I focuses on the 3D Patterson analysis based on experimental data, Part II reports modeling of structural disorder in decagonal Al-Co-Ni.« less

Kinetic manipulation of silicide phase formation in Si nanowire templates.

PubMed

Chen, Yu; Lin, Yung-Chen; Zhong, Xing; Cheng, Hung-Chieh; Duan, Xiangfeng; Huang, Yu

2013-08-14

The phase formation sequence of silicides in two-dimensional (2-D) structures has been well-investigated due to their significance in microelectronics. Applying high-quality silicides as contacts in nanoscale silicon (Si) devices has caught considerable attention recently for their potential in improving and introducing new functions in nanodevices. However, nucleation and diffusion mechanisms are found to be very different in one-dimensional (1-D) nanostructures, and thus the phase manipulation of silicides is yet to be achieved there. In this work, we report kinetic phase modulations to selectively enhance or hinder the growth rates of targeted nickel (Ni) silicides in a Si nanowire (NW) and demonstrate that Ni31Si12, δ-Ni2Si, θ-Ni2Si, NiSi, and NiSi2 can emerge as the first contacting phase at the silicide/Si interface through these modulations. First, the growth rates of silicides are selectively tuned through template structure modifications. It is demonstrated that the growth rate of diffusion limited phases can be enhanced in a porous Si NW due to a short diffusion path, which suppresses the formation of interface limited NiSi2. In addition, we show that a confining thick shell can be applied around the Si NW to hinder the growth of the silicides with large volume expansion during silicidation, including Ni31Si12, δ-Ni2Si, and θ-Ni2Si. Second, a platinum (Pt) interlayer between the Ni source and the Si NW is shown to effectively suppress the formation of the phases with low Pt solubility, including the dominating NiSi2. Lastly, we show that with the combined applications of the above-mentioned approaches, the lowest resistive NiSi phase can form as the first phase in a solid NW with a Pt interlayer to suppress NiSi2 and a thick shell to hinder Ni31Si12, δ-Ni2Si, and θ-Ni2Si simultaneously. The resistivity and maximum current density of NiSi agree reasonably to reported values.

Electron Transport in Quasi-Two-Dimensional Porous Network of Titania Nanoparticles, Incorporating Electrical and Optical Advantages in Dye-Sensitized Solar Cells.

PubMed

Javadi, Mohammad; Alizadeh, Saba; Khosravi, Yusef; Abdi, Yaser

2016-11-04

The integration of fast electron transport and large effective surface area is critical to attaining higher gains in the nanostructured photovoltaic devices. Here, we report facilitated electron transport in the quasi-two-dimensional (Q2D) porous TiO 2 . Liquid electrolyte dye-sensitized solar cells were prepared by utilizing photoanodes based on the Q2D porous substructures. Due to electron confinement in a microscale porous medium, directional diffusion toward collecting electrode is induced into the electron transport. Our measurements based on the photocurrent and photovoltage time-of-flight transients show that at higher Fermi levels, the electron diffusion coefficient in the Q2D porous TiO 2 is about one order of magnitude higher when compared with the conventional layer of porous TiO 2 . The results show that microstructuring of the porous TiO 2 leads to an approximately threefold improvement in the electron diffusion length. Such a modification may considerably affects the electrical functionality of moderate or low performance dye-sensitized solar cells for which the internal gain or collection efficiency is typically low. © 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

A nonlinear equation for ionic diffusion in a strong binary electrolyte

PubMed Central

Ghosal, Sandip; Chen, Zhen

2010-01-01

The problem of the one-dimensional electro-diffusion of ions in a strong binary electrolyte is considered. The mathematical description, known as the Poisson–Nernst–Planck (PNP) system, consists of a diffusion equation for each species augmented by transport owing to a self-consistent electrostatic field determined by the Poisson equation. This description is also relevant to other important problems in physics, such as electron and hole diffusion across semiconductor junctions and the diffusion of ions in plasmas. If concentrations do not vary appreciably over distances of the order of the Debye length, the Poisson equation can be replaced by the condition of local charge neutrality first introduced by Planck. It can then be shown that both species diffuse at the same rate with a common diffusivity that is intermediate between that of the slow and fast species (ambipolar diffusion). Here, we derive a more general theory by exploiting the ratio of the Debye length to a characteristic length scale as a small asymptotic parameter. It is shown that the concentration of either species may be described by a nonlinear partial differential equation that provides a better approximation than the classical linear equation for ambipolar diffusion, but reduces to it in the appropriate limit. PMID:21818176

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.

Heat and mass transfer models to understand the drying mechanisms of a porous substrate.

PubMed

Songok, Joel; Bousfield, Douglas W; Gane, Patrick A C; Toivakka, Martti

2016-02-01

While drying of paper and paper coatings is expensive, with significant energy requirements, the rate controlling mechanisms are not currently fully understood. Two two-dimensional models are used as a first approximation to predict the heat transfer during hot air drying and to evaluate the role of various parameters on the drying rates of porous coatings. The models help determine the structural limiting factors during the drying process, while applying for the first time the recently known values of coating thermal diffusivity. The results indicate that the thermal conductivity of the coating structure is not the controlling factor, but the drying rate is rather determined by the thermal transfer process at the structure surface. This underlines the need for ensuring an efficient thermal transfer from hot air to coating surface during drying, before considering further measures to increase the thermal conductivity of porous coatings.

Dissociative diffusion mechanism in vacancy-rich materials according to mass action kinetics

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

Biderman, N. J.; Sundaramoorthy, R.; Haldar, Pradeep

We conducted two sets of diffusion-reaction numerical simulations using a finite difference method (FDM) in order to investigate fast impurity diffusion via interstitial sites in vacancy-rich materials such as Cu(In,Ga)Se 2 (CIGS) and Cu 2ZnSn(S, Se) 4 (CZTSSe or CZTS) via the dissociative diffusion mechanism where the interstitial diffuser ultimately reacts with a vacancy to produce a substitutional. The first set of simulations extends the standard interstitial-limited dissociative diffusion theory to vacancy-rich material conditions where vacancies are annihilated in large amounts, introducing non-equilibrium vacancy concentration profiles. The second simulation set explores the vacancy-limited dissociative diffusion where impurity incorporation increases themore » equilibrium vacancy concentration. In addition to diffusion profiles of varying concentrations and shapes that were obtained in all simulations, some of the profiles can be fitted with the constant- and limited-source solutions of Fick’s second law despite the non-equilibrium condition induced by the interstitial-vacancy reaction. The first set of simulations reveals that the dissociative diffusion coefficient in vacancy-rich materials is inversely proportional to the initial vacancy concentration. In the second set of numerical simulations, impurity-induced changes in the vacancy concentration lead to distinctive diffusion profile shapes. The simulation results are also compared with published data of impurity diffusion in CIGS. And according to the characteristic properties of diffusion profiles from the two set of simulations, experimental detection of the dissociative diffusion mechanism in vacancy-rich materials may be possible.« less

Dissociative diffusion mechanism in vacancy-rich materials according to mass action kinetics

DOE PAGES

Biderman, N. J.; Sundaramoorthy, R.; Haldar, Pradeep; ...

2016-05-13

We conducted two sets of diffusion-reaction numerical simulations using a finite difference method (FDM) in order to investigate fast impurity diffusion via interstitial sites in vacancy-rich materials such as Cu(In,Ga)Se 2 (CIGS) and Cu 2ZnSn(S, Se) 4 (CZTSSe or CZTS) via the dissociative diffusion mechanism where the interstitial diffuser ultimately reacts with a vacancy to produce a substitutional. The first set of simulations extends the standard interstitial-limited dissociative diffusion theory to vacancy-rich material conditions where vacancies are annihilated in large amounts, introducing non-equilibrium vacancy concentration profiles. The second simulation set explores the vacancy-limited dissociative diffusion where impurity incorporation increases themore » equilibrium vacancy concentration. In addition to diffusion profiles of varying concentrations and shapes that were obtained in all simulations, some of the profiles can be fitted with the constant- and limited-source solutions of Fick’s second law despite the non-equilibrium condition induced by the interstitial-vacancy reaction. The first set of simulations reveals that the dissociative diffusion coefficient in vacancy-rich materials is inversely proportional to the initial vacancy concentration. In the second set of numerical simulations, impurity-induced changes in the vacancy concentration lead to distinctive diffusion profile shapes. The simulation results are also compared with published data of impurity diffusion in CIGS. And according to the characteristic properties of diffusion profiles from the two set of simulations, experimental detection of the dissociative diffusion mechanism in vacancy-rich materials may be possible.« less

Effect of Annealing on Exciton Diffusion in a High Performance Small Molecule Organic Photovoltaic Material.

PubMed

Long, Yun; Hedley, Gordon J; Ruseckas, Arvydas; Chowdhury, Mithun; Roland, Thomas; Serrano, Luis A; Cooke, Graeme; Samuel, Ifor D W

2017-05-03

Singlet exciton diffusion was studied in the efficient organic photovoltaic electron donor material DTS(FBTTh 2 ) 2 . Three complementary time-resolved fluorescence measurements were performed: quenching in planar heterojunctions with an electron acceptor, exciton-exciton annihilation, and fluorescence depolarization. The average exciton diffusivity increases upon annealing from 1.6 × 10 -3 to 3.6 × 10 -3 cm 2 s -1 , resulting in an enhancement of the mean two-dimensional exciton diffusion length (L D = (4Dτ) 1/2 ) from 15 to 27 nm. About 30% of the excitons get trapped very quickly in as-cast films. The high exciton diffusion coefficient of the material leads to it being able to harvest excitons efficiently from large donor domains in bulk heterojunctions.

Effect of Annealing on Exciton Diffusion in a High Performance Small Molecule Organic Photovoltaic Material

PubMed Central

2017-01-01

Singlet exciton diffusion was studied in the efficient organic photovoltaic electron donor material DTS(FBTTh2)2. Three complementary time-resolved fluorescence measurements were performed: quenching in planar heterojunctions with an electron acceptor, exciton–exciton annihilation, and fluorescence depolarization. The average exciton diffusivity increases upon annealing from 1.6 × 10–3 to 3.6 × 10–3 cm2 s–1, resulting in an enhancement of the mean two-dimensional exciton diffusion length (LD = (4Dτ)1/2) from 15 to 27 nm. About 30% of the excitons get trapped very quickly in as-cast films. The high exciton diffusion coefficient of the material leads to it being able to harvest excitons efficiently from large donor domains in bulk heterojunctions. PMID:28358189

Concentration dependence of lipopolymer self-diffusion in supported bilayer membranes

PubMed Central

Zhang, Huai-Ying; Hill, Reghan J.

2011-01-01

Self-diffusion coefficients of poly(ethylene glycol)2k-derivatized lipids (DSPE-PEG2k-CF) in glass-supported DOPC phospholipid bilayers are ascertained from quantitative fluorescence recovery after photobleaching (FRAP). We developed a first-order reaction–diffusion model to ascertain the bleaching constant, mobile fraction and lipopolymer self-diffusion coefficient Ds at concentrations in the range c ≈ 0.5–5 mol%. In contrast to control experiments with 1,2-dioleoyl-sn-glycero-3-phosphoethanolamine-N-(7-nitro-2-1,3-benzoxadiazol-4-yl) (ammonium salt) (DOPE-NBD) in 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC), the lipopolymer self-diffusion coefficient decreases monotonically with increasing concentration, without a distinguishing mushroom-to-brush transition. Our data yield a correlation Ds = D0/(1 + αc), where D0 ≈ 3.36 µm2 s−1 and α ≈ 0.56 (with c expressed as a mole percent). Interpreting the dilute limit with the Scalettar–Abney–Owicki statistical mechanical theory for transmembrane proteins yields an effective disc radius ae ≈ 2.41 nm. On the other hand, the Bussell–Koch–Hammer theory, which includes hydrodynamic interactions, yields ae ≈ 2.92 nm. As expected, both measures are smaller than the Flory radius of the 2 kDa poly(ethylene glycol) (PEG) chains, RF ≈ 3.83 nm, and significantly larger than the nominal radius of the phospholipid heads, al ≈ 0.46 nm. The diffusion coefficient at infinite dilution D0 was interpreted using the Evans–Sackmann theory, furnishing an inter-leaflet frictional drag coefficient bs ≈ 1.33 × 108 N s m−3. Our results suggest that lipopolymer interactions are dominated by the excluded volume of the PEG-chain segments, with frictional drag dominated by the two-dimensional bilayer hydrodynamics. PMID:20504804

Ellipsoidal Brownian self-driven particles in a magnetic field

NASA Astrophysics Data System (ADS)

Fan, Wai-Tong Louis; Pak, On Shun; Sandoval, Mario

2017-03-01

We study the two-dimensional Brownian dynamics of an ellipsoidal paramagnetic microswimmer moving at a low Reynolds number and subject to a magnetic field. Its corresponding mean-square displacement, showing the effect of a particles's shape, activity, and magnetic field on the microswimmer's diffusion, is analytically obtained. Comparison between analytical and computational results shows good agreement. In addition, the effect of self-propulsion on the transition time from anisotropic to isotropic diffusion of the ellipse is investigated.

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.

Three-Dimensional Flow of Nanofluid Induced by an Exponentially Stretching Sheet: An Application to Solar Energy

PubMed Central

Khan, Junaid Ahmad; Mustafa, M.; Hayat, T.; Sheikholeslami, M.; Alsaedi, A.

2015-01-01

This work deals with the three-dimensional flow of nanofluid over a bi-directional exponentially stretching sheet. The effects of Brownian motion and thermophoretic diffusion of nanoparticles are considered in the mathematical model. The temperature and nanoparticle volume fraction at the sheet are also distributed exponentially. Local similarity solutions are obtained by an implicit finite difference scheme known as Keller-box method. The results are compared with the existing studies in some limiting cases and found in good agreement. The results reveal the existence of interesting Sparrow-Gregg-type hills for temperature distribution corresponding to some range of parametric values. PMID:25785857

Suitability of the first-order mass transfer concept for describing cyclic diffusive mass transfer in stagnant zones

NASA Astrophysics Data System (ADS)

Griffioen, Jasper

1998-10-01

The concept of first-order mass transfer between mobile and immobile regions, which mathematically simplifies the concept of Fickian diffusion in stagnant areas, has often been used to describe physical nonequilibrium transport of solutes into natural porous media. This study compares the two concepts, using analytical expressions describing cyclic mass transfer into and out of stagnant layers. The results show that the first-order mass transfer concept cannot describe continuous diffusion into the immobile zone during period of net outward diffusion if the immobile zone has not filled completely during the period of net inward diffusion. This sets phenomenological limitations to the first-order mass transfer concept when short periods of relative time are involved; these limitations have to be compared with the practical limitations to the Fickian diffusion concept.

Entropy and temperature from black-hole/near-horizon-CFT duality

NASA Astrophysics Data System (ADS)

Rodriguez, Leo; Yildirim, Tuna

2010-08-01

We construct a two-dimensional CFT, in the form of a Liouville theory, in the near-horizon limit of four- and three-dimensional black holes. The near-horizon CFT assumes two-dimensional black hole solutions first introduced by Christensen and Fulling (1977 Phys. Rev. D 15 2088-104) and expanded to a greater class of black holes via Robinson and Wilczek (2005 Phys. Rev. Lett. 95 011303). The two-dimensional black holes admit a Diff(S1) subalgebra, which upon quantization in the horizon limit becomes Virasoro with calculable central charge. This charge and the lowest Virasoro eigen-mode reproduce the correct Bekenstein-Hawking entropy of the four- and three-dimensional black holes via the known Cardy formula (Blöte et al 1986 Phys. Rev. Lett. 56 742; Cardy 1986 Nucl. Phys. B 270 186). Furthermore, the two-dimensional CFT's energy-momentum tensor is anomalous. However, in the horizon limit the energy-momentum tensor becomes holomorphic equaling the Hawking flux of the four- and three-dimensional black holes. This encoding of both entropy and temperature provides a uniformity in the calculation of black hole thermodynamic and statistical quantities for the non-local effective action approach.

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

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

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

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

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

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

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

DOE PAGES

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

2017-12-05

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

Large-scale Instability during Gravitational Collapse with Neutrino Transport and a Core-Collapse Supernova

NASA Astrophysics Data System (ADS)

Aksenov, A. G.; Chechetkin, V. M.

2018-04-01

Most of the energy released in the gravitational collapse of the cores of massive stars is carried away by neutrinos. Neutrinos play a pivotal role in explaining core-collape supernovae. Currently, mathematical models of the gravitational collapse are based on multi-dimensional gas dynamics and thermonuclear reactions, while neutrino transport is considered in a simplified way. Multidimensional gas dynamics is used with neutrino transport in the flux-limited diffusion approximation to study the role of multi-dimensional effects. The possibility of large-scale convection is discussed, which is interesting both for explaining SN II and for setting up observations to register possible high-energy (≳10MeV) neutrinos from the supernova. A new multi-dimensional, multi-temperature gas dynamics method with neutrino transport is presented.

An approximate stationary solution for multi-allele neutral diffusion with low mutation rates.

PubMed

Burden, Conrad J; Tang, Yurong

2016-12-01

We address the problem of determining the stationary distribution of the multi-allelic, neutral-evolution Wright-Fisher model in the diffusion limit. A full solution to this problem for an arbitrary K×K mutation rate matrix involves solving for the stationary solution of a forward Kolmogorov equation over a (K-1)-dimensional simplex, and remains intractable. In most practical situations mutations rates are slow on the scale of the diffusion limit and the solution is heavily concentrated on the corners and edges of the simplex. In this paper we present a practical approximate solution for slow mutation rates in the form of a set of line densities along the edges of the simplex. The method of solution relies on parameterising the general non-reversible rate matrix as the sum of a reversible part and a set of (K-1)(K-2)/2 independent terms corresponding to fluxes of probability along closed paths around faces of the simplex. The solution is potentially a first step in estimating non-reversible evolutionary rate matrices from observed allele frequency spectra. Copyright © 2016 Elsevier Inc. All rights reserved.

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.

Numerical simulation of multi-dimensional NMR response in tight sandstone

NASA Astrophysics Data System (ADS)

Guo, Jiangfeng; Xie, Ranhong; Zou, Youlong; Ding, Yejiao

2016-06-01

Conventional logging methods have limitations in the evaluation of tight sandstone reservoirs. The multi-dimensional nuclear magnetic resonance (NMR) logging method has the advantage that it can simultaneously measure transverse relaxation time (T 2), longitudinal relaxation time (T 1) and diffusion coefficient (D). In this paper, we simulate NMR measurements of tight sandstone with different wettability and saturations by the random walk method and obtain the magnetization decays of Carr-Purcell-Meiboom-Gill pulse sequences with different wait times (TW) and echo spacings (TE) under a magnetic field gradient, resulting in D-T 2-T 1 maps by the multiple echo trains joint inversion method. We also study the effects of wettability, saturation, signal-to-noise ratio (SNR) of data and restricted diffusion on the D-T 2-T 1 maps in tight sandstone. The results show that with decreasing wetting fluid saturation, the surface relaxation rate of the wetting fluid gradually increases and the restricted diffusion phenomenon becomes more and more obvious, which leads to the wetting fluid signal moving along the direction of short relaxation and the direction of the diffusion coefficient decreasing in D-T 2-T 1 maps. Meanwhile, the non-wetting fluid position in D-T 2-T 1 maps does not change with saturation variation. With decreasing SNR, the ability to identify water and oil signals based on NMR maps gradually decreases. The wetting fluid D-T 1 and D-T 2 correlations in NMR diffusion-relaxation maps of tight sandstone are obtained through expanding the wetting fluid restricted diffusion models, and are further applied to recognize the wetting fluid in simulated D-T 2 maps and D-T 1 maps.

Diffusion-controlled formation and collapse of a d-dimensional A-particle island in the B-particle sea.

PubMed

Shipilevsky, Boris M

2017-06-01

We consider diffusion-controlled evolution of a d-dimensional A-particle island in the B-particle sea at propagation of the sharp reaction front A+B→0 at equal species diffusivities. The A-particle island is formed by a localized (point) A-source with a strength λ that acts for a finite time T. We reveal the conditions under which the island collapse time t_{c} becomes much longer than the injection period T (long-living island) and demonstrate that regardless of d the evolution of the long-living island radius r_{f}(t) is described by the universal law ζ_{f}=r_{f}/r_{f}^{M}=sqrt[eτ|lnτ|], where τ=t/t_{c} and r_{f}^{M} is the maximal island expansion radius at the front turning point t_{M}=t_{c}/e. We find that in the long-living island regime the ratio t_{c}/T changes with the increase of the injection period T by the law ∝(λ^{2}T^{2-d})^{1/d}, i.e., increases with the increase of T in the one-dimensional (1D) case, does not change with the increase of T in the 2D case and decreases with the increase of T in the 3D case. We derive the scaling laws for particles death in the long-living island and determine the limits of their applicability. We demonstrate also that these laws describe asymptotically the evolution of the d-dimensional spherical island with a uniform initial particle distribution generalizing the results obtained earlier for the quasi-one-dimensional geometry. As striking results, we present a systematic analysis of the front relative width evolution for fluctuation, logarithmically modified, and mean-field regimes, and we demonstrate that in a wide range of parameters the front remains sharp up to a narrow vicinity of the collapse point.

Inertial-range dynamics and scaling laws of two-dimensional magnetohydrodynamic turbulence in the weak-field regime.

PubMed

Blackbourn, Luke A K; Tran, Chuong V

2014-08-01

We study inertial-range dynamics and scaling laws in unforced two-dimensional magnetohydrodynamic turbulence in the regime of moderately small and small initial magnetic-to-kinetic-energy ratio r(0), with an emphasis on the latter. The regime of small r(0) corresponds to a relatively weak field and strong magnetic stretching, whereby the turbulence is characterized by an intense conversion of kinetic into magnetic energy (dynamo action in the three-dimensional context). This conversion is an inertial-range phenomenon and, upon becoming quasisaturated, deposits the converted energy within the inertial range rather than transferring it to the small scales. As a result, the magnetic-energy spectrum E(b)(k) in the inertial range can become quite shallow and may not be adequately explained or understood in terms of conventional cascade theories. It is demonstrated by numerical simulations at high Reynolds numbers (and unity magnetic Prandtl number) that the energetics and inertial-range scaling depend strongly on r(0). In particular, for fully developed turbulence with r(0) in the range [1/4,1/4096], E(b)(k) is found to scale as k(α), where α≳-1, including α>0. The extent of such a shallow spectrum is limited, becoming broader as r(0) is decreased. The slope α increases as r(0) is decreased, appearing to tend to +1 in the limit of small r(0). This implies equipartition of magnetic energy among the Fourier modes of the inertial range and the scaling k(-1) of the magnetic potential variance, whose flux is direct rather than inverse. This behavior of the potential resembles that of a passive scalar. However, unlike a passive scalar whose variance dissipation rate slowly vanishes in the diffusionless limit, the dissipation rate of the magnetic potential variance scales linearly with the diffusivity in that limit. Meanwhile, the kinetic-energy spectrum is relatively steep, followed by a much shallower tail due to strong antidynamo excitation. This gives rise to a total-energy spectrum poorly obeying a power-law scaling.

Strongly nonlinear dynamics of electrolytes in large ac voltages.

PubMed

Højgaard Olesen, Laurits; Bazant, Martin Z; Bruus, Henrik

2010-07-01

We study the response of a model microelectrochemical cell to a large ac voltage of frequency comparable to the inverse cell relaxation time. To bring out the basic physics, we consider the simplest possible model of a symmetric binary electrolyte confined between parallel-plate blocking electrodes, ignoring any transverse instability or fluid flow. We analyze the resulting one-dimensional problem by matched asymptotic expansions in the limit of thin double layers and extend previous work into the strongly nonlinear regime, which is characterized by two features--significant salt depletion in the electrolyte near the electrodes and, at very large voltage, the breakdown of the quasiequilibrium structure of the double layers. The former leads to the prediction of "ac capacitive desalination" since there is a time-averaged transfer of salt from the bulk to the double layers, via oscillating diffusion layers. The latter is associated with transient diffusion limitation, which drives the formation and collapse of space-charge layers, even in the absence of any net Faradaic current through the cell. We also predict that steric effects of finite ion sizes (going beyond dilute-solution theory) act to suppress the strongly nonlinear regime in the limit of concentrated electrolytes, ionic liquids, and molten salts. Beyond the model problem, our reduced equations for thin double layers, based on uniformly valid matched asymptotic expansions, provide a useful mathematical framework to describe additional nonlinear responses to large ac voltages, such as Faradaic reactions, electro-osmotic instabilities, and induced-charge electrokinetic phenomena.

Diffusion Tensor Analysis by Two-Dimensional Pair Correlation of Fluorescence Fluctuations in Cells.

PubMed

Di Rienzo, Carmine; Cardarelli, Francesco; Di Luca, Mariagrazia; Beltram, Fabio; Gratton, Enrico

2016-08-23

In a living cell, the movement of biomolecules is highly regulated by the cellular organization into subcompartments that impose barriers to diffusion, can locally break the spatial isotropy, and ultimately guide these molecules to their targets. Despite the pivotal role of these processes, experimental tools to fully probe the complex connectivity (and accessibility) of the cell interior with adequate spatiotemporal resolution are still lacking. Here, we show how the heterogeneity of molecular dynamics and the location of barriers to molecular motion can be mapped in live cells by exploiting a two-dimensional (2D) extension of the pair correlation function (pCF) analysis. Starting from a time series of images collected for the same field of view, the resulting 2D pCF is calculated in the proximity of each point for each time delay and allows us to probe the spatial distribution of the molecules that started from a given pixel. This 2D pCF yields an accurate description of the preferential diffusive routes. Furthermore, we combine this analysis with the image-derived mean-square displacement approach and gain information on the average nanoscopic molecular displacements in different directions. Through these quantities, we build a fluorescence-fluctuation-based diffusion tensor that contains information on speed and directionality of the local dynamical processes. Contrary to classical fluorescence correlation spectroscopy and related methods, this combined approach can distinguish between isotropic and anisotropic local diffusion. We argue that the measurement of this iMSD tensor will contribute to advance our understanding of the role played by the intracellular environment in the regulation of molecular diffusion at the nanoscale. Copyright © 2016 Biophysical Society. Published by Elsevier Inc. All rights reserved.

Nanoscale charge transfer and diffusion at the MoS2/SiO2 interface by atomic force microscopy: contact injection versus triboelectrification.

PubMed

Xu, Rui; Ye, Shili; Xu, Kunqi; Lei, Le; Hussain, Sabir; Zheng, Zhiyue; Pang, Fei; Xing, Shuya; Liu, Xinmeng; Ji, Wei; Cheng, Zhihai

2018-08-31

Understanding the process of charge generation, transfer, and diffusion between two-dimensional (2D) materials and their supporting substrates is very important for potential applications of 2D materials. Compared with the systematic studies of triboelectric charging in a bulk sample, a fundamental understanding of the triboelectrification of the 2D material/insulator system is rather limited. Here, the charge transfer and diffusion of both the SiO 2 surface and MoS 2 /SiO 2 interface through contact electrification and frictional electrification are investigated systematically in situ by scanning Kelvin probe microscopy and dual-harmonic electrostatic force microscopy. Different from the simple static charge transfer between SiO 2 and the PtSi alloy atomic force microscope (AFM) tip, the charge transfer between the tip and the MoS 2 /SiO 2 system is complicated. Triboelectric charges, generated by contact or frictional electrification with the AFM tip, are trapped at the MoS 2 /SiO 2 interface and act as floating gates. The local charge discharge processes can be obtained by monitoring the surface potential. The charge decay time (τ) of the MoS 2 /SiO 2 interface is one (or two) orders of magnitude larger than the decay time τ of the SiO 2 surface. This work facilitates an understanding of the triboelectric and de-electrification of the interface between 2D materials and substrates. In addition to the charge transfer and diffusion, we demonstrate the nanopatterns of surface and interfacial charges, which have great potential for the application of self-assembly of charged nanostructures.

Microscopic origin and macroscopic implications of lane formation in mixtures of oppositely driven particles

NASA Astrophysics Data System (ADS)

Klymko, Katherine; Geissler, Phillip L.; Whitelam, Stephen

2016-08-01

Colloidal particles of two types, driven in opposite directions, can segregate into lanes [Vissers et al., Soft Matter 7, 2352 (2011), 10.1039/c0sm01343a]. This phenomenon can be reproduced by two-dimensional Brownian dynamics simulations of model particles [Dzubiella et al., Phys. Rev. E 65, 021402 (2002), 10.1103/PhysRevE.65.021402]. Here we use computer simulation to assess the generality of lane formation with respect to variation of particle type and dynamical protocol. We find that laning results from rectification of diffusion on the scale of a particle diameter: oppositely driven particles must, in the time taken to encounter each other in the direction of the drive, diffuse in the perpendicular direction by about one particle diameter. This geometric constraint implies that the diffusion constant of a particle, in the presence of those of the opposite type, grows approximately linearly with the Péclet number, a prediction confirmed by our numerics over a range of model parameters. Such environment-dependent diffusion is statistically similar to an effective interparticle attraction; consistent with this observation, we find that oppositely driven nonattractive colloids display features characteristic of the simplest model system possessing both interparticle attractions and persistent motion, the driven Ising lattice gas [Katz, Leibowitz, and Spohn, J. Stat. Phys. 34, 497 (1984), 10.1007/BF01018556]. These features include long-ranged correlations in the disordered regime, a critical regime characterized by a change in slope of the particle current with the Péclet number, and fluctuations that grow with system size. By analogy, we suggest that lane formation in the driven colloid system is a phase transition in the macroscopic limit, but that macroscopic phase separation would not occur in finite time upon starting from disordered initial conditions.

Simulations of Cyclic Voltammetry for Electric Double Layers in Asymmetric Electrolytes: A Generalized Modified Poisson-Nernst-Planck Model

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

Wang, Hainan; Thiele, Alexander; Pilon, Laurent

2013-11-15

This paper presents a generalized modified Poisson–Nernst–Planck (MPNP) model derived from first principles based on excess chemical potential and Langmuir activity coefficient to simulate electric double-layer dynamics in asymmetric electrolytes. The model accounts simultaneously for (1) asymmetric electrolytes with (2) multiple ion species, (3) finite ion sizes, and (4) Stern and diffuse layers along with Ohmic potential drop in the electrode. It was used to simulate cyclic voltammetry (CV) measurements for binary asymmetric electrolytes. The results demonstrated that the current density increased significantly with decreasing ion diameter and/or increasing valency |z i| of either ion species. By contrast, the ionmore » diffusion coefficients affected the CV curves and capacitance only at large scan rates. Dimensional analysis was also performed, and 11 dimensionless numbers were identified to govern the CV measurements of the electric double layer in binary asymmetric electrolytes between two identical planar electrodes of finite thickness. A self-similar behavior was identified for the electric double-layer integral capacitance estimated from CV measurement simulations. Two regimes were identified by comparing the half cycle period τ CV and the “RC time scale” τ RC corresponding to the characteristic time of ions’ electrodiffusion. For τ RC ← τ CV, quasi-equilibrium conditions prevailed and the capacitance was diffusion-independent while for τ RC → τ CV, the capacitance was diffusion-limited. The effect of the electrode was captured by the dimensionless electrode electrical conductivity representing the ratio of characteristic times associated with charge transport in the electrolyte and that in the electrode. The model developed here will be useful for simulating and designing various practical electrochemical, colloidal, and biological systems for a wide range of applications.« less

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

Experimental Observations on a Low Strain Counter-Flow Diffusion Flame: Flow and Bouyancy Effects

NASA Technical Reports Server (NTRS)

Sutula, J. A.; Torero, J. L.; Ezekoye, O. A.

1999-01-01

Diffusion flames are of great interest in fire safety and many industrial processes. The counter-flow configuration provides a constant strain flow, and therefore is ideal to study the structure of diffusion flames. Most studies have concentrated on the high velocity, high strain limit, since buoyantly induced instabilities will disintegrate the planar flame as the velocity decreases. Only recently, experimental studies in microgravity conditions have begun to explore the low strain regimes. Numerical work has shown the coupling between gas phase reaction rates, soot reaction rates, and radiation. For these programs, size, geometry and experimental conditions have been chosen to keep the flame unaffected by the physical boundaries. When the physical boundaries can not be considered infinitely far from the reaction zone discrepancies arise. A computational study that includes boundary effects and accounts for the deviations occurring when the major potential flow assumptions are relaxed was presented by Borlik et al. This development properly incorporates all heat loss terms and shows the possibility of extinction in the low strain regime. A major constraint of studying the low strain regime is buoyancy. Buoyant instabilities have been shown to have a significant effect on the nature of reactants and heat transport, and can introduce instabilities on the flow that result in phenomena such as flickering or fingering. The counter-flow configuration has been shown to provide a flame with no symmetry disrupting instabilities for inlet velocities greater than 50 mm/s. As the velocity approaches this limit, the characteristic length of the experiment has to be reduced to a few millimetres so as to keep the Rayleigh number (Ra(sub L) = (Beta)(g(sub 0))(L(exp 3) del T)/(alpha(v))) below 2000. In this work, a rectangular counter-flow burner was used to study a two-dimensional counter-flow diffusion flame. Flow visualisation and Particle Image Velocimetry served to describe the nature of the stagnation plane for strain rates smaller than 100 (1/s). These experiments were conducted with a non-reacting flow. Video images of a propane air diffusion flame were used to describe the behaviour of a diffusion flame in this regime. Flame geometry and pulsation frequency are described.

Role of Rayleigh numbers on characteristics of double diffusive salt fingers

NASA Astrophysics Data System (ADS)

Rehman, F.; Singh, O. P.

2018-05-01

Double diffusion convection, driven by two constituents of the fluid with different molecular diffusivity, is widely applied in oceanography and large number of other fields like astrophysics, geology, chemistry and metallurgy. In case of ocean, heat (T) and salinity (S) are the two components with varying diffusivity, where heat diffuses hundred times faster than salt. Component (T) stabilizes the system whereas components (S) destabilizes the system with overall density remains stable and forms the rising and sinking fingers known as salt fingers. Recent observations suggest that salt finger characteristics such as growth rates, wavenumber, and fluxes are strongly depending on the Rayleigh numbers as major driving force. In this paper, we corroborate this observation with the help of experiments, numerical simulations and linear theory. An eigenvalue expression for growth rate is derived from the linearized governing equations with explicit dependence on Rayleigh numbers, density stability ratio, Prandtl number and diffusivity ratio. Expressions for fastest growing fingers are also derived as a function various non-dimensional parameter. The predicted results corroborate well with the data reported from the field measurements, experiments and numerical simulations.

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.

Phonons, Diffusons, and the Boson Peak in Two-Dimensional Lattices with Random Bonds

NASA Astrophysics Data System (ADS)

Konyukh, D. A.; Bel'tyukov, Ya. M.; Parshin, D. A.

2018-02-01

Within the model of stable random matrices possessing translational invariance, a two-dimensional (on a square lattice) disordered oscillatory system with random strongly fluctuating bonds is considered. By a numerical analysis of the dynamic structure factor S( q, ω), it is shown that vibrations with frequencies below the Ioffe-Regel frequency ωIR are ordinary phonons with a linear dispersion law ω( q) ∝ q and a reciprocal lifetime б q 3. Vibrations with frequencies above ωIR, although being delocalized, cannot be described by plane waves with a definite dispersion law ω( q). They are characterized by a diffusion structure factor with a reciprocal lifetime б q 2, which is typical of a diffusion process. In the literature, they are often referred to as diffusons. It is shown that, as in the three-dimensional model, the boson peak at the frequency ωb in the reduced density of vibrational states g(ω)/ω is on the order of the frequency ωIR. It is located in the transition region between phonons and diffusons and is proportional to the Young's modulus of the lattice, ω b ≃ E.

Wideband radar cross section reduction using two-dimensional phase gradient metasurfaces

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

Li, Yongfeng; Qu, Shaobo; Wang, Jiafu

2014-06-02

Phase gradient metasurface (PGMs) are artificial surfaces that can provide pre-defined in-plane wave-vectors to manipulate the directions of refracted/reflected waves. In this Letter, we propose to achieve wideband radar cross section (RCS) reduction using two-dimensional (2D) PGMs. A 2D PGM was designed using a square combination of 49 split-ring sub-unit cells. The PGM can provide additional wave-vectors along the two in-plane directions simultaneously, leading to either surface wave conversion, deflected reflection, or diffuse reflection. Both the simulation and experiment results verified the wide-band, polarization-independent, high-efficiency RCS reduction induced by the 2D PGM.

Electron energization mechanisms in collisionless magnetic reconnection for different guide-field intensities

NASA Astrophysics Data System (ADS)

Pucci, F.; Usami, S.; Guo, X.; Ji, H.; Horiuchi, R.; Okamura, S.

2017-12-01

Electron dynamics and energization are a key component of magnetic field dissipation in collisionless reconnection. Indeed, in 2D reconnection, the main mechanism that limits the current density and provides the resistivity most probably relies on the electron pressure tensor term which has been shown to break the frozen-in condition at the x-point (Ishizawa and Horiuchi 2005; Horiuchi et al. 2014). In addition the electron-meandering-orbit scale controls the width of the electron dissipation region around the x-point, where the electron temperature is observed to increase, so understanding the electron heating mechanism is fundamental for magnetic reconnection. It has been shown by Guo et al. 2017 that for a 2D high guide field configuration (Bz/B0 = 3) electron perpendicular heating is mainly due to the breaking of magnetic moment conservation in the separatrix region while electron perpendicular acceleration takes place mainly in the downstream near the X-point. Electron velocity distributions have been shown to exhibit highly structured features within a few electron skin depths from the X line (Bessho et al. 2014) as well as in the exhaust (Shuster et al. 2014). By means of two-dimensional, full-particle simulations in an open system (Pei et al. 2001; Ohtani and R. Horiuchi 2009), we investigate how the energization mechanism depends on the guide field intensity. We compare electron distribution functions as well as particles orbits, in the electron diffusion region and the exhaust, in order to clarify the preferential electron heating/acceleration in two-dimensional systems. We will then compare our results with observations using the present catalogue of MMS diffusion region crossings.