Spatial pattern dynamics due to the fitness gradient flux in evolutionary games.

PubMed

deForest, Russ; Belmonte, Andrew

2013-06-01

We introduce a nondiffusive spatial coupling term into the replicator equation of evolutionary game theory. The spatial flux is based on motion due to local gradients in the relative fitness of each strategy, providing a game-dependent alternative to diffusive coupling. We study numerically the development of patterns in one dimension (1D) for two-strategy games including the coordination game and the prisoner's dilemma, and in two dimensions (2D) for the rock-paper-scissors game. In 1D we observe modified traveling wave solutions in the presence of diffusion, and asymptotic attracting states under a frozen-strategy assumption without diffusion. In 2D we observe spiral formation and breakup in the frozen-strategy rock-paper-scissors game without diffusion. A change of variables appropriate to replicator dynamics is shown to correctly capture the 1D asymptotic steady state via a nonlinear diffusion equation.

Quantum Transmission Conditions for Diffusive Transport in Graphene with Steep Potentials

NASA Astrophysics Data System (ADS)

Barletti, Luigi; Negulescu, Claudia

2018-05-01

We present a formal derivation of a drift-diffusion model for stationary electron transport in graphene, in presence of sharp potential profiles, such as barriers and steps. Assuming the electric potential to have steep variations within a strip of vanishing width on a macroscopic scale, such strip is viewed as a quantum interface that couples the classical regions at its left and right sides. In the two classical regions, where the potential is assumed to be smooth, electron and hole transport is described in terms of semiclassical kinetic equations. The diffusive limit of the kinetic model is derived by means of a Hilbert expansion and a boundary layer analysis, and consists of drift-diffusion equations in the classical regions, coupled by quantum diffusive transmission conditions through the interface. The boundary layer analysis leads to the discussion of a four-fold Milne (half-space, half-range) transport problem.

Spatial pattern dynamics due to the fitness gradient flux in evolutionary games

NASA Astrophysics Data System (ADS)

deForest, Russ; Belmonte, Andrew

2013-06-01

We introduce a nondiffusive spatial coupling term into the replicator equation of evolutionary game theory. The spatial flux is based on motion due to local gradients in the relative fitness of each strategy, providing a game-dependent alternative to diffusive coupling. We study numerically the development of patterns in one dimension (1D) for two-strategy games including the coordination game and the prisoner's dilemma, and in two dimensions (2D) for the rock-paper-scissors game. In 1D we observe modified traveling wave solutions in the presence of diffusion, and asymptotic attracting states under a frozen-strategy assumption without diffusion. In 2D we observe spiral formation and breakup in the frozen-strategy rock-paper-scissors game without diffusion. A change of variables appropriate to replicator dynamics is shown to correctly capture the 1D asymptotic steady state via a nonlinear diffusion equation.

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.

Coupling of light into the fundamental diffusion mode of a scattering medium (Conference Presentation)

NASA Astrophysics Data System (ADS)

Ojambati, Oluwafemi S.; Yılmaz, Hasan; Lagendijk, Ad; Mosk, Allard P.; Vos, Willem L.

2016-03-01

Diffusion equation describes the energy density inside a scattering medium such as biological tissues and paint [1]. The solution of the diffusion equation is a sum over a complete set of eigensolutions that shows a characteristic linear decrease with depth in the medium. It is of particular interest if one could launch energy in the fundamental eigensolution, as this opens the opportunity to achieve a much greater internal energy density. For applications in optics, an enhanced energy density is vital for solid-state lighting, light harvesting in solar cells, low-threshold random lasers, and biomedical optics. Here we demonstrate the first ever selective coupling of optical energy into a diffusion eigensolution of a scattering medium of zinc oxide (ZnO) paint. To this end, we exploit wavefront shaping to selectively couple energy into the fundamental diffusion mode, employing fluorescence of nanoparticles randomly positioned inside the medium as a probe of the energy density. We observe an enhanced fluorescence in case of optimized incident wavefronts, and the enhancement increases with sample thickness, a typical mesoscopic control parameter. We interpret successfully our result by invoking the fundamental eigensolution of the diffusion equation, and we obtain excellent agreement with our observations, even in absence of adjustable parameters [2]. References [1] R. Pierrat, P. Ambichl, S. Gigan, A. Haber, R. Carminati, and R. Rotter, Proc. Natl. Acad. Sci. U.S.A. 111, 17765 (2014). [2] O. S. Ojambati, H. Yilmaz, A. Lagendijk, A. P. Mosk, and W. L. Vos, arXiv:1505.08103.

Quasilinear diffusion coefficients in a finite Larmor radius expansion for ion cyclotron heated plasmas

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

Lee, Jungpyo; Wright, John; Bertelli, Nicola

In this study, a reduced model of quasilinear velocity diffusion by a small Larmor radius approximation is derived to couple the Maxwell’s equations and the Fokker Planck equation self-consistently for the ion cyclotron range of frequency waves in a tokamak. The reduced model ensures the important properties of the full model by Kennel-Engelmann diffusion, such as diffusion directions, wave polarizations, and H-theorem. The kinetic energy change (Wdot ) is used to derive the reduced model diffusion coefficients for the fundamental damping (n = 1) and the second harmonic damping (n = 2) to the lowest order of the finite Larmormore » radius expansion. The quasilinear diffusion coefficients are implemented in a coupled code (TORIC-CQL3D) with the equivalent reduced model of the dielectric tensor. We also present the simulations of the ITER minority heating scenario, in which the reduced model is verified within the allowable errors from the full model results.« less

Quasilinear diffusion coefficients in a finite Larmor radius expansion for ion cyclotron heated plasmas

DOE PAGES

Lee, Jungpyo; Wright, John; Bertelli, Nicola; ...

2017-04-24

In this study, a reduced model of quasilinear velocity diffusion by a small Larmor radius approximation is derived to couple the Maxwell’s equations and the Fokker Planck equation self-consistently for the ion cyclotron range of frequency waves in a tokamak. The reduced model ensures the important properties of the full model by Kennel-Engelmann diffusion, such as diffusion directions, wave polarizations, and H-theorem. The kinetic energy change (Wdot ) is used to derive the reduced model diffusion coefficients for the fundamental damping (n = 1) and the second harmonic damping (n = 2) to the lowest order of the finite Larmormore » radius expansion. The quasilinear diffusion coefficients are implemented in a coupled code (TORIC-CQL3D) with the equivalent reduced model of the dielectric tensor. We also present the simulations of the ITER minority heating scenario, in which the reduced model is verified within the allowable errors from the full model results.« less

Generalized two-temperature model for coupled phonon-magnon diffusion.

PubMed

Liao, Bolin; Zhou, Jiawei; Chen, Gang

2014-07-11

We generalize the two-temperature model [Sanders and Walton, Phys. Rev. B 15, 1489 (1977)] for coupled phonon-magnon diffusion to include the effect of the concurrent magnetization flow, with a particular emphasis on the thermal consequence of the magnon flow driven by a nonuniform magnetic field. Working within the framework of the Boltzmann transport equation, we derive the constitutive equations for coupled phonon-magnon transport driven by gradients of both temperature and external magnetic fields, and the corresponding conservation laws. Our equations reduce to the original Sanders-Walton two-temperature model under a uniform external field, but predict a new magnon cooling effect driven by a nonuniform magnetic field in a homogeneous single-domain ferromagnet. We estimate the magnitude of the cooling effect in an yttrium iron garnet, and show it is within current experimental reach. With properly optimized materials, the predicted cooling effect can potentially supplement the conventional magnetocaloric effect in cryogenic applications in the future.

A computational method for the coupled solution of reaction-diffusion equations on evolving domains and manifolds: Application to a model of cell migration and chemotaxis.

PubMed

MacDonald, G; Mackenzie, J A; Nolan, M; Insall, R H

2016-03-15

In this paper, we devise a moving mesh finite element method for the approximate solution of coupled bulk-surface reaction-diffusion equations on an evolving two dimensional domain. Fundamental to the success of the method is the robust generation of bulk and surface meshes. For this purpose, we use a novel moving mesh partial differential equation (MMPDE) approach. The developed method is applied to model problems with known analytical solutions; these experiments indicate second-order spatial and temporal accuracy. Coupled bulk-surface problems occur frequently in many areas; in particular, in the modelling of eukaryotic cell migration and chemotaxis. We apply the method to a model of the two-way interaction of a migrating cell in a chemotactic field, where the bulk region corresponds to the extracellular region and the surface to the cell membrane.

Surge dynamics coupled to pore-pressure evolution in debris flows

USGS Publications Warehouse

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

2003-01-01

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

A new mathematical solution for predicting char activation reactions

USGS Publications Warehouse

Rafsanjani, H.H.; Jamshidi, E.; Rostam-Abadi, M.

2002-01-01

The differential conservation equations that describe typical gas-solid reactions, such as activation of coal chars, yield a set of coupled second-order partial differential equations. The solution of these coupled equations by exact analytical methods is impossible. In addition, an approximate or exact solution only provides predictions for either reaction- or diffusion-controlling cases. A new mathematical solution, the quantize method (QM), was applied to predict the gasification rates of coal char when both chemical reaction and diffusion through the porous char are present. Carbon conversion rates predicted by the QM were in closer agreement with the experimental data than those predicted by the random pore model and the simple particle model. ?? 2002 Elsevier Science Ltd. All rights reserved.

Coupling of atom-by-atom calculations of extended defects with B kick-out equations: application to the simulation of boron ted

NASA Astrophysics Data System (ADS)

Lampin, E.; Cristiano, F.; Lamrani, Y.; Colombeau, B.

2004-02-01

We present simulations of B TED based on a complete calculation of the extended defect growth/shrinkage during annealing. The Si self-interstitial supersaturation calculated at the extended defect depth is coupled to the set of equations for the B kick-out diffusion through a generation/recombination term in the diffusion equation of the Si self-interstitials. The simulations are compared to the measurements performed on a Si wafer containing several B marker layers, where the amount of TED varies from one peak to the other. The good agreement obtained on this experiment is very promising for the application of these calculations to the case of ultra-shallow B + implants.

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

NASA Astrophysics Data System (ADS)

Zhang, Xiaolong; Zhong, Zheng

2017-10-01

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

Modeling the sound transmission between rooms coupled through partition walls by using a diffusion model.

PubMed

Billon, Alexis; Foy, Cédric; Picaut, Judicaël; Valeau, Vincent; Sakout, Anas

2008-06-01

In this paper, a modification of the diffusion model for room acoustics is proposed to account for sound transmission between two rooms, a source room and an adjacent room, which are coupled through a partition wall. A system of two diffusion equations, one for each room, together with a set of two boundary conditions, one for the partition wall and one for the other walls of a room, is obtained and numerically solved. The modified diffusion model is validated by numerical comparisons with the statistical theory for several coupled-room configurations by varying the coupling area surface, the absorption coefficient of each room, and the volume of the adjacent room. An experimental comparison is also carried out for two coupled classrooms. The modified diffusion model results agree very well with both the statistical theory and the experimental data. The diffusion model can then be used as an alternative to the statistical theory, especially when the statistical theory is not applicable, that is, when the reverberant sound field is not diffuse. Moreover, the diffusion model allows the prediction of the spatial distribution of sound energy within each coupled room, while the statistical theory gives only one sound level for each room.

Calculation of two-dimension radial electric field in boundary plasmas by using BOUT++

NASA Astrophysics Data System (ADS)

Li, N. M.; Xu, X. Q.; Rognlien, T. D.; Gui, B.; Sun, J. Z.; Wang, D. Z.

2018-07-01

The steady state radial electric field (Er) is calculated by coupling a plasma transport model with the quasi-neutrality constraint and the vorticity equation within the BOUT++ framework. Based on the experimentally measured plasma density and temperature profiles in Alcator C-Mod discharges, the effective radial particle and heat diffusivities are inferred from the set of plasma transport equations. The effective diffusivities are then extended into the scrape-off layer (SOL) to calculate the plasma density, temperature and flow profiles across the separatrix into the SOL with the electrostatic sheath boundary conditions (SBC) applied on the divertor plates. Given these diffusivities, the electric field can be calculated self-consistently across the separatrix from the vorticity equation with SBC coupled to the plasma transport equations. The sheath boundary conditions act to generate a large and positive Er in the SOL, which is consistent with experimental measurements. The effect of magnetic particle drifts is shown to play a significant role on local particle transport and Er by inducing a net particle flow in both the edge and SOL regions.

Analysis of a diffuse interface model of multispecies tumor growth

NASA Astrophysics Data System (ADS)

Dai, Mimi; Feireisl, Eduard; Rocca, Elisabetta; Schimperna, Giulio; Schonbek, Maria E.

2017-04-01

We consider a diffuse interface model for tumor growth recently proposed in Chen et al (2014 Int. J. Numer. Methods Biomed. Eng. 30 726-54). In this new approach sharp interfaces are replaced by narrow transition layers arising due to adhesive forces among the cell species. Hence, a continuum thermodynamically consistent model is introduced. The resulting PDE system couples four different types of equations: a Cahn-Hilliard type equation for the tumor cells (which include proliferating and dead cells), a Darcy law for the tissue velocity field, whose divergence may be different from 0 and depend on the other variables, a transport equation for the proliferating (viable) tumor cells, and a quasi-static reaction diffusion equation for the nutrient concentration. We establish existence of weak solutions for the PDE system coupled with suitable initial and boundary conditions. In particular, the proliferation function at the boundary is supposed to be nonnegative on the set where the velocity \\mathbf{u} satisfies \\mathbf{u}\\centerdot ν >0 , where ν is the outer normal to the boundary of the domain.

A Model to Couple Flow, Thermal and Reactive Chemical Transport, and Geo-mechanics in Variably Saturated Media

NASA Astrophysics Data System (ADS)

Yeh, G. T.; Tsai, C. H.

2015-12-01

This paper presents the development of a THMC (thermal-hydrology-mechanics-chemistry) process model in variably saturated media. The governing equations for variably saturated flow and reactive chemical transport are obtained based on the mass conservation principle of species transport supplemented with Darcy's law, constraint of species concentration, equation of states, and constitutive law of K-S-P (Conductivity-Degree of Saturation-Capillary Pressure). The thermal transport equation is obtained based on the conservation of energy. The geo-mechanic displacement is obtained based on the assumption of equilibrium. Conventionally, these equations have been implicitly coupled via the calculations of secondary variables based on primary variables. The mechanisms of coupling have not been obvious. In this paper, governing equations are explicitly coupled for all primary variables. The coupling is accomplished via the storage coefficients, transporting velocities, and conduction-dispersion-diffusion coefficient tensor; one set each for every primary variable. With this new system of equations, the coupling mechanisms become clear. Physical interpretations of every term in the coupled equations will be discussed. Examples will be employed to demonstrate the intuition and superiority of these explicit coupling approaches. Keywords: Variably Saturated Flow, Thermal Transport, Geo-mechanics, Reactive Transport.

Reconstruction of ensembles of coupled time-delay systems from time series.

PubMed

Sysoev, I V; Prokhorov, M D; Ponomarenko, V I; Bezruchko, B P

2014-06-01

We propose a method to recover from time series the parameters of coupled time-delay systems and the architecture of couplings between them. The method is based on a reconstruction of model delay-differential equations and estimation of statistical significance of couplings. It can be applied to networks composed of nonidentical nodes with an arbitrary number of unidirectional and bidirectional couplings. We test our method on chaotic and periodic time series produced by model equations of ensembles of diffusively coupled time-delay systems in the presence of noise, and apply it to experimental time series obtained from electronic oscillators with delayed feedback coupled by resistors.

The Marriage of Gas and Dust

NASA Astrophysics Data System (ADS)

Price, D. J.; Laibe, G.

2015-10-01

Dust-gas mixtures are the simplest example of a two fluid mixture. We show that when simulating such mixtures with particles or with particles coupled to grids a problem arises due to the need to resolve a very small length scale when the coupling is strong. Since this is occurs in the limit when the fluids are well coupled, we show how the dust-gas equations can be reformulated to describe a single fluid mixture. The equations are similar to the usual fluid equations supplemented by a diffusion equation for the dust-to-gas ratio or alternatively the dust fraction. This solves a number of numerical problems as well as making the physics clear.

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

Garcia, Andres

Transport and reaction in zeolites and other porous materials, such as mesoporous silica particles, has been a focus of interest in recent years. This is in part due to the possibility of anomalous transport effects (e.g. single-file diffusion) and its impact in the reaction yield in catalytic processes. Computational simulations are often used to study these complex nonequilibrium systems. Computer simulations using Molecular Dynamics (MD) techniques are prohibitive, so instead coarse grained one-dimensional models with the aid of Kinetic Monte Carlo (KMC) simulations are used. Both techniques can be computationally expensive, both time and resource wise. These coarse-grained systems canmore » be exactly described by a set of coupled stochastic master equations, that describe the reaction-diffusion kinetics of the system. The equations can be written exactly, however, coupling between the equations and terms within the equations make it impossible to solve them exactly; approximations must be made. One of the most common methods to obtain approximate solutions is to use Mean Field (MF) theory. MF treatments yield reasonable results at high ratios of reaction rate k to hop rate h of the particles, but fail completely at low k=h due to the over-estimation of fluxes of particles within the pore. We develop a method to estimate fluxes and intrapore diffusivity in simple one- dimensional reaction-diffusion models at high and low k=h, where the pores are coupled to an equilibrated three-dimensional fluid. We thus successfully describe analytically these simple reaction-diffusion one-dimensional systems. Extensions to models considering behavior with long range steric interactions and wider pores require determination of multiple boundary conditions. We give a prescription to estimate the required parameters for these simulations. For one dimensional systems, if single-file diffusion is relaxed, additional parameters to describe particle exchange have to be introduced. We use Langevin Molecular Dynamics (MD) simulations to assess these parameters.« less

Turbulent transport of a passive-scalar field by using a renormalization-group method

NASA Technical Reports Server (NTRS)

Hossain, Murshed

1992-01-01

A passive-scalar field is considered to evolve under the influence of a turbulent fluid governed by the Navier-Stokes equation. Turbulent-transport coefficients are calculated by small-scale elimination using a renormalization-group method. Turbulent processes couple both the viscosity and the diffusivity. In the absence of any correlation between the passive-scalar fluctuations and any component of the fluid velocity, the renormalized diffusivity is essentially the same as if the fluid velocity were frozen, although the renormalized equation does contain higher-order nonlinear terms involving viscosity. This arises due to the nonlinear interaction of the velocity with itself. In the presence of a finite correlation, the turbulent diffusivity becomes coupled with both the velocity field and the viscosity. There is then a dependence of the turbulent decay of the passive scalar on the turbulent Prandtl number.

DEVELOPMENT OF SPLIT-OPERATOR, PETROV-GALERKIN METHODS TO SIMULATE TRANSPORT AND DIFFUSION PROBLEMS

EPA Science Inventory

The rate at which contaminants in groundwater undergo sorption and desorption is routinely described using diffusion models. Such approaches, when incorporated into transport models, lead to large systems of coupled equations, often nonlinear. This has restricted applications of ...

Hybrid simplified spherical harmonics with diffusion equation for light propagation in tissues.

PubMed

Chen, Xueli; Sun, Fangfang; Yang, Defu; Ren, Shenghan; Zhang, Qian; Liang, Jimin

2015-08-21

Aiming at the limitations of the simplified spherical harmonics approximation (SPN) and diffusion equation (DE) in describing the light propagation in tissues, a hybrid simplified spherical harmonics with diffusion equation (HSDE) based diffuse light transport model is proposed. In the HSDE model, the living body is first segmented into several major organs, and then the organs are divided into high scattering tissues and other tissues. DE and SPN are employed to describe the light propagation in these two kinds of tissues respectively, which are finally coupled using the established boundary coupling condition. The HSDE model makes full use of the advantages of SPN and DE, and abandons their disadvantages, so that it can provide a perfect balance between accuracy and computation time. Using the finite element method, the HSDE is solved for light flux density map on body surface. The accuracy and efficiency of the HSDE are validated with both regular geometries and digital mouse model based simulations. Corresponding results reveal that a comparable accuracy and much less computation time are achieved compared with the SPN model as well as a much better accuracy compared with the DE one.

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.

Stress, deformation and diffusion interactions in solids - A simulation study

NASA Astrophysics Data System (ADS)

Fischer, F. D.; Svoboda, J.

2015-05-01

Equations of diffusion treated in the frame of Manning's concept, are completed by equations for generation/annihilation of vacancies at non-ideal sources and sinks, by conservation laws, by equations for generation of an eigenstrain state and by a strain-stress analysis. The stress-deformation-diffusion interactions are demonstrated on the evolution of a diffusion couple consisting of two thin layers of different chemical composition forming a free-standing plate without external loading. The equations are solved for different material parameters represented by the values of diffusion coefficients of individual components and by the intensity of sources and sinks for vacancies. The results of simulations indicate that for low intensity of sources and sinks for vacancies a significant eigenstress state can develop and the interdiffusion process is slowed down. For high intensity of sources and sinks for vacancies a significant eigenstrain state can develop and the eigenstress state quickly relaxes. If the difference in the diffusion coefficients of individual components is high, then the intensity of sources and sinks for vacancies influences the interdiffusion process considerably. For such systems their description only by diffusion coefficients is insufficient and must be completed by a microstructure characterization.

Thermodynamics of viscoelastic rate-type fluids with stress diffusion

NASA Astrophysics Data System (ADS)

Málek, Josef; Průša, Vít; Skřivan, Tomáš; Süli, Endre

2018-02-01

We propose thermodynamically consistent models for viscoelastic fluids with a stress diffusion term. In particular, we derive variants of compressible/incompressible Maxwell/Oldroyd-B models with a stress diffusion term in the evolution equation for the extra stress tensor. It is shown that the stress diffusion term can be interpreted either as a consequence of a nonlocal energy storage mechanism or as a consequence of a nonlocal entropy production mechanism, while different interpretations of the stress diffusion mechanism lead to different evolution equations for the temperature. The benefits of the knowledge of the thermodynamical background of the derived models are documented in the study of nonlinear stability of equilibrium rest states. The derived models open up the possibility to study fully coupled thermomechanical problems involving viscoelastic rate-type fluids with stress diffusion.

Stratified Shear Flows In Pipe Geometries

NASA Astrophysics Data System (ADS)

Harabin, George; Camassa, Roberto; McLaughlin, Richard; UNC Joint Fluids Lab Team Team

2015-11-01

Exact and series solutions to the full Navier-Stokes equations coupled to the advection diffusion equation are investigated in tilted three-dimensional pipe geometries. Analytic techniques for studying the three-dimensional problem provide a means for tackling interesting questions such as the optimal domain for mass transport, and provide new avenues for experimental investigation of diffusion driven flows. Both static and time dependent solutions will be discussed. NSF RTG DMS-0943851, NSF RTG ARC-1025523, NSF DMS-1009750.

Equation-of-motion coupled-cluster method for doubly ionized states with spin-orbit coupling.

PubMed

Wang, Zhifan; Hu, Shu; Wang, Fan; Guo, Jingwei

2015-04-14

In this work, we report implementation of the equation-of-motion coupled-cluster method for doubly ionized states (EOM-DIP-CC) with spin-orbit coupling (SOC) using a closed-shell reference. Double ionization potentials (DIPs) are calculated in the space spanned by 2h and 3h1p determinants with the EOM-DIP-CC approach at the CC singles and doubles level (CCSD). Time-reversal symmetry together with spatial symmetry is exploited to reduce computational effort. To circumvent the problem of unstable dianion references when diffuse basis functions are included, nuclear charges are scaled. Effect of this stabilization potential on DIPs is estimated based on results from calculations using a small basis set without diffuse basis functions. DIPs and excitation energies of some low-lying states for a series of open-shell atoms and molecules containing heavy elements with two unpaired electrons have been calculated with the EOM-DIP-CCSD approach. Results show that this approach is able to afford a reliable description on SOC splitting. Furthermore, the EOM-DIP-CCSD approach is shown to provide reasonable excitation energies for systems with a dianion reference when diffuse basis functions are not employed.

Equation-of-motion coupled-cluster method for doubly ionized states with spin-orbit coupling

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

Wang, Zhifan; Hu, Shu; Guo, Jingwei

2015-04-14

In this work, we report implementation of the equation-of-motion coupled-cluster method for doubly ionized states (EOM-DIP-CC) with spin-orbit coupling (SOC) using a closed-shell reference. Double ionization potentials (DIPs) are calculated in the space spanned by 2h and 3h1p determinants with the EOM-DIP-CC approach at the CC singles and doubles level (CCSD). Time-reversal symmetry together with spatial symmetry is exploited to reduce computational effort. To circumvent the problem of unstable dianion references when diffuse basis functions are included, nuclear charges are scaled. Effect of this stabilization potential on DIPs is estimated based on results from calculations using a small basis setmore » without diffuse basis functions. DIPs and excitation energies of some low-lying states for a series of open-shell atoms and molecules containing heavy elements with two unpaired electrons have been calculated with the EOM-DIP-CCSD approach. Results show that this approach is able to afford a reliable description on SOC splitting. Furthermore, the EOM-DIP-CCSD approach is shown to provide reasonable excitation energies for systems with a dianion reference when diffuse basis functions are not employed.« less

Convective Sedimentation of Colloidal Particles in a Bowl.

PubMed

Stiles; Kagan

1999-08-01

A physical model, which regards a colloidal dispersion as a single fluid continuum, is used to investigate cellular convection accompanying gravitational sedimentation in a hemispherical bowl with a thin cylindrical shaft along its vertical axis of symmetry. We have adapted the stream-function-vorticity form of the Navier-Stokes equations to describe momentum conservation in axially symmetric containers. These hydrodynamic equations have been coupled to the mass balance equation for binary hydrodynamic diffusion in the presence of a vertical gravitational field. Using finite-element software we have solved the equations governing coupled diffusive and hydrodynamic flow. A rapidly intensifying horizontal toroidal vortex develops around the axis of the bowl. This vortex is characterized by downward barycentric flow along the curved surface of the bowl and upward flow in the vicinity of its axis. We find that after a short period of time this large-scale cellular convection associated with the curved boundary of the bowl greatly enhances the rate of sedimentation. Copyright 1999 Academic Press.

Partitioned coupling of advection-diffusion-reaction systems and Brinkman flows

NASA Astrophysics Data System (ADS)

Lenarda, Pietro; Paggi, Marco; Ruiz Baier, Ricardo

2017-09-01

We present a partitioned algorithm aimed at extending the capabilities of existing solvers for the simulation of coupled advection-diffusion-reaction systems and incompressible, viscous flow. The space discretisation of the governing equations is based on mixed finite element methods defined on unstructured meshes, whereas the time integration hinges on an operator splitting strategy that exploits the differences in scales between the reaction, advection, and diffusion processes, considering the global system as a number of sequentially linked sets of partial differential, and algebraic equations. The flow solver presents the advantage that all unknowns in the system (here vorticity, velocity, and pressure) can be fully decoupled and thus turn the overall scheme very attractive from the computational perspective. The robustness of the proposed method is illustrated with a series of numerical tests in 2D and 3D, relevant in the modelling of bacterial bioconvection and Boussinesq systems.

A Corresponding Lie Algebra of a Reductive homogeneous Group and Its Applications

NASA Astrophysics Data System (ADS)

Zhang, Yu-Feng; Wu, Li-Xin; Rui, Wen-Juan

2015-05-01

With the help of a Lie algebra of a reductive homogeneous space G/K, where G is a Lie group and K is a resulting isotropy group, we introduce a Lax pair for which an expanding (2+1)-dimensional integrable hierarchy is obtained by applying the binormial-residue representation (BRR) method, whose Hamiltonian structure is derived from the trace identity for deducing (2+1)-dimensional integrable hierarchies, which was proposed by Tu, et al. We further consider some reductions of the expanding integrable hierarchy obtained in the paper. The first reduction is just right the (2+1)-dimensional AKNS hierarchy, the second-type reduction reveals an integrable coupling of the (2+1)-dimensional AKNS equation (also called the Davey-Stewartson hierarchy), a kind of (2+1)-dimensional Schrödinger equation, which was once reobtained by Tu, Feng and Zhang. It is interesting that a new (2+1)-dimensional integrable nonlinear coupled equation is generated from the reduction of the part of the (2+1)-dimensional integrable coupling, which is further reduced to the standard (2+1)-dimensional diffusion equation along with a parameter. In addition, the well-known (1+1)-dimensional AKNS hierarchy, the (1+1)-dimensional nonlinear Schrödinger equation are all special cases of the (2+1)-dimensional expanding integrable hierarchy. Finally, we discuss a few discrete difference equations of the diffusion equation whose stabilities are analyzed by making use of the von Neumann condition and the Fourier method. Some numerical solutions of a special stationary initial value problem of the (2+1)-dimensional diffusion equation are obtained and the resulting convergence and estimation formula are investigated. Supported by the Innovation Team of Jiangsu Province hosted by China University of Mining and Technology (2014), the National Natural Science Foundation of China under Grant No. 11371361, the Fundamental Research Funds for the Central Universities (2013XK03), and the Natural Science Foundation of Shandong Province under Grant No. ZR2013AL016

Algorithm refinement for stochastic partial differential equations: II. Correlated systems

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

Alexander, Francis J.; Garcia, Alejandro L.; Tartakovsky, Daniel M.

2005-08-10

We analyze a hybrid particle/continuum algorithm for a hydrodynamic system with long ranged correlations. Specifically, we consider the so-called train model for viscous transport in gases, which is based on a generalization of the random walk process for the diffusion of momentum. This discrete model is coupled with its continuous counterpart, given by a pair of stochastic partial differential equations. At the interface between the particle and continuum computations the coupling is by flux matching, giving exact mass and momentum conservation. This methodology is an extension of our stochastic Algorithm Refinement (AR) hybrid for simple diffusion [F. Alexander, A. Garcia,more » D. Tartakovsky, Algorithm refinement for stochastic partial differential equations: I. Linear diffusion, J. Comput. Phys. 182 (2002) 47-66]. Results from a variety of numerical experiments are presented for steady-state scenarios. In all cases the mean and variance of density and velocity are captured correctly by the stochastic hybrid algorithm. For a non-stochastic version (i.e., using only deterministic continuum fluxes) the long-range correlations of velocity fluctuations are qualitatively preserved but at reduced magnitude.« less

Dynamical spike solutions in a nonlocal model of pattern formation

NASA Astrophysics Data System (ADS)

Marciniak-Czochra, Anna; Härting, Steffen; Karch, Grzegorz; Suzuki, Kanako

2018-05-01

Coupling a reaction-diffusion equation with ordinary differential equa- tions (ODE) may lead to diffusion-driven instability (DDI) which, in contrast to the classical reaction-diffusion models, causes destabilization of both, constant solutions and Turing patterns. Using a shadow-type limit of a reaction-diffusion-ODE model, we show that in such cases the instability driven by nonlocal terms (a counterpart of DDI) may lead to formation of unbounded spike patterns.

Study of Solid-State Diffusion of Bi in Polycrystalline Sn Using Electron Probe Microanalysis

NASA Astrophysics Data System (ADS)

Delhaise, André M.; Perovic, Doug D.

2018-03-01

Current lead-free solders such as SAC305 exhibit degradation in microstructure, properties, and reliability. Current third-generation alloys containing bismuth (Bi) demonstrate preservation of strength after aging; this is accompanied by homogenization of the Bi precipitates in the tin (Sn) matrix, driven via solid-state diffusion. This study quantifies the diffusion of Bi in Sn. Diffusion couples were prepared by mating together polished samples of pure Sn and Bi. Couples were annealed at one of three temperatures, viz. 85°C for 7 days, 100°C for 2 days, or 125°C for 1 day. After cross-sectioning the couples to examine the diffusion microstructure and grain size, elemental analysis was performed using electron probe microanalysis. For this study, it was assumed that the diffusivity of Bi in Sn is concentration dependent, therefore inverse methods were used to solve Fick's non-steady-state diffusion equation. In addition, Darken analysis was used to extract the impurity diffusivity of Bi in Sn at each temperature, allowing estimation of the Arrhenius parameters D 0 and k A.

Transport of water and ions in partially water-saturated porous media. Part 1. Constitutive equations

NASA Astrophysics Data System (ADS)

Revil, A.

2017-05-01

I developed a model of cross-coupled flow in partially saturated porous media based on electrokinetic coupling including the effect of ion filtration (normal and reverse osmosis) and the multi-component nature of the pore water (wetting) phase. The model also handles diffusion and membrane polarization but is valid only for saturations above the irreducible water saturation. I start with the local Nernst-Planck and Stokes equations and I use a volume-averaging procedure to obtain the generalized Ohm, Fick, and Darcy equations with cross-coupling terms at the scale of a representative elementary volume of the porous rock. These coupling terms obey Onsager's reciprocity, which is a required condition, at the macroscale, to keep the total dissipation function of the system positive. Rather than writing the electrokinetic terms in terms of zeta potential (the double layer electrical potential on the slipping plane located in the pore water), I developed the model in terms of an effective charge density dragged by the flow of the pore water. This effective charge density is found to be strongly controlled by the permeability and the water saturation. I also developed an electrical conductivity equation including the effect of saturation on both bulk and surface conductivities, the surface conductivity being associated with electromigration in the electrical diffuse layer coating the grains. This surface conductivity depends on the CEC of the porous material.

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

NASA Astrophysics Data System (ADS)

Yan, David

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

Particle Transport through Scattering Regions with Clear Layers and Inclusions

NASA Astrophysics Data System (ADS)

Bal, Guillaume

2002-08-01

This paper introduces generalized diffusion models for the transport of particles in scattering media with nonscattering inclusions. Classical diffusion is known as a good approximation of transport only in scattering media. Based on asymptotic expansions and the coupling of transport and diffusion models, generalized diffusion equations with nonlocal interface conditions are proposed which offer a computationally cheap, yet accurate, alternative to solving the full phase-space transport equations. The paper shows which computational model should be used depending on the size and shape of the nonscattering inclusions in the simplified setting of two space dimensions. An important application is the treatment of clear layers in near-infrared (NIR) spectroscopy, an imaging technique based on the propagation of NIR photons in human tissues.

New Quantum Diffusion Monte Carlo Method for strong field time dependent problems

NASA Astrophysics Data System (ADS)

Kalinski, Matt

2017-04-01

We have recently formulated the Quantum Diffusion Quantum Monte Carlo (QDMC) method for the solution of the time-dependent Schrödinger equation when it is equivalent to the reaction-diffusion system coupled by the highly nonlinear potentials of the type of Shay. Here we formulate a new Time Dependent QDMC method free of the nonlinearities described by the constant stochastic process of the coupled diffusion with transmutation. As before two kinds of diffusing particles (color walkers) are considered but which can further also transmute one into the other. Each of the species undergoes the hypothetical Einstein random walk progression with transmutation. The progressed particles transmute into the particles of the other kind before contributing to or annihilating the other particles density. This fully emulates the Time Dependent Schrödinger equation for any number of quantum particles. The negative sign of the real and the imaginary parts of the wave function is handled by the ``spinor'' densities carrying the sign as the degree of freedom. We apply the method for the exact time-dependent observation of our discovered two-electron Langmuir configurations in the magnetic and circularly polarized fields.

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

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

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

2016-01-15

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

Temperature Variations in Lubricating Films Induced by Viscous Dissipation

NASA Astrophysics Data System (ADS)

Mozaffari, Farshad; Metcalfe, Ralph

2015-11-01

We have studied temperature distributions of lubricating films. The study has applications in tribology where temperature-reduced viscosity decreases load carrying capacity of bearings, or degrades elastomeric seals. The viscosity- temperature dependency is modeled according to ASTM D341-09. We have modeled the film temperature distribution by our finite element program. The program is made up of three modules: the first one solves the general form of Reynolds equation for the film pressure and velocity gradients. The other two solve the energy equation for the film and its solid boundary temperature distributions. The modules are numerically coupled and iteratively converged to the solutions. We have shown that the temperature distribution in the film is strongly coupled with the thermal response at the boundary. In addition, only thermal diffusion across film thickness is dominant. Moreover, thermal diffusion in the lateral directions, as well as all the convection terms, are negligible. The approximation reduces the energy equation to an ordinary differential equation, which significantly simplifies the modeling of temperature -viscosity effects in thin films. Supported by Kalsi Engineering, Inc.

Roles of Vacancy/Interstitial Diffusion and Segregation in the Microchemistry at Grain Boundaries of Irradiated Fe-Cr-Ni alloys

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

Yang, Ying; Field, Kevin G.; Allen, Todd R.

2016-02-23

A detailed analysis of the diffusion fluxes near and at grain boundaries of irradiated Fe–Cr–Ni alloys, induced by preferential atom-vacancy and atom-interstitial coupling, is presented. The diffusion flux equations were based on the Perks model formulated through the linear theory of the thermodynamics of irreversible processes. The preferential atom-vacancy coupling was described by the mobility model, whereas the preferential atom-interstitial coupling was described by the interstitial binding model. The composition dependence of the thermodynamic factor was modeled using the CALPHAD approach. The calculated fluxes up to 10 dpa suggested the dominant diffusion mechanism for chromium and iron is via vacancy,more » while that for nickel can swing from the vacancy to the interstitial dominant mechanism. The diffusion flux in the vicinity of a grain boundary was found to be greatly modified by the segregation induced by irradiation, leading to the oscillatory behavior of alloy compositions in this region.« less

Primal-mixed formulations for reaction-diffusion systems on deforming domains

NASA Astrophysics Data System (ADS)

Ruiz-Baier, Ricardo

2015-10-01

We propose a finite element formulation for a coupled elasticity-reaction-diffusion system written in a fully Lagrangian form and governing the spatio-temporal interaction of species inside an elastic, or hyper-elastic body. A primal weak formulation is the baseline model for the reaction-diffusion system written in the deformed domain, and a finite element method with piecewise linear approximations is employed for its spatial discretization. On the other hand, the strain is introduced as mixed variable in the equations of elastodynamics, which in turn acts as coupling field needed to update the diffusion tensor of the modified reaction-diffusion system written in a deformed domain. The discrete mechanical problem yields a mixed finite element scheme based on row-wise Raviart-Thomas elements for stresses, Brezzi-Douglas-Marini elements for displacements, and piecewise constant pressure approximations. The application of the present framework in the study of several coupled biological systems on deforming geometries in two and three spatial dimensions is discussed, and some illustrative examples are provided and extensively analyzed.

A coupling strategy for nonlocal and local diffusion models with mixed volume constraints and boundary conditions

DOE PAGES

D'Elia, Marta; Perego, Mauro; Bochev, Pavel B.; ...

2015-12-21

We develop and analyze an optimization-based method for the coupling of nonlocal and local diffusion problems with mixed volume constraints and boundary conditions. The approach formulates the coupling as a control problem where the states are the solutions of the nonlocal and local equations, the objective is to minimize their mismatch on the overlap of the nonlocal and local domains, and the controls are virtual volume constraints and boundary conditions. When some assumptions on the kernel functions hold, we prove that the resulting optimization problem is well-posed and discuss its implementation using Sandia’s agile software components toolkit. As a result,more » the latter provides the groundwork for the development of engineering analysis tools, while numerical results for nonlocal diffusion in three-dimensions illustrate key properties of the optimization-based coupling method.« less

A double medium model for diffusion in fluid-bearing rock

NASA Astrophysics Data System (ADS)

Wang, H. F.

1993-09-01

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

Double diffusivity model under stochastic forcing

NASA Astrophysics Data System (ADS)

Chattopadhyay, Amit K.; Aifantis, Elias C.

2017-05-01

The "double diffusivity" model was proposed in the late 1970s, and reworked in the early 1980s, as a continuum counterpart to existing discrete models of diffusion corresponding to high diffusivity paths, such as grain boundaries and dislocation lines. It was later rejuvenated in the 1990s to interpret experimental results on diffusion in polycrystalline and nanocrystalline specimens where grain boundaries and triple grain boundary junctions act as high diffusivity paths. Technically, the model pans out as a system of coupled Fick-type diffusion equations to represent "regular" and "high" diffusivity paths with "source terms" accounting for the mass exchange between the two paths. The model remit was extended by analogy to describe flow in porous media with double porosity, as well as to model heat conduction in media with two nonequilibrium local temperature baths, e.g., ion and electron baths. Uncoupling of the two partial differential equations leads to a higher-ordered diffusion equation, solutions of which could be obtained in terms of classical diffusion equation solutions. Similar equations could also be derived within an "internal length" gradient (ILG) mechanics formulation applied to diffusion problems, i.e., by introducing nonlocal effects, together with inertia and viscosity, in a mechanics based formulation of diffusion theory. While being remarkably successful in studies related to various aspects of transport in inhomogeneous media with deterministic microstructures and nanostructures, its implications in the presence of stochasticity have not yet been considered. This issue becomes particularly important in the case of diffusion in nanopolycrystals whose deterministic ILG-based theoretical calculations predict a relaxation time that is only about one-tenth of the actual experimentally verified time scale. This article provides the "missing link" in this estimation by adding a vital element in the ILG structure, that of stochasticity, that takes into account all boundary layer fluctuations. Our stochastic-ILG diffusion calculation confirms rapprochement between theory and experiment, thereby benchmarking a new generation of gradient-based continuum models that conform closer to real-life fluctuating environments.

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

The Transport Equation in Optically Thick Media: Discussion of IMC and its Diffusion Limit

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

Szoke, A.; Brooks, E. D.

2016-07-12

We discuss the limits of validity of the Implicit Monte Carlo (IMC) method for the transport of thermally emitted radiation. The weakened coupling between the radiation and material energy of the IMC method causes defects in handling problems with strong transients. We introduce an approach to asymptotic analysis for the transport equation that emphasizes the fact that the radiation and material temperatures are always different in time-dependent problems, and we use it to show that IMC does not produce the correct diffusion limit. As this is a defect of IMC in the continuous equations, no improvement to its discretization canmore » remedy it.« less

Unimodal dynamical systems: Comparison principles, spreading speeds and travelling waves

NASA Astrophysics Data System (ADS)

Yi, Taishan; Chen, Yuming; Wu, Jianhong

Reaction diffusion equations with delayed nonlinear reaction terms are used as prototypes to motivate an appropriate abstract formulation of dynamical systems with unimodal nonlinearity. For such non-monotone dynamical systems, we develop a general comparison principle and show how this general comparison principle, coupled with some existing results for monotone dynamical systems, can be used to establish results on the asymptotic speeds of spread and travelling waves. We illustrate our main results by an integral equation which includes a nonlocal delayed reaction diffusion equation and a nonlocal delayed lattice differential system in an unbounded domain, with the non-monotone nonlinearities including the Ricker birth function and the Mackey-Glass hematopoiesis feedback.

Diffuse-Interface Capturing Methods for Compressible Two-Phase Flows

NASA Astrophysics Data System (ADS)

Saurel, Richard; Pantano, Carlos

2018-01-01

Simulation of compressible flows became a routine activity with the appearance of shock-/contact-capturing methods. These methods can determine all waves, particularly discontinuous ones. However, additional difficulties may appear in two-phase and multimaterial flows due to the abrupt variation of thermodynamic properties across the interfacial region, with discontinuous thermodynamical representations at the interfaces. To overcome this difficulty, researchers have developed augmented systems of governing equations to extend the capturing strategy. These extended systems, reviewed here, are termed diffuse-interface models, because they are designed to compute flow variables correctly in numerically diffused zones surrounding interfaces. In particular, they facilitate coupling the dynamics on both sides of the (diffuse) interfaces and tend to the proper pure fluid-governing equations far from the interfaces. This strategy has become efficient for contact interfaces separating fluids that are governed by different equations of state, in the presence or absence of capillary effects, and with phase change. More sophisticated materials than fluids (e.g., elastic-plastic materials) have been considered as well.

A generalized spin diffusion equation with four electrochemical potentials for channels with spin-orbit coupling

NASA Astrophysics Data System (ADS)

Sayed, Shehrin; Hong, Seokmin; Datta, Supriyo

We will present a general semiclassical theory for an arbitrary channel with spin-orbit coupling (SOC), that uses four electrochemical potential (U + , D + , U - , and D -) depending on the sign of z-component of the spin (up (U) , down (D)) and the sign of the x-component of the group velocity (+ , -) . This can be considered as an extension of the standard spin diffusion equation that uses two electrochemical potentials for up and down spin states, allowing us to take into account the unique coupling between charge and spin degrees of freedom in channels with SOC. We will describe applications of this model to answer a number of interesting questions in this field such as: (1) whether topological insulators can switch magnets, (2) how the charge to spin conversion is influenced by the channel resistivity, and (3) how device structures can be designed to enhance spin injection. This work was supported by FAME, one of six centers of STARnet, a Semiconductor Research Corporation program sponsored by MARCO and DARPA.

Smoothed particle hydrodynamics model for Landau-Lifshitz-Navier-Stokes and advection-diffusion equations

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

Kordilla, Jannes, E-mail: jkordil@gwdg.de; Pan, Wenxiao, E-mail: Wenxiao.Pan@pnnl.gov; Tartakovsky, Alexandre, E-mail: alexandre.tartakovsky@pnnl.gov

2014-12-14

We propose a novel smoothed particle hydrodynamics (SPH) discretization of the fully coupled Landau-Lifshitz-Navier-Stokes (LLNS) and stochastic advection-diffusion equations. The accuracy of the SPH solution of the LLNS equations is demonstrated by comparing the scaling of velocity variance and the self-diffusion coefficient with kinetic temperature and particle mass obtained from the SPH simulations and analytical solutions. The spatial covariance of pressure and velocity fluctuations is found to be in a good agreement with theoretical models. To validate the accuracy of the SPH method for coupled LLNS and advection-diffusion equations, we simulate the interface between two miscible fluids. We study formationmore » of the so-called “giant fluctuations” of the front between light and heavy fluids with and without gravity, where the light fluid lies on the top of the heavy fluid. We find that the power spectra of the simulated concentration field are in good agreement with the experiments and analytical solutions. In the absence of gravity, the power spectra decay as the power −4 of the wavenumber—except for small wavenumbers that diverge from this power law behavior due to the effect of finite domain size. Gravity suppresses the fluctuations, resulting in much weaker dependence of the power spectra on the wavenumber. Finally, the model is used to study the effect of thermal fluctuation on the Rayleigh-Taylor instability, an unstable dynamics of the front between a heavy fluid overlaying a light fluid. The front dynamics is shown to agree well with the analytical solutions.« less

Smoothed particle hydrodynamics model for Landau-Lifshitz-Navier-Stokes and advection-diffusion equations.

PubMed

Kordilla, Jannes; Pan, Wenxiao; Tartakovsky, Alexandre

2014-12-14

We propose a novel smoothed particle hydrodynamics (SPH) discretization of the fully coupled Landau-Lifshitz-Navier-Stokes (LLNS) and stochastic advection-diffusion equations. The accuracy of the SPH solution of the LLNS equations is demonstrated by comparing the scaling of velocity variance and the self-diffusion coefficient with kinetic temperature and particle mass obtained from the SPH simulations and analytical solutions. The spatial covariance of pressure and velocity fluctuations is found to be in a good agreement with theoretical models. To validate the accuracy of the SPH method for coupled LLNS and advection-diffusion equations, we simulate the interface between two miscible fluids. We study formation of the so-called "giant fluctuations" of the front between light and heavy fluids with and without gravity, where the light fluid lies on the top of the heavy fluid. We find that the power spectra of the simulated concentration field are in good agreement with the experiments and analytical solutions. In the absence of gravity, the power spectra decay as the power -4 of the wavenumber-except for small wavenumbers that diverge from this power law behavior due to the effect of finite domain size. Gravity suppresses the fluctuations, resulting in much weaker dependence of the power spectra on the wavenumber. Finally, the model is used to study the effect of thermal fluctuation on the Rayleigh-Taylor instability, an unstable dynamics of the front between a heavy fluid overlaying a light fluid. The front dynamics is shown to agree well with the analytical solutions.

Smoothed particle hydrodynamics model for Landau-Lifshitz Navier-Stokes and advection-diffusion equations

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

Kordilla, Jannes; Pan, Wenxiao; Tartakovsky, Alexandre M.

2014-12-14

We propose a novel Smoothed Particle Hydrodynamics (SPH) discretization of the fully-coupled Landau-Lifshitz-Navier-Stokes (LLNS) and advection-diffusion equations. The accuracy of the SPH solution of the LLNS equations is demonstrated by comparing the scaling of velocity variance and self-diffusion coefficient with kinetic temperature and particle mass obtained from the SPH simulations and analytical solutions. The spatial covariance of pressure and velocity fluctuations are found to be in a good agreement with theoretical models. To validate the accuracy of the SPH method for the coupled LLNS and advection-diffusion equations, we simulate the interface between two miscible fluids. We study the formation ofmore » the so-called giant fluctuations of the front between light and heavy fluids with and without gravity, where the light fluid lays on the top of the heavy fluid. We find that the power spectra of the simulated concentration field is in good agreement with the experiments and analytical solutions. In the absence of gravity the the power spectra decays as the power -4 of the wave number except for small wave numbers which diverge from this power law behavior due to the effect of finite domain size. Gravity suppresses the fluctuations resulting in the much weaker dependence of the power spectra on the wave number. Finally the model is used to study the effect of thermal fluctuation on the Rayleigh-Taylor instability, an unstable dynamics of the front between a heavy fluid overlying a light fluid. The front dynamics is shown to agree well with the analytical solutions.« less

Using hybrid implicit Monte Carlo diffusion to simulate gray radiation hydrodynamics

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

Cleveland, Mathew A., E-mail: cleveland7@llnl.gov; Gentile, Nick

This work describes how to couple a hybrid Implicit Monte Carlo Diffusion (HIMCD) method with a Lagrangian hydrodynamics code to evaluate the coupled radiation hydrodynamics equations. This HIMCD method dynamically applies Implicit Monte Carlo Diffusion (IMD) [1] to regions of a problem that are opaque and diffusive while applying standard Implicit Monte Carlo (IMC) [2] to regions where the diffusion approximation is invalid. We show that this method significantly improves the computational efficiency as compared to a standard IMC/Hydrodynamics solver, when optically thick diffusive material is present, while maintaining accuracy. Two test cases are used to demonstrate the accuracy andmore » performance of HIMCD as compared to IMC and IMD. The first is the Lowrie semi-analytic diffusive shock [3]. The second is a simple test case where the source radiation streams through optically thin material and heats a thick diffusive region of material causing it to rapidly expand. We found that HIMCD proves to be accurate, robust, and computationally efficient for these test problems.« less

Theory and Simulation of Self- and Mutual-Diffusion of Carrier Density and Temperature in Semiconductor Lasers

NASA Technical Reports Server (NTRS)

Li, Jian-Zhong; Cheung, Samson H.; Ning, C. Z.

2001-01-01

Carrier diffusion and thermal conduction play a fundamental role in the operation of high-power, broad-area semiconductor lasers. Restricted geometry, high pumping level and dynamic instability lead to inhomogeneous spatial distribution of plasma density, temperature, as well as light field, due to strong light-matter interaction. Thus, modeling and simulation of such optoelectronic devices rely on detailed descriptions of carrier dynamics and energy transport in the system. A self-consistent description of lasing and heating in large-aperture, inhomogeneous edge- or surface-emitting lasers (VCSELs) require coupled diffusion equations for carrier density and temperature. In this paper, we derive such equations from the Boltzmann transport equation for the carrier distributions. The derived self- and mutual-diffusion coefficients are in general nonlinear functions of carrier density and temperature including many-body interactions. We study the effects of many-body interactions on these coefficients, as well as the nonlinearity of these coefficients for large-area VCSELs. The effects of mutual diffusions on carrier and temperature distributions in gain-guided VCSELs will be also presented.

Transition and separation process in brine channels formation

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

Berti, Alessia, E-mail: alessia.berti@unibs.it; Bochicchio, Ivana, E-mail: ibochicchio@unisa.it; Fabrizio, Mauro, E-mail: mauro.fabrizio@unibo.it

2016-02-15

In this paper, we discuss the formation of brine channels in sea ice. The model includes a time-dependent Ginzburg-Landau equation for the solid-liquid phase change, a diffusion equation of the Cahn-Hilliard kind for the solute dynamics, and the heat equation for the temperature change. The macroscopic motion of the fluid is also considered, so the resulting differential system couples with the Navier-Stokes equation. The compatibility of this system with the thermodynamic laws and a maximum theorem is proved.

Is the kinetic equation for turbulent gas-particle flows ill posed?

PubMed

Reeks, M; Swailes, D C; Bragg, A D

2018-02-01

This paper is about the kinetic equation for gas-particle flows, in particular its well-posedness and realizability and its relationship to the generalized Langevin model (GLM) probability density function (PDF) equation. Previous analyses, e.g. [J.-P. Minier and C. Profeta, Phys. Rev. E 92, 053020 (2015)PLEEE81539-375510.1103/PhysRevE.92.053020], have concluded that this kinetic equation is ill posed, that in particular it has the properties of a backward heat equation, and as a consequence, its solution will in the course of time exhibit finite-time singularities. We show that this conclusion is fundamentally flawed because it ignores the coupling between the phase space variables in the kinetic equation and the time and particle inertia dependence of the phase space diffusion tensor. This contributes an extra positive diffusion that always outweighs the negative diffusion associated with the dispersion along one of the principal axes of the phase space diffusion tensor. This is confirmed by a numerical evaluation of analytic solutions of these positive and negative contributions to the particle diffusion coefficient along this principal axis. We also examine other erroneous claims and assumptions made in previous studies that demonstrate the apparent superiority of the GLM PDF approach over the kinetic approach. In so doing, we have drawn attention to the limitations of the GLM approach, which these studies have ignored or not properly considered, to give a more balanced appraisal of the benefits of both PDF approaches.

Drift-wave turbulence and zonal flow generation.

PubMed

Balescu, R

2003-10-01

Drift-wave turbulence in a plasma is analyzed on the basis of the wave Liouville equation, describing the evolution of the distribution function of wave packets (quasiparticles) characterized by position x and wave vector k. A closed kinetic equation is derived for the ensemble-averaged part of this function by the methods of nonequilibrium statistical mechanics. It has the form of a non-Markovian advection-diffusion equation describing coupled diffusion processes in x and k spaces. General forms of the diffusion coefficients are obtained in terms of Lagrangian velocity correlations. The latter are calculated in the decorrelation trajectory approximation, a method recently developed for an accurate measure of the important trapping phenomena of particles in the rugged electrostatic potential. The analysis of individual decorrelation trajectories provides an illustration of the fragmentation of drift-wave structures in the radial direction and the generation of long-wavelength structures in the poloidal direction that are identified as zonal flows.

Modelling of soot formation in laminar diffusion flames using a comprehensive CFD-PBE model with detailed gas-phase chemistry

NASA Astrophysics Data System (ADS)

Akridis, Petros; Rigopoulos, Stelios

2017-01-01

A discretised population balance equation (PBE) is coupled with an in-house computational fluid dynamics (CFD) code in order to model soot formation in laminar diffusion flames. The unsteady Navier-Stokes, species and enthalpy transport equations and the spatially-distributed discretised PBE for the soot particles are solved in a coupled manner, together with comprehensive gas-phase chemistry and an optically thin radiation model, thus yielding the complete particle size distribution of the soot particles. Nucleation, surface growth and oxidation are incorporated into the PBE using an acetylene-based soot model. The potential of the proposed methodology is investigated by comparing with experimental results from the Santoro jet burner [Santoro, Semerjian and Dobbins, Soot particle measurements in diffusion flames, Combustion and Flame, Vol. 51 (1983), pp. 203-218; Santoro, Yeh, Horvath and Semerjian, The transport and growth of soot particles in laminar diffusion flames, Combustion Science and Technology, Vol. 53 (1987), pp. 89-115] for three laminar axisymmetric non-premixed ethylene flames: a non-smoking, an incipient smoking and a smoking flame. Overall, good agreement is observed between the numerical and the experimental results.

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

PubMed

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

2001-06-01

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

Effect of interface reaction and diffusion on stress-oxidation coupling at high temperature

NASA Astrophysics Data System (ADS)

Yue, Mengkun; Dong, Xuelin; Fang, Xufei; Feng, Xue

2018-04-01

High-temperature structural materials undergo oxidation during the service, and stress would generate in the oxide film. Understanding the coupling effect between stress and oxidation contributes to the understanding of material degradation and failure during the oxidation process. Here, we propose a model to investigative the coupling effect of stress and oxidation at high temperature by considering the three-stage oxidation process, where both the interface reaction and the diffusion process are present. The governing equations including the oxidation kinetics and stress equilibrium for isothermal oxidation under stress-oxidation coupling effect have been derived. The theory is validated by comparing with the experimental results of SiO2 grown on Si substrate. Results show that the coupling of stress and oxidation influences the growth of the oxide film by affecting all three stages of the oxidation process.

Fluctuation-enhanced electric conductivity in electrolyte solutions.

PubMed

Péraud, Jean-Philippe; Nonaka, Andrew J; Bell, John B; Donev, Aleksandar; Garcia, Alejandro L

2017-10-10

We analyze the effects of an externally applied electric field on thermal fluctuations for a binary electrolyte fluid. We show that the fluctuating Poisson-Nernst-Planck (PNP) equations for charged multispecies diffusion coupled with the fluctuating fluid momentum equation result in enhanced charge transport via a mechanism distinct from the well-known enhancement of mass transport that accompanies giant fluctuations. Although the mass and charge transport occurs by advection by thermal velocity fluctuations, it can macroscopically be represented as electrodiffusion with renormalized electric conductivity and a nonzero cation-anion diffusion coefficient. Specifically, we predict a nonzero cation-anion Maxwell-Stefan coefficient proportional to the square root of the salt concentration, a prediction that agrees quantitatively with experimental measurements. The renormalized or effective macroscopic equations are different from the starting PNP equations, which contain no cross-diffusion terms, even for rather dilute binary electrolytes. At the same time, for infinitely dilute solutions the renormalized electric conductivity and renormalized diffusion coefficients are consistent and the classical PNP equations with renormalized coefficients are recovered, demonstrating the self-consistency of the fluctuating hydrodynamics equations. Our calculations show that the fluctuating hydrodynamics approach recovers the electrophoretic and relaxation corrections obtained by Debye-Huckel-Onsager theory, while elucidating the physical origins of these corrections and generalizing straightforwardly to more complex multispecies electrolytes. Finally, we show that strong applied electric fields result in anisotropically enhanced "giant" velocity fluctuations and reduced fluctuations of salt concentration.

Fluctuation-enhanced electric conductivity in electrolyte solutions

PubMed Central

Péraud, Jean-Philippe; Nonaka, Andrew J.; Bell, John B.; Donev, Aleksandar; Garcia, Alejandro L.

2017-01-01

We analyze the effects of an externally applied electric field on thermal fluctuations for a binary electrolyte fluid. We show that the fluctuating Poisson–Nernst–Planck (PNP) equations for charged multispecies diffusion coupled with the fluctuating fluid momentum equation result in enhanced charge transport via a mechanism distinct from the well-known enhancement of mass transport that accompanies giant fluctuations. Although the mass and charge transport occurs by advection by thermal velocity fluctuations, it can macroscopically be represented as electrodiffusion with renormalized electric conductivity and a nonzero cation–anion diffusion coefficient. Specifically, we predict a nonzero cation–anion Maxwell–Stefan coefficient proportional to the square root of the salt concentration, a prediction that agrees quantitatively with experimental measurements. The renormalized or effective macroscopic equations are different from the starting PNP equations, which contain no cross-diffusion terms, even for rather dilute binary electrolytes. At the same time, for infinitely dilute solutions the renormalized electric conductivity and renormalized diffusion coefficients are consistent and the classical PNP equations with renormalized coefficients are recovered, demonstrating the self-consistency of the fluctuating hydrodynamics equations. Our calculations show that the fluctuating hydrodynamics approach recovers the electrophoretic and relaxation corrections obtained by Debye–Huckel–Onsager theory, while elucidating the physical origins of these corrections and generalizing straightforwardly to more complex multispecies electrolytes. Finally, we show that strong applied electric fields result in anisotropically enhanced “giant” velocity fluctuations and reduced fluctuations of salt concentration. PMID:28973890

Heat and Mass Transfer in an L Shaped Porous Medium

NASA Astrophysics Data System (ADS)

Salman Ahmed, N. J.; Azeem; Yunus Khan, T. M.

2017-08-01

This article is an extension to the heat transfer in L-shaped porous medium by including the mass diffusion. The heat and mass transfer in the porous domain is represented by three coupled partial differential equations representing the fluid movement, energy transport and mass transport. The equations are converted into algebraic form of equations by the application of finite element method that can be conveniently solved by matrix method. An iterative approach is adopted to solve the coupled equations by setting suitable convergence criterion. The results are discussed in terms of heat transfer characteristics influenced by physical parameters such as buoyancy ratio, Lewis number, Rayleigh number etc. It is found that these physical parameters have significant effect on heat and mass transfer behavior of L-shaped porous medium.

Pattern formation for NO+N H3 on Pt(100): Two-dimensional numerical results

NASA Astrophysics Data System (ADS)

Uecker, Hannes

2005-01-01

The Lombardo-Fink-Imbihl model of the NO+NH3 reaction on a Pt(100) surface consists of seven coupled ordinary differential equations (ODE) and shows stable relaxation oscillations with sharp transitions in the relevant temperature range. Here we study numerically the effect of coupling of these oscillators by surface diffusion in two dimensions. We find different types of patterns, in particular phase clusters and standing waves. In models of related surface reactions such clustered solutions are known to exist only under a global coupling through the gas phase. This global coupling is replaced here by relatively fast diffusion of two variables which are kinetically slaved in the ODE. We also compare our simulations with experimental results and discuss some shortcomings of the model.

Square Turing patterns in reaction-diffusion systems with coupled layers

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

Li, Jing; Wang, Hongli, E-mail: hlwang@pku.edu.cn, E-mail: qi@pku.edu.cn; Center for Quantitative Biology, Peking University, Beijing 100871

Square Turing patterns are usually unstable in reaction-diffusion systems and are rarely observed in corresponding experiments and simulations. We report here an example of spontaneous formation of square Turing patterns with the Lengyel-Epstein model of two coupled layers. The squares are found to be a result of the resonance between two supercritical Turing modes with an appropriate ratio. Besides, the spatiotemporal resonance of Turing modes resembles to the mode-locking phenomenon. Analysis of the general amplitude equations for square patterns reveals that the fixed point corresponding to square Turing patterns is stationary when the parameters adopt appropriate values.

Pattern formation in diffusive excitable systems under magnetic flow effects

NASA Astrophysics Data System (ADS)

Mvogo, Alain; Takembo, Clovis N.; Ekobena Fouda, H. P.; Kofané, Timoléon C.

2017-07-01

We study the spatiotemporal formation of patterns in a diffusive FitzHugh-Nagumo network where the effect of electromagnetic induction has been introduced in the standard mathematical model by using magnetic flux, and the modulation of magnetic flux on membrane potential is realized by using memristor coupling. We use the multi-scale expansion to show that the system equations can be reduced to a single differential-difference nonlinear equation. The linear stability analysis is performed and discussed with emphasis on the impact of magnetic flux. It is observed that the effect of memristor coupling importantly modifies the features of modulational instability. Our analytical results are supported by the numerical experiments, which reveal that the improved model can lead to nonlinear quasi-periodic spatiotemporal patterns with some features of synchronization. It is observed also the generation of pulses and rhythmics behaviors like breathing or swimming which are important in brain researches.

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.

Performance of a parallel algebraic multilevel preconditioner for stabilized finite element semiconductor device modeling

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

Lin, Paul T.; Shadid, John N.; Sala, Marzio

In this study results are presented for the large-scale parallel performance of an algebraic multilevel preconditioner for solution of the drift-diffusion model for semiconductor devices. The preconditioner is the key numerical procedure determining the robustness, efficiency and scalability of the fully-coupled Newton-Krylov based, nonlinear solution method that is employed for this system of equations. The coupled system is comprised of a source term dominated Poisson equation for the electric potential, and two convection-diffusion-reaction type equations for the electron and hole concentration. The governing PDEs are discretized in space by a stabilized finite element method. Solution of the discrete system ismore » obtained through a fully-implicit time integrator, a fully-coupled Newton-based nonlinear solver, and a restarted GMRES Krylov linear system solver. The algebraic multilevel preconditioner is based on an aggressive coarsening graph partitioning of the nonzero block structure of the Jacobian matrix. Representative performance results are presented for various choices of multigrid V-cycles and W-cycles and parameter variations for smoothers based on incomplete factorizations. Parallel scalability results are presented for solution of up to 10{sup 8} unknowns on 4096 processors of a Cray XT3/4 and an IBM POWER eServer system.« less

Direct Coupling Method for Time-Accurate Solution of Incompressible Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Soh, Woo Y.

1992-01-01

A noniterative finite difference numerical method is presented for the solution of the incompressible Navier-Stokes equations with second order accuracy in time and space. Explicit treatment of convection and diffusion terms and implicit treatment of the pressure gradient give a single pressure Poisson equation when the discretized momentum and continuity equations are combined. A pressure boundary condition is not needed on solid boundaries in the staggered mesh system. The solution of the pressure Poisson equation is obtained directly by Gaussian elimination. This method is tested on flow problems in a driven cavity and a curved duct.

Integrated Coupling of Surface and Subsurface Flow with HYDRUS-2D

NASA Astrophysics Data System (ADS)

Hartmann, Anne; Šimůnek, Jirka; Wöhling, Thomas; Schütze, Niels

2016-04-01

Describing interactions between surface and subsurface flow processes is important to adequately define water flow in natural systems. Since overland flow generation is highly influenced by rainfall and infiltration, both highly spatially heterogeneous processes, overland flow is unsteady and varies spatially. The prediction of overland flow needs to include an appropriate description of the interactions between the surface and subsurface flow. Coupling surface and subsurface water flow is a challenging task. Different approaches have been developed during the last few years, each having its own advantages and disadvantages. A new approach by Weill et al. (2009) to couple overland flow and subsurface flow based on a generalized Richards equation was implemented into the well-known subsurface flow model HYDRUS-2D (Šimůnek et al., 2011). This approach utilizes the one-dimensional diffusion wave equation to model overland flow. The diffusion wave model is integrated in HYDRUS-2D by replacing the terms of the Richards equation in a pre-defined runoff layer by terms defining the diffusion wave equation. Using this approach, pressure and flux continuity along the interface between both flow domains is provided. This direct coupling approach provides a strong coupling of both systems based on the definition of a single global system matrix to numerically solve the coupled flow problem. The advantage of the direct coupling approach, compared to the loosely coupled approach, is supposed to be a higher robustness, when many convergence problems can be avoided (Takizawa et al., 2014). The HYDRUS-2D implementation was verified using a) different test cases, including a direct comparison with the results of Weill et al. (2009), b) an analytical solution of the kinematic wave equation, and c) the results of a benchmark test of Maxwell et al. (2014), that included several known coupled surface subsurface flow models. Additionally, a sensitivity analysis evaluating the effects of various model parameters on simulated overland flow (while considering or neglecting the effects of subsurface flow) was carried out to verify the applicability of the model to different problems. The model produced reasonable results in describing the diffusion wave approximation and its interactions with subsurface flow processes. The model could handle coupled surface-subsurface processes for conditions involving runoff generated by infiltration excess, saturation excess, or run-on, as well as a combination of these runoff generating processes. Several standard features of the HYDRUS 2D model, such as root water uptake and evaporation from the soil surface, as well as evaporation from runoff layer, can still be considered by the new model. The code required relatively small time steps when overland flow was active, resulting in long simulation times, and sometimes produced poor mass balance. The model nevertheless showed potential to be a useful tool for addressing various issues related to irrigation research and to natural generation of overland flow at the hillslope scale. Maxwell, R., Putti, M., Meyerhoff, S., Delf, J., Ferguson, I., Ivanov, V., Kim, J., Kolditz, O., Kollet, S., Kumar, M., Lopez, S., Niu, J., Paniconi, C., Park, Y.-J., Phanikumar, M., Shen, C., Sudicky, E., and Sulis, M. (2014). Surface-subsurface model intercomparison: A first set of benchmark results to diagnose integrated hydrology and feedbacks. Water Resourc. Res., 50:1531-1549. Šimůnek, J., van Genuchten, M. T., and Šejna, M. (2011). The HYDRUS Software Package for Simulating Two- and Three-Dimensional Movement of Water, Heat, and Multiple Solutes in Variably-Saturated Media. Technical Manual, Version 2.0, PC Progress, Prague, Czech Republic. Takizawa, K., Bazilevs Y., Tezduyar, T. E., Long, C.C., Marsden, A. L. and Schjodt.K., Patient-Specific Cardiovascular Fluid Mechanics Analysis with the ST and ALE-VMS Method in Idelsohn, S. R. (2014). Numerical Simulations of Coupled Problems in Engineering. Springer. Weill, S., Mouche, E., and Patin, J. (2009). A generalized Richards equation for surface/subsurface flow modelling. Journal of Hydrology, 366:9-20.

Dynamics of one- and two-dimensional fronts in a bistable equation with time-delayed global feedback: Propagation failure and control mechanisms

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

Boubendir, Yassine; Mendez, Vicenc; Rotstein, Horacio G.

2010-09-15

We study the evolution of fronts in a bistable equation with time-delayed global feedback in the fast reaction and slow diffusion regime. This equation generalizes the Hodgkin-Grafstein and Allen-Cahn equations. We derive a nonlinear equation governing the motion of fronts, which includes a term with delay. In the one-dimensional case this equation is linear. We study the motion of one- and two-dimensional fronts, finding a much richer dynamics than for the previously studied cases (without time-delayed global feedback). We explain the mechanism by which localized fronts created by inhibitory global coupling loose stability in a Hopf bifurcation as the delaymore » time increases. We show that for certain delay times, the prevailing phase is different from that corresponding to the system in the absence of global coupling. Numerical simulations of the partial differential equation are in agreement with the analytical predictions.« less

The 3-D numerical study of airflow in the compressor/combustor prediffuser and dump diffuser of an industrial gas turbine

NASA Technical Reports Server (NTRS)

Agrawal, Ajay K.; Yang, Tah-Teh

1993-01-01

This paper describes the 3D computations of a flow field in the compressor/combustor diffusers of an industrial gas turbine. The geometry considered includes components such as the combustor support strut, the transition piece and the impingement sleeve with discrete cooling air holes on its surface. Because the geometry was complex and 3D, the airflow path was divided into two computational domains sharing an interface region. The body-fitted grid was generated independently in each of the two domains. The governing equations for incompressible Navier-Stokes equations were solved using the finite volume approach. The results show that the flow in the prediffuser is strongly coupled with the flow in the dump diffuser and vice versa. The computations also revealed that the flow in the dump diffuser is highly nonuniform.

Numerical simulation of double‐diffusive finger convection

USGS Publications Warehouse

Hughes, Joseph D.; Sanford, Ward E.; Vacher, H. Leonard

2005-01-01

A hybrid finite element, integrated finite difference numerical model is developed for the simulation of double‐diffusive and multicomponent flow in two and three dimensions. The model is based on a multidimensional, density‐dependent, saturated‐unsaturated transport model (SUTRA), which uses one governing equation for fluid flow and another for solute transport. The solute‐transport equation is applied sequentially to each simulated species. Density coupling of the flow and solute‐transport equations is accounted for and handled using a sequential implicit Picard iterative scheme. High‐resolution data from a double‐diffusive Hele‐Shaw experiment, initially in a density‐stable configuration, is used to verify the numerical model. The temporal and spatial evolution of simulated double‐diffusive convection is in good agreement with experimental results. Numerical results are very sensitive to discretization and correspond closest to experimental results when element sizes adequately define the spatial resolution of observed fingering. Numerical results also indicate that differences in the molecular diffusivity of sodium chloride and the dye used to visualize experimental sodium chloride concentrations are significant and cause inaccurate mapping of sodium chloride concentrations by the dye, especially at late times. As a result of reduced diffusion, simulated dye fingers are better defined than simulated sodium chloride fingers and exhibit more vertical mass transfer.

Posterior quantum dynamics for a continuous diffusion observation of a coherent channel

NASA Astrophysics Data System (ADS)

Dąbrowska, Anita; Staszewski, Przemysław

2012-11-01

We present the Belavkin filtering equation for the intense balanced heterodyne detection in a unitary model of an indirect observation. The measuring apparatus modelled by a Bose field is initially prepared in a coherent state and the observed process is a diffusion one. We prove that this filtering equation is relaxing: any initial square-integrable function tends asymptotically to a coherent state with an amplitude depending on the coupling constant and the initial state of the apparatus. The time-development of a squeezed coherent state is studied and compared with the previous results obtained for the measuring apparatus prepared initially in the vacuum state.

DREAM3D simulations of inner-belt dynamics

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

Cunningham, Gregory Scott

2015-05-26

A 1973 paper by Lyons and Thorne explains the two-belt structure for electrons in the inner magnetosphere as a balance between inward radial diffusion and loss to the atmosphere, where the loss to the atmosphere is enabled by pitch-angle scattering from Coulomb and wave-particle interactions. In the 1973 paper, equilibrium solutions to a decoupled set of 1D radial diffusion equations, one for each value of the first invariant of motion, μ, were computed to produce the equilibrium two-belt structure. Each 1D radial diffusion equation incorporated an L-and μ-dependent `lifetime' due to the Coulomb and wave-particle interactions. This decoupling of themore » problem is appropriate under the assumption that radial diffusion is slow in comparison to pitch-angle scattering. However, for some values of μ and L the lifetime associated with pitch-angle scattering is comparable to the timescale associated with radial diffusion, suggesting that the true equilibrium solutions might reflect `coupled modes' involving pitch-angle scattering and radial diffusion and thus requiring a 3D diffusion model. In the work we show here, we have computed the equilibrium solutions using our 3D diffusion model, DREAM3D, that allows for such coupling. We find that the 3D equilibrium solutions are quite similar to the solutions shown in the 1973 paper when we use the same physical models for radial diffusion and pitch-angle scattering from hiss. However, we show that the equilibrium solutions are quite sensitive to various aspects of the physics model employed in the 1973 paper that can be improved, suggesting that additional work needs to be done to understand the two-belt structure.« less

The weak coupling limit as a quantum functional central limit

NASA Astrophysics Data System (ADS)

Accardi, L.; Frigerio, A.; Lu, Y. G.

1990-08-01

We show that, in the weak coupling limit, the laser model process converges weakly in the sense of the matrix elements to a quantum diffusion whose equation is explicitly obtained. We prove convergence, in the same sense, of the Heisenberg evolution of an observable of the system to the solution of a quantum Langevin equation. As a corollary of this result, via the quantum Feynman-Kac technique, one can recover previous results on the quantum master equation for reduced evolutions of open systems. When applied to some particular model (e.g. the free Boson gas) our results allow to interpret the Lamb shift as an Ito correction term and to express the pumping rates in terms of quantities related to the original Hamiltonian model.

Analysis of opposed jet hydrogen-air counter flow diffusion flame

NASA Technical Reports Server (NTRS)

Ho, Y. H.; Isaac, K. M.

1989-01-01

A computational simulation of the opposed-jet diffusion flame is performed to study its structure and extinction limits. The present analysis concentrates on the nitrogen-diluted hydrogen-air diffusion flame, which provides the basic information for many vehicle designs such as the aerospace plane for which hydrogen is a candidate as the fuel. The computer program uses the time-marching technique to solve the energy and species equations coupled with the momentum equation solved by the collocation method. The procedure is implemented in two stages. In the first stage, a one-step forward overal chemical reaction is chosen with the gas phase chemical reaction rate determined by comparison with experimental data. In the second stage, a complete chemical reaction mechanism is introduced with detailed thermodynamic and transport property calculations. Comparison between experimental extinction data and theoretical predictions is discussed. The effects of thermal diffusion as well as Lewis number and Prandtl number variations on the diffusion flame are also presented.

Excitation of turbulence by density waves

NASA Technical Reports Server (NTRS)

Tichen, C. M.

1985-01-01

A nonlinear system describes the microdynamical state of turbulence that is excited by density waves. It consists of an equation of propagation and a master equation. A group-scaling generates the scaled equations of many interacting groups of distribution functions. The two leading groups govern the transport processes of evolution and eddy diffusivity. The remaining sub-groups represent the relaxation for the approach of diffusivity to equilibrium. In strong turbulence, the sub-groups disperse themselves and the ensemble acts like a medium that offers an effective damping to close the hierarchy. The kinetic equation of turbulence is derived. It calculates the eddy viscosity and identifies the effective damping of the assumed medium self-consistently. It formulates the coupling mechanism for the intensification of the turbulent energy at the expense of the wave energy, and the transfer mechanism for the cascade. The spectra of velocity and density fluctuations find the power law k sup-2 and k sup-4, respectively.

Fluctuation-enhanced electric conductivity in electrolyte solutions

DOE PAGES

Péraud, Jean-Philippe; Nonaka, Andrew J.; Bell, John B.; ...

2017-09-26

In this work, we analyze the effects of an externally applied electric field on thermal fluctuations for a binary electrolyte fluid. We show that the fluctuating Poisson–Nernst–Planck (PNP) equations for charged multispecies diffusion coupled with the fluctuating fluid momentum equation result in enhanced charge transport via a mechanism distinct from the well-known enhancement of mass transport that accompanies giant fluctuations. Although the mass and charge transport occurs by advection by thermal velocity fluctuations, it can macroscopically be represented as electrodiffusion with renormalized electric conductivity and a nonzero cation–anion diffusion coefficient. Specifically, we predict a nonzero cation–anion Maxwell– Stefan coefficient proportionalmore » to the square root of the salt concentration, a prediction that agrees quantitatively with experimental measurements. The renormalized or effective macroscopic equations are different from the starting PNP equations, which contain no cross-diffusion terms, even for rather dilute binary electrolytes. At the same time, for infinitely dilute solutions the renormalized electric conductivity and renormalized diffusion coefficients are consistent and the classical PNP equations with renormalized coefficients are recovered, demonstrating the self-consistency of the fluctuating hydrodynamics equations. Our calculations show that the fluctuating hydrodynamics approach recovers the electrophoretic and relaxation corrections obtained by Debye–Huckel–Onsager theory, while elucidating the physical origins of these corrections and generalizing straightforwardly to more complex multispecies electrolytes. Lastly, we show that strong applied electric fields result in anisotropically enhanced “giant” velocity fluctuations and reduced fluctuations of salt concentration.« less

Fluctuation-enhanced electric conductivity in electrolyte solutions

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

Péraud, Jean-Philippe; Nonaka, Andrew J.; Bell, John B.

In this work, we analyze the effects of an externally applied electric field on thermal fluctuations for a binary electrolyte fluid. We show that the fluctuating Poisson–Nernst–Planck (PNP) equations for charged multispecies diffusion coupled with the fluctuating fluid momentum equation result in enhanced charge transport via a mechanism distinct from the well-known enhancement of mass transport that accompanies giant fluctuations. Although the mass and charge transport occurs by advection by thermal velocity fluctuations, it can macroscopically be represented as electrodiffusion with renormalized electric conductivity and a nonzero cation–anion diffusion coefficient. Specifically, we predict a nonzero cation–anion Maxwell– Stefan coefficient proportionalmore » to the square root of the salt concentration, a prediction that agrees quantitatively with experimental measurements. The renormalized or effective macroscopic equations are different from the starting PNP equations, which contain no cross-diffusion terms, even for rather dilute binary electrolytes. At the same time, for infinitely dilute solutions the renormalized electric conductivity and renormalized diffusion coefficients are consistent and the classical PNP equations with renormalized coefficients are recovered, demonstrating the self-consistency of the fluctuating hydrodynamics equations. Our calculations show that the fluctuating hydrodynamics approach recovers the electrophoretic and relaxation corrections obtained by Debye–Huckel–Onsager theory, while elucidating the physical origins of these corrections and generalizing straightforwardly to more complex multispecies electrolytes. Lastly, we show that strong applied electric fields result in anisotropically enhanced “giant” velocity fluctuations and reduced fluctuations of salt concentration.« less

Development of a robust modeling tool for radiation-induced segregation in austenitic stainless steels

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

Yang, Ying; Field, Kevin G; Allen, Todd R.

2015-09-01

Irradiation-assisted stress corrosion cracking (IASCC) of austenitic stainless steels in Light Water Reactor (LWR) components has been linked to changes in grain boundary composition due to irradiation induced segregation (RIS). This work developed a robust RIS modeling tool to account for thermodynamics and kinetics of the atom and defect transportation under combined thermal and radiation conditions. The diffusion flux equations were based on the Perks model formulated through the linear theory of the thermodynamics of irreversible processes. Both cross and non-cross phenomenological diffusion coefficients in the flux equations were considered and correlated to tracer diffusion coefficients through Manning’s relation. Themore » preferential atomvacancy coupling was described by the mobility model, whereas the preferential atom-interstitial coupling was described by the interstitial binding model. The composition dependence of the thermodynamic factor was modeled using the CALPHAD approach. Detailed analysis on the diffusion fluxes near and at grain boundaries of irradiated austenitic stainless steels suggested the dominant diffusion mechanism for chromium and iron is via vacancy, while that for nickel can swing from the vacancy to the interstitial dominant mechanism. The diffusion flux in the vicinity of a grain boundary was found to be greatly influenced by the composition gradient formed from the transient state, leading to the oscillatory behavior of alloy compositions in this region. This work confirms that both vacancy and interstitial diffusion, and segregation itself, have important roles in determining the microchemistry of Fe, Cr, and Ni at irradiated grain boundaries in austenitic stainless steels.« less

Time-independent hybrid enrichment for finite element solution of transient conduction–radiation in diffusive grey media

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

Mohamed, M. Shadi, E-mail: m.s.mohamed@durham.ac.uk; Seaid, Mohammed; Trevelyan, Jon

2013-10-15

We investigate the effectiveness of the partition-of-unity finite element method for transient conduction–radiation problems in diffusive grey media. The governing equations consist of a semi-linear transient heat equation for the temperature field and a stationary diffusion approximation to the radiation in grey media. The coupled equations are integrated in time using a semi-implicit method in the finite element framework. We show that for the considered problems, a combination of hyperbolic and exponential enrichment functions based on an approximation of the boundary layer leads to improved accuracy compared to the conventional finite element method. It is illustrated that this approach canmore » be more efficient than using h adaptivity to increase the accuracy of the finite element method near the boundary walls. The performance of the proposed partition-of-unity method is analyzed on several test examples for transient conduction–radiation problems in two space dimensions.« less

Vertical distribution of vibrational energy of molecular nitrogen in a stable auroral red arc and its effect on ionospheric electron densities. Ph.D. Thesis - Catholic Univ. of Am.

NASA Technical Reports Server (NTRS)

Newton, G. P.

1973-01-01

Previous solutions of the problem of the distribution of vibrationally excited molecular nitrogen in the thermosphere have either assumed a Boltzmann distribution and considered diffusion as one of the loss processes or solved for the energy level populations and neglected diffusion. Both of the previous approaches are combined by solving the time dependent continuity equations, including the diffusion process, for the first six energy levels of molecular nitrogen for conditions in the thermosphere corresponding to a stable auroral red arc. The primary source of molecular nitrogen excitation was subexcitation, and inelastic collisions between thermal electrons and molecular nitrogen. The reaction rates for this process were calculated from published cross section calculations. The loss processes for vibrational energy were electron and atomic oxygen quenching and vibrational energy exchange. The coupled sets of nonlinear, partial differential equations were solved numerically by employing finite difference equations.

Thermal coupling effect on the vortex dynamics of superconducting thin films: time-dependent Ginzburg–Landau simulations

NASA Astrophysics Data System (ADS)

Jing, Ze; Yong, Huadong; Zhou, Youhe

2018-05-01

In this paper, vortex dynamics of superconducting thin films are numerically investigated by the generalized time-dependent Ginzburg–Landau (TDGL) theory. Interactions between vortex motion and the motion induced energy dissipation is considered by solving the coupled TDGL equation and the heat diffusion equation. It is found that thermal coupling has significant effects on the vortex dynamics of superconducting thin films. Branching in the vortex penetration path originates from the coupling between vortex motion and the motion induced energy dissipation. In addition, the environment temperature, the magnetic field ramp rate and the geometry of the superconducting film also greatly influence the vortex dynamic behaviors. Our results provide new insights into the dynamics of superconducting vortices, and give a mesoscopic understanding on the channeling and branching of vortex penetration paths during flux avalanches.

Viscosity and diffusivity in melts: from unary to multicomponent systems

NASA Astrophysics Data System (ADS)

Chen, Weimin; Zhang, Lijun; Du, Yong; Huang, Baiyun

2014-05-01

Viscosity and diffusivity, two important transport coefficients, are systematically investigated from unary melt to binary to multicomponent melts in the present work. By coupling with Kaptay's viscosity equation of pure liquid metals and effective radii of diffusion species, the Sutherland equation is modified by taking the size effect into account, and further derived into an Arrhenius formula for the convenient usage. Its reliability for predicting self-diffusivity and impurity diffusivity in unary liquids is then validated by comparing the calculated self-diffusivities and impurity diffusivities in liquid Al- and Fe-based alloys with the experimental and the assessed data. Moreover, the Kozlov model was chosen among various viscosity models as the most reliable one to reproduce the experimental viscosities in binary and multicomponent melts. Based on the reliable viscosities calculated from the Kozlov model, the modified Sutherland equation is utilized to predict the tracer diffusivities in binary and multicomponent melts, and validated in Al-Cu, Al-Ni and Al-Ce-Ni melts. Comprehensive comparisons between the calculated results and the literature data indicate that the experimental tracer diffusivities and the theoretical ones can be well reproduced by the present calculations. In addition, the vacancy-wind factor in binary liquid Al-Ni alloys with the increasing temperature is also discussed. What's more, the calculated inter-diffusivities in liquid Al-Cu, Al-Ni and Al-Ag-Cu alloys are also in excellent agreement with the measured and theoretical data. Comparisons between the simulated concentration profiles and the measured ones in Al-Cu, Al-Ce-Ni and Al-Ag-Cu melts are further used to validate the present calculation method.

Effective electrodiffusion equation for non-uniform nanochannels.

PubMed

Marini Bettolo Marconi, Umberto; Melchionna, Simone; Pagonabarraga, Ignacio

2013-06-28

We derive a one-dimensional formulation of the Planck-Nernst-Poisson equation to describe the dynamics of a symmetric binary electrolyte in channels whose section is nanometric and varies along the axial direction. The approach is in the spirit of the Fick-Jacobs diffusion equation and leads to a system of coupled equations for the partial densities which depends on the charge sitting at the walls in a non-trivial fashion. We consider two kinds of non-uniformities, those due to the spatial variation of charge distribution and those due to the shape variation of the pore and report one- and three-dimensional solutions of the electrokinetic equations.

EFFECTS OF TURBULENCE AND ELECTROHYDRODYAMICS ON THE PERFORMANCE OF ELECTROSTATIC PRECIPITATORS

EPA Science Inventory

Numerical simulations of the turbulent diffusion equation coupled with the electrohydrodynamics (EHD) are carried out for the plate-plate and wire-plate ESPs. The local particle concentration profiles and fractional collection efficiencies have been evaluated as a function of thr...

Coupled Protein Diffusion and Folding in the Cell

PubMed Central

Guo, Minghao; Gelman, Hannah; Gruebele, Martin

2014-01-01

When a protein unfolds in the cell, its diffusion coefficient is affected by its increased hydrodynamic radius and by interactions of exposed hydrophobic residues with the cytoplasmic matrix, including chaperones. We characterize protein diffusion by photobleaching whole cells at a single point, and imaging the concentration change of fluorescent-labeled protein throughout the cell as a function of time. As a folded reference protein we use green fluorescent protein. The resulting region-dependent anomalous diffusion is well characterized by 2-D or 3-D diffusion equations coupled to a clustering algorithm that accounts for position-dependent diffusion. Then we study diffusion of a destabilized mutant of the enzyme phosphoglycerate kinase (PGK) and of its stable control inside the cell. Unlike the green fluorescent protein control's diffusion coefficient, PGK's diffusion coefficient is a non-monotonic function of temperature, signaling ‘sticking’ of the protein in the cytosol as it begins to unfold. The temperature-dependent increase and subsequent decrease of the PGK diffusion coefficient in the cytosol is greater than a simple size-scaling model suggests. Chaperone binding of the unfolding protein inside the cell is one plausible candidate for even slower diffusion of PGK, and we test the plausibility of this hypothesis experimentally, although we do not rule out other candidates. PMID:25436502

Coupled protein diffusion and folding in the cell.

PubMed

Guo, Minghao; Gelman, Hannah; Gruebele, Martin

2014-01-01

When a protein unfolds in the cell, its diffusion coefficient is affected by its increased hydrodynamic radius and by interactions of exposed hydrophobic residues with the cytoplasmic matrix, including chaperones. We characterize protein diffusion by photobleaching whole cells at a single point, and imaging the concentration change of fluorescent-labeled protein throughout the cell as a function of time. As a folded reference protein we use green fluorescent protein. The resulting region-dependent anomalous diffusion is well characterized by 2-D or 3-D diffusion equations coupled to a clustering algorithm that accounts for position-dependent diffusion. Then we study diffusion of a destabilized mutant of the enzyme phosphoglycerate kinase (PGK) and of its stable control inside the cell. Unlike the green fluorescent protein control's diffusion coefficient, PGK's diffusion coefficient is a non-monotonic function of temperature, signaling 'sticking' of the protein in the cytosol as it begins to unfold. The temperature-dependent increase and subsequent decrease of the PGK diffusion coefficient in the cytosol is greater than a simple size-scaling model suggests. Chaperone binding of the unfolding protein inside the cell is one plausible candidate for even slower diffusion of PGK, and we test the plausibility of this hypothesis experimentally, although we do not rule out other candidates.

Global cluster synchronization in nonlinearly coupled community networks with heterogeneous coupling delays.

PubMed

Tseng, Jui-Pin

2017-02-01

This investigation establishes the global cluster synchronization of complex networks with a community structure based on an iterative approach. The units comprising the network are described by differential equations, and can be non-autonomous and involve time delays. In addition, units in the different communities can be governed by different equations. The coupling configuration of the network is rather general. The coupling terms can be non-diffusive, nonlinear, asymmetric, and with heterogeneous coupling delays. Based on this approach, both delay-dependent and delay-independent criteria for global cluster synchronization are derived. We implement the present approach for a nonlinearly coupled neural network with heterogeneous coupling delays. Two numerical examples are given to show that neural networks can behave in a variety of new collective ways under the synchronization criteria. These examples also demonstrate that neural networks remain synchronized in spite of coupling delays between neurons across different communities; however, they may lose synchrony if the coupling delays between the neurons within the same community are too large, such that the synchronization criteria are violated. Copyright © 2016 Elsevier Ltd. All rights reserved.

A novel coupled system of non-local integro-differential equations modelling Young's modulus evolution, nutrients' supply and consumption during bone fracture healing

NASA Astrophysics Data System (ADS)

Lu, Yanfei; Lekszycki, Tomasz

2016-10-01

During fracture healing, a series of complex coupled biological and mechanical phenomena occurs. They include: (i) growth and remodelling of bone, whose Young's modulus varies in space and time; (ii) nutrients' diffusion and consumption by living cells. In this paper, we newly propose to model these evolution phenomena. The considered features include: (i) a new constitutive equation for growth simulation involving the number of sensor cells; (ii) an improved equation for nutrient concentration accounting for the switch between Michaelis-Menten kinetics and linear consumption regime; (iii) a new constitutive equation for Young's modulus evolution accounting for its dependence on nutrient concentration and variable number of active cells. The effectiveness of the model and its predictive capability are qualitatively verified by numerical simulations (using COMSOL) describing the healing of bone in the presence of damaged tissue between fractured parts.

Hydrodynamics of bacterial colonies: A model

NASA Astrophysics Data System (ADS)

Lega, J.; Passot, T.

2003-03-01

We propose a hydrodynamic model for the evolution of bacterial colonies growing on soft agar plates. This model consists of reaction-diffusion equations for the concentrations of nutrients, water, and bacteria, coupled to a single hydrodynamic equation for the velocity field of the bacteria-water mixture. It captures the dynamics inside the colony as well as on its boundary and allows us to identify a mechanism for collective motion towards fresh nutrients, which, in its modeling aspects, is similar to classical chemotaxis. As shown in numerical simulations, our model reproduces both usual colony shapes and typical hydrodynamic motions, such as the whirls and jets recently observed in wet colonies of Bacillus subtilis. The approach presented here could be extended to different experimental situations and provides a general framework for the use of advection-reaction-diffusion equations in modeling bacterial colonies.

Variational Implicit Solvation with Solute Molecular Mechanics: From Diffuse-Interface to Sharp-Interface Models.

PubMed

Li, Bo; Zhao, Yanxiang

2013-01-01

Central in a variational implicit-solvent description of biomolecular solvation is an effective free-energy functional of the solute atomic positions and the solute-solvent interface (i.e., the dielectric boundary). The free-energy functional couples together the solute molecular mechanical interaction energy, the solute-solvent interfacial energy, the solute-solvent van der Waals interaction energy, and the electrostatic energy. In recent years, the sharp-interface version of the variational implicit-solvent model has been developed and used for numerical computations of molecular solvation. In this work, we propose a diffuse-interface version of the variational implicit-solvent model with solute molecular mechanics. We also analyze both the sharp-interface and diffuse-interface models. We prove the existence of free-energy minimizers and obtain their bounds. We also prove the convergence of the diffuse-interface model to the sharp-interface model in the sense of Γ-convergence. We further discuss properties of sharp-interface free-energy minimizers, the boundary conditions and the coupling of the Poisson-Boltzmann equation in the diffuse-interface model, and the convergence of forces from diffuse-interface to sharp-interface descriptions. Our analysis relies on the previous works on the problem of minimizing surface areas and on our observations on the coupling between solute molecular mechanical interactions with the continuum solvent. Our studies justify rigorously the self consistency of the proposed diffuse-interface variational models of implicit solvation.

Quantum cybernetics: a new perspective for Nelson's stochastic theory, nonlocality, and the Klein-Gordon equation

NASA Astrophysics Data System (ADS)

Grössing, Gerhard

2002-04-01

The Klein-Gordon equation is shown to be equivalent to coupled partial differential equations for a sub-quantum Brownian movement of a “particle”, which is both passively affected by, and actively affecting, a diffusion process of its generally nonlocal environment. This indicates circularly causal, or “cybernetic”, relationships between “particles” and their surroundings. Moreover, in the relativistic domain, the original stochastic theory of Nelson is shown to hold as a limiting case only, i.e., for a vanishing quantum potential.

Travelling fronts of the CO oxidation on Pd(111) with coverage-dependent diffusion

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

Cisternas, Jaime, E-mail: jecisternas@miuandes.cl; Karpitschka, Stefan; Wehner, Stefan

2014-10-28

In this work, we study a surface reaction on Pd(111) crystals under ultra-high-vacuum conditions that can be modeled by two coupled reaction-diffusion equations. In the bistable regime, the reaction exhibits travelling fronts that can be observed experimentally using photo electron emission microscopy. The spatial profile of the fronts reveals a coverage-dependent diffusivity for one of the species. We propose a method to solve the nonlinear eigenvalue problem and compute the direction and the speed of the fronts based on a geometrical construction in phase-space. This method successfully captures the dependence of the speed on control parameters and diffusivities.

Transport mechanisms of contaminants released from fine sediment in rivers

NASA Astrophysics Data System (ADS)

Cheng, Pengda; Zhu, Hongwei; Zhong, Baochang; Wang, Daozeng

2015-12-01

Contaminants released from sediment into rivers are one of the main problems to study in environmental hydrodynamics. For contaminants released into the overlying water under different hydrodynamic conditions, the mechanical mechanisms involved can be roughly divided into convective diffusion, molecular diffusion, and adsorption/desorption. Because of the obvious environmental influence of fine sediment (D_{90}= 0.06 mm), non-cohesive fine sediment, and cohesive fine sediment are researched in this paper, and phosphorus is chosen for a typical adsorption of a contaminant. Through theoretical analysis of the contaminant release process, according to different hydraulic conditions, the contaminant release coupling mathematical model can be established by the N-S equation, the Darcy equation, the solute transport equation, and the adsorption/desorption equation. Then, the experiments are completed in an open water flume. The simulation results and experimental results show that convective diffusion dominates the contaminant release both in non-cohesive and cohesive fine sediment after their suspension, and that they contribute more than 90 % of the total release. Molecular diffusion and desorption have more of a contribution for contaminant release from unsuspended sediment. In unsuspension sediment, convective diffusion is about 10-50 times larger than molecular diffusion during the initial stages under high velocity; it is close to molecular diffusion in the later stages. Convective diffusion is about 6 times larger than molecular diffusion during the initial stages under low velocity, it is about a quarter of molecular diffusion in later stages, and has a similar level with desorption/adsorption. In unsuspended sediment, a seepage boundary layer exists below the water-sediment interface, and various release mechanisms in that layer mostly dominate the contaminant release process. In non-cohesive fine sediment, the depth of that layer increases linearly with shear stress. In cohesive fine sediment, the range seepage boundary is different from that in non-cohesive sediment, and that phenomenon is more obvious under a lower shear stress.

Traveling waves in a coupled reaction-diffusion and difference model of hematopoiesis

NASA Astrophysics Data System (ADS)

Adimy, M.; Chekroun, A.; Kazmierczak, B.

2017-04-01

The formation and development of blood cells is a very complex process, called hematopoiesis. This process involves a small population of cells called hematopoietic stem cells (HSCs). The HSCs are undifferentiated cells, located in the bone marrow before they become mature blood cells and enter the blood stream. They have a unique ability to produce either similar cells (self-renewal), or cells engaged in one of different lineages of blood cells: red blood cells, white cells and platelets (differentiation). The HSCs can be either in a proliferating or in a quiescent phase. In this paper, we distinguish between dividing cells that enter directly to the quiescent phase and dividing cells that return to the proliferating phase to divide again. We propose a mathematical model describing the dynamics of HSC population, taking into account their spatial distribution. The resulting model is a coupled reaction-diffusion equation and difference equation with delay. We study the existence of monotone traveling wave fronts and the asymptotic speed of spread.

A hybrid algorithm for coupling partial differential equation and compartment-based dynamics.

PubMed

Harrison, Jonathan U; Yates, Christian A

2016-09-01

Stochastic simulation methods can be applied successfully to model exact spatio-temporally resolved reaction-diffusion systems. However, in many cases, these methods can quickly become extremely computationally intensive with increasing particle numbers. An alternative description of many of these systems can be derived in the diffusive limit as a deterministic, continuum system of partial differential equations (PDEs). Although the numerical solution of such PDEs is, in general, much more efficient than the full stochastic simulation, the deterministic continuum description is generally not valid when copy numbers are low and stochastic effects dominate. Therefore, to take advantage of the benefits of both of these types of models, each of which may be appropriate in different parts of a spatial domain, we have developed an algorithm that can be used to couple these two types of model together. This hybrid coupling algorithm uses an overlap region between the two modelling regimes. By coupling fluxes at one end of the interface and using a concentration-matching condition at the other end, we ensure that mass is appropriately transferred between PDE- and compartment-based regimes. Our methodology gives notable reductions in simulation time in comparison with using a fully stochastic model, while maintaining the important stochastic features of the system and providing detail in appropriate areas of the domain. We test our hybrid methodology robustly by applying it to several biologically motivated problems including diffusion and morphogen gradient formation. Our analysis shows that the resulting error is small, unbiased and does not grow over time. © 2016 The Authors.

A hybrid algorithm for coupling partial differential equation and compartment-based dynamics

PubMed Central

Yates, Christian A.

2016-01-01

Stochastic simulation methods can be applied successfully to model exact spatio-temporally resolved reaction–diffusion systems. However, in many cases, these methods can quickly become extremely computationally intensive with increasing particle numbers. An alternative description of many of these systems can be derived in the diffusive limit as a deterministic, continuum system of partial differential equations (PDEs). Although the numerical solution of such PDEs is, in general, much more efficient than the full stochastic simulation, the deterministic continuum description is generally not valid when copy numbers are low and stochastic effects dominate. Therefore, to take advantage of the benefits of both of these types of models, each of which may be appropriate in different parts of a spatial domain, we have developed an algorithm that can be used to couple these two types of model together. This hybrid coupling algorithm uses an overlap region between the two modelling regimes. By coupling fluxes at one end of the interface and using a concentration-matching condition at the other end, we ensure that mass is appropriately transferred between PDE- and compartment-based regimes. Our methodology gives notable reductions in simulation time in comparison with using a fully stochastic model, while maintaining the important stochastic features of the system and providing detail in appropriate areas of the domain. We test our hybrid methodology robustly by applying it to several biologically motivated problems including diffusion and morphogen gradient formation. Our analysis shows that the resulting error is small, unbiased and does not grow over time. PMID:27628171

Output Feedback-Based Boundary Control of Uncertain Coupled Semilinear Parabolic PDE Using Neurodynamic Programming.

PubMed

Talaei, Behzad; Jagannathan, Sarangapani; Singler, John

2018-04-01

In this paper, neurodynamic programming-based output feedback boundary control of distributed parameter systems governed by uncertain coupled semilinear parabolic partial differential equations (PDEs) under Neumann or Dirichlet boundary control conditions is introduced. First, Hamilton-Jacobi-Bellman (HJB) equation is formulated in the original PDE domain and the optimal control policy is derived using the value functional as the solution of the HJB equation. Subsequently, a novel observer is developed to estimate the system states given the uncertain nonlinearity in PDE dynamics and measured outputs. Consequently, the suboptimal boundary control policy is obtained by forward-in-time estimation of the value functional using a neural network (NN)-based online approximator and estimated state vector obtained from the NN observer. Novel adaptive tuning laws in continuous time are proposed for learning the value functional online to satisfy the HJB equation along system trajectories while ensuring the closed-loop stability. Local uniformly ultimate boundedness of the closed-loop system is verified by using Lyapunov theory. The performance of the proposed controller is verified via simulation on an unstable coupled diffusion reaction process.

Effective equations governing an active poroelastic medium

PubMed Central

2017-01-01

In this work, we consider the spatial homogenization of a coupled transport and fluid–structure interaction model, to the end of deriving a system of effective equations describing the flow, elastic deformation and transport in an active poroelastic medium. The ‘active’ nature of the material results from a morphoelastic response to a chemical stimulant, in which the growth time scale is strongly separated from other elastic time scales. The resulting effective model is broadly relevant to the study of biological tissue growth, geophysical flows (e.g. swelling in coals and clays) and a wide range of industrial applications (e.g. absorbant hygiene products). The key contribution of this work is the derivation of a system of homogenized partial differential equations describing macroscale growth, coupled to transport of solute, that explicitly incorporates details of the structure and dynamics of the microscopic system, and, moreover, admits finite growth and deformation at the pore scale. The resulting macroscale model comprises a Biot-type system, augmented with additional terms pertaining to growth, coupled to an advection–reaction–diffusion equation. The resultant system of effective equations is then compared with other recent models under a selection of appropriate simplifying asymptotic limits. PMID:28293138

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.

A Model for the Oxidation of C/SiC Composite Structures

NASA Technical Reports Server (NTRS)

Sullivan, Roy M.

2003-01-01

A mathematical theory and an accompanying numerical scheme have been developed for predicting the oxidation behavior of C/SiC composite structures. The theory is derived from the mechanics of the flow of ideal gases through a porous solid. Within the mathematical formulation, two diffusion mechanisms are possible: (1) the relative diffusion of one species with respect to the mixture, which is concentration gradient driven and (2) the diffusion associated with the average velocity of the gas mixture, which is total gas pressure gradient driven. The result of the theoretical formulation is a set of two coupled nonlinear differential equations written in terms of the oxidant and oxide partial pressures. The differential equations must be solved simultaneously to obtain the partial vapor pressures of the oxidant and oxides as a function of space and time. The local rate of carbon oxidation is determined as a function of space and time using the map of the local oxidant partial vapor pressure along with the Arrhenius rate equation. The nonlinear differential equations are cast into matrix equations by applying the Bubnov-Galerkin weighted residual method, allowing for the solution of the differential equations numerically. The end result is a numerical scheme capable of determining the variation of the local carbon oxidation rates as a function of space and time for any arbitrary C/SiC composite structures.

Non-canonical distribution and non-equilibrium transport beyond weak system-bath coupling regime: A polaron transformation approach

NASA Astrophysics Data System (ADS)

Xu, Dazhi; Cao, Jianshu

2016-08-01

The concept of polaron, emerged from condense matter physics, describes the dynamical interaction of moving particle with its surrounding bosonic modes. This concept has been developed into a useful method to treat open quantum systems with a complete range of system-bath coupling strength. Especially, the polaron transformation approach shows its validity in the intermediate coupling regime, in which the Redfield equation or Fermi's golden rule will fail. In the polaron frame, the equilibrium distribution carried out by perturbative expansion presents a deviation from the canonical distribution, which is beyond the usual weak coupling assumption in thermodynamics. A polaron transformed Redfield equation (PTRE) not only reproduces the dissipative quantum dynamics but also provides an accurate and efficient way to calculate the non-equilibrium steady states. Applications of the PTRE approach to problems such as exciton diffusion, heat transport and light-harvesting energy transfer are presented.

A fully implicit finite element method for bidomain models of cardiac electromechanics

PubMed Central

Dal, Hüsnü; Göktepe, Serdar; Kaliske, Michael; Kuhl, Ellen

2012-01-01

We propose a novel, monolithic, and unconditionally stable finite element algorithm for the bidomain-based approach to cardiac electromechanics. We introduce the transmembrane potential, the extracellular potential, and the displacement field as independent variables, and extend the common two-field bidomain formulation of electrophysiology to a three-field formulation of electromechanics. The intrinsic coupling arises from both excitation-induced contraction of cardiac cells and the deformation-induced generation of intra-cellular currents. The coupled reaction-diffusion equations of the electrical problem and the momentum balance of the mechanical problem are recast into their weak forms through a conventional isoparametric Galerkin approach. As a novel aspect, we propose a monolithic approach to solve the governing equations of excitation-contraction coupling in a fully coupled, implicit sense. We demonstrate the consistent linearization of the resulting set of non-linear residual equations. To assess the algorithmic performance, we illustrate characteristic features by means of representative three-dimensional initial-boundary value problems. The proposed algorithm may open new avenues to patient specific therapy design by circumventing stability and convergence issues inherent to conventional staggered solution schemes. PMID:23175588

Asymptotic properties of blow-up solutions in reaction-diffusion equations with nonlocal boundary flux

NASA Astrophysics Data System (ADS)

Liu, Bingchen; Dong, Mengzhen; Li, Fengjie

2018-04-01

This paper deals with a reaction-diffusion problem with coupled nonlinear inner sources and nonlocal boundary flux. Firstly, we propose the critical exponents on nonsimultaneous blow-up under some conditions on the initial data. Secondly, we combine the scaling technique and the Green's identity method to determine four kinds of simultaneous blow-up rates. Thirdly, the lower and the upper bounds of blow-up time are derived by using Sobolev-type differential inequalities.

Fem Formulation for Heat and Mass Transfer in Porous Medium

NASA Astrophysics Data System (ADS)

Azeem; Soudagar, Manzoor Elahi M.; Salman Ahmed, N. J.; Anjum Badruddin, Irfan

2017-08-01

Heat and mass transfer in porous medium can be modelled using three partial differential equations namely, momentum equation, energy equation and mass diffusion. These three equations are coupled to each other by some common terms that turn the whole phenomenon into a complex problem with inter-dependable variables. The current article describes the finite element formulation of heat and mass transfer in porous medium with respect to Cartesian coordinates. The problem under study is formulated into algebraic form of equations by using Galerkin's method with the help of two-node linear triangular element having three nodes. The domain is meshed with smaller sized elements near the wall region and bigger size away from walls.

Introduction to Physical Intelligence

NASA Technical Reports Server (NTRS)

Zak, Michail

2011-01-01

A slight deviation from Newtonian dynamics can lead to new effects associated with the concept of physical intelligence. Non-Newtonian effects such as deviation from classical thermodynamic as well as quantum-like properties have been analyzed. A self-supervised (intelligent) particle that can escape from Brownian motion autonomously is introduced. Such a capability is due to a coupling of the particle governing equation with its own Liouville equation via an appropriate feedback. As a result, the governing equation is self-stabilized, and random oscillations are suppressed, while the Liouville equation takes the form of the Fokker-Planck equation with negative diffusion. Non- Newtonian properties of such a dynamical system as well as thermodynamical implications have been evaluated.

Field theory and diffusion creep predictions in polycrystalline aggregates

NASA Astrophysics Data System (ADS)

Villani, A.; Busso, E. P.; Forest, S.

2015-07-01

In polycrystals, stress-driven vacancy diffusion at high homologous temperatures leads to inelastic deformation. In this work, a novel continuum mechanics framework is proposed to describe the strain fields resulting from such a diffusion-driven process in a polycrystalline aggregate where grains and grain boundaries are explicitly considered. The choice of an anisotropic eigenstrain in the grain boundary region provides the driving force for the diffusive creep processes. The corresponding inelastic strain rate is shown to be related to the gradient of the vacancy flux. Dislocation driven deformation is then introduced as an additional mechanism, through standard crystal plasticity constitutive equations. The fully coupled diffusion-mechanical model is implemented into the finite element method and then used to describe the biaxial creep behaviour of FCC polycrystalline aggregates. The corresponding results revealed for the first time that such a coupled diffusion-stress approach, involving the gradient of the vacancy flux, can accurately predict the well-known macroscopic strain rate dependency on stress and grain size in the diffusion creep regime. They also predict strongly heterogeneous viscoplastic strain fields, especially close to grain boundaries triple junctions. Finally, a smooth transition from Herring and Coble to dislocation creep behaviour is predicted and compared to experimental results for copper.

A discrete model to study reaction-diffusion-mechanics systems.

PubMed

Weise, Louis D; Nash, Martyn P; Panfilov, Alexander V

2011-01-01

This article introduces a discrete reaction-diffusion-mechanics (dRDM) model to study the effects of deformation on reaction-diffusion (RD) processes. The dRDM framework employs a FitzHugh-Nagumo type RD model coupled to a mass-lattice model, that undergoes finite deformations. The dRDM model describes a material whose elastic properties are described by a generalized Hooke's law for finite deformations (Seth material). Numerically, the dRDM approach combines a finite difference approach for the RD equations with a Verlet integration scheme for the equations of the mass-lattice system. Using this framework results were reproduced on self-organized pacemaking activity that have been previously found with a continuous RD mechanics model. Mechanisms that determine the period of pacemakers and its dependency on the medium size are identified. Finally it is shown how the drift direction of pacemakers in RDM systems is related to the spatial distribution of deformation and curvature effects.

A Discrete Model to Study Reaction-Diffusion-Mechanics Systems

PubMed Central

Weise, Louis D.; Nash, Martyn P.; Panfilov, Alexander V.

2011-01-01

This article introduces a discrete reaction-diffusion-mechanics (dRDM) model to study the effects of deformation on reaction-diffusion (RD) processes. The dRDM framework employs a FitzHugh-Nagumo type RD model coupled to a mass-lattice model, that undergoes finite deformations. The dRDM model describes a material whose elastic properties are described by a generalized Hooke's law for finite deformations (Seth material). Numerically, the dRDM approach combines a finite difference approach for the RD equations with a Verlet integration scheme for the equations of the mass-lattice system. Using this framework results were reproduced on self-organized pacemaking activity that have been previously found with a continuous RD mechanics model. Mechanisms that determine the period of pacemakers and its dependency on the medium size are identified. Finally it is shown how the drift direction of pacemakers in RDM systems is related to the spatial distribution of deformation and curvature effects. PMID:21804911

New imaging algorithm in diffusion tomography

NASA Astrophysics Data System (ADS)

Klibanov, Michael V.; Lucas, Thomas R.; Frank, Robert M.

1997-08-01

A novel imaging algorithm for diffusion/optical tomography is presented for the case of the time dependent diffusion equation. Numerical tests are conducted for ranges of parameters realistic for applications to an early breast cancer diagnosis using ultrafast laser pulses. This is a perturbation-like method which works for both homogeneous a heterogeneous background media. Its main innovation lies in a new approach for a novel linearized problem (LP). Such an LP is derived and reduced to a boundary value problem for a coupled system of elliptic partial differential equations. As is well known, the solution of such a system amounts to the factorization of well conditioned, sparse matrices with few non-zero entries clustered along the diagonal, which can be done very rapidly. Thus, the main advantages of this technique are that it is fast and accurate. The authors call this approach the elliptic systems method (ESM). The ESM can be extended for other data collection schemes.

Unified implicit kinetic scheme for steady multiscale heat transfer based on the phonon Boltzmann transport equation

NASA Astrophysics Data System (ADS)

Zhang, Chuang; Guo, Zhaoli; Chen, Songze

2017-12-01

An implicit kinetic scheme is proposed to solve the stationary phonon Boltzmann transport equation (BTE) for multiscale heat transfer problem. Compared to the conventional discrete ordinate method, the present method employs a macroscopic equation to accelerate the convergence in the diffusive regime. The macroscopic equation can be taken as a moment equation for phonon BTE. The heat flux in the macroscopic equation is evaluated from the nonequilibrium distribution function in the BTE, while the equilibrium state in BTE is determined by the macroscopic equation. These two processes exchange information from different scales, such that the method is applicable to the problems with a wide range of Knudsen numbers. Implicit discretization is implemented to solve both the macroscopic equation and the BTE. In addition, a memory reduction technique, which is originally developed for the stationary kinetic equation, is also extended to phonon BTE. Numerical comparisons show that the present scheme can predict reasonable results both in ballistic and diffusive regimes with high efficiency, while the memory requirement is on the same order as solving the Fourier law of heat conduction. The excellent agreement with benchmark and the rapid converging history prove that the proposed macro-micro coupling is a feasible solution to multiscale heat transfer problems.

Construction of Fluid - solid Coupling Model with Improved Richards - BP & Its Engineering Application

NASA Astrophysics Data System (ADS)

Xie, Chengyu; Jia, Nan; Shi, Dongping; Lu, Hao

2017-10-01

In order to study the slurry diffusion law during grouting, Richards unsaturated-saturated model was introduced, the definition of the grouting model is clear, the Richards model control equation was established, And the BP neural network was introduced, the improved fluid-solid coupling model was constructed, Through the use of saturated - unsaturated seepage flow model, As well as the overflow boundary iterative solution of the mixed boundary conditions, the free surface is calculated. Engineering practice for an example, with the aid of multi - field coupling analysis software, the diffusion law of slurry was simulated numerically. The results show that the slurry diffusion rule is affected by grouting material, initial pressure and other factors. When the slurry starts, it flows in the cracks along the upper side of the grouting hole, when the pressure gradient is reduced to the critical pressure, that is, to the lower side of the flow, when the slurry diffusion stability, and ultimately its shape like an 8. The slurry is spread evenly from the overall point of view, from the grouting mouth toward the surrounding evenly spread, it gradually reaches saturation by non-saturation, and it is not a purely saturated flow, when the slurry spread and reach a saturated state, the diffusion time is the engineering grouting time.

Solving regularly and singularly perturbed reaction-diffusion equations in three space dimensions

NASA Astrophysics Data System (ADS)

Moore, Peter K.

2007-06-01

In [P.K. Moore, Effects of basis selection and h-refinement on error estimator reliability and solution efficiency for higher-order methods in three space dimensions, Int. J. Numer. Anal. Mod. 3 (2006) 21-51] a fixed, high-order h-refinement finite element algorithm, Href, was introduced for solving reaction-diffusion equations in three space dimensions. In this paper Href is coupled with continuation creating an automatic method for solving regularly and singularly perturbed reaction-diffusion equations. The simple quasilinear Newton solver of Moore, (2006) is replaced by the nonlinear solver NITSOL [M. Pernice, H.F. Walker, NITSOL: a Newton iterative solver for nonlinear systems, SIAM J. Sci. Comput. 19 (1998) 302-318]. Good initial guesses for the nonlinear solver are obtained using continuation in the small parameter ɛ. Two strategies allow adaptive selection of ɛ. The first depends on the rate of convergence of the nonlinear solver and the second implements backtracking in ɛ. Finally a simple method is used to select the initial ɛ. Several examples illustrate the effectiveness of the algorithm.

Plasma Equilibrium in a Magnetic Field with Stochastic Field-Line Trajectories

NASA Astrophysics Data System (ADS)

Krommes, J. A.; Reiman, A. H.

2008-11-01

The nature of plasma equilibrium in a magnetic field with stochastic field lines is examined, expanding upon the ideas first described by Reiman et al. The magnetic partial differential equation (PDE) that determines the equilibrium Pfirsch-Schlüter currents is treated as a passive stochastic PDE for μj/B. Renormalization leads to a stochastic Langevin equation for μ in which the resonances at the rational surfaces are broadened by the stochastic diffusion of the field lines; even weak radial diffusion can significantly affect the equilibrium, which need not be flattened in the stochastic region. Particular attention is paid to satisfying the periodicity constraints in toroidal configurations with sheared magnetic fields. A numerical scheme that couples the renormalized Langevin equation to Ampere's law is described. A. Reiman et al, Nucl. Fusion 47, 572--8 (2007). J. A. Krommes, Phys. Reports 360, 1--351.

A Stochastic Diffusion Process for the Dirichlet Distribution

DOE PAGES

Bakosi, J.; Ristorcelli, J. R.

2013-03-01

The method of potential solutions of Fokker-Planck equations is used to develop a transport equation for the joint probability ofNcoupled stochastic variables with the Dirichlet distribution as its asymptotic solution. To ensure a bounded sample space, a coupled nonlinear diffusion process is required: the Wiener processes in the equivalent system of stochastic differential equations are multiplicative with coefficients dependent on all the stochastic variables. Individual samples of a discrete ensemble, obtained from the stochastic process, satisfy a unit-sum constraint at all times. The process may be used to represent realizations of a fluctuating ensemble ofNvariables subject to a conservation principle.more » Similar to the multivariate Wright-Fisher process, whose invariant is also Dirichlet, the univariate case yields a process whose invariant is the beta distribution. As a test of the results, Monte Carlo simulations are used to evolve numerical ensembles toward the invariant Dirichlet distribution.« less

Adaptive hierarchical grid model of water-borne pollutant dispersion

NASA Astrophysics Data System (ADS)

Borthwick, A. G. L.; Marchant, R. D.; Copeland, G. J. M.

Water pollution by industrial and agricultural waste is an increasingly major public health issue. It is therefore important for water engineers and managers to be able to predict accurately the local behaviour of water-borne pollutants. This paper describes the novel and efficient coupling of dynamically adaptive hierarchical grids with standard solvers of the advection-diffusion equation. Adaptive quadtree grids are able to focus on regions of interest such as pollutant fronts, while retaining economy in the total number of grid elements through selective grid refinement. Advection is treated using Lagrangian particle tracking. Diffusion is solved separately using two grid-based methods; one is by explicit finite differences, the other a diffusion-velocity approach. Results are given in two dimensions for pure diffusion of an initially Gaussian plume, advection-diffusion of the Gaussian plume in the rotating flow field of a forced vortex, and the transport of species in a rectangular channel with side wall boundary layers. Close agreement is achieved with analytical solutions of the advection-diffusion equation and simulations from a Lagrangian random walk model. An application to Sepetiba Bay, Brazil is included to demonstrate the method with complex flows and topography.

Modeling of transport phenomena in concrete porous media.

PubMed

Plecas, Ilija

2014-02-01

Two fundamental concerns must be addressed when attempting to isolate low-level waste in a disposal facility on land. The first concern is isolating the waste from water, or hydrologic isolation. The second is preventing movement of the radionuclides out of the disposal facility, or radionuclide migration. Particularly, we have investigated here the latter modified scenario. To assess the safety for disposal of radioactive waste-concrete composition, the leakage of 60Co from a waste composite into a surrounding fluid has been studied. Leakage tests were carried out by the original method, developed at the Vinča Institute. Transport phenomena involved in the leaching of a radioactive material from a cement composite matrix are investigated using three methods based on theoretical equations. These are: the diffusion equation for a plane source: an equation for diffusion coupled to a first-order equation, and an empirical method employing a polynomial equation. The results presented in this paper are from a 25-y mortar and concrete testing project that will influence the design choices for radioactive waste packaging for a future Serbian radioactive waste disposal center.

Spin-diffusions and diffusive molecular dynamics

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

Magnetosphere-Ionosphere Energy Interchange in the Electron Diffuse Aurora

NASA Technical Reports Server (NTRS)

Khazanov, George V.; Glocer, Alex; Himwich, E. W.

2014-01-01

The diffuse aurora has recently been shown to be a major contributor of energy flux into the Earth's ionosphere. Therefore, a comprehensive theoretical analysis is required to understand its role in energy redistribution in the coupled ionosphere-magnetosphere system. In previous theoretical descriptions of precipitated magnetospheric electrons (E is approximately 1 keV), the major focus has been the ionization and excitation rates of the neutral atmosphere and the energy deposition rate to thermal ionospheric electrons. However, these precipitating electrons will also produce secondary electrons via impact ionization of the neutral atmosphere. This paper presents the solution of the Boltzman-Landau kinetic equation that uniformly describes the entire electron distribution function in the diffuse aurora, including the affiliated production of secondary electrons (E greater than 600 eV) and their ionosphere-magnetosphere coupling processes. In this article, we discuss for the first time how diffuse electron precipitation into the atmosphere and the associated secondary electron production participate in ionosphere-magnetosphere energy redistribution.

Elimination of numerical diffusion in 1 - phase and 2 - phase flows

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

Rajamaeki, M.

1997-07-01

The new hydraulics solution method PLIM (Piecewise Linear Interpolation Method) is capable of avoiding the excessive errors, numerical diffusion and also numerical dispersion. The hydraulics solver CFDPLIM uses PLIM and solves the time-dependent one-dimensional flow equations in network geometry. An example is given for 1-phase flow in the case when thermal-hydraulics and reactor kinetics are strongly coupled. Another example concerns oscillations in 2-phase flow. Both the example computations are not possible with conventional methods.

Three-temperature plasma shock solutions with gray radiation diffusion

DOE PAGES

Johnson, Bryan M.; Klein, Richard I.

2016-04-19

Here we discuss the effects of radiation on the structure of shocks in a fully ionized plasma are investigated by solving the steady-state fluid equations for ions, electrons, and radiation. The electrons and ions are assumed to have the same bulk velocity but separate temperatures, and the radiation is modeled with the gray diffusion approximation. Both electron and ion conduction are included, as well as ion viscosity. When the material is optically thin, three-temperature behavior occurs. When the diffusive flux of radiation is important but radiation pressure is not, two-temperature behavior occurs, with the electrons strongly coupled to the radiation.more » Since the radiation heats the electrons on length scales that are much longer than the electron–ion Coulomb coupling length scale, these solutions resemble radiative shock solutions rather than plasma shock solutions that neglect radiation. When radiation pressure is important, all three components are strongly coupled. Results with constant values for the transport and coupling coefficients are compared to a full numerical simulation with a good match between the two, demonstrating that steady shock solutions constitute a straightforward and comprehensive verification test methodology for multi-physics numerical algorithms.« less

Three-temperature plasma shock solutions with gray radiation diffusion

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

Johnson, Bryan M.; Klein, Richard I.

Here we discuss the effects of radiation on the structure of shocks in a fully ionized plasma are investigated by solving the steady-state fluid equations for ions, electrons, and radiation. The electrons and ions are assumed to have the same bulk velocity but separate temperatures, and the radiation is modeled with the gray diffusion approximation. Both electron and ion conduction are included, as well as ion viscosity. When the material is optically thin, three-temperature behavior occurs. When the diffusive flux of radiation is important but radiation pressure is not, two-temperature behavior occurs, with the electrons strongly coupled to the radiation.more » Since the radiation heats the electrons on length scales that are much longer than the electron–ion Coulomb coupling length scale, these solutions resemble radiative shock solutions rather than plasma shock solutions that neglect radiation. When radiation pressure is important, all three components are strongly coupled. Results with constant values for the transport and coupling coefficients are compared to a full numerical simulation with a good match between the two, demonstrating that steady shock solutions constitute a straightforward and comprehensive verification test methodology for multi-physics numerical algorithms.« less

Spectral method for pricing options in illiquid markets

NASA Astrophysics Data System (ADS)

Pindza, Edson; Patidar, Kailash C.

2012-09-01

We present a robust numerical method to solve a problem of pricing options in illiquid markets. The governing equation is described by a nonlinear Black-Scholes partial differential equation (BS-PDE) of the reaction-diffusion-advection type. To discretise this BS-PDE numerically, we use a spectral method in the asset (spatial) direction and couple it with a fifth order RADAU method for the discretisation in the time direction. Numerical experiments illustrate that our approach is very efficient for pricing financial options in illiquid markets.

Fourier's law of heat conduction: quantum mechanical master equation analysis.

PubMed

Wu, Lian-Ao; Segal, Dvira

2008-06-01

We derive the macroscopic Fourier's Law of heat conduction from the exact gain-loss time convolutionless quantum master equation under three assumptions for the interaction kernel. To second order in the interaction, we show that the first two assumptions are natural results of the long time limit. The third assumption can be satisfied by a family of interactions consisting of an exchange effect. The pure exchange model directly leads to energy diffusion in a weakly coupled spin- 12 chain.

Compact scheme for systems of equations applied to fundamental problems of mechanics of continua

NASA Technical Reports Server (NTRS)

Klimkowski, Jerzy Z.

1990-01-01

Compact scheme formulation was used in the treatment of boundary conditions for a system of coupled diffusion and Poisson equations. Models and practical solutions of specific engineering problems arising in solid mechanics, chemical engineering, heat transfer and fuid mechanics are described and analyzed for efficiency and accuracy. Only 2-D cases are discussed and a new method of numerical treatment of boundary conditions common in the fundamental problems of mechanics of continua is presented.

Mathematical modeling of microbially induced crown corrosion in wastewater collection systems and laboratory investigation and modeling of sulfuric acid corrosion of concrete

NASA Astrophysics Data System (ADS)

Jahani, Fereidoun

In the model for microbially induced crown corrosion, the diffusion of sulfide inside the concrete pores, its biological conversion to sulfuric acid, and the corrosion of calcium carbonate aggregates are represented. The corrosion front is modeled as a moving boundary. The location of the interface between the corrosion layer and the concrete is determined as part of the solution to the model equations. This model consisted of a system of one dimensional reaction-diffusion equations coupled to an equation describing the movement of the corrosion front. The equations were solved numerically using finite element Galerkin approximation. The concentration profiles of sulfide in the air and the liquid phases, the pH as a function of concrete depth, and the position of the corrosion front. A new equation for the corrosion rate was also derived. A more specific model for the degradation of a concrete specimen exposed to a sulfuric acid solution was also studied. In this model, diffusion of hydrogen ions and their reaction with alkaline components of concrete were expressed using Fick's Law of diffusion. The model equations described the moving boundary, the dissolution rate of alkaline components in the concrete, volume increase of sulfuric acid solution over the concrete specimen, and the boundary conditions on the surface of the concrete. An apparatus was designed and experiments were performed to measure pH changes on the surface of concrete. The data were used to calculate the dissolution rate of the concrete and, with the model, to determine the diffusion rate of sulfuric acid in the corrosion layer and corrosion layer thickness. Electrochemical Impedance Spectroscopy (EIS) was used to study the corrosion rate of iron pins embedded in the concrete sample. The open circuit potential (OCP) determined the onset of corrosion on the surface of the pins. Visual observation of the corrosion layer thickness was in good agreement with the simulation results.

Discrete and continuum links to a nonlinear coupled transport problem of interacting populations

NASA Astrophysics Data System (ADS)

Duong, M. H.; Muntean, A.; Richardson, O. M.

2017-07-01

We are interested in exploring interacting particle systems that can be seen as microscopic models for a particular structure of coupled transport flux arising when different populations are jointly evolving. The scenarios we have in mind are inspired by the dynamics of pedestrian flows in open spaces and are intimately connected to cross-diffusion and thermo-diffusion problems holding a variational structure. The tools we use include a suitable structure of the relative entropy controlling TV-norms, the construction of Lyapunov functionals and particular closed-form solutions to nonlinear transport equations, a hydrodynamics limiting procedure due to Philipowski, as well as the construction of numerical approximates to both the continuum limit problem in 2D and to the original interacting particle systems.

Spin Hall and Spin Swapping Torques in Diffusive Ferromagnets

NASA Astrophysics Data System (ADS)

Pauyac, Christian Ortiz; Chshiev, Mairbek; Manchon, Aurelien; Nikolaev, Sergey A.

2018-04-01

A complete set of the generalized drift-diffusion equations for a coupled charge and spin dynamics in ferromagnets in the presence of extrinsic spin-orbit coupling is derived from the quantum kinetic approach, covering major transport phenomena, such as the spin and anomalous Hall effects, spin swapping, spin precession, and relaxation processes. We argue that the spin swapping effect in ferromagnets is enhanced due to spin polarization, while the overall spin texture induced by the interplay of spin-orbital and spin precession effects displays a complex spatial dependence that can be exploited to generate torques and nucleate or propagate domain walls in centrosymmetric geometries without the use of external polarizers, as opposed to the conventional understanding of spin-orbit mediated torques.

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

Novascone, Stephen Rhead; Peterson, John William

Abstract This report documents the progress of simulating pore migration in ceramic (UO 2 and mixed oxide or MOX) fuel using BISON. The porosity field is treated as a function of space and time whose evolution is governed by a custom convection-diffusion-reaction equation (described here) which is coupled to the heat transfer equation via the temperature field. The porosity is initialized to a constant value at every point in the domain, and as the temperature (and its gradient) are increased by application of a heat source, the pores move up the thermal gradient and accumulate at the center of themore » fuel in a time-frame that is consistent with observations from experiments. There is an inverse dependence of the fuel’s thermal conductivity on porosity (increasing porosity decreases thermal conductivity, and vice-versa) which is also accounted for, allowing the porosity equation to couple back into the heat transfer equation. Results from an example simulation are shown to demonstrate the new capability.« less

Overdamping by weakly coupled environments

NASA Astrophysics Data System (ADS)

Esposito, Massimiliano; Haake, Fritz

2005-12-01

A quantum system weakly interacting with a fast environment usually undergoes a relaxation with complex frequencies whose imaginary parts are damping rates quadratic in the coupling to the environment in accord with Fermi’s “golden rule.” We show for various models (spin damped by harmonic-oscillator or random-matrix baths, quantum diffusion, and quantum Brownian motion) that upon increasing the coupling up to a critical value still small enough to allow for weak-coupling Markovian master equations, a different relaxation regime can occur. In that regime, complex frequencies lose their real parts such that the process becomes overdamped. Our results call into question the standard belief that overdamping is exclusively a strong coupling feature.

Instabilities and diffusion in a hydrodynamic model of a fluid membrane coupled to a thin active fluid layer.

PubMed

Sarkar, N; Basu, A

2012-11-01

We construct a coarse-grained effective two-dimensional (2d hydrodynamic theory as a theoretical model for a coupled system of a fluid membrane and a thin layer of a polar active fluid in its ordered state that is anchored to the membrane. We show that such a system is prone to generic instabilities through the interplay of nonequilibrium drive, polar order and membrane fluctuation. We use our model equations to calculate diffusion coefficients of an inclusion in the membrane and show that their values depend strongly on the system size, in contrast to their equilibrium values. Our work extends the work of S. Sankararaman and S. Ramaswamy (Phys. Rev. Lett., 102, 118107 (2009)) to a coupled system of a fluid membrane and an ordered active fluid layer. Our model is broadly inspired by and should be useful as a starting point for theoretical descriptions of the coupled dynamics of a cell membrane and a cortical actin layer anchored to it.

Initial Coupling of the RELAP-7 and PRONGHORN Applications

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

J. Ortensi; D. Andrs; A.A. Bingham

2012-10-01

Modern nuclear reactor safety codes require the ability to solve detailed coupled neutronic- thermal fluids problems. For larger cores, this implies fully coupled higher dimensionality spatial dynamics with appropriate feedback models that can provide enough resolution to accurately compute core heat generation and removal during steady and unsteady conditions. The reactor analysis code PRONGHORN is being coupled to RELAP-7 as a first step to extend RELAP’s current capabilities. This report details the mathematical models, the type of coupling, and the testing results from the integrated system. RELAP-7 is a MOOSE-based application that solves the continuity, momentum, and energy equations inmore » 1-D for a compressible fluid. The pipe and joint capabilities enable it to model parts of the power conversion unit. The PRONGHORN application, also developed on the MOOSE infrastructure, solves the coupled equations that define the neutron diffusion, fluid flow, and heat transfer in a full core model. The two systems are loosely coupled to simplify the transition towards a more complex infrastructure. The integration is tested on a simplified version of the OECD/NEA MHTGR-350 Coupled Neutronics-Thermal Fluids benchmark model.« less

Fractional Diffusion Equations and Anomalous Diffusion

NASA Astrophysics Data System (ADS)

Evangelista, Luiz Roberto; Kaminski Lenzi, Ervin

2018-01-01

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

A three-dimensional, finite element model for coastal and estuarine circulation

USGS Publications Warehouse

Walters, R.A.

1992-01-01

This paper describes the development and application of a three-dimensional model for coastal and estuarine circulation. The model uses a harmonic expansion in time and a finite element discretization in space. All nonlinear terms are retained, including quadratic bottom stress, advection and wave transport (continuity nonlinearity). The equations are solved as a global and a local problem, where the global problem is the solution of the wave equation formulation of the shallow water equations, and the local problem is the solution of the momentum equation for the vertical velocity profile. These equations are coupled to the advection-diffusion equation for salt so that density gradient forcing is included in the momentum equations. The model is applied to a study of Delaware Bay, U.S.A., where salinity intrusion is the primary focus. ?? 1991.

Multiscale model reduction for shale gas transport in poroelastic fractured media

NASA Astrophysics Data System (ADS)

Akkutlu, I. Yucel; Efendiev, Yalchin; Vasilyeva, Maria; Wang, Yuhe

2018-01-01

Inherently coupled flow and geomechanics processes in fractured shale media have implications for shale gas production. The system involves highly complex geo-textures comprised of a heterogeneous anisotropic fracture network spatially embedded in an ultra-tight matrix. In addition, nonlinearities due to viscous flow, diffusion, and desorption in the matrix and high velocity gas flow in the fractures complicates the transport. In this paper, we develop a multiscale model reduction approach to couple gas flow and geomechanics in fractured shale media. A Discrete Fracture Model (DFM) is used to treat the complex network of fractures on a fine grid. The coupled flow and geomechanics equations are solved using a fixed stress-splitting scheme by solving the pressure equation using a continuous Galerkin method and the displacement equation using an interior penalty discontinuous Galerkin method. We develop a coarse grid approximation and coupling using the Generalized Multiscale Finite Element Method (GMsFEM). GMsFEM constructs the multiscale basis functions in a systematic way to capture the fracture networks and their interactions with the shale matrix. Numerical results and an error analysis is provided showing that the proposed approach accurately captures the coupled process using a few multiscale basis functions, i.e. a small fraction of the degrees of freedom of the fine-scale problem.

Similarity solutions of reaction–diffusion equation with space- and time-dependent diffusion and reaction terms

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

Ho, C.-L.; Lee, C.-C., E-mail: chieh.no27@gmail.com

2016-01-15

We consider solvability of the generalized reaction–diffusion equation with both space- and time-dependent diffusion and reaction terms by means of the similarity method. By introducing the similarity variable, the reaction–diffusion equation is reduced to an ordinary differential equation. Matching the resulting ordinary differential equation with known exactly solvable equations, one can obtain corresponding exactly solvable reaction–diffusion systems. Several representative examples of exactly solvable reaction–diffusion equations are presented.

A finite elements method to solve the Bloch-Torrey equation applied to diffusion magnetic resonance imaging

NASA Astrophysics Data System (ADS)

Nguyen, Dang Van; Li, Jing-Rebecca; Grebenkov, Denis; Le Bihan, Denis

2014-04-01

The complex transverse water proton magnetization subject to diffusion-encoding magnetic field gradient pulses in a heterogeneous medium can be modeled by the multiple compartment Bloch-Torrey partial differential equation (PDE). In addition, steady-state Laplace PDEs can be formulated to produce the homogenized diffusion tensor that describes the diffusion characteristics of the medium in the long time limit. In spatial domains that model biological tissues at the cellular level, these two types of PDEs have to be completed with permeability conditions on the cellular interfaces. To solve these PDEs, we implemented a finite elements method that allows jumps in the solution at the cell interfaces by using double nodes. Using a transformation of the Bloch-Torrey PDE we reduced oscillations in the searched-for solution and simplified the implementation of the boundary conditions. The spatial discretization was then coupled to the adaptive explicit Runge-Kutta-Chebyshev time-stepping method. Our proposed method is second order accurate in space and second order accurate in time. We implemented this method on the FEniCS C++ platform and show time and spatial convergence results. Finally, this method is applied to study some relevant questions in diffusion MRI.

Emergent dynamics of Cucker-Smale particles under the effects of random communication and incompressible fluids

NASA Astrophysics Data System (ADS)

Ha, Seung-Yeal; Xiao, Qinghua; Zhang, Xiongtao

2018-04-01

We study the dynamics of infinitely many Cucker-Smale (C-S) flocking particles under the interplay of random communication and incompressible fluids. For the dynamics of an ensemble of flocking particles, we use the kinetic Cucker-Smale-Fokker-Planck (CS-FP) equation with a degenerate diffusion, whereas for the fluid component, we use the incompressible Navier-Stokes (N-S) equations. These two subsystems are coupled via the drag force. For this coupled model, we present the global existence of weak and strong solutions in Rd (d = 2 , 3). Under the extra regularity assumptions of the initial data, the unique solvability of strong solutions is also established in R2. In a large coupling regime and periodic spatial domain T2 : =R2 /Z2, we show that the velocities of C-S particles and fluids are asymptotically aligned to two constant velocities which may be different.

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

A minimal model of an autonomous thermal motor

NASA Astrophysics Data System (ADS)

Fogedby, Hans C.; Imparato, Alberto

2017-09-01

We consider a model of a Brownian motor composed of two coupled overdamped degrees of freedom moving in periodic potentials and driven by two heat reservoirs. This model exhibits a spontaneous breaking of symmetry and gives rise to directed transport in the case of a non-vanishing interparticle interaction strength. For strong coupling between the particles we derive an expression for the propagation velocity valid for arbitrary periodic potentials. In the limit of strong coupling the model is equivalent to the Büttiker-Landauer model for a single particle diffusing in an environment with position-dependent temperature. By using numerical calculations of the Fokker-Planck equation and simulations of the Langevin equations we study the model for arbitrary coupling, retrieving many features of the strong-coupling limit. In particular, directed transport emerges even for symmetric potentials. For distinct heat reservoirs the heat currents are well-defined quantities allowing a study of the motor efficiency. We show that the optimal working regime occurs for moderate coupling. Finally, we introduce a model with discrete phase space which captures the essential features of the continuous model, can be solved in the limit of weak coupling, and exhibits a larger efficiency than the continuous counterpart.

Accelerated ions and self-excited Alfvén waves at the Earth's bow shock

NASA Astrophysics Data System (ADS)

Berezhko, E. G.; Taneev, S. N.; Trattner, K. J.

2011-07-01

The diffuse energetic ion event and related Alfvén waves upstream of the Earth's bow shock, measured by AMPTE/IRM satellite on 29 September 1984, 06:42-07:22 UT, was studied using a self-consistent quasi-linear theory of ion diffusive shock acceleration and associated Alfvén wave generation. The wave energy density satisfies a wave kinetic equation, and the ion distribution function satisfies the diffusive transport equation. These coupled equations are solved numerically, and calculated ion and wave spectra are compared with observations. It is shown that calculated steady state ion and Alfvén wave spectra are established during the time period of about 1000 s. Alfvén waves excited by accelerated ions are confined within the frequency range (10-2 to 1) Hz, and their spectral peak with the wave amplitude δB ≈ B comparable to the interplanetary magnetic field value B corresponds to the frequency 2 × 10-2 Hz. The high-frequency part of the wave spectrum undergoes absorption by thermal protons. It is shown that the observed ion spectra and the associated Alfvén wave spectra are consistent with the theoretical prediction.

Iontophoretic transdermal drug delivery: a multi-layered approach.

PubMed

Pontrelli, Giuseppe; Lauricella, Marco; Ferreira, José A; Pena, Gonçalo

2017-12-11

We present a multi-layer mathematical model to describe the transdermal drug release from an iontophoretic system. The Nernst-Planck equation describes the basic convection-diffusion process, with the electric potential obtained by solving the Laplace's equation. These equations are complemented with suitable interface and boundary conditions in a multi-domain. The stability of the mathematical problem is discussed in different scenarios and a finite-difference method is used to solve the coupled system. Numerical experiments are included to illustrate the drug dynamics under different conditions. © The authors 2016. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Diffusion approximation of the radiative-conductive heat transfer model with Fresnel matching conditions

NASA Astrophysics Data System (ADS)

Chebotarev, Alexander Yu.; Grenkin, Gleb V.; Kovtanyuk, Andrey E.; Botkin, Nikolai D.; Hoffmann, Karl-Heinz

2018-04-01

The paper is concerned with a problem of diffraction type. The study starts with equations of complex (radiative and conductive) heat transfer in a multicomponent domain with Fresnel matching conditions at the interfaces. Applying the diffusion, P1, approximation yields a pair of coupled nonlinear PDEs describing the radiation intensity and temperature for each component of the domain. Matching conditions for these PDEs, imposed at the interfaces between the domain components, are derived. The unique solvability of the obtained problem is proven, and numerical experiments are conducted.

A generalized electron energy probability function for inductively coupled plasmas under conditions of nonlocal electron kinetics

NASA Astrophysics Data System (ADS)

Mouchtouris, S.; Kokkoris, G.

2018-01-01

A generalized equation for the electron energy probability function (EEPF) of inductively coupled Ar plasmas is proposed under conditions of nonlocal electron kinetics and diffusive cooling. The proposed equation describes the local EEPF in a discharge and the independent variable is the kinetic energy of electrons. The EEPF consists of a bulk and a depleted tail part and incorporates the effect of the plasma potential, Vp, and pressure. Due to diffusive cooling, the break point of the EEPF is eVp. The pressure alters the shape of the bulk and the slope of the tail part. The parameters of the proposed EEPF are extracted by fitting to measure EEPFs (at one point in the reactor) at different pressures. By coupling the proposed EEPF with a hybrid plasma model, measurements in the gaseous electronics conference reference reactor concerning (a) the electron density and temperature and the plasma potential, either spatially resolved or at different pressure (10-50 mTorr) and power, and (b) the ion current density of the electrode, are well reproduced. The effect of the choice of the EEPF on the results is investigated by a comparison to an EEPF coming from the Boltzmann equation (local electron kinetics approach) and to a Maxwellian EEPF. The accuracy of the results and the fact that the proposed EEPF is predefined renders its use a reliable alternative with a low computational cost compared to stochastic electron kinetic models at low pressure conditions, which can be extended to other gases and/or different electron heating mechanisms.

First passage times for multiple particles with reversible target-binding kinetics

NASA Astrophysics Data System (ADS)

Grebenkov, Denis S.

2017-10-01

We investigate the first passage problem for multiple particles that diffuse towards a target, partially adsorb there, and then desorb after a finite exponentially distributed residence time. We search for the first time when m particles undergoing such reversible target-binding kinetics are found simultaneously on the target that may trigger an irreversible chemical reaction or a biophysical event. Even if the particles are independent, the finite residence time on the target yields an intricate temporal coupling between particles. We compute analytically the mean first passage time (MFPT) for two independent particles by mapping the original problem to higher-dimensional surface-mediated diffusion and solving the coupled partial differential equations. The respective effects of the adsorption and desorption rates on the MFPT are revealed and discussed.

The effect of coupled transport phenomena in the Opalinus Clay and implications for radionuclide transport

NASA Astrophysics Data System (ADS)

Soler, Josep M.

2001-12-01

In this study, the potential effects of coupled transport phenomena on radionuclide transport in the vicinity of a repository for vitrified high-level radioactive waste (HLW) and spent nuclear fuel (SF) hosted by the Opalinus Clay in Switzerland, at times equal to or greater than the expected lifetime of the waste canisters (about 1000 years), are addressed. The solute fluxes associated with advection, chemical diffusion, thermal and chemical osmosis, hyperfiltration and thermal diffusion have been incorporated into a simple one-dimensional transport equation. The analytical solution of this equation, with appropriate parameters, shows that thermal osmosis is the only coupled transport mechanism that could, on its own, have a strong effect on repository performance. Based on the results from the analytical model, two-dimensional finite-difference models incorporating advection and thermal osmosis, and taking conservation of fluid mass into account, have been formulated. The results show that, under the conditions in the vicinity of the repository at the time scales of interest, and due to the constraints imposed by conservation of fluid mass, the advective component of flow will oppose and cancel the thermal-osmotic component. The overall conclusion is that coupled phenomena will only have a very minor impact on radionuclide transport in the Opalinus Clay, in terms of fluid and solute fluxes, at least under the conditions prevailing at times equal to or greater than the expected lifetime of the waste canisters (about 1000 years).

Marangoni Convection during Free Electron Laser Nitriding of Titanium

NASA Astrophysics Data System (ADS)

Höche, Daniel; Müller, Sven; Rapin, Gerd; Shinn, Michelle; Remdt, Elvira; Gubisch, Maik; Schaaf, Peter

2009-08-01

Pure titanium was treated by free electron laser (FEL) radiation in a nitrogen atmosphere. As a result, nitrogen diffusion occurs and a TiN coating was synthesized. Local gradients of interfacial tension due to the local heating lead to a Marangoni convection, which determines the track properties. Because of the experimental inaccessibility of time-dependent occurrences, finite element calculations were performed, to determine the physical processes such as heat transfer, melt flow, and mass transport. In order to calculate the surface deformation of the gas-liquid interface, the level set approach was used. The equations were modified and coupled with heat-transfer and diffusion equations. The process was characterized by dimensionless numbers such as the Reynolds, Peclet, and capillary numbers, to obtain more information about the acting forces and the coating development. Moreover, the nitrogen distribution was calculated using the corresponding transport equation. The simulations were compared with cross-sectional micrographs of the treated titanium sheets and checked for their validity. Finally, the process presented is discussed and compared with similar laser treatments.

The Stressing Effect of Electromigration from the Maxwell Stress and a Preliminary Mean-Time-to-Failure Analysis

NASA Astrophysics Data System (ADS)

Zhou, Peng

2013-06-01

As temperature increases, it is suggested that atoms on lattice sites serve as dynamic defects and cause a much more homogeneous distribution of the Maxwell stress throughout the crystal lattice compared with that caused by static defects. Though this stressing effect mostly leads to Joule heating, it also results in distortion of the crystal lattice, which leads to a decrease in the activation energy for atomic diffusion and causes enhancements in the phase growth rates at both interfaces of diffusion couples. Due to this stressing effect, the decrease in the activation energy is proportional to a square term of the current density J. A mean-time-to-failure analysis is performed for failure caused by excessive growth of intermediate phases, and a mean-time-to-failure (MTTF) equation is found. This equation appears similar to Black's equation but with an extra exponential term arising from the stressing effect of the crystal lattice.

Dissipative particle dynamics of diffusion-NMR requires high Schmidt-numbers

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

Azhar, Mueed; Greiner, Andreas; Korvink, Jan G., E-mail: jan.korvink@kit.edu, E-mail: david.kauzlaric@imtek.uni-freiburg.de

We present an efficient mesoscale model to simulate the diffusion measurement with nuclear magnetic resonance (NMR). On the level of mesoscopic thermal motion of fluid particles, we couple the Bloch equations with dissipative particle dynamics (DPD). Thereby we establish a physically consistent scaling relation between the diffusion constant measured for DPD-particles and the diffusion constant of a real fluid. The latter is based on a splitting into a centre-of-mass contribution represented by DPD, and an internal contribution which is not resolved in the DPD-level of description. As a consequence, simulating the centre-of-mass contribution with DPD requires high Schmidt numbers. Aftermore » a verification for fundamental pulse sequences, we apply the NMR-DPD method to NMR diffusion measurements of anisotropic fluids, and of fluids restricted by walls of microfluidic channels. For the latter, the free diffusion and the localisation regime are considered.« less

Transport behaviors of locally fractional coupled Brownian motors with fluctuating interactions

NASA Astrophysics Data System (ADS)

Wang, Huiqi; Ni, Feixiang; Lin, Lifeng; Lv, Wangyong; Zhu, Hongqiang

2018-09-01

In some complex viscoelastic mediums, it is ubiquitous that absorbing and desorbing surrounding Brownian particles randomly occur in coupled systems. The conventional method is to model a variable-mass system driven by both multiplicative and additive noises. In this paper, an improved mathematical model is created based on generalized Langevin equations (GLE) to characterize the random interaction with locally fluctuating number of coupled particles in the elastically coupled factional Brownian motors (FBM). By the numerical simulations, the effect of fluctuating interactions on collective transport behaviors is investigated, and some abnormal phenomena, such as cooperative behaviors, stochastic resonance (SR) and anomalous transport, are observed in the regime of sub-diffusion.

Hamiltonian chaos acts like a finite energy reservoir: accuracy of the Fokker-Planck approximation.

PubMed

Riegert, Anja; Baba, Nilüfer; Gelfert, Katrin; Just, Wolfram; Kantz, Holger

2005-02-11

The Hamiltonian dynamics of slow variables coupled to fast degrees of freedom is modeled by an effective stochastic differential equation. Formal perturbation expansions, involving a Markov approximation, yield a Fokker-Planck equation in the slow subspace which respects conservation of energy. A detailed numerical and analytical analysis of suitable model systems demonstrates the feasibility of obtaining the system specific drift and diffusion terms and the accuracy of the stochastic approximation on all time scales. Non-Markovian and non-Gaussian features of the fast variables are negligible.

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.

A Three-Wave Model of the Stratosphere with Coupled Dynamics, Radiation and Photochemistry. Appendix M

NASA Technical Reports Server (NTRS)

Shia, Run-Lie; Zhou, Shuntai; Ko, Malcolm K. W.; Sze, Nien-Dak; Salstein, David; Cady-Pereira, Karen

1997-01-01

A zonal mean chemistry transport model (2-D CTM) coupled with a semi-spectral dynamical model is used to simulate the distributions of trace gases in the present day atmosphere. The zonal-mean and eddy equations for the velocity and the geopotential height are solved in the semi-spectral dynamical model. The residual mean circulation is derived from these dynamical variables and used to advect the chemical species in the 2- D CTM. Based on a linearized wave transport equation, the eddy diffusion coefficients for chemical tracers are expressed in terms of the amplitude, frequency and growth rate of dynamical waves; local chemical loss rates; and a time constant parameterizing small scale mixing. The contributions to eddy flux are from the time varying wave amplitude (transient eddy), chemical reactions (chemical eddy) and small scale mixing. In spite of the high truncation in the dynamical module (only three longest waves are resolved), the model has simulated many observed characteristics of stratospheric dynamics and distribution of chemical species including ozone. Compared with the values commonly used in 2-D CTMs, the eddy diffusion coefficients for chemical species calculated in this model are smaller, especially in the subtropics. It is also found that the chemical eddy diffusion has only a small effects in determining the distribution of most slow species, including ozone in the stratosphere.

Phase field approaches of bone remodeling based on TIP

NASA Astrophysics Data System (ADS)

Ganghoffer, Jean-François; Rahouadj, Rachid; Boisse, Julien; Forest, Samuel

2016-01-01

The process of bone remodeling includes a cycle of repair, renewal, and optimization. This adaptation process, in response to variations in external loads and chemical driving factors, involves three main types of bone cells: osteoclasts, which remove the old pre-existing bone; osteoblasts, which form the new bone in a second phase; osteocytes, which are sensing cells embedded into the bone matrix, trigger the aforementioned sequence of events. The remodeling process involves mineralization of the bone in the diffuse interface separating the marrow, which contains all specialized cells, from the newly formed bone. The main objective advocated in this contribution is the setting up of a modeling and simulation framework relying on the phase field method to capture the evolution of the diffuse interface between the new bone and the marrow at the scale of individual trabeculae. The phase field describes the degree of mineralization of this diffuse interface; it varies continuously between the lower value (no mineral) and unity (fully mineralized phase, e.g. new bone), allowing the consideration of a diffuse moving interface. The modeling framework is the theory of continuous media, for which field equations for the mechanical, chemical, and interfacial phenomena are written, based on the thermodynamics of irreversible processes. Additional models for the cellular activity are formulated to describe the coupling of the cell activity responsible for bone production/resorption to the kinetics of the internal variables. Kinetic equations for the internal variables are obtained from a pseudo-potential of dissipation. The combination of the balance equations for the microforce associated to the phase field and the kinetic equations lead to the Ginzburg-Landau equation satisfied by the phase field with a source term accounting for the dissipative microforce. Simulations illustrating the proposed framework are performed in a one-dimensional situation showing the evolution of the diffuse interface separating new bone from marrow.

Coupled Particle Transport and Pattern Formation in a Nonlinear Leaky-Box Model

NASA Technical Reports Server (NTRS)

Barghouty, A. F.; El-Nemr, K. W.; Baird, J. K.

2009-01-01

Effects of particle-particle coupling on particle characteristics in nonlinear leaky-box type descriptions of the acceleration and transport of energetic particles in space plasmas are examined in the framework of a simple two-particle model based on the Fokker-Planck equation in momentum space. In this model, the two particles are assumed coupled via a common nonlinear source term. In analogy with a prototypical mathematical system of diffusion-driven instability, this work demonstrates that steady-state patterns with strong dependence on the magnetic turbulence but a rather weak one on the coupled particles attributes can emerge in solutions of a nonlinearly coupled leaky-box model. The insight gained from this simple model may be of wider use and significance to nonlinearly coupled leaky-box type descriptions in general.

Geophysical aspects of underground fluid dynamics and mineral transformation process

NASA Astrophysics Data System (ADS)

Khramchenkov, Maxim; Khramchenkov, Eduard

2014-05-01

The description of processes of mass exchange between fluid and poly-minerals material in porous media from various kinds of rocks (primarily, sedimentary rocks) have been examined. It was shown that in some important cases there is a storage equation of non-linear diffusion equation type. In addition, process of filtration in un-swelling soils, swelling porous rocks and coupled process of consolidation and chemical interaction between fluid and particles material were considered. In the latter case equations of physical-chemical mechanics of conservation of mass for fluid and particles material were used. As it is well known, the mechanics of porous media is theoretical basis of such branches of science as rock mechanics, soil physics and so on. But at the same moment some complex processes in the geosystems lacks full theoretical description. The example of such processes is metamorphosis of rocks and correspondent variations of stress-strain state. In such processes chemical transformation of solid and fluid components, heat release and absorption, phase transitions, rock destruction occurs. Extensive usage of computational resources in limits of traditional models of the mechanics of porous media cannot guarantee full correctness of obtained models and results. The process of rocks consolidation which happens due to filtration of underground fluids is described from the position of rock mechanics. As an additional impact, let us consider the porous media consolidating under the weight of overlying rock with coupled complex geological processes, as a continuous porous medium of variable mass. Problems of obtaining of correct storage equations for coupled processes of consolidation and mass exchange between underground fluid and skeleton material are often met in catagenesi processes description. The example of such processes is metamorphosis of rocks and correspondent variations of stress-strain state. In such processes chemical transformation of solid and fluid components, heat release and absorption, phase transitions, rock destruction occurs. Extensive usage of computational resources in limits of traditional models of the mechanics of porous media cannot guarantee full correctness of obtained models and results. The present work is dedicated to the retrieval of new ways to formulate and construct such models. It was shown that in some important cases there is a governing equation of non-linear diffusion equation type (well-known Fisher equation). In addition, some geophysical aspects of filtration process in usual non-swelling soils, swelling porous rocks and coupled process of consolidation and chemical interaction between fluid and skeleton material, including earth quakes, are considered.

Simulating Donnan equilibria based on the Nernst-Planck equation

NASA Astrophysics Data System (ADS)

Gimmi, Thomas; Alt-Epping, Peter

2018-07-01

Understanding ion transport through clays and clay membranes is important for many geochemical and environmental applications. Ion transport is affected by electrostatic forces exerted by charged clay surfaces. Anions are partly excluded from pore water near these surfaces, whereas cations are enriched. Such effects can be modeled by the Donnan approach. Here we introduce a new, comparatively simple way to represent Donnan equilibria in transport simulations. We include charged surfaces as immobile ions in the balance equation and calculate coupled transport of all components, including the immobile charges, with the Nernst-Planck equation. This results in an additional diffusion potential that influences ion transport, leading to Donnan ion distributions while maintaining local charge balance. The validity of our new approach was demonstrated by comparing Nernst-Planck simulations using the reactive transport code Flotran with analytical solutions available for simple Donnan systems. Attention has to be paid to the numerical evaluation of the electrochemical migration term in the Nernst-Planck equation to obtain correct results for asymmetric electrolytes. Sensitivity simulations demonstrate the influence of various Donnan model parameters on simulated anion accessible porosities. It is furthermore shown that the salt diffusion coefficient in a Donnan pore depends on local concentrations, in contrast to the aqueous salt diffusion coefficient. Our approach can be easily implemented into other transport codes. It is versatile and facilitates, for instance, assessing the implications of different activity models for the Donnan porosity.

Probability density function approach for compressible turbulent reacting flows

NASA Technical Reports Server (NTRS)

Hsu, A. T.; Tsai, Y.-L. P.; Raju, M. S.

1994-01-01

The objective of the present work is to extend the probability density function (PDF) tubulence model to compressible reacting flows. The proability density function of the species mass fractions and enthalpy are obtained by solving a PDF evolution equation using a Monte Carlo scheme. The PDF solution procedure is coupled with a compression finite-volume flow solver which provides the velocity and pressure fields. A modeled PDF equation for compressible flows, capable of treating flows with shock waves and suitable to the present coupling scheme, is proposed and tested. Convergence of the combined finite-volume Monte Carlo solution procedure is discussed. Two super sonic diffusion flames are studied using the proposed PDF model and the results are compared with experimental data; marked improvements over solutions without PDF are observed.

The coupling between flame surface dynamics and species mass conservation in premixed turbulent combustion

NASA Technical Reports Server (NTRS)

Trouve, A.; Veynante, D.; Bray, K. N. C.; Mantel, T.

1994-01-01

Current flamelot models based on a description of the flame surface dynamics require the closure of two inter-related equations: a transport equation for the mean reaction progress variable, (tilde)c, and a transport equation for the flame surface density, Sigma. The coupling between these two equations is investigated using direct numerical simulations (DNS) with emphasis on the correlation between the turbulent fluxes of (tilde)c, bar(pu''c''), and Sigma, (u'')(sub S)Sigma. Two different DNS databases are used in the present work: a database developed at CTR by A. Trouve and a database developed by C. J. Rutland using a different code. Both databases correspond to statistically one-dimensional premixed flames in isotropic turbulent flow. The run parameters, however, are significantly different, and the two databases correspond to different combustion regimes. It is found that in all simulated flames, the correlation between bar(pu''c'') and (u'')(sub S)Sigma is always strong. The sign, however, of the turbulent flux of (tilde)c or Sigma with respect to the mean gradients, delta(tilde)c/delta(x) or delta(Sigma)/delta(x), is case-dependent. The CTR database is found to exhibit gradient turbulent transport of (tilde)c and Sigma, whereas the Rutland DNS features counter-gradient diffusion. The two databases are analyzed and compared using various tools (a local analysis of the flow field near the flame, a classical analysis of the conservation equation for (tilde)(u''c''), and a thin flame theoretical analysis). A mechanism is then proposed to explain the discrepancies between the two databases and a preliminary simple criterion is derived to predict the occurrence of gradient/counter-gradient turbulent diffusion.

A spatially nonlocal model for polymer-penetrant diffusion

NASA Astrophysics Data System (ADS)

Edwards, D. A.

Diffusion of a penetrant in a polymer entanglement network cannot be described by Fick's Law alone; rather, one must incorporate other nonlocal effects. In contrast to previous viscoelastic models which have modeled these effects through hereditary integrals in time, a new model is presented exploiting the disparate lengths of the polymer in the glassy (dry) and rubbery (saturated) states. This model leads to a partial integrodifferential equation which is nonlocal in space. The system is recast as a moving boundary-value problem between sets of coupled partial differential equations. Using singular perturbation techniques, sorption in a semi-infinite polymer is studied on several time scales with varying exposed interface conditions. Though some of the results match with those from viscoelastic models, new physically relevant behaviors also appear. These include the formation of stopping fronts and overshoot in the pseudostress.

A COMPUTATIONAL ANALYSIS OF BONE FORMATION IN THE CRANIAL VAULT USING A COUPLED REACTION-DIFFUSION-STRAIN MODEL

PubMed Central

LEE, CHANYOUNG; RICHTSMEIER, JOAN T.; KRAFT, REUBEN H.

2017-01-01

Bones of the murine cranial vault are formed by differentiation of mesenchymal cells into osteoblasts, a process that is primarily understood to be controlled by a cascade of reactions between extracellular molecules and cells. We assume that the process can be modeled using Turing’s reaction-diffusion equations, a mathematical model describing the pattern formation controlled by two interacting molecules (activator and inhibitor). In addition to the processes modeled by reaction-diffusion equations, we hypothesize that mechanical stimuli of the cells due to growth of the underlying brain contribute significantly to the process of cell differentiation in cranial vault development. Structural analysis of the surface of the brain was conducted to explore the effects of the mechanical strain on bone formation. We propose a mechanobiological model for the formation of cranial vault bones by coupling the reaction-diffusion model with structural mechanics. The mathematical formulation was solved using the finite volume method. The computational domain and model parameters are determined using a large collection of experimental data that provide precise three dimensional (3D) measures of murine cranial geometry and cranial vault bone formation for specific embryonic time points. The results of this study suggest that mechanical strain contributes information to specific aspects of bone formation. Our mechanobiological model predicts some key features of cranial vault bone formation that were verified by experimental observations including the relative location of ossification centers of individual vault bones, the pattern of cranial vault bone growth over time, and the position of cranial vault sutures. PMID:29225392

The effect of the physical properties of the substrate on the kinetics of cell adhesion and crawling studied by an axisymmetric diffusion-energy balance coupled model.

PubMed

Samadi-Dooki, Aref; Shodja, Hossein M; Malekmotiei, Leila

2015-05-14

In this paper an analytical approach to study the effect of the substrate physical properties on the kinetics of adhesion and motility behavior of cells is presented. Cell adhesion is mediated by the binding of cell wall receptors and substrate's complementary ligands, and tight adhesion is accomplished by the recruitment of the cell wall binders to the adhesion zone. The binders' movement is modeled as their axisymmetric diffusion in the fluid-like cell membrane. In order to preserve the thermodynamic consistency, the energy balance for the cell-substrate interaction is imposed on the diffusion equation. Solving the axisymmetric diffusion-energy balance coupled equations, it turns out that the physical properties of the substrate (substrate's ligand spacing and stiffness) have considerable effects on the cell adhesion and motility kinetics. For a rigid substrate with uniform distribution of immobile ligands, the maximum ligand spacing which does not interrupt adhesion growth is found to be about 57 nm. It is also found that as a consequence of the reduction in the energy dissipation in the isolated adhesion system, cell adhesion is facilitated by increasing substrate's stiffness. Moreover, the directional movement of cells on a substrate with gradients in mechanical compliance is explored with an extension of the adhesion formulation. It is shown that cells tend to move from soft to stiff regions of the substrate, but their movement is decelerated as the stiffness of the substrate increases. These findings based on the proposed theoretical model are in excellent agreement with the previous experimental observations.

Modelling uncertainty in incompressible flow simulation using Galerkin based generalized ANOVA

NASA Astrophysics Data System (ADS)

Chakraborty, Souvik; Chowdhury, Rajib

2016-11-01

This paper presents a new algorithm, referred to here as Galerkin based generalized analysis of variance decomposition (GG-ANOVA) for modelling input uncertainties and its propagation in incompressible fluid flow. The proposed approach utilizes ANOVA to represent the unknown stochastic response. Further, the unknown component functions of ANOVA are represented using the generalized polynomial chaos expansion (PCE). The resulting functional form obtained by coupling the ANOVA and PCE is substituted into the stochastic Navier-Stokes equation (NSE) and Galerkin projection is employed to decompose it into a set of coupled deterministic 'Navier-Stokes alike' equations. Temporal discretization of the set of coupled deterministic equations is performed by employing Adams-Bashforth scheme for convective term and Crank-Nicolson scheme for diffusion term. Spatial discretization is performed by employing finite difference scheme. Implementation of the proposed approach has been illustrated by two examples. In the first example, a stochastic ordinary differential equation has been considered. This example illustrates the performance of proposed approach with change in nature of random variable. Furthermore, convergence characteristics of GG-ANOVA has also been demonstrated. The second example investigates flow through a micro channel. Two case studies, namely the stochastic Kelvin-Helmholtz instability and stochastic vortex dipole, have been investigated. For all the problems results obtained using GG-ANOVA are in excellent agreement with benchmark solutions.

CFD-ACE+: a CAD system for simulation and modeling of MEMS

NASA Astrophysics Data System (ADS)

Stout, Phillip J.; Yang, H. Q.; Dionne, Paul; Leonard, Andy; Tan, Zhiqiang; Przekwas, Andrzej J.; Krishnan, Anantha

1999-03-01

Computer aided design (CAD) systems are a key to designing and manufacturing MEMS with higher performance/reliability, reduced costs, shorter prototyping cycles and improved time- to-market. One such system is CFD-ACE+MEMS, a modeling and simulation environment for MEMS which includes grid generation, data visualization, graphical problem setup, and coupled fluidic, thermal, mechanical, electrostatic, and magnetic physical models. The fluid model is a 3D multi- block, structured/unstructured/hybrid, pressure-based, implicit Navier-Stokes code with capabilities for multi- component diffusion, multi-species transport, multi-step gas phase chemical reactions, surface reactions, and multi-media conjugate heat transfer. The thermal model solves the total enthalpy from of the energy equation. The energy equation includes unsteady, convective, conductive, species energy, viscous dissipation, work, and radiation terms. The electrostatic model solves Poisson's equation. Both the finite volume method and the boundary element method (BEM) are available for solving Poisson's equation. The BEM method is useful for unbounded problems. The magnetic model solves for the vector magnetic potential from Maxwell's equations including eddy currents but neglecting displacement currents. The mechanical model is a finite element stress/deformation solver which has been coupled to the flow, heat, electrostatic, and magnetic calculations to study flow, thermal electrostatically, and magnetically included deformations of structures. The mechanical or structural model can accommodate elastic and plastic materials, can handle large non-linear displacements, and can model isotropic and anisotropic materials. The thermal- mechanical coupling involves the solution of the steady state Navier equation with thermoelastic deformation. The electrostatic-mechanical coupling is a calculation of the pressure force due to surface charge on the mechanical structure. Results of CFD-ACE+MEMS modeling of MEMS such as cantilever beams, accelerometers, and comb drives are discussed.

On the transition from the Ginzburg-Landau equation to the extended Fisher-Kolmogorov equation

NASA Astrophysics Data System (ADS)

Rottschäfer, Vivi; Doelman, Arjen

1998-07-01

The Ginzburg-Landau (GL) equation ‘generically’ describes the behaviour of small perturbations of a marginally unstable basic state in systems on unbounded domains. In this paper we consider the transition from this generic situation to a degenerate (co-dimension 2) case in which the GL approach is no longer valid. Instead of studying a general underlying model problem, we consider a two-dimensional system of coupled reaction-diffusion equations in one spatial dimension. We show that near the degeneration the behaviour of small perturbations is governed by the extended Fisher-Kolmogorov (eFK) equation (at leading order). The relation between the GL-equation and the eFK-equation is quite subtle, but can be analysed in detail. The main goal of this paper is to study this relation, which we do asymptotically. The asymptotic analysis is compared to numerical simulations of the full reaction-diffusion system. As one approaches the co-dimension 2 point, we observe that the stable stationary periodic patterns predicted by the GL-equation evolve towards various different families of stable, stationary (but not necessarily periodic) so-called ‘multi-bump’ solutions. In the literature, these multi-bump patterns are shown to exist as solutions of the eFK-equation, but there is no proof of the asymptotic stability of these solutions. Our results suggest that these multi-bump patterns can also be asymptotically stable in large classes of model problems.

Coupled thermo-chemical boundary conditions in double-diffusive geodynamo models at arbitrary Lewis numbers.

NASA Astrophysics Data System (ADS)

Bouffard, M.

2016-12-01

Convection in the Earth's outer core is driven by the combination of two buoyancy sources: a thermal source directly related to the Earth's secular cooling, the release of latent heat and possibly the heat generated by radioactive decay, and a compositional source due to the crystallization of the growing inner core which releases light elements into the liquid outer core. The dynamics of fusion/crystallization being dependent on the heat flux distribution, the thermochemical boundary conditions are coupled at the inner core boundary which may affect the dynamo in various ways, particularly if heterogeneous conditions are imposed at one boundary. In addition, the thermal and compositional molecular diffusivities differ by three orders of magnitude. This can produce significant differences in the convective dynamics compared to pure thermal or compositional convection due to the potential occurence of double-diffusive phenomena. Traditionally, temperature and composition have been combined into one single variable called codensity under the assumption that turbulence mixes all physical properties at an "eddy-diffusion" rate. This description does not allow for a proper treatment of the thermochemical coupling and is certainly incorrect within stratified layers in which double-diffusive phenomena can be expected. For a more general and rigorous approach, two distinct transport equations should therefore be solved for temperature and composition. However, the weak compositional diffusivity is technically difficult to handle in current geodynamo codes and requires the use of a semi-Lagrangian description to minimize numerical diffusion. We implemented a "particle-in-cell" method into a geodynamo code to properly describe the compositional field. The code is suitable for High Parallel Computing architectures and was successfully tested on two benchmarks. Following the work by Aubert et al. (2008) we use this new tool to perform dynamo simulations including thermochemical coupling at the inner core boundary as well as exploration of the infinite Lewis number limit to study the effect of a heterogeneous core mantle boundary heat flow on the inner core growth.

A finite elements method to solve the Bloch–Torrey equation applied to diffusion magnetic resonance imaging

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

Nguyen, Dang Van; NeuroSpin, Bat145, Point Courrier 156, CEA Saclay Center, 91191 Gif-sur-Yvette Cedex; Li, Jing-Rebecca, E-mail: jingrebecca.li@inria.fr

2014-04-15

The complex transverse water proton magnetization subject to diffusion-encoding magnetic field gradient pulses in a heterogeneous medium can be modeled by the multiple compartment Bloch–Torrey partial differential equation (PDE). In addition, steady-state Laplace PDEs can be formulated to produce the homogenized diffusion tensor that describes the diffusion characteristics of the medium in the long time limit. In spatial domains that model biological tissues at the cellular level, these two types of PDEs have to be completed with permeability conditions on the cellular interfaces. To solve these PDEs, we implemented a finite elements method that allows jumps in the solution atmore » the cell interfaces by using double nodes. Using a transformation of the Bloch–Torrey PDE we reduced oscillations in the searched-for solution and simplified the implementation of the boundary conditions. The spatial discretization was then coupled to the adaptive explicit Runge–Kutta–Chebyshev time-stepping method. Our proposed method is second order accurate in space and second order accurate in time. We implemented this method on the FEniCS C++ platform and show time and spatial convergence results. Finally, this method is applied to study some relevant questions in diffusion MRI.« less

On the dynamics of some grid adaption schemes

NASA Technical Reports Server (NTRS)

Sweby, Peter K.; Yee, Helen C.

1994-01-01

The dynamics of a one-parameter family of mesh equidistribution schemes coupled with finite difference discretisations of linear and nonlinear convection-diffusion model equations is studied numerically. It is shown that, when time marched to steady state, the grid adaption not only influences the stability and convergence rate of the overall scheme, but can also introduce spurious dynamics to the numerical solution procedure.

Data fitting and image fine-tuning approach to solve the inverse problem in fluorescence molecular imaging

NASA Astrophysics Data System (ADS)

Gorpas, Dimitris; Politopoulos, Kostas; Yova, Dido; Andersson-Engels, Stefan

2008-02-01

One of the most challenging problems in medical imaging is to "see" a tumour embedded into tissue, which is a turbid medium, by using fluorescent probes for tumour labeling. This problem, despite the efforts made during the last years, has not been fully encountered yet, due to the non-linear nature of the inverse problem and the convergence failures of many optimization techniques. This paper describes a robust solution of the inverse problem, based on data fitting and image fine-tuning techniques. As a forward solver the coupled radiative transfer equation and diffusion approximation model is proposed and compromised via a finite element method, enhanced with adaptive multi-grids for faster and more accurate convergence. A database is constructed by application of the forward model on virtual tumours with known geometry, and thus fluorophore distribution, embedded into simulated tissues. The fitting procedure produces the best matching between the real and virtual data, and thus provides the initial estimation of the fluorophore distribution. Using this information, the coupled radiative transfer equation and diffusion approximation model has the required initial values for a computational reasonable and successful convergence during the image fine-tuning application.

Chlorine dioxide-induced and Congo red-inhibited Marangoni effect on the chlorite-trithionate reaction front

NASA Astrophysics Data System (ADS)

Liu, Yang; Ren, Xingfeng; Pan, Changwei; Zheng, Ting; Yuan, Ling; Zheng, Juhua; Gao, Qingyu

2017-10-01

Hydrodynamic flows can exert multiple effects on an exothermal autocatalytic reaction, such as buoyancy and the Marangoni convection, which can change the structure and velocity of chemical waves. Here we report that in the chlorite-trithionate reaction, the production and consumption of chlorine dioxide can induce and inhibit Marangoni flow, respectively, leading to different chemo-hydrodynamic patterns. The horizontal propagation of a reaction-diffusion-convection front was investigated with the upper surface open to the air. The Marangoni convection, induced by gaseous chlorine dioxide on the surface, produced from chlorite disproportionation after the proton autocatalysis, has the same effect as the heat convection. When the Marangoni effect is removed by the reaction of chlorine dioxide with the Congo red (CR) indicator, an oscillatory propagation of the front tip is observed under suitable conditions. Replacing CR with bromophenol blue (BPB) distinctly enhanced the floating, resulting in multiple vortexes, owing to the coexistence between BPB and chlorine dioxide. Using the incompressible Navier-Stokes equations coupled with reaction-diffusion and heat conduction equations, we numerically obtain various experimental scenarios of front instability for the exothermic autocatalytic reaction coupled with buoyancy-driven convection and Marangoni convection.

Analytic Couple Modeling Introducing Device Design Factor, Fin Factor, Thermal Diffusivity Factor, and Inductance Factor

NASA Technical Reports Server (NTRS)

Mackey, Jon; Sehirlioglu, Alp; Dynys, Fred

2014-01-01

A set of convenient thermoelectric device solutions have been derived in order to capture a number of factors which are previously only resolved with numerical techniques. The concise conversion efficiency equations derived from governing equations provide intuitive and straight-forward design guidelines. These guidelines allow for better device design without requiring detailed numerical modeling. The analytical modeling accounts for factors such as i) variable temperature boundary conditions, ii) lateral heat transfer, iii) temperature variable material properties, and iv) transient operation. New dimensionless parameters, similar to the figure of merit, are introduced including the device design factor, fin factor, thermal diffusivity factor, and inductance factor. These new device factors allow for the straight-forward description of phenomenon generally only captured with numerical work otherwise. As an example a device design factor of 0.38, which accounts for thermal resistance of the hot and cold shoes, can be used to calculate a conversion efficiency of 2.28 while the ideal conversion efficiency based on figure of merit alone would be 6.15. Likewise an ideal couple with efficiency of 6.15 will be reduced to 5.33 when lateral heat is accounted for with a fin factor of 1.0.

A novel simulation theory and model system for multi-field coupling pipe-flow system

NASA Astrophysics Data System (ADS)

Chen, Yang; Jiang, Fan; Cai, Guobiao; Xu, Xu

2017-09-01

Due to the lack of a theoretical basis for multi-field coupling in many system-level models, a novel set of system-level basic equations for flow/heat transfer/combustion coupling is put forward. Then a finite volume model of quasi-1D transient flow field for multi-species compressible variable-cross-section pipe flow is established by discretising the basic equations on spatially staggered grids. Combining with the 2D axisymmetric model for pipe-wall temperature field and specific chemical reaction mechanisms, a finite volume model system is established; a set of specific calculation methods suitable for multi-field coupling system-level research is structured for various parameters in this model; specific modularisation simulation models can be further derived in accordance with specific structures of various typical components in a liquid propulsion system. This novel system can also be used to derive two sub-systems: a flow/heat transfer two-field coupling pipe-flow model system without chemical reaction and species diffusion; and a chemical equilibrium thermodynamic calculation-based multi-field coupling system. The applicability and accuracy of two sub-systems have been verified through a series of dynamic modelling and simulations in earlier studies. The validity of this system is verified in an air-hydrogen combustion sample system. The basic equations and the model system provide a unified universal theory and numerical system for modelling and simulation and even virtual testing of various pipeline systems.

Numerical Solution of the Extended Nernst-Planck Model.

PubMed

Samson; Marchand

1999-07-01

The main features of a numerical model aiming at predicting the drift of ions in an electrolytic solution upon a chemical potential gradient are presented. The mechanisms of ionic diffusion are described by solving the extended Nernst-Planck system of equations. The electrical coupling between the various ionic fluxes is accounted for by the Poisson equation. Furthermore, chemical activity effects are considered in the model. The whole system of nonlinear equations is solved using the finite-element method. Results yielded by the model for simple test cases are compared to those obtained using an analytical solution. Applications of the model to more complex problems are also presented and discussed. Copyright 1999 Academic Press.

Hybrid diffusion-P3 equation in N-layered turbid media: steady-state domain.

PubMed

Shi, Zhenzhi; Zhao, Huijuan; Xu, Kexin

2011-10-01

This paper discusses light propagation in N-layered turbid media. The hybrid diffusion-P3 equation is solved for an N-layered finite or infinite turbid medium in the steady-state domain for one point source using the extrapolated boundary condition. The Fourier transform formalism is applied to derive the analytical solutions of the fluence rate in Fourier space. Two inverse Fourier transform methods are developed to calculate the fluence rate in real space. In addition, the solutions of the hybrid diffusion-P3 equation are compared to the solutions of the diffusion equation and the Monte Carlo simulation. For the case of small absorption coefficients, the solutions of the N-layered diffusion equation and hybrid diffusion-P3 equation are almost equivalent and are in agreement with the Monte Carlo simulation. For the case of large absorption coefficients, the model of the hybrid diffusion-P3 equation is more precise than that of the diffusion equation. In conclusion, the model of the hybrid diffusion-P3 equation can replace the diffusion equation for modeling light propagation in the N-layered turbid media for a wide range of absorption coefficients.

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

NASA Astrophysics Data System (ADS)

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

2017-03-01

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

Generalized Cahn-Hilliard equation for solutions with drastically different diffusion coefficients. Application to exsolution in ternary feldspar

NASA Astrophysics Data System (ADS)

Petrishcheva, E.; Abart, R.

2012-04-01

We address mathematical modeling and computer simulations of phase decomposition in a multicomponent system. As opposed to binary alloys with one common diffusion parameter, our main concern is phase decomposition in real geological systems under influence of strongly different interdiffusion coefficients, as it is frequently encountered in mineral solid solutions with coupled diffusion on different sub-lattices. Our goal is to explain deviations from equilibrium element partitioning which are often observed in nature, e.g., in a cooled ternary feldspar. To this end we first adopt the standard Cahn-Hilliard model to the multicomponent diffusion problem and account for arbitrary diffusion coefficients. This is done by using Onsager's approach such that flux of each component results from the combined action of chemical potentials of all components. In a second step the generalized Cahn-Hilliard equation is solved numerically using finite-elements approach. We introduce and investigate several decomposition scenarios that may produce systematic deviations from the equilibrium element partitioning. Both ideal solutions and ternary feldspar are considered. Typically, the slowest component is initially "frozen" and the decomposition effectively takes place only for two "fast" components. At this stage the deviations from the equilibrium element partitioning are indeed observed. These deviations may became "frozen" under conditions of cooling. The final equilibration of the system occurs on a considerably slower time scale. Therefore the system may indeed remain unaccomplished at the observation point. Our approach reveals the intrinsic reasons for the specific phase separation path and rigorously describes it by direct numerical solution of the generalized Cahn-Hilliard equation.

Macro and micro analysis of small molecule diffusion in amorphous polymers

NASA Astrophysics Data System (ADS)

Putta, Santosh Krishna

In this study, both macroscopic and microscopic numerical techniques have been explored, to model and understand the diffusion behavior of small molecules in amorphous polymers, which very often do not follow the classical Fickian law. It was attempted to understand the influence of various aspects of the molecular structure of a polymer on its macroscopic diffusion behavior. At the macroscopic level, a hybrid finite-element/finite-difference model is developed to implement the coupled diffusion and deformation constitutive equations. A viscoelasticity theory, combined with time-freevolume superposition is used to model the deformation processes. A freevolume-based model is used to model the diffusion processes. The freevolume in the polymer is used as a coupling factor between the deformation and the diffusion processes. The model is shown to qualitatively describe some of the typical non-Fickian diffusion behavior in polymers. However, it does not directly involve the microstructure of a polymer. Further, some of the input parameters to the model are difficult to obtain experimentally. A numerical microscopic approach is therefore adopted to study the molecular structure of polymers. A molecular mechanics and dynamics technique combined with a modified Rotational Isomeric State (RIS) approach, is followed to generate the molecular structure for two types of polycarbonates, and, two types of polyacrylates, starting only with their chemical structures. A new efficient 3-D algorithm for Delaunay Tessellation is developed, and, then applied to discretize the molecular structure into Delaunay Tetrahedra. By using the dicretized molecular structure, size, shape, and, connectivity of free-spaces for small molecule diffusion in the above mentioned polymers, are then studied in relation to their diffusion properties. The influence of polymer and side chain flexibility, and diffusant-diffusant and diffusant-polymer molecular interactions, is also discussed with respect to the diffusion properties.

Diffusion for holographic lattices

NASA Astrophysics Data System (ADS)

Donos, Aristomenis; Gauntlett, Jerome P.; Ziogas, Vaios

2018-03-01

We consider black hole spacetimes that are holographically dual to strongly coupled field theories in which spatial translations are broken explicitly. We discuss how the quasinormal modes associated with diffusion of heat and charge can be systematically constructed in a long wavelength perturbative expansion. We show that the dispersion relation for these modes is given in terms of the thermoelectric DC conductivity and static susceptibilities of the dual field theory and thus we derive a generalised Einstein relation from Einstein's equations. A corollary of our results is that thermodynamic instabilities imply specific types of dynamical instabilities of the associated black hole solutions.

Steady-State Electrodiffusion from the Nernst-Planck Equation Coupled to Local Equilibrium Monte Carlo Simulations.

PubMed

Boda, Dezső; Gillespie, Dirk

2012-03-13

We propose a procedure to compute the steady-state transport of charged particles based on the Nernst-Planck (NP) equation of electrodiffusion. To close the NP equation and to establish a relation between the concentration and electrochemical potential profiles, we introduce the Local Equilibrium Monte Carlo (LEMC) method. In this method, Grand Canonical Monte Carlo simulations are performed using the electrochemical potential specified for the distinct volume elements. An iteration procedure that self-consistently solves the NP and flux continuity equations with LEMC is shown to converge quickly. This NP+LEMC technique can be used in systems with diffusion of charged or uncharged particles in complex three-dimensional geometries, including systems with low concentrations and small applied voltages that are difficult for other particle simulation techniques.

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

PubMed

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

2006-02-01

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

Intrinsic electric fields and proton diffusion in immobilized protein membranes. Effects of electrolytes and buffers.

PubMed Central

Zabusky, N J; Deem, G S

1979-01-01

We present a theory for proton diffusion through an immobilized protein membrane perfused with an electrolyte and a buffer. Using a Nernst-Planck equation for each species and assuming local charge neutrality, we obtain two coupled nonlinear diffusion equations with new diffusion coefficients dependent on the concentration of all species, the diffusion constants or mobilities of the buffers and salts, the pH-derivative of the titration curves of the mobile buffer and the immobilized protein, and the derivative with respect to ionic strength of the protein titration curve. Transient time scales are locally pH-dependent because of protonation-deprotonation reactions with the fixed protein and are ionic strength-dependent because salts provide charge carriers to shield internal electric fields. Intrinsic electric fields arise proportional to the gradient of an "effective" charge concentration. The field may reverse locally if buffer concentrations are large (greater to or equal to 0.1 M) and if the diffusivity of the electrolyte species is sufficiently small. The "ideal" electrolyte case (where each species has the same diffusivity) reduces to a simple form. We apply these theoretical considerations to membranes composed of papain and bovine serum albumin (BSA) and show that intrinsic electric fields greatly enhance the mobility of protons when the ionic strength of the salts is smaller than 0.1 M. These results are consistent with experiments where pH changes are observed to depend strongly on buffer, salt, and proton concentrations in baths adjacent to the membranes. PMID:233570

Coarse mesh and one-cell block inversion based diffusion synthetic acceleration

NASA Astrophysics Data System (ADS)

Kim, Kang-Seog

DSA (Diffusion Synthetic Acceleration) has been developed to accelerate the SN transport iteration. We have developed solution techniques for the diffusion equations of FLBLD (Fully Lumped Bilinear Discontinuous), SCB (Simple Comer Balance) and UCB (Upstream Corner Balance) modified 4-step DSA in x-y geometry. Our first multi-level method includes a block Gauss-Seidel iteration for the discontinuous diffusion equation, uses the continuous diffusion equation derived from the asymptotic analysis, and avoids void cell calculation. We implemented this multi-level procedure and performed model problem calculations. The results showed that the FLBLD, SCB and UCB modified 4-step DSA schemes with this multi-level technique are unconditionally stable and rapidly convergent. We suggested a simplified multi-level technique for FLBLD, SCB and UCB modified 4-step DSA. This new procedure does not include iterations on the diffusion calculation or the residual calculation. Fourier analysis results showed that this new procedure was as rapidly convergent as conventional modified 4-step DSA. We developed new DSA procedures coupled with 1-CI (Cell Block Inversion) transport which can be easily parallelized. We showed that 1-CI based DSA schemes preceded by SI (Source Iteration) are efficient and rapidly convergent for LD (Linear Discontinuous) and LLD (Lumped Linear Discontinuous) in slab geometry and for BLD (Bilinear Discontinuous) and FLBLD in x-y geometry. For 1-CI based DSA without SI in slab geometry, the results showed that this procedure is very efficient and effective for all cases. We also showed that 1-CI based DSA in x-y geometry was not effective for thin mesh spacings, but is effective and rapidly convergent for intermediate and thick mesh spacings. We demonstrated that the diffusion equation discretized on a coarse mesh could be employed to accelerate the transport equation. Our results showed that coarse mesh DSA is unconditionally stable and is as rapidly convergent as fine mesh DSA in slab geometry. For x-y geometry our coarse mesh DSA is very effective for thin and intermediate mesh spacings independent of the scattering ratio, but is not effective for purely scattering problems and high aspect ratio zoning. However, if the scattering ratio is less than about 0.95, this procedure is very effective for all mesh spacing.

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

Transverse particle acceleration and diffusion in a planetary magnetic field

NASA Technical Reports Server (NTRS)

Barbosa, D. D.

1994-01-01

A general model of particle acceleration by plasma waves coupled with adiabatic radial diffusion in a planetary magnetic field is developed. The model assumes that a spectrum of lower hybird waves is present to resonantly accelerate ions transverse to the magnetic field. The steady state Green's function for the combined radial diffusion and wave acceleration equation is found in terms of a series expansion. The results provide a rigorous demonstration of how a quasi-Maxwellian distribution function is formed in the absence of particle collisons and elucidate the nature of turbulent heating of magnetospheric plasmas. The solution is applied to the magnetosphere of Neptune for which a number of examples are given illustrating how the spectrum of pickup N(+) ions from Triton evolves.

Stable two-dimensional solitary pulses in linearly coupled dissipative Kadomtsev-Petviashvili equations.

PubMed

Feng, Bao-Feng; Malomed, Boris A; Kawahara, Takuji

2002-11-01

We present a two-dimensional (2D) generalization of the stabilized Kuramoto-Sivashinsky system, based on the Kadomtsev-Petviashvili (KP) equation including dissipation of the generic [Newell-Whitehead-Segel (NWS)] type and gain. The system directly applies to the description of gravity-capillary waves on the surface of a liquid layer flowing down an inclined plane, with a surfactant diffusing along the layer's surface. Actually, the model is quite general, offering a simple way to stabilize nonlinear media, combining the weakly 2D dispersion of the KP type with gain and NWS dissipation. Other applications are internal waves in multilayer fluids flowing down an inclined plane, double-front flames in gaseous mixtures, etc. Parallel to this weakly 2D model, we also introduce and study a semiphenomenological one, whose dissipative terms are isotropic, rather than of the NWS type, in order to check if qualitative results are sensitive to the exact form of the lossy terms. The models include an additional linear equation of the advection-diffusion type, linearly coupled to the main KP-NWS equation. The extra equation provides for stability of the zero background in the system, thus opening a way for the existence of stable localized pulses. We focus on the most interesting case, when the dispersive part of the system is of the KP-I type, which corresponds, e.g., to capillary waves, and makes the existence of completely localized 2D pulses possible. Treating the losses and gain as small perturbations and making use of the balance equation for the field momentum, we find that the equilibrium between the gain and losses may select two steady-state solitons from their continuous family existing in the absence of the dissipative terms (the latter family is found in an exact analytical form, and is numerically demonstrated to be stable). The selected soliton with the larger amplitude is expected to be stable. Direct simulations completely corroborate the analytical predictions, for both the physical and phenomenological models.

Hydrodynamic and Thermal Slip Effect on Double-Diffusive Free Convective Boundary Layer Flow of a Nanofluid Past a Flat Vertical Plate in the Moving Free Stream

PubMed Central

Khan, Waqar A.; Uddin, Md Jashim; Ismail, A. I. Md.

2013-01-01

The effects of hydrodynamic and thermal slip boundary conditions on the double-diffusive free convective flow of a nanofluid along a semi-infinite flat solid vertical plate are investigated numerically. It is assumed that free stream is moving. The governing boundary layer equations are non-dimensionalized and transformed into a system of nonlinear, coupled similarity equations. The effects of the controlling parameters on the dimensionless velocity, temperature, solute and nanofluid concentration as well as on the reduced Nusselt number, reduced Sherwood number and the reduced nanoparticle Sherwood number are investigated and presented graphically. To the best of our knowledge, the effects of hydrodynamic and thermal slip boundary conditions have not been investigated yet. It is found that the reduced local Nusselt, local solute and the local nanofluid Sherwood numbers increase with hydrodynamic slip and decrease with thermal slip parameters. PMID:23533566

Characterization of chaotic electroconvection near flat electrodes under oscillatory voltages

NASA Astrophysics Data System (ADS)

Kim, Jeonglae; Davidson, Scott; Mani, Ali

2017-11-01

Onset of hydrodynamic instability and chaotic electroconvection in aqueous systems are studied by directly solving the two-dimensional coupled Poisson-Nernst-Planck and Navier-Stokes equations. An aqueous binary electrolyte is bounded by two planar electrodes where time-harmonic voltage is applied at a constant oscillation frequency. The governing equations are solved using a fully-conservative second-order-accurate finite volume discretization and a second-order implicit Euler time advancement. At a sufficiently high amplitude of applied voltage, the system exhibits chaotic behaviors involving strong hydrodynamic mixing and enhanced electroconvection. The system responses are characterized as a function of oscillation frequency, voltage magnitude, and the ratio of diffusivities of two ion species. Our results indicate that electroconvection is most enhanced for frequencies on the order of inverse system RC time scale. We will discuss the dependence of this optimal frequency on the asymmetry of the diffusion coefficients of ionic species. Supported by the Stanford's Precourt Institute.

Mathematical modeling and computer simulation of isoelectric focusing with electrochemically defined ampholytes

NASA Technical Reports Server (NTRS)

Palusinski, O. A.; Allgyer, T. T.; Mosher, R. A.; Bier, M.; Saville, D. A.

1981-01-01

A mathematical model of isoelectric focusing at the steady state has been developed for an M-component system of electrochemically defined ampholytes. The model is formulated from fundamental principles describing the components' chemical equilibria, mass transfer resulting from diffusion and electromigration, and electroneutrality. The model consists of ordinary differential equations coupled with a system of algebraic equations. The model is implemented on a digital computer using FORTRAN-based simulation software. Computer simulation data are presented for several two-component systems showing the effects of varying the isoelectric points and dissociation constants of the constituents.

A Closely Coupled Experimental and Numerical Approach for Hypersonic and High Enthalpy Flow Investigations Utilising the HEG Shock Tunnel and the DLR TAU Code

DTIC Science & Technology

2010-04-01

factorization scheme (Lower-Upper Symmetric Gauss- Seidel ) can be used for time integration. Additional convergence acceleration is achieved by the...of the full Stefan -Maxwell equations. The diffusive mass flux of species S is computed according to: for 1 for jS S S Sm j jm S j eS jd S S S j j j...approximate factorization scheme (Lower-Upper Symmetric Gauss- Seidel ). For steady state problems, equation (69) reduces to R=0 because ddU t

Multistage adsorption of diffusing macromolecules and viruses

NASA Astrophysics Data System (ADS)

Chou, Tom; D'Orsogna, Maria R.

2007-09-01

We derive the equations that describe adsorption of diffusing particles onto a surface followed by additional surface kinetic steps before being transported across the interface. Multistage surface kinetics occurs during membrane protein insertion, cell signaling, and the infection of cells by virus particles. For example, viral entry into healthy cells is possible only after a series of receptor and coreceptor binding events occurs at the cellular surface. We couple the diffusion of particles in the bulk phase with the multistage surface kinetics and derive an effective, integrodifferential boundary condition that contains a memory kernel embodying the delay induced by the surface reactions. This boundary condition takes the form of a singular perturbation problem in the limit where particle-surface interactions are short ranged. Moreover, depending on the surface kinetics, the delay kernel induces a nonmonotonic, transient replenishment of the bulk particle concentration near the interface. The approach generalizes that of Ward and Tordai [J. Chem. Phys. 14, 453 (1946)] and Diamant and Andelman [Colloids Surf. A 183-185, 259 (2001)] to include surface kinetics, giving rise to qualitatively new behaviors. Our analysis also suggests a simple scheme by which stochastic surface reactions may be coupled to deterministic bulk diffusion.

Diffuse Optical Tomography for Brain Imaging: Continuous Wave Instrumentation and Linear Analysis Methods

NASA Astrophysics Data System (ADS)

Giacometti, Paolo; Diamond, Solomon G.

Diffuse optical tomography (DOT) is a functional brain imaging technique that measures cerebral blood oxygenation and blood volume changes. This technique is particularly useful in human neuroimaging measurements because of the coupling between neural and hemodynamic activity in the brain. DOT is a multichannel imaging extension of near-infrared spectroscopy (NIRS). NIRS uses laser sources and light detectors on the scalp to obtain noninvasive hemodynamic measurements from spectroscopic analysis of the remitted light. This review explains how NIRS data analysis is performed using a combination of the modified Beer-Lambert law (MBLL) and the diffusion approximation to the radiative transport equation (RTE). Laser diodes, photodiode detectors, and optical terminals that contact the scalp are the main components in most NIRS systems. Placing multiple sources and detectors over the surface of the scalp allows for tomographic reconstructions that extend the individual measurements of NIRS into DOT. Mathematically arranging the DOT measurements into a linear system of equations that can be inverted provides a way to obtain tomographic reconstructions of hemodynamics in the brain.

Hydrodynamic dispersion within porous biofilms

NASA Astrophysics Data System (ADS)

Davit, Y.; Byrne, H.; Osborne, J.; Pitt-Francis, J.; Gavaghan, D.; Quintard, M.

2013-01-01

Many microorganisms live within surface-associated consortia, termed biofilms, that can form intricate porous structures interspersed with a network of fluid channels. In such systems, transport phenomena, including flow and advection, regulate various aspects of cell behavior by controlling nutrient supply, evacuation of waste products, and permeation of antimicrobial agents. This study presents multiscale analysis of solute transport in these porous biofilms. We start our analysis with a channel-scale description of mass transport and use the method of volume averaging to derive a set of homogenized equations at the biofilm-scale in the case where the width of the channels is significantly smaller than the thickness of the biofilm. We show that solute transport may be described via two coupled partial differential equations or telegrapher's equations for the averaged concentrations. These models are particularly relevant for chemicals, such as some antimicrobial agents, that penetrate cell clusters very slowly. In most cases, especially for nutrients, solute penetration is faster, and transport can be described via an advection-dispersion equation. In this simpler case, the effective diffusion is characterized by a second-order tensor whose components depend on (1) the topology of the channels' network; (2) the solute's diffusion coefficients in the fluid and the cell clusters; (3) hydrodynamic dispersion effects; and (4) an additional dispersion term intrinsic to the two-phase configuration. Although solute transport in biofilms is commonly thought to be diffusion dominated, this analysis shows that hydrodynamic dispersion effects may significantly contribute to transport.

Counterflow diffusion flames: effects of thermal expansion and non-unity Lewis numbers

NASA Astrophysics Data System (ADS)

Koundinyan, Sushilkumar P.; Matalon, Moshe; Stewart, D. Scott

2018-05-01

In this work we re-examine the counterflow diffusion flame problem focusing in particular on the flame-flow interactions due to thermal expansion and its influence on various flame properties such as flame location, flame temperature, reactant leakage and extinction conditions. The analysis follows two different procedures: an asymptotic approximation for large activation energy chemical reactions, and a direct numerical approach. The asymptotic treatment follows the general theory of Cheatham and Matalon, which consists of a free-boundary problem with jump conditions across the surface representing the reaction sheet, and is well suited for variable-density flows and for mixtures with non-unity and distinct Lewis numbers for the fuel and oxidiser. Due to density variations, the species and energy transport equations are coupled to the Navier-Stokes equations and the problem does not possess an analytical solution. We thus propose and implement a methodology for solving the free-boundary problem numerically. Results based on the asymptotic approximation are then verified against those obtained from the 'exact' numerical integration of the governing equations, comparing predictions of the various flame properties.

OpenCMISS: a multi-physics & multi-scale computational infrastructure for the VPH/Physiome project.

PubMed

Bradley, Chris; Bowery, Andy; Britten, Randall; Budelmann, Vincent; Camara, Oscar; Christie, Richard; Cookson, Andrew; Frangi, Alejandro F; Gamage, Thiranja Babarenda; Heidlauf, Thomas; Krittian, Sebastian; Ladd, David; Little, Caton; Mithraratne, Kumar; Nash, Martyn; Nickerson, David; Nielsen, Poul; Nordbø, Oyvind; Omholt, Stig; Pashaei, Ali; Paterson, David; Rajagopal, Vijayaraghavan; Reeve, Adam; Röhrle, Oliver; Safaei, Soroush; Sebastián, Rafael; Steghöfer, Martin; Wu, Tim; Yu, Ting; Zhang, Heye; Hunter, Peter

2011-10-01

The VPH/Physiome Project is developing the model encoding standards CellML (cellml.org) and FieldML (fieldml.org) as well as web-accessible model repositories based on these standards (models.physiome.org). Freely available open source computational modelling software is also being developed to solve the partial differential equations described by the models and to visualise results. The OpenCMISS code (opencmiss.org), described here, has been developed by the authors over the last six years to replace the CMISS code that has supported a number of organ system Physiome projects. OpenCMISS is designed to encompass multiple sets of physical equations and to link subcellular and tissue-level biophysical processes into organ-level processes. In the Heart Physiome project, for example, the large deformation mechanics of the myocardial wall need to be coupled to both ventricular flow and embedded coronary flow, and the reaction-diffusion equations that govern the propagation of electrical waves through myocardial tissue need to be coupled with equations that describe the ion channel currents that flow through the cardiac cell membranes. In this paper we discuss the design principles and distributed memory architecture behind the OpenCMISS code. We also discuss the design of the interfaces that link the sets of physical equations across common boundaries (such as fluid-structure coupling), or between spatial fields over the same domain (such as coupled electromechanics), and the concepts behind CellML and FieldML that are embodied in the OpenCMISS data structures. We show how all of these provide a flexible infrastructure for combining models developed across the VPH/Physiome community. Copyright © 2011 Elsevier Ltd. All rights reserved.

Simultaneous Heat and Mass Transfer Model for Convective Drying of Building Material

NASA Astrophysics Data System (ADS)

Upadhyay, Ashwani; Chandramohan, V. P.

2018-04-01

A mathematical model of simultaneous heat and moisture transfer is developed for convective drying of building material. A rectangular brick is considered for sample object. Finite-difference method with semi-implicit scheme is used for solving the transient governing heat and mass transfer equation. Convective boundary condition is used, as the product is exposed in hot air. The heat and mass transfer equations are coupled through diffusion coefficient which is assumed as the function of temperature of the product. Set of algebraic equations are generated through space and time discretization. The discretized algebraic equations are solved by Gauss-Siedel method via iteration. Grid and time independent studies are performed for finding the optimum number of nodal points and time steps respectively. A MATLAB computer code is developed to solve the heat and mass transfer equations simultaneously. Transient heat and mass transfer simulations are performed to find the temperature and moisture distribution inside the brick.

Euler equation computations for the flow over a hovering helicopter rotor

NASA Technical Reports Server (NTRS)

Roberts, Thomas Wesley

1988-01-01

A numerical solution technique is developed for computing the flow field around an isolated helicopter rotor in hover. The flow is governed by the compressible Euler equations which are integrated using a finite volume approach. The Euler equations are coupled to a free wake model of the rotary wing vortical wake. This wake model is incorporated into the finite volume solver using a prescribed flow, or perturbation, technique which eliminates the numerical diffusion of vorticity due to the artificial viscosity of the scheme. The work is divided into three major parts: (1) comparisons of Euler solutions to experimental data for the flow around isolated wings show good agreement with the surface pressures, but poor agreement with the vortical wake structure; (2) the perturbation method is developed and used to compute the interaction of a streamwise vortex with a semispan wing. The rapid diffusion of the vortex when only the basic Euler solver is used is illustrated, and excellent agreement with experimental section lift coefficients is demonstrated when using the perturbation approach; and (3) the free wake solution technique is described and the coupling of the wake to the Euler solver for an isolated rotor is presented. Comparisons with experimental blade load data for several cases show good agreement, with discrepancies largely attributable to the neglect of viscous effects. The computed wake geometries agree less well with experiment, the primary difference being that too rapid a wake contraction is predicted for all the cases.

Cellular Automata for Spatiotemporal Pattern Formation from Reaction-Diffusion Partial Differential Equations

NASA Astrophysics Data System (ADS)

Ohmori, Shousuke; Yamazaki, Yoshihiro

2016-01-01

Ultradiscrete equations are derived from a set of reaction-diffusion partial differential equations, and cellular automaton rules are obtained on the basis of the ultradiscrete equations. Some rules reproduce the dynamical properties of the original reaction-diffusion equations, namely, bistability and pulse annihilation. Furthermore, other rules bring about soliton-like preservation and periodic pulse generation with a pacemaker, which are not obtained from the original reaction-diffusion equations.

Quantum Brownian motion with inhomogeneous damping and diffusion

NASA Astrophysics Data System (ADS)

Massignan, Pietro; Lampo, Aniello; Wehr, Jan; Lewenstein, Maciej

2015-03-01

We analyze the microscopic model of quantum Brownian motion, describing a Brownian particle interacting with a bosonic bath through a coupling which is linear in the creation and annihilation operators of the bath, but may be a nonlinear function of the position of the particle. Physically, this corresponds to a configuration in which damping and diffusion are spatially inhomogeneous. We derive systematically the quantum master equation for the Brownian particle in the Born-Markov approximation and we discuss the appearance of additional terms, for various polynomials forms of the coupling. We discuss the cases of linear and quadratic coupling in great detail and we derive, using Wigner function techniques, the stationary solutions of the master equation for a Brownian particle in a harmonic trapping potential. We predict quite generally Gaussian stationary states, and we compute the aspect ratio and the spread of the distributions. In particular, we find that these solutions may be squeezed (superlocalized) with respect to the position of the Brownian particle. We analyze various restrictions to the validity of our theory posed by non-Markovian effects and by the Heisenberg principle. We further study the dynamical stability of the system, by applying a Gaussian approximation to the time-dependent Wigner function, and we compute the decoherence rates of coherent quantum superpositions in position space. Finally, we propose a possible experimental realization of the physics discussed here, by considering an impurity particle embedded in a degenerate quantum gas.

A minimally-resolved immersed boundary model for reaction-diffusion problems

NASA Astrophysics Data System (ADS)

Pal Singh Bhalla, Amneet; Griffith, Boyce E.; Patankar, Neelesh A.; Donev, Aleksandar

2013-12-01

We develop an immersed boundary approach to modeling reaction-diffusion processes in dispersions of reactive spherical particles, from the diffusion-limited to the reaction-limited setting. We represent each reactive particle with a minimally-resolved "blob" using many fewer degrees of freedom per particle than standard discretization approaches. More complicated or more highly resolved particle shapes can be built out of a collection of reactive blobs. We demonstrate numerically that the blob model can provide an accurate representation at low to moderate packing densities of the reactive particles, at a cost not much larger than solving a Poisson equation in the same domain. Unlike multipole expansion methods, our method does not require analytically computed Green's functions, but rather, computes regularized discrete Green's functions on the fly by using a standard grid-based discretization of the Poisson equation. This allows for great flexibility in implementing different boundary conditions, coupling to fluid flow or thermal transport, and the inclusion of other effects such as temporal evolution and even nonlinearities. We develop multigrid-based preconditioners for solving the linear systems that arise when using implicit temporal discretizations or studying steady states. In the diffusion-limited case the resulting linear system is a saddle-point problem, the efficient solution of which remains a challenge for suspensions of many particles. We validate our method by comparing to published results on reaction-diffusion in ordered and disordered suspensions of reactive spheres.

Deformations of a pre-stretched and lubricated finite elastic membrane driven by non-uniform external forcing

NASA Astrophysics Data System (ADS)

Boyko, Evgeniy; Gat, Amir; Bercovici, Moran

2017-11-01

We study viscous-elastic dynamics of a fluid confined between a rigid plate and a finite pre-stretched circular elastic membrane, pinned at its boundaries. The membrane is subjected to forces acting either directly on the membrane or through a pressure distribution in the fluid. Under the assumptions of strong pre-stretching and small deformations of the elastic sheet, and by applying the lubrication approximation for the flow, we derive the Green's function for the resulting linearized 4th order diffusion equation governing the deformation field in cylindrical coordinates. In addition, defining an asymptotic expansion with the ratio of the induced to prescribed tension serving as the small parameter, we reduce the coupled Reynolds and non-linear von-Karman equations to a set of three one-way coupled linear equations. The solutions to these equations provide insight onto the effects of induced tension, and enable simplified prediction of the correction for the deformation field. Funded by the European Research Council (ERC) under the European Union'sHorizon 2020 Research and Innovation Programme, Grant Agreement No. 678734 (MetamorphChip). E.B. is supported by the Adams Fellowship Program.

Radial Diffusion study of the 1 June 2013 CME event using MHD simulations.

NASA Astrophysics Data System (ADS)

Patel, M.; Hudson, M.; Wiltberger, M. J.; Li, Z.; Boyd, A. J.

2016-12-01

The June 1, 2013 storm was a CME-shock driven geomagnetic storm (Dst = -119 nT) that caused a dropout affecting all radiation belt electron energies measured by the Energetic Particle, Composition and Thermal Plasma Suite (ECT) instrument on Van Allen Probes at higher L-shells following dynamic pressure enhancement in the solar wind. Lower energies (up to about 700 keV) were enhanced by the storm while MeV electrons were depleted throughout the belt. We focus on depletion through radial diffusion caused by the enhanced ULF wave activity due to the CME-shock. This study utilities the Lyon-Fedder-Mobarry (LFM) model, a 3D global magnetospheric simulation code based on the ideal MHD equations, coupled with the Magnetosphere Ionosphere Coupler (MIX) and Rice Convection Model (RCM). The MHD electric and magnetic fields with equations described by Fei et al. [JGR, 2006] are used to calculate radial diffusion coefficients (DLL). These DLL values are input into a radial diffusion code to recreate the dropouts observed by the Van Allen Probes. The importance of understanding the complex role that ULF waves play in radial transport and the effects of CME-driven storms on the relativistic energy electrons in the radiation belts can be accomplished using MHD simulations to obtain diffusion coefficients, initial phase space density and the outer boundary condition from the ECT instrument suite and a radial diffusion model to reproduce observed fluxes which compare favorably with Van Allen Probes ECT measurements.

Spreading of nonmotile bacteria on a hard agar plate: Comparison between agent-based and stochastic simulations

NASA Astrophysics Data System (ADS)

Rana, Navdeep; Ghosh, Pushpita; Perlekar, Prasad

2017-11-01

We study spreading of a nonmotile bacteria colony on a hard agar plate by using agent-based and continuum models. We show that the spreading dynamics depends on the initial nutrient concentration, the motility, and the inherent demographic noise. Population fluctuations are inherent in an agent-based model, whereas for the continuum model we model them by using a stochastic Langevin equation. We show that the intrinsic population fluctuations coupled with nonlinear diffusivity lead to a transition from a diffusion limited aggregation type of morphology to an Eden-like morphology on decreasing the initial nutrient concentration.

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

Fractional Diffusion Processes: Probability Distributions and Continuous Time Random Walk

NASA Astrophysics Data System (ADS)

Gorenflo, R.; Mainardi, F.

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

Comparisons of hybrid radiosity-diffusion model and diffusion equation for bioluminescence tomography in cavity cancer detection

NASA Astrophysics Data System (ADS)

Chen, Xueli; Yang, Defu; Qu, Xiaochao; Hu, Hao; Liang, Jimin; Gao, Xinbo; Tian, Jie

2012-06-01

Bioluminescence tomography (BLT) has been successfully applied to the detection and therapeutic evaluation of solid cancers. However, the existing BLT reconstruction algorithms are not accurate enough for cavity cancer detection because of neglecting the void problem. Motivated by the ability of the hybrid radiosity-diffusion model (HRDM) in describing the light propagation in cavity organs, an HRDM-based BLT reconstruction algorithm was provided for the specific problem of cavity cancer detection. HRDM has been applied to optical tomography but is limited to simple and regular geometries because of the complexity in coupling the boundary between the scattering and void region. In the provided algorithm, HRDM was first applied to three-dimensional complicated and irregular geometries and then employed as the forward light transport model to describe the bioluminescent light propagation in tissues. Combining HRDM with the sparse reconstruction strategy, the cavity cancer cells labeled with bioluminescent probes can be more accurately reconstructed. Compared with the diffusion equation based reconstruction algorithm, the essentiality and superiority of the HRDM-based algorithm were demonstrated with simulation, phantom and animal studies. An in vivo gastric cancer-bearing nude mouse experiment was conducted, whose results revealed the ability and feasibility of the HRDM-based algorithm in the biomedical application of gastric cancer detection.

Comparisons of hybrid radiosity-diffusion model and diffusion equation for bioluminescence tomography in cavity cancer detection.

PubMed

Chen, Xueli; Yang, Defu; Qu, Xiaochao; Hu, Hao; Liang, Jimin; Gao, Xinbo; Tian, Jie

2012-06-01

Bioluminescence tomography (BLT) has been successfully applied to the detection and therapeutic evaluation of solid cancers. However, the existing BLT reconstruction algorithms are not accurate enough for cavity cancer detection because of neglecting the void problem. Motivated by the ability of the hybrid radiosity-diffusion model (HRDM) in describing the light propagation in cavity organs, an HRDM-based BLT reconstruction algorithm was provided for the specific problem of cavity cancer detection. HRDM has been applied to optical tomography but is limited to simple and regular geometries because of the complexity in coupling the boundary between the scattering and void region. In the provided algorithm, HRDM was first applied to three-dimensional complicated and irregular geometries and then employed as the forward light transport model to describe the bioluminescent light propagation in tissues. Combining HRDM with the sparse reconstruction strategy, the cavity cancer cells labeled with bioluminescent probes can be more accurately reconstructed. Compared with the diffusion equation based reconstruction algorithm, the essentiality and superiority of the HRDM-based algorithm were demonstrated with simulation, phantom and animal studies. An in vivo gastric cancer-bearing nude mouse experiment was conducted, whose results revealed the ability and feasibility of the HRDM-based algorithm in the biomedical application of gastric cancer detection.

Diffusion in shear flow

NASA Astrophysics Data System (ADS)

Dufty, J. W.

1984-09-01

Diffusion of a tagged particle in a fluid with uniform shear flow is described. The continuity equation for the probability density describing the position of the tagged particle is considered. The diffusion tensor is identified by expanding the irreversible part of the probability current to first order in the gradient of the probability density, but with no restriction on the shear rate. The tensor is expressed as the time integral of a nonequilibrium autocorrelation function for the velocity of the tagged particle in its local fluid rest frame, generalizing the Green-Kubo expression to the nonequilibrium state. The tensor is evaluated from results obtained previously for the velocity autocorrelation function that are exact for Maxwell molecules in the Boltzmann limit. The effects of viscous heating are included and the dependence on frequency and shear rate is displayed explicitly. The mode-coupling contributions to the frequency and shear-rate dependent diffusion tensor are calculated.

PDF approach for compressible turbulent reacting flows

NASA Technical Reports Server (NTRS)

Hsu, A. T.; Tsai, Y.-L. P.; Raju, M. S.

1993-01-01

The objective of the present work is to develop a probability density function (pdf) turbulence model for compressible reacting flows for use with a CFD flow solver. The probability density function of the species mass fraction and enthalpy are obtained by solving a pdf evolution equation using a Monte Carlo scheme. The pdf solution procedure is coupled with a compressible CFD flow solver which provides the velocity and pressure fields. A modeled pdf equation for compressible flows, capable of capturing shock waves and suitable to the present coupling scheme, is proposed and tested. Convergence of the combined finite-volume Monte Carlo solution procedure is discussed, and an averaging procedure is developed to provide smooth Monte-Carlo solutions to ensure convergence. Two supersonic diffusion flames are studied using the proposed pdf model and the results are compared with experimental data; marked improvements over CFD solutions without pdf are observed. Preliminary applications of pdf to 3D flows are also reported.

Coupled numerical approach combining finite volume and lattice Boltzmann methods for multi-scale multi-physicochemical processes

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

Chen, Li; He, Ya-Ling; Kang, Qinjun

2013-12-15

A coupled (hybrid) simulation strategy spatially combining the finite volume method (FVM) and the lattice Boltzmann method (LBM), called CFVLBM, is developed to simulate coupled multi-scale multi-physicochemical processes. In the CFVLBM, computational domain of multi-scale problems is divided into two sub-domains, i.e., an open, free fluid region and a region filled with porous materials. The FVM and LBM are used for these two regions, respectively, with information exchanged at the interface between the two sub-domains. A general reconstruction operator (RO) is proposed to derive the distribution functions in the LBM from the corresponding macro scalar, the governing equation of whichmore » obeys the convection–diffusion equation. The CFVLBM and the RO are validated in several typical physicochemical problems and then are applied to simulate complex multi-scale coupled fluid flow, heat transfer, mass transport, and chemical reaction in a wall-coated micro reactor. The maximum ratio of the grid size between the FVM and LBM regions is explored and discussed. -- Highlights: •A coupled simulation strategy for simulating multi-scale phenomena is developed. •Finite volume method and lattice Boltzmann method are coupled. •A reconstruction operator is derived to transfer information at the sub-domains interface. •Coupled multi-scale multiple physicochemical processes in micro reactor are simulated. •Techniques to save computational resources and improve the efficiency are discussed.« less

Multiphysics modelling of the separation of suspended particles via frequency ramping of ultrasonic standing waves.

PubMed

Trujillo, Francisco J; Eberhardt, Sebastian; Möller, Dirk; Dual, Jurg; Knoerzer, Kai

2013-03-01

A model was developed to determine the local changes of concentration of particles and the formations of bands induced by a standing acoustic wave field subjected to a sawtooth frequency ramping pattern. The mass transport equation was modified to incorporate the effect of acoustic forces on the concentration of particles. This was achieved by balancing the forces acting on particles. The frequency ramping was implemented as a parametric sweep for the time harmonic frequency response in time steps of 0.1s. The physics phenomena of piezoelectricity, acoustic fields and diffusion of particles were coupled and solved in COMSOL Multiphysics™ (COMSOL AB, Stockholm, Sweden) following a three step approach. The first step solves the governing partial differential equations describing the acoustic field by assuming that the pressure field achieves a pseudo steady state. In the second step, the acoustic radiation force is calculated from the pressure field. The final step allows calculating the locally changing concentration of particles as a function of time by solving the modified equation of particle transport. The diffusivity was calculated as function of concentration following the Garg and Ruthven equation which describes the steep increase of diffusivity when the concentration approaches saturation. However, it was found that this steep increase creates numerical instabilities at high voltages (in the piezoelectricity equations) and high initial particle concentration. The model was simplified to a pseudo one-dimensional case due to computation power limitations. The predicted particle distribution calculated with the model is in good agreement with the experimental data as it follows accurately the movement of the bands in the centre of the chamber. Crown Copyright © 2012. Published by Elsevier B.V. All rights reserved.

Continuum simulations of acetylcholine consumption by acetylcholinesterase: a Poisson-Nernst-Planck approach.

PubMed

Zhou, Y C; Lu, Benzhuo; Huber, Gary A; Holst, Michael J; McCammon, J Andrew

2008-01-17

The Poisson-Nernst-Planck (PNP) equation provides a continuum description of electrostatic-driven diffusion and is used here to model the diffusion and reaction of acetylcholine (ACh) with acetylcholinesterase (AChE) enzymes. This study focuses on the effects of ion and substrate concentrations on the reaction rate and rate coefficient. To this end, the PNP equations are numerically solved with a hybrid finite element and boundary element method at a wide range of ion and substrate concentrations, and the results are compared with the partially coupled Smoluchowski-Poisson-Boltzmann model. The reaction rate is found to depend strongly on the concentrations of both the substrate and ions; this is explained by the competition between the intersubstrate repulsion and the ionic screening effects. The reaction rate coefficient is independent of the substrate concentration only at very high ion concentrations, whereas at low ion concentrations the behavior of the rate depends strongly on the substrate concentration. Moreover, at physiological ion concentrations, variations in substrate concentration significantly affect the transient behavior of the reaction. Our results offer a reliable estimate of reaction rates at various conditions and imply that the concentrations of charged substrates must be coupled with the electrostatic computation to provide a more realistic description of neurotransmission and other electrodiffusion and reaction processes.

Some Properties of the Fractional Equation of Continuity and the Fractional Diffusion Equation

NASA Astrophysics Data System (ADS)

Fukunaga, Masataka

2006-05-01

The fractional equation of continuity (FEC) and the fractional diffusion equation (FDE) show peculiar behaviors that are in the opposite sense to those expected from the equation of continuity and the diffusion equation, respectively. The behaviors are interpreted in terms of the memory effect of the fractional time derivatives included in the equations. Some examples are given by solutions of the FDE.

Solution of a modified fractional diffusion equation

NASA Astrophysics Data System (ADS)

Langlands, T. A. M.

2006-07-01

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

Steady MHD free convection heat and mass transfer flow about a vertical porous surface with thermal diffusion and induced magnetic field

NASA Astrophysics Data System (ADS)

Touhid Hossain, M. M.; Afruz-Zaman, Md.; Rahman, Fouzia; Hossain, M. Arif

2013-09-01

In this study the thermal diffusion effect on the steady laminar free convection flow and heat transfer of viscous incompressible MHD electrically conducting fluid above a vertical porous surface is considered under the influence of an induced magnetic field. The governing non-dimensional equations relevant to the problem, containing the partial differential equations, are transformed by usual similarity transformations into a system of coupled non-linear ordinary differential equations and will be solved analytically by using the perturbation technique. On introducing the non-dimensional concept and applying Boussinesq's approximation, the solutions for velocity field, temperature distribution and induced magnetic field to the second order approximations are obtained for large suction with different selected values of the established dimensionless parameters. The influences of these various establish parameters on the velocity and temperature fields and on the induced magnetic fields are exhibited under certain assumptions and are studied graphically in the present analysis. It is observed that the effects of thermal-diffusion and large suction have great importance on the velocity, temperature and induced magnetic fields and mass concentration for several fluids considered, so that their effects should be taken into account with other useful parameters associated. It is also found that the dimensionless Prandtl number, Grashof number, Modified Grashof number and magnetic parameter have an appreciable influence on the concerned independent variables.

Quasi-two-layer morphodynamic model for bedload-dominated problems: bed slope-induced morphological diffusion

NASA Astrophysics Data System (ADS)

Maldonado, Sergio; Borthwick, Alistair G. L.

2018-02-01

We derive a two-layer depth-averaged model of sediment transport and morphological evolution for application to bedload-dominated problems. The near-bed transport region is represented by the lower (bedload) layer which has an arbitrarily constant, vanishing thickness (of approx. 10 times the sediment particle diameter), and whose average sediment concentration is free to vary. Sediment is allowed to enter the upper layer, and hence the total load may also be simulated, provided that concentrations of suspended sediment remain low. The model conforms with established theories of bedload, and is validated satisfactorily against empirical expressions for sediment transport rates and the morphodynamic experiment of a migrating mining pit by Lee et al. (1993 J. Hydraul. Eng. 119, 64-80 (doi:10.1061/(ASCE)0733-9429(1993)119:1(64))). Investigation into the effect of a local bed gradient on bedload leads to derivation of an analytical, physically meaningful expression for morphological diffusion induced by a non-zero local bed slope. Incorporation of the proposed morphological diffusion into a conventional morphodynamic model (defined as a coupling between the shallow water equations, Exner equation and an empirical formula for bedload) improves model predictions when applied to the evolution of a mining pit, without the need either to resort to special numerical treatment of the equations or to use additional tuning parameters.

Quasi-two-layer morphodynamic model for bedload-dominated problems: bed slope-induced morphological diffusion.

PubMed

Maldonado, Sergio; Borthwick, Alistair G L

2018-02-01

We derive a two-layer depth-averaged model of sediment transport and morphological evolution for application to bedload-dominated problems. The near-bed transport region is represented by the lower (bedload) layer which has an arbitrarily constant, vanishing thickness (of approx. 10 times the sediment particle diameter), and whose average sediment concentration is free to vary. Sediment is allowed to enter the upper layer, and hence the total load may also be simulated, provided that concentrations of suspended sediment remain low. The model conforms with established theories of bedload, and is validated satisfactorily against empirical expressions for sediment transport rates and the morphodynamic experiment of a migrating mining pit by Lee et al. (1993 J. Hydraul. Eng. 119 , 64-80 (doi:10.1061/(ASCE)0733-9429(1993)119:1(64))). Investigation into the effect of a local bed gradient on bedload leads to derivation of an analytical, physically meaningful expression for morphological diffusion induced by a non-zero local bed slope. Incorporation of the proposed morphological diffusion into a conventional morphodynamic model (defined as a coupling between the shallow water equations, Exner equation and an empirical formula for bedload) improves model predictions when applied to the evolution of a mining pit, without the need either to resort to special numerical treatment of the equations or to use additional tuning parameters.

Modelling gait transition in two-legged animals

NASA Astrophysics Data System (ADS)

Pinto, Carla M. A.; Santos, Alexandra P.

2011-12-01

The study of locomotor patterns has been a major research goal in the last decades. Understanding how intralimb and interlimb coordination works out so well in animals' locomotion is a hard and challenging task. Many models have been proposed to model animal's rhythms. These models have also been applied to the control of rhythmic movements of adaptive legged robots, namely biped, quadruped and other designs. In this paper we study gait transition in a central pattern generator (CPG) model for bipeds, the 4-cells model. This model is proposed by Golubitsky, Stewart, Buono and Collins and is studied further by Pinto and Golubitsky. We briefly resume the work done by Pinto and Golubitsky. We compute numerically gait transition in the 4-cells CPG model for bipeds. We use Morris-Lecar equations and Wilson-Cowan equations as the internal dynamics for each cell. We also consider two types of coupling between the cells: diffusive and synaptic. We obtain secondary gaits by bifurcation of primary gaits, by varying the coupling strengths. Nevertheless, some bifurcating branches could not be obtained, emphasizing the fact that despite analytically those bifurcations exist, finding them is a hard task and requires variation of other parameters of the equations. We note that the type of coupling did not influence the results.

On two parabolic systems: Convergence and blowup

NASA Astrophysics Data System (ADS)

Huang, Yamin

1998-12-01

This dissertation studies two parabolic systems. It consists of two parts. In part one (chapter one), we prove a convergence result, namely, the solution (AK,/ BK) of a system of chemical diffusion-reaction equations (with reaction rate K) converges to the solution (A, B) of a diffusion- instantaneous-reaction equation. To prove our main result, we use some L1 and L2 'energy' estimates and a compactness result due to Aubin (1). As a by-product we also prove that as K approaches infinity, the limit solution exhibits phase separation between A and B. In part two (chapter two), we study the blowup rate for a system of heat equations ut=/Delta u,/ vt=/Delta v in a bounded domain Ωtimes(0,T) coupled in the nonlinear Neumann boundary conditions [/partial u/over/partial n]=vp,/ [/partial v/over/partial n]=uq on ∂Omega×[ 0,T), where p>0,/ q>0,/ pq>1 and n is the exterior normal vector on ∂Omega. Under certain assumptions, we establish exact blowup rate which generalizes the corresponding results of some authors' recent work including Deng (2), Deng-Fila-Levine (3) and Hu-Yin (4). ftn (1) J. P. A scUBIN, Un theoreme de compacite, C. R. Acad. Sci., 256(1963), pp. 5042-5044. (2) K. D scENG, Blow-up rates for parabolic systems, Z. Angew. Math. Phys., 47(1996), No. 1, pp. 132-143. (3) K. D scENG, M. F scILA AND H. A. L scEVINE, On critical exponents for a system of heat equations coupled in the boundary conditions, Acta Math. Univ. Comenian. (N.S.), 36(1994), No. 2, pp. 169-192. (4) B. H scU scAND H. M. Y scIN, The profile near blowup time for solutions of the heat equation with a nonlinear boundary condition, Trans. Amer. Math. Soc., 346(1994), pp. 117-135.

Fully implicit moving mesh adaptive algorithm

NASA Astrophysics Data System (ADS)

Chacon, Luis

2005-10-01

In many problems of interest, the numerical modeler is faced with the challenge of dealing with multiple time and length scales. The former is best dealt with with fully implicit methods, which are able to step over fast frequencies to resolve the dynamical time scale of interest. The latter requires grid adaptivity for efficiency. Moving-mesh grid adaptive methods are attractive because they can be designed to minimize the numerical error for a given resolution. However, the required grid governing equations are typically very nonlinear and stiff, and of considerably difficult numerical treatment. Not surprisingly, fully coupled, implicit approaches where the grid and the physics equations are solved simultaneously are rare in the literature, and circumscribed to 1D geometries. In this study, we present a fully implicit algorithm for moving mesh methods that is feasible for multidimensional geometries. A crucial element is the development of an effective multilevel treatment of the grid equation.ootnotetextL. Chac'on, G. Lapenta, A fully implicit, nonlinear adaptive grid strategy, J. Comput. Phys., accepted (2005) We will show that such an approach is competitive vs. uniform grids both from the accuracy (due to adaptivity) and the efficiency standpoints. Results for a variety of models 1D and 2D geometries, including nonlinear diffusion, radiation-diffusion, Burgers equation, and gas dynamics will be presented.

Implementation of a diffusion convection surface evolution model in WallDYN

NASA Astrophysics Data System (ADS)

Schmid, K.

2013-07-01

In thermonuclear fusion experiments with multiple plasma facing materials the formation of mixed materials is inevitable. The formation of these mixed material layers is a dynamic process driven the tight interaction between transport in the plasma scrape off layer and erosion/(re-) deposition at the surface. To track this global material erosion/deposition balance and the resulting formation of mixed material layers the WallDYN code has been developed which couples surface processes and plasma transport. The current surface model in WallDYN cannot fully handle the growth of layers nor does it include diffusion. However at elevated temperatures diffusion is a key process in the formation of mixed materials. To remedy this shortcoming a new surface model has been developed which, for the first time, describes both layer growth/recession and diffusion in a single continuous diffusion/convection equation. The paper will detail the derivation of the new surface model and compare it to TRIDYN calculations.

Diffuse interface models of locally inextensible vesicles in a viscous fluid

PubMed Central

Aland, Sebastian; Egerer, Sabine; Lowengrub, John; Voigt, Axel

2014-01-01

We present a new diffuse interface model for the dynamics of inextensible vesicles in a viscous fluid with inertial forces. A new feature of this work is the implementation of the local inextensibility condition in the diffuse interface context. Local inextensibility is enforced by using a local Lagrange multiplier, which provides the necessary tension force at the interface. We introduce a new equation for the local Lagrange multiplier whose solution essentially provides a harmonic extension of the multiplier off the interface while maintaining the local inextensibility constraint near the interface. We also develop a local relaxation scheme that dynamically corrects local stretching/compression errors thereby preventing their accumulation. Asymptotic analysis is presented that shows that our new system converges to a relaxed version of the inextensible sharp interface model. This is also verified numerically. To solve the equations, we use an adaptive finite element method with implicit coupling between the Navier-Stokes and the diffuse interface inextensibility equations. Numerical simulations of a single vesicle in a shear flow at different Reynolds numbers demonstrate that errors in enforcing local inextensibility may accumulate and lead to large differences in the dynamics in the tumbling regime and smaller differences in the inclination angle of vesicles in the tank-treading regime. The local relaxation algorithm is shown to prevent the accumulation of stretching and compression errors very effectively. Simulations of two vesicles in an extensional flow show that local inextensibility plays an important role when vesicles are in close proximity by inhibiting fluid drainage in the near contact region. PMID:25246712

Poisson-Nernst-Planck Equations for Simulating Biomolecular Diffusion-Reaction Processes II: Size Effects on Ionic Distributions and Diffusion-Reaction Rates

PubMed Central

Lu, Benzhuo; Zhou, Y.C.

2011-01-01

The effects of finite particle size on electrostatics, density profiles, and diffusion have been a long existing topic in the study of ionic solution. The previous size-modified Poisson-Boltzmann and Poisson-Nernst-Planck models are revisited in this article. In contrast to many previous works that can only treat particle species with a single uniform size or two sizes, we generalize the Borukhov model to obtain a size-modified Poisson-Nernst-Planck (SMPNP) model that is able to treat nonuniform particle sizes. The numerical tractability of the model is demonstrated as well. The main contributions of this study are as follows. 1), We show that an (arbitrarily) size-modified PB model is indeed implied by the SMPNP equations under certain boundary/interface conditions, and can be reproduced through numerical solutions of the SMPNP. 2), The size effects in the SMPNP effectively reduce the densities of highly concentrated counterions around the biomolecule. 3), The SMPNP is applied to the diffusion-reaction process for the first time, to our knowledge. In the case of low substrate density near the enzyme reactive site, it is observed that the rate coefficients predicted by SMPNP model are considerably larger than those by the PNP model, suggesting both ions and substrates are subject to finite size effects. 4), An accurate finite element method and a convergent Gummel iteration are developed for the numerical solution of the completely coupled nonlinear system of SMPNP equations. PMID:21575582

Fokker-Planck description of electron and photon transport in homogeneous media

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

Akcasu, A.Z.; Holloway, J.P.

1997-06-01

Starting from a Fokker-Planck description of particle transport, which is valid when the scattering is forwardly peaked and the energy change in scattering is small, we systematically obtain an approximate diffusionlike equation for the particle density by eliminating the direction variable {bold {cflx {Omega}}} with an elimination scheme based on Zwanzig{close_quote}s projection operator formalism in the interaction representation. The elimination procedure closely follows one described by Grigolini and Marchesoni [in {ital Memory Function Approaches to Stochastic Problems in Condensed Matter}, edited by Myron W. Evans, Paolo Grigolini, and Guiseppe P. Parravicini, Advances in Physical Chemistry, Vol. 62 (Wiley-Interscience, New York,more » 1985), Chap. II, p. 29], but with a different projection operator. The resulting diffusion equation is correct up to the second order in the coupling operator between the particle direction and position variable. The diffusion coefficients and mobility in the resulting diffusion equation depend on the initial distribution of the particles in direction and on the path length traveled by the particles. The full solution is obtained for a monoenergetic and monodirectional pulsed point source of particles in an infinite homogeneous medium. This solution is used to study the penetration and the transverse and longitudinal spread of the particles as they are transported through the medium. Application to diffusive wave spectroscopy in calculating the path-length distribution of photons, as well as application to dose calculations in tissue due to an electron beam are mentioned. {copyright} {ital 1997} {ital The American Physical Society}« less

DREAM3D simulations of inner-belt dynamics

NASA Astrophysics Data System (ADS)

Cunningham, G.

2015-12-01

A 1973 paper by Lyons and Thorne explains the two-belt structure for electrons in the inner magnetosphere as a balance between inward radial diffusion and loss to the atmosphere due to pitch-angle scattering from Coulomb and VLF wave-particle interactions. In this paper, equilibrium solutions to a set of 1D radial diffusion equations, one for each value of the first invariant of motion, μ, were computed to produce the equilibrium structure. Each diffusion equation incorporated an L- and μ-dependent `lifetime' due to the Coulomb and wave-particle interactions. This model is appropriate under the assumption that radial diffusion is slow in comparison to pitch-angle scattering, and that there is no acceleration caused by the VLF wave-particle interactions. We have revisited this model using our DREAM3D 3D diffusion code, which allows the user to explicitly model the diffusion in pitch-angle and momentum rather than using a lifetime. We find that a) replacing the lifetimes with an explicit model of pitch-angle diffusion, thus allowing for coupling between radial and pitch-angle diffusion, affects the equilibrium structure, and b) over the long time scales needed to reach equilibrium, significant acceleration due to VLF wave particle interactions takes place due to the 'cross-terms' in pitch-angle and momentum and the sharp gradient in the equilibrium pitch-angle distributions. We also find that the equilibrium solutions are quite sensitive to various aspects of the physics model employed in the 1973 paper that can be improved, suggesting that additional work needs to be done to fully understand the equilibirum nature of the trapped electron radiation belts.

Long-range intercellular Ca2+ wave patterns

NASA Astrophysics Data System (ADS)

Tabi, C. B.; Maïna, I.; Mohamadou, A.; Ekobena, H. P. F.; Kofané, T. C.

2015-10-01

Modulational instability is utilized to investigate intercellular Ca2+ wave propagation in an array of diffusively coupled cells. Cells are supposed to be connected via paracrine signaling, where long-range effects, due to the presence of extracellular messengers, are included. The multiple-scale expansion is used to show that the whole dynamics of Ca2+ waves, from the endoplasmic reticulum to the cytosol, can be reduced to a single differential-difference nonlinear equation whose solutions are assumed to be plane waves. Their linear stability analysis is studied, with emphasis on the impact of long-range coupling, via the range parameter s. It is shown that s, as well as the number of interacting cells, importantly modifies the features of modulational instability, as small values of s imply a strong coupling, and increasing its value rather reduces the problem to a first-neighbor one. Our theoretical findings are numerically tested, as the generic equations are fully integrated, leading to the emergence of nonlinear patterns of Ca2+ waves. Strong long-range coupling is pictured by extended trains of breather-like structures whose frequency decreases with increasing s. We also show numerically that the number of interacting cells plays on the spatio-temporal formation of Ca2+ patterns, whilst the quasi-perfect intercellular communication depends on the paracrine coupling parameter.

Modelling Growth and Form of the Scleractinian Coral Pocillopora verrucosa and the Influence of Hydrodynamics

PubMed Central

Chindapol, Nol; Kaandorp, Jaap A.; Cronemberger, Carolina; Mass, Tali; Genin, Amatzia

2013-01-01

The growth of scleractinian corals is strongly influenced by the effect of water motion. Corals are known to have a high level of phenotypic variation and exhibit a diverse range of growth forms, which often contain a high level of geometric complexity. Due to their complex shape, simulation models represent an important option to complement experimental studies of growth and flow. In this work, we analyzed the impact of flow on coral's morphology by an accretive growth model coupled with advection-diffusion equations. We performed simulations under no-flow and uni-directional flow setup with the Reynolds number constant. The relevant importance of diffusion to advection was investigated by varying the diffusion coefficient, rather than the flow speed in Péclet number. The flow and transport equations were coupled and solved using COMSOL Multiphysics. We then compared the simulated morphologies with a series of Computed Tomography (CT) scans of scleractinian corals Pocillopora verrucosa exposed to various flow conditions in the in situ controlled flume setup. As a result, we found a similar trend associated with the increasing Péclet for both simulated forms and in situ corals; that is uni-directional current tends to facilitate asymmetrical growth response resulting in colonies with branches predominantly developed in the upstream direction. A closer look at the morphological traits yielded an interesting property about colony symmetry and plasticity induced by uni-directional flow. Both simulated and in situ corals exhibit a tendency where the degree of symmetry decreases and compactification increases in conjunction with the augmented Péclet thus indicates the significant importance of hydrodynamics. PMID:23326222

Diffusion Coefficients from Molecular Dynamics Simulations in Binary and Ternary Mixtures

NASA Astrophysics Data System (ADS)

Liu, Xin; Schnell, Sondre K.; Simon, Jean-Marc; Krüger, Peter; Bedeaux, Dick; Kjelstrup, Signe; Bardow, André; Vlugt, Thijs J. H.

2013-07-01

Multicomponent diffusion in liquids is ubiquitous in (bio)chemical processes. It has gained considerable and increasing interest as it is often the rate limiting step in a process. In this paper, we review methods for calculating diffusion coefficients from molecular simulation and predictive engineering models. The main achievements of our research during the past years can be summarized as follows: (1) we introduced a consistent method for computing Fick diffusion coefficients using equilibrium molecular dynamics simulations; (2) we developed a multicomponent Darken equation for the description of the concentration dependence of Maxwell-Stefan diffusivities. In the case of infinite dilution, the multicomponent Darken equation provides an expression for [InlineEquation not available: see fulltext.] which can be used to parametrize the generalized Vignes equation; and (3) a predictive model for self-diffusivities was proposed for the parametrization of the multicomponent Darken equation. This equation accurately describes the concentration dependence of self-diffusivities in weakly associating systems. With these methods, a sound framework for the prediction of mutual diffusion in liquids is achieved.

Statistical Mechanical Theory of Coupled Slow Dynamics in Glassy Polymer-Molecule Mixtures

NASA Astrophysics Data System (ADS)

Zhang, Rui; Schweizer, Kenneth

The microscopic Elastically Collective Nonlinear Langevin Equation theory of activated relaxation in one-component supercooled liquids and glasses is generalized to polymer-molecule mixtures. The key idea is to account for dynamic coupling between molecule and polymer segment motion. For describing the molecule hopping event, a temporal casuality condition is formulated to self-consistently determine a dimensionless degree of matrix distortion relative to the molecule jump distance based on the concept of coupled dynamic free energies. Implementation for real materials employs an established Kuhn sphere model of the polymer liquid and a quantitative mapping to a hard particle reference system guided by the experimental equation-of-state. The theory makes predictions for the mixture dynamic shear modulus, activated relaxation time and diffusivity of both species, and mixture glass transition temperature as a function of molecule-Kuhn segment size ratio and attraction strength, composition and temperature. Model calculations illustrate the dynamical behavior in three distinct mixture regimes (fully miscible, bridging, clustering) controlled by the molecule-polymer interaction or chi-parameter. Applications to specific experimental systems will be discussed.

Systematic derivation of reaction-diffusion equations with distributed delays and relations to fractional reaction-diffusion equations and hyperbolic transport equations: application to the theory of Neolithic transition.

PubMed

Vlad, Marcel Ovidiu; Ross, John

2002-12-01

We introduce a general method for the systematic derivation of nonlinear reaction-diffusion equations with distributed delays. We study the interactions among different types of moving individuals (atoms, molecules, quasiparticles, biological organisms, etc). The motion of each species is described by the continuous time random walk theory, analyzed in the literature for transport problems, whereas the interactions among the species are described by a set of transformation rates, which are nonlinear functions of the local concentrations of the different types of individuals. We use the time interval between two jumps (the transition time) as an additional state variable and obtain a set of evolution equations, which are local in time. In order to make a connection with the transport models used in the literature, we make transformations which eliminate the transition time and derive a set of nonlocal equations which are nonlinear generalizations of the so-called generalized master equations. The method leads under different specified conditions to various types of nonlocal transport equations including a nonlinear generalization of fractional diffusion equations, hyperbolic reaction-diffusion equations, and delay-differential reaction-diffusion equations. Thus in the analysis of a given problem we can fit to the data the type of reaction-diffusion equation and the corresponding physical and kinetic parameters. The method is illustrated, as a test case, by the study of the neolithic transition. We introduce a set of assumptions which makes it possible to describe the transition from hunting and gathering to agriculture economics by a differential delay reaction-diffusion equation for the population density. We derive a delay evolution equation for the rate of advance of agriculture, which illustrates an application of our analysis.

Stochastic Feshbach Projection for the Dynamics of Open Quantum Systems

NASA Astrophysics Data System (ADS)

Link, Valentin; Strunz, Walter T.

2017-11-01

We present a stochastic projection formalism for the description of quantum dynamics in bosonic or spin environments. The Schrödinger equation in the coherent state representation with respect to the environmental degrees of freedom can be reformulated by employing the Feshbach partitioning technique for open quantum systems based on the introduction of suitable non-Hermitian projection operators. In this picture the reduced state of the system can be obtained as a stochastic average over pure state trajectories, for any temperature of the bath. The corresponding non-Markovian stochastic Schrödinger equations include a memory integral over the past states. In the case of harmonic environments and linear coupling the approach gives a new form of the established non-Markovian quantum state diffusion stochastic Schrödinger equation without functional derivatives. Utilizing spin coherent states, the evolution equation for spin environments resembles the bosonic case with, however, a non-Gaussian average for the reduced density operator.

Horizontal density-gradient effects on simulation of flow and transport in the Potomac Estuary

USGS Publications Warehouse

Schaffranek, Raymond W.; Baltzer, Robert A.; ,

1990-01-01

A two-dimensional, depth-integrated, hydrodynamic/transport model of the Potomac Estuary between Indian Head and Morgantown, Md., has been extended to include treatment of baroclinic forcing due to horizontal density gradients. The finite-difference model numerically integrates equations of mass and momentum conservation in conjunction with a transport equation for heat, salt, and constituent fluxes. Lateral and longitudinal density gradients are determined from salinity distributions computed from the convection-diffusion equation and an equation of state that expresses density as a function of temperature and salinity; thus, the hydrodynamic and transport computations are directly coupled. Horizontal density variations are shown to contribute significantly to momentum fluxes determined in the hydrodynamic computation. These fluxes lead to enchanced tidal pumping, and consequently greater dispersion, as is evidenced by numerical simulations. Density gradient effects on tidal propagation and transport behavior are discussed and demonstrated.

The role of fractional time-derivative operators on anomalous diffusion

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

Experimental characterization and modelization of ion exchange kinetics for a carboxylic resin in infinite solution volume conditions. Application to monovalent-trivalent cations exchange.

PubMed

Picart, Sébastien; Ramière, Isabelle; Mokhtari, Hamid; Jobelin, Isabelle

2010-09-02

This study is devoted to the characterization of ion exchange inside a microsphere of carboxylic resin. It aims at describing the kinetics of this exchange reaction which is known to be controlled by interdiffusion in the particle. The fractional attainment of equilibrium function of time depends on the concentration of the cations in the resin which can be modelized by the Nernst-Planck equation. A powerful approach for the numerical resolution of this equation is introduced in this paper. This modeling is based on the work of Helfferich but involves an implicit numerical scheme which reduces the computational cost. Knowing the diffusion coefficients of the cations in the resin and the radius of the spherical exchanger, the kinetics can be hence completely determined. When those diffusion parameters are missing, they can be deduced by fitting experimental data of fractional attainment of equilibrium. An efficient optimization tool coupled with the implicit resolution has been developed for this purpose. A monovalent/trivalent cation exchange had been experimentally characterized for a carboxylic resin. Diffusion coefficients and concentration profiles in the resin were then deduced through this new model.

Product interactions and feedback in diffusion-controlled reactions

NASA Astrophysics Data System (ADS)

Roa, Rafael; Siegl, Toni; Kim, Won Kyu; Dzubiella, Joachim

2018-02-01

Steric or attractive interactions among reactants or between reactants and inert crowders can substantially influence the total rate of a diffusion-influenced reaction in the liquid phase. However, the role of the product species, which has typically different physical properties than the reactant species, has been disregarded so far. Here we study the effects of reactant-product and product-product interactions as well as asymmetric diffusion properties on the rate of diffusion-controlled reactions in the classical Smoluchowski-setup for chemical transformations at a perfect catalytic sphere. For this, we solve the diffusion equation with appropriate boundary conditions coupled by a mean-field approach on the second virial level to account for the particle interactions. We find that all particle spatial distributions and the total rate can change significantly, depending on the diffusion and interaction properties of the accumulated products. Complex competing and self-regulating (homeostatic) or self-amplifying effects are observed for the system, leading to both decrease and increase in the rates, as the presence of interacting products feeds back to the reactant flux and thus the rate with which the products are generated.

Strong diffusion formulation of Markov chain ensembles and its optimal weaker reductions

NASA Astrophysics Data System (ADS)

Güler, Marifi

2017-10-01

Two self-contained diffusion formulations, in the form of coupled stochastic differential equations, are developed for the temporal evolution of state densities over an ensemble of Markov chains evolving independently under a common transition rate matrix. Our first formulation derives from Kurtz's strong approximation theorem of density-dependent Markov jump processes [Stoch. Process. Their Appl. 6, 223 (1978), 10.1016/0304-4149(78)90020-0] and, therefore, strongly converges with an error bound of the order of lnN /N for ensemble size N . The second formulation eliminates some fluctuation variables, and correspondingly some noise terms, within the governing equations of the strong formulation, with the objective of achieving a simpler analytic formulation and a faster computation algorithm when the transition rates are constant or slowly varying. There, the reduction of the structural complexity is optimal in the sense that the elimination of any given set of variables takes place with the lowest attainable increase in the error bound. The resultant formulations are supported by numerical simulations.

Background-Error Correlation Model Based on the Implicit Solution of a Diffusion Equation

DTIC Science & Technology

2010-01-01

1 Background- Error Correlation Model Based on the Implicit Solution of a Diffusion Equation Matthew J. Carrier* and Hans Ngodock...4. TITLE AND SUBTITLE Background- Error Correlation Model Based on the Implicit Solution of a Diffusion Equation 5a. CONTRACT NUMBER 5b. GRANT...2001), which sought to model error correlations based on the explicit solution of a generalized diffusion equation. The implicit solution is

Perturbation expansions of stochastic wavefunctions for open quantum systems

NASA Astrophysics Data System (ADS)

Ke, Yaling; Zhao, Yi

2017-11-01

Based on the stochastic unravelling of the reduced density operator in the Feynman path integral formalism for an open quantum system in touch with harmonic environments, a new non-Markovian stochastic Schrödinger equation (NMSSE) has been established that allows for the systematic perturbation expansion in the system-bath coupling to arbitrary order. This NMSSE can be transformed in a facile manner into the other two NMSSEs, i.e., non-Markovian quantum state diffusion and time-dependent wavepacket diffusion method. Benchmarked by numerically exact results, we have conducted a comparative study of the proposed method in its lowest order approximation, with perturbative quantum master equations in the symmetric spin-boson model and the realistic Fenna-Matthews-Olson complex. It is found that our method outperforms the second-order time-convolutionless quantum master equation in the whole parameter regime and even far better than the fourth-order in the slow bath and high temperature cases. Besides, the method is applicable on an equal footing for any kind of spectral density function and is expected to be a powerful tool to explore the quantum dynamics of large-scale systems, benefiting from the wavefunction framework and the time-local appearance within a single stochastic trajectory.

Magnetically Driven Flows of Suspensions of Rods to Deliver Clot-Busting Drugs to Dead-End Arteries

NASA Astrophysics Data System (ADS)

Bonnecaze, Roger; Clements, Michael

2014-11-01

Suspensions of iron particles in the presence of a magnetic field create flows that could significantly increase the delivery of drugs to dissolve clots in stroke victims. An explanation of this flow rests on the foundation of the seminal works by Prof. Acrivos and his students on effective magnetic permittivity of suspensions of rods, hydrodynamic diffusion of particles, and the flow of suspensions. Intravenous administration of the clot dissolving tissue plasminogen activator (tPA) is the most used therapy for stroke. This therapy is often unsuccessful because the tPA delivery is diffusion-limited and too slow to be effective. Observations show that added iron particles in a rotating magnetic field form rotating rods along the wall of the occluded vessel, creating a convective flow that can carry tPA much faster than diffusion. We present a proposed mechanism for this magnetically driven flow in the form of coupled particle-scale and vessel-scale flow models. At the particle-scale, particles chain up to form rods that rotate, diffuse and translate in the presence of the flow and magnetic fields. Localized vorticity created by the rotating particles drives a macroscopic convective flow in the vessel. Suspension transport equations describe the flow at the vessel-scale. The flow affects the convection and diffusion of the suspension of particles, linking the two scales. The model equations are solved asymptotically and numerically to understand how to create convective flows in dead-end or blocked vessels.

Hybrid Multiscale Finite Volume Method for Advection-Diffusion Equations Subject to Heterogeneous Reactive Boundary Conditions

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

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

2016-10-13

We present a hybrid scheme for the coupling of macro and microscale continuum models for reactive contaminant transport in fractured and porous media. The transport model considered is the advection-dispersion equation, subject to linear heterogeneous reactive boundary conditions. The Multiscale Finite Volume method (MsFV) is employed to define an approximation to the microscale concentration field defined in terms of macroscopic or \\emph{global} degrees of freedom, together with local interpolator and corrector functions capturing microscopic spatial variability. The macroscopic mass balance relations for the MsFV global degrees of freedom are coupled with the macroscopic model, resulting in a global problem for the simultaneous time-stepping of all macroscopic degrees of freedom throughout the domain. In order to perform the hybrid coupling, the micro and macroscale models are applied over overlapping subdomains of the simulation domain, with the overlap denoted as the handshake subdomainmore » $$\\Omega^{hs}$$, over which continuity of concentration and transport fluxes between models is enforced. Continuity of concentration is enforced by posing a restriction relation between models over $$\\Omega^{hs}$$. Continuity of fluxes is enforced by prolongating the macroscopic model fluxes across the boundary of $$\\Omega^{hs}$$ to microscopic resolution. The microscopic interpolator and corrector functions are solutions to local microscopic advection-diffusion problems decoupled from the global degrees of freedom and from each other by virtue of the MsFV decoupling ansatz. The error introduced by the decoupling ansatz is reduced iteratively by the preconditioned GMRES algorithm, with the hybrid MsFV operator serving as the preconditioner.« less

Asymptotic analysis of noisy fitness maximization, applied to metabolism & growth

NASA Astrophysics Data System (ADS)

De Martino, Daniele; Masoero, Davide

2016-12-01

We consider a population dynamics model coupling cell growth to a diffusion in the space of metabolic phenotypes as it can be obtained from realistic constraints-based modeling. In the asymptotic regime of slow diffusion, that coincides with the relevant experimental range, the resulting non-linear Fokker-Planck equation is solved for the steady state in the WKB approximation that maps it into the ground state of a quantum particle in an Airy potential plus a centrifugal term. We retrieve scaling laws for growth rate fluctuations and time response with respect to the distance from the maximum growth rate suggesting that suboptimal populations can have a faster response to perturbations.

Spin-orbit torque in a thin film of the topological insulator Bi2Se3: Crossover from the ballistic to diffusive regime

NASA Astrophysics Data System (ADS)

Ren, Y. J.; Deng, W. Y.; Geng, H.; Shen, R.; Shao, L. B.; Sheng, L.; Xing, D. Y.

2017-12-01

The spin-orbit torque provides an efficient method for switching the direction of a magnetization by using an electric field. Owing to the spin-orbit coupling, when an electric field is applied, a nonequilibrium spin density is generated, which exerts a torque on the local magnetization. Here, we investigate the spin-orbit torque in a thin film of topological insulator \\text{Bi}2\\text{Se}3 based upon a Boltzmann equation, with proper boundary conditions, which is applicable from the ballistic regime to the diffusive regime. It is shown that due to the spin-momentum interlocking of the electron surface states, the magnitude of the field-like torque is simply in linear proportion to the longitudinal electrical current. For a fixed electric field, the spin-orbit torque is proportional to the sample length in the ballistic limit, and saturates to a constant in the diffusive limit. The dependence of the torque on the magnetization direction and exchange coupling strength is also studied. Our theory may offer useful guidance for experimental investigations of the spin-orbit torque in finite-size systems.

Diffusion of Charged Species in Liquids

NASA Astrophysics Data System (ADS)

Del Río, J. A.; Whitaker, S.

2016-11-01

In this study the laws of mechanics for multi-component systems are used to develop a theory for the diffusion of ions in the presence of an electrostatic field. The analysis begins with the governing equation for the species velocity and it leads to the governing equation for the species diffusion velocity. Simplification of this latter result provides a momentum equation containing three dominant forces: (a) the gradient of the partial pressure, (b) the electrostatic force, and (c) the diffusive drag force that is a central feature of the Maxwell-Stefan equations. For ideal gas mixtures we derive the classic Nernst-Planck equation. For liquid-phase diffusion we encounter a situation in which the Nernst-Planck contribution to diffusion differs by several orders of magnitude from that obtained for ideal gases.

Diffusion of Charged Species in Liquids.

PubMed

Del Río, J A; Whitaker, S

2016-11-04

In this study the laws of mechanics for multi-component systems are used to develop a theory for the diffusion of ions in the presence of an electrostatic field. The analysis begins with the governing equation for the species velocity and it leads to the governing equation for the species diffusion velocity. Simplification of this latter result provides a momentum equation containing three dominant forces: (a) the gradient of the partial pressure, (b) the electrostatic force, and (c) the diffusive drag force that is a central feature of the Maxwell-Stefan equations. For ideal gas mixtures we derive the classic Nernst-Planck equation. For liquid-phase diffusion we encounter a situation in which the Nernst-Planck contribution to diffusion differs by several orders of magnitude from that obtained for ideal gases.

Diffusion of Charged Species in Liquids

PubMed Central

del Río, J. A.; Whitaker, S.

2016-01-01

In this study the laws of mechanics for multi-component systems are used to develop a theory for the diffusion of ions in the presence of an electrostatic field. The analysis begins with the governing equation for the species velocity and it leads to the governing equation for the species diffusion velocity. Simplification of this latter result provides a momentum equation containing three dominant forces: (a) the gradient of the partial pressure, (b) the electrostatic force, and (c) the diffusive drag force that is a central feature of the Maxwell-Stefan equations. For ideal gas mixtures we derive the classic Nernst-Planck equation. For liquid-phase diffusion we encounter a situation in which the Nernst-Planck contribution to diffusion differs by several orders of magnitude from that obtained for ideal gases. PMID:27811959

Microscopic Interpretation and Generalization of the Bloch-Torrey Equation for Diffusion Magnetic Resonance

PubMed Central

Seroussi, Inbar; Grebenkov, Denis S.; Pasternak, Ofer; Sochen, Nir

2017-01-01

In order to bridge microscopic molecular motion with macroscopic diffusion MR signal in complex structures, we propose a general stochastic model for molecular motion in a magnetic field. The Fokker-Planck equation of this model governs the probability density function describing the diffusion-magnetization propagator. From the propagator we derive a generalized version of the Bloch-Torrey equation and the relation to the random phase approach. This derivation does not require assumptions such as a spatially constant diffusion coefficient, or ad-hoc selection of a propagator. In particular, the boundary conditions that implicitly incorporate the microstructure into the diffusion MR signal can now be included explicitly through a spatially varying diffusion coefficient. While our generalization is reduced to the conventional Bloch-Torrey equation for piecewise constant diffusion coefficients, it also predicts scenarios in which an additional term to the equation is required to fully describe the MR signal. PMID:28242566

Study on monostable and bistable reaction-diffusion equations by iteration of travelling wave maps

NASA Astrophysics Data System (ADS)

Yi, Taishan; Chen, Yuming

2017-12-01

In this paper, based on the iterative properties of travelling wave maps, we develop a new method to obtain spreading speeds and asymptotic propagation for monostable and bistable reaction-diffusion equations. Precisely, for Dirichlet problems of monostable reaction-diffusion equations on the half line, by making links between travelling wave maps and integral operators associated with the Dirichlet diffusion kernel (the latter is NOT invariant under translation), we obtain some iteration properties of the Dirichlet diffusion and some a priori estimates on nontrivial solutions of Dirichlet problems under travelling wave transformation. We then provide the asymptotic behavior of nontrivial solutions in the space-time region for Dirichlet problems. These enable us to develop a unified method to obtain results on heterogeneous steady states, travelling waves, spreading speeds, and asymptotic spreading behavior for Dirichlet problem of monostable reaction-diffusion equations on R+ as well as of monostable/bistable reaction-diffusion equations on R.

Effects of Gravity on Soot Formation in a Coflow Laminar Methane/Air Diffusion Flame

NASA Astrophysics Data System (ADS)

Kong, Wenjun; Liu, Fengshan

2010-04-01

Simulations of a laminar coflow methane/air diffusion flame at atmospheric pressure are conducted to gain better understanding of the effects of gravity on soot formation by using detailed gas-phase chemistry, complex thermal and transport properties coupled with a semiempirical two-equation soot model and a nongray radiation model. Soot oxidation by O2, OH and O was considered. Thermal radiation was calculated using the discrete ordinate method coupled with a statistical narrow-band correlated-K model. The spectral absorption coefficient of soot was obtained by Rayleigh's theory for small particles. The results show that the peak temperature decreases with the decrease of the gravity level. The peak soot volume fraction in microgravity is about twice of that in normal gravity under the present conditions. The numerical results agree very well with available experimental results. The predicted results also show that gravity affects the location and intensity for soot nucleation and surface growth.

Geometrically nonlinear continuum thermomechanics with surface energies coupled to diffusion

NASA Astrophysics Data System (ADS)

McBride, A. T.; Javili, A.; Steinmann, P.; Bargmann, S.

2011-10-01

Surfaces can have a significant influence on the overall response of a continuum body but are often neglected or accounted for in an ad hoc manner. This work is concerned with a nonlinear continuum thermomechanics formulation which accounts for surface structures and includes the effects of diffusion and viscoelasticity. The formulation is presented within a thermodynamically consistent framework and elucidates the nature of the coupling between the various fields, and the surface and the bulk. Conservation principles are used to determine the form of the constitutive relations and the evolution equations. Restrictions on the jump in the temperature and the chemical potential between the surface and the bulk are not a priori assumptions, rather they arise from the reduced dissipation inequality on the surface and are shown to be satisfiable without imposing the standard assumptions of thermal and chemical slavery. The nature of the constitutive relations is made clear via an example wherein the form of the Helmholtz energy is explicitly given.

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

Dimensionless numbers and correlating equations for the analysis of the membrane-gas diffusion electrode assembly in polymer electrolyte fuel cells

NASA Astrophysics Data System (ADS)

Gyenge, E. L.

The Quraishi-Fahidy method [Can. J. Chem. Eng. 59 (1981) 563] was employed to derive characteristic dimensionless numbers for the membrane-electrolyte, cathode catalyst layer and gas diffuser, respectively, based on the model presented by Bernardi and Verbrugge for polymer electrolyte fuel cells [AIChE J. 37 (1991) 1151]. Monomial correlations among dimensionless numbers were developed and tested against experimental and mathematical modeling results. Dimensionless numbers comparing the bulk and surface-convective ionic conductivities, the electric and viscous forces and the current density and the fixed surface charges, were employed to describe the membrane ohmic drop and its non-linear dependence on current density due to membrane dehydration. The analysis of the catalyst layer yielded electrode kinetic equivalents of the second Damköhler number and Thiele modulus, influencing the penetration depth of the oxygen reduction front based on the pseudohomogeneous film model. The correlating equations for the catalyst layer could describe in a general analytical form, all the possible electrode polarization scenarios such as electrode kinetic control coupled or not with ionic and/or oxygen mass transport limitation. For the gas diffusion-backing layer correlations are presented in terms of the Nusselt number for mass transfer in electrochemical systems. The dimensionless number-based correlating equations for the membrane electrode assembly (MEA) could provide a practical approach to quantify single-cell polarization results obtained under a variety of experimental conditions and to implement them in models of the fuel cell stack.

Numerical Modeling of Interstitial Fluid Flow Coupled with Blood Flow through a Remodeled Solid Tumor Microvascular Network

PubMed Central

Soltani, M.; Chen, P.

2013-01-01

Modeling of interstitial fluid flow involves processes such as fluid diffusion, convective transport in extracellular matrix, and extravasation from blood vessels. To date, majority of microvascular flow modeling has been done at different levels and scales mostly on simple tumor shapes with their capillaries. However, with our proposed numerical model, more complex and realistic tumor shapes and capillary networks can be studied. Both blood flow through a capillary network, which is induced by a solid tumor, and fluid flow in tumor’s surrounding tissue are formulated. First, governing equations of angiogenesis are implemented to specify the different domains for the network and interstitium. Then, governing equations for flow modeling are introduced for different domains. The conservation laws for mass and momentum (including continuity equation, Darcy’s law for tissue, and simplified Navier–Stokes equation for blood flow through capillaries) are used for simulating interstitial and intravascular flows and Starling’s law is used for closing this system of equations and coupling the intravascular and extravascular flows. This is the first study of flow modeling in solid tumors to naturalistically couple intravascular and extravascular flow through a network. This network is generated by sprouting angiogenesis and consisting of one parent vessel connected to the network while taking into account the non-continuous behavior of blood, adaptability of capillary diameter to hemodynamics and metabolic stimuli, non-Newtonian blood flow, and phase separation of blood flow in capillary bifurcation. The incorporation of the outlined components beyond the previous models provides a more realistic prediction of interstitial fluid flow pattern in solid tumors and surrounding tissues. Results predict higher interstitial pressure, almost two times, for realistic model compared to the simplified model. PMID:23840579

Combined Excitatory and Inhibitory Coupling in a 1-D Array of Belousov-Zhabotinsky Droplets

DTIC Science & Technology

2014-01-01

with numerical chemical models of the BZ reaction in which components that participate in the excitatory (bromine dioxide and bromous acid) and...verify the transport through the fluorinated oil of chlorine dioxide and several weak acids, including malonic acid. 1. Introduction Recent studies1...finite element model (COMSOLs) of the reaction - diffusion equation in 1-D, 2-D and 3-D, where each drop is modeled as a point, disk or sphere

A Flux-Corrected Transport Based Hydrodynamic Model for the Plasmasphere Refilling Problem following Geomagnetic Storms

NASA Astrophysics Data System (ADS)

Chatterjee, K.; Schunk, R. W.

2017-12-01

The refilling of the plasmasphere following a geomagnetic storm remains one of the longstanding problems in the area of ionosphere-magnetosphere coupling. Both diffusion and hydrodynamic approximations have been adopted for the modeling and solution of this problem. The diffusion approximation neglects the nonlinear inertial term in the momentum equation and so this approximation is not rigorously valid immediately after the storm. Over the last few years, we have developed a hydrodynamic refilling model using the flux-corrected transport method, a numerical method that is extremely well suited to handling nonlinear problems with shocks and discontinuities. The plasma transport equations are solved along 1D closed magnetic field lines that connect conjugate ionospheres and the model currently includes three ion (H+, O+, He+) and two neutral (O, H) species. In this work, each ion species under consideration has been modeled as two separate streams emanating from the conjugate hemispheres and the model correctly predicts supersonic ion speeds and the presence of high levels of Helium during the early hours of refilling. The ultimate objective of this research is the development of a 3D model for the plasmasphere refilling problem and with additional development, the same methodology can potentially be applied to the study of other complex space plasma coupling problems in closed flux tube geometries. Index Terms: 2447 Modeling and forecasting [IONOSPHERE] 2753 Numerical modeling [MAGNETOSPHERIC PHYSICS] 7959 Models [SPACE WEATHER

Inversion of geothermal heat flux in a thermomechanically coupled nonlinear Stokes ice sheet model

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

Zhu, Hongyu; Petra, Noemi; Stadler, Georg

We address the inverse problem of inferring the basal geothermal heat flux from surface velocity observations using a steady-state thermomechanically coupled nonlinear Stokes ice flow model. This is a challenging inverse problem since the map from basal heat flux to surface velocity observables is indirect: the heat flux is a boundary condition for the thermal advection–diffusion equation, which couples to the nonlinear Stokes ice flow equations; together they determine the surface ice flow velocity. This multiphysics inverse problem is formulated as a nonlinear least-squares optimization problem with a cost functional that includes the data misfit between surface velocity observations andmore » model predictions. A Tikhonov regularization term is added to render the problem well posed. We derive adjoint-based gradient and Hessian expressions for the resulting partial differential equation (PDE)-constrained optimization problem and propose an inexact Newton method for its solution. As a consequence of the Petrov–Galerkin discretization of the energy equation, we show that discretization and differentiation do not commute; that is, the order in which we discretize the cost functional and differentiate it affects the correctness of the gradient. Using two- and three-dimensional model problems, we study the prospects for and limitations of the inference of the geothermal heat flux field from surface velocity observations. The results show that the reconstruction improves as the noise level in the observations decreases and that short-wavelength variations in the geothermal heat flux are difficult to recover. We analyze the ill-posedness of the inverse problem as a function of the number of observations by examining the spectrum of the Hessian of the cost functional. Motivated by the popularity of operator-split or staggered solvers for forward multiphysics problems – i.e., those that drop two-way coupling terms to yield a one-way coupled forward Jacobian – we study the effect on the inversion of a one-way coupling of the adjoint energy and Stokes equations. Here, we show that taking such a one-way coupled approach for the adjoint equations can lead to an incorrect gradient and premature termination of optimization iterations. This is due to loss of a descent direction stemming from inconsistency of the gradient with the contours of the cost functional. Nevertheless, one may still obtain a reasonable approximate inverse solution particularly if important features of the reconstructed solution emerge early in optimization iterations, before the premature termination.« less

Inversion of geothermal heat flux in a thermomechanically coupled nonlinear Stokes ice sheet model

DOE PAGES

Zhu, Hongyu; Petra, Noemi; Stadler, Georg; ...

2016-07-13

We address the inverse problem of inferring the basal geothermal heat flux from surface velocity observations using a steady-state thermomechanically coupled nonlinear Stokes ice flow model. This is a challenging inverse problem since the map from basal heat flux to surface velocity observables is indirect: the heat flux is a boundary condition for the thermal advection–diffusion equation, which couples to the nonlinear Stokes ice flow equations; together they determine the surface ice flow velocity. This multiphysics inverse problem is formulated as a nonlinear least-squares optimization problem with a cost functional that includes the data misfit between surface velocity observations andmore » model predictions. A Tikhonov regularization term is added to render the problem well posed. We derive adjoint-based gradient and Hessian expressions for the resulting partial differential equation (PDE)-constrained optimization problem and propose an inexact Newton method for its solution. As a consequence of the Petrov–Galerkin discretization of the energy equation, we show that discretization and differentiation do not commute; that is, the order in which we discretize the cost functional and differentiate it affects the correctness of the gradient. Using two- and three-dimensional model problems, we study the prospects for and limitations of the inference of the geothermal heat flux field from surface velocity observations. The results show that the reconstruction improves as the noise level in the observations decreases and that short-wavelength variations in the geothermal heat flux are difficult to recover. We analyze the ill-posedness of the inverse problem as a function of the number of observations by examining the spectrum of the Hessian of the cost functional. Motivated by the popularity of operator-split or staggered solvers for forward multiphysics problems – i.e., those that drop two-way coupling terms to yield a one-way coupled forward Jacobian – we study the effect on the inversion of a one-way coupling of the adjoint energy and Stokes equations. Here, we show that taking such a one-way coupled approach for the adjoint equations can lead to an incorrect gradient and premature termination of optimization iterations. This is due to loss of a descent direction stemming from inconsistency of the gradient with the contours of the cost functional. Nevertheless, one may still obtain a reasonable approximate inverse solution particularly if important features of the reconstructed solution emerge early in optimization iterations, before the premature termination.« less

Inversion of geothermal heat flux in a thermomechanically coupled nonlinear Stokes ice sheet model

NASA Astrophysics Data System (ADS)

Zhu, Hongyu; Petra, Noemi; Stadler, Georg; Isaac, Tobin; Hughes, Thomas J. R.; Ghattas, Omar

2016-07-01

We address the inverse problem of inferring the basal geothermal heat flux from surface velocity observations using a steady-state thermomechanically coupled nonlinear Stokes ice flow model. This is a challenging inverse problem since the map from basal heat flux to surface velocity observables is indirect: the heat flux is a boundary condition for the thermal advection-diffusion equation, which couples to the nonlinear Stokes ice flow equations; together they determine the surface ice flow velocity. This multiphysics inverse problem is formulated as a nonlinear least-squares optimization problem with a cost functional that includes the data misfit between surface velocity observations and model predictions. A Tikhonov regularization term is added to render the problem well posed. We derive adjoint-based gradient and Hessian expressions for the resulting partial differential equation (PDE)-constrained optimization problem and propose an inexact Newton method for its solution. As a consequence of the Petrov-Galerkin discretization of the energy equation, we show that discretization and differentiation do not commute; that is, the order in which we discretize the cost functional and differentiate it affects the correctness of the gradient. Using two- and three-dimensional model problems, we study the prospects for and limitations of the inference of the geothermal heat flux field from surface velocity observations. The results show that the reconstruction improves as the noise level in the observations decreases and that short-wavelength variations in the geothermal heat flux are difficult to recover. We analyze the ill-posedness of the inverse problem as a function of the number of observations by examining the spectrum of the Hessian of the cost functional. Motivated by the popularity of operator-split or staggered solvers for forward multiphysics problems - i.e., those that drop two-way coupling terms to yield a one-way coupled forward Jacobian - we study the effect on the inversion of a one-way coupling of the adjoint energy and Stokes equations. We show that taking such a one-way coupled approach for the adjoint equations can lead to an incorrect gradient and premature termination of optimization iterations. This is due to loss of a descent direction stemming from inconsistency of the gradient with the contours of the cost functional. Nevertheless, one may still obtain a reasonable approximate inverse solution particularly if important features of the reconstructed solution emerge early in optimization iterations, before the premature termination.

Topology optimisation for natural convection problems

NASA Astrophysics Data System (ADS)

Alexandersen, Joe; Aage, Niels; Andreasen, Casper Schousboe; Sigmund, Ole

2014-12-01

This paper demonstrates the application of the density-based topology optimisation approach for the design of heat sinks and micropumps based on natural convection effects. The problems are modelled under the assumptions of steady-state laminar flow using the incompressible Navier-Stokes equations coupled to the convection-diffusion equation through the Boussinesq approximation. In order to facilitate topology optimisation, the Brinkman approach is taken to penalise velocities inside the solid domain and the effective thermal conductivity is interpolated in order to accommodate differences in thermal conductivity of the solid and fluid phases. The governing equations are discretised using stabilised finite elements and topology optimisation is performed for two different problems using discrete adjoint sensitivity analysis. The study shows that topology optimisation is a viable approach for designing heat sink geometries cooled by natural convection and micropumps powered by natural convection.

Day and night models of the Venus thermosphere

NASA Technical Reports Server (NTRS)

Massie, S. T.; Hunten, D. M.; Sowell, D. R.

1983-01-01

A model atmosphere of Venus for altitudes between 100 and 178 km is presented for the dayside and nightside. Densities of CO2, CO, O, N2, He, and O2 on the dayside, for 0800 and 1600 hours local time, are obtained by simultaneous solution of continuity equations. These equations couple ionospheric and neutral chemistry and the transport processes of molecular and eddy diffusion. Photodissociation and photoionization J coefficients are presented to facilitate the incorporation of chemistry into circulation models of the Venus atmosphere. Midnight densities of CO2 CO, O, N2, He, and N are derived from integration of the continuity equations, subject to specified fluxes. The nightside densities and fluxes are consistent with the observed airglow of NO and O2(1 Delta). The homopause of Venus is located near 133 km on both the dayside and nightside.

Prediction of stream volatilization coefficients

USGS Publications Warehouse

Rathbun, Ronald E.

1990-01-01

Equations are developed for predicting the liquid-film and gas-film reference-substance parameters for quantifying volatilization of organic solutes from streams. Molecular weight and molecular-diffusion coefficients of the solute are used as correlating parameters. Equations for predicting molecular-diffusion coefficients of organic solutes in water and air are developed, with molecular weight and molal volume as parameters. Mean absolute errors of prediction for diffusion coefficients in water are 9.97% for the molecular-weight equation, 6.45% for the molal-volume equation. The mean absolute error for the diffusion coefficient in air is 5.79% for the molal-volume equation. Molecular weight is not a satisfactory correlating parameter for diffusion in air because two equations are necessary to describe the values in the data set. The best predictive equation for the liquid-film reference-substance parameter has a mean absolute error of 5.74%, with molal volume as the correlating parameter. The best equation for the gas-film parameter has a mean absolute error of 7.80%, with molecular weight as the correlating parameter.

Causal Diffusion and the Survival of Charge Fluctuations

NASA Astrophysics Data System (ADS)

Abdel-Aziz, Mohamed; Gavin, Sean

2004-10-01

Diffusion may obliterate fluctuation signals of the QCD phase transition in nuclear collisions at SPS and RHIC energies. We propose a hyperbolic diffusion equation to study the dissipation of net charge fluctuations [1]. This equation is needed in a relativistic context, because the classic parabolic diffusion equation violates causality. We find that causality substantially limits the extent to which diffusion can dissipate these fluctuations. [1] M. Abdel-Aziz and S. Gavin, nucl-th/0404058

Conditional and unconditional Gaussian quantum dynamics

NASA Astrophysics Data System (ADS)

Genoni, Marco G.; Lami, Ludovico; Serafini, Alessio

2016-07-01

This article focuses on the general theory of open quantum systems in the Gaussian regime and explores a number of diverse ramifications and consequences of the theory. We shall first introduce the Gaussian framework in its full generality, including a classification of Gaussian (also known as 'general-dyne') quantum measurements. In doing so, we will give a compact proof for the parametrisation of the most general Gaussian completely positive map, which we believe to be missing in the existing literature. We will then move on to consider the linear coupling with a white noise bath, and derive the diffusion equations that describe the evolution of Gaussian states under such circumstances. Starting from these equations, we outline a constructive method to derive general master equations that apply outside the Gaussian regime. Next, we include the general-dyne monitoring of the environmental degrees of freedom and recover the Riccati equation for the conditional evolution of Gaussian states. Our derivation relies exclusively on the standard quantum mechanical update of the system state, through the evaluation of Gaussian overlaps. The parametrisation of the conditional dynamics we obtain is novel and, at variance with existing alternatives, directly ties in to physical detection schemes. We conclude our study with two examples of conditional dynamics that can be dealt with conveniently through our formalism, demonstrating how monitoring can suppress the noise in optical parametric processes as well as stabilise systems subject to diffusive scattering.

Exciton Transport Simulations in Phenyl Cored Thiophene Dendrimers

NASA Astrophysics Data System (ADS)

Kim, Kwiseon; Erkan Kose, Muhammet; Graf, Peter; Kopidakis, Nikos; Rumbles, Garry; Shaheen, Sean E.

2009-03-01

Phenyl cored 3-arm and 4-arm thiophene dendrimers are promising materials for use in photovoltaic devices. It is important to understand the energy transfer mechanisms in these molecules to guide the synthesis of novel dendrimers with improved efficiency. A method is developed to estimate the exciton diffusion lengths for the dendrimers and similar chromophores in amorphous films. The approach exploits Fermi's Golden Rule to estimate the energy transfer rates for an ensemble of bimolecular complexes in random orientations. Using Poisson's equation to evaluate Coulomb integrals led to efficient calculation of excitonic couplings between the transition densities. Monte-Carlo simulations revealed the dynamics of energy transport in the dendrimers. Experimental exciton diffusion lengths of the dendrimers range 10 ˜ 20 nm, increasing with the size of the dendrimer. Simulated diffusion lengths correlate well with experiments. The chemical structure of the chromophore, the shape of the transition densities and the exciton lifetime are found to be the most important factors that determine the exciton diffusion length in amorphous films.

Theoretical Relationships between Luminescence and Hillslope Soil Vertical Diffusivity: a Numerical Modeling Approach

NASA Astrophysics Data System (ADS)

Gray, H. J.; Tucker, G. E.; Mahan, S.

2017-12-01

Luminescence is a property of matter that can be used to obtain depositional ages from fine sand. Luminescence generates due to exposure to background ionizing radiation and is removed by sunlight exposure in a process known as bleaching. There is evidence to suggest that luminescence can also serve as a sediment tracer in fluvial and hillslope environments. For hillslope environments, it has been suggested that the magnitude of luminescence as a function of soil depth is related to the strength of soil mixing. Hillslope soils with a greater extent of mixing will have previously surficial sand grains moved to greater depths in a soil column. These previously surface-exposed grains will contain a lower luminescence than those which have never seen the surface. To attempt to connect luminescence profiles with soil mixing rate, here defined as the soil vertical diffusivity, I conduct numerical modelling of particles in hillslope soils coupled with equations describing the physics of luminescence. I use recently published equations describing the trajectories of particles under both exponential and uniform soil velocity soils profiles and modify them to include soil diffusivity. Results from the model demonstrates a strong connection between soil diffusivity and luminescence. Both the depth profiles of luminescence and the total percent of surface exposed grains will change drastically based on the magnitude of the diffusivity. This suggests that luminescence could potentially be used to infer the magnitude of soil diffusivity. However, I test other variables such as the soil production rate, e-folding length of soil velocity, background dose rate, and soil thickness, and I find these other variables can also affect the relationship between luminescence and diffusivity. This suggests that these other variables may need to be constrained prior to any inferences of soil diffusivity from luminescence measurements. Further field testing of the model in areas where the soil vertical diffusivity and other parameters are independently known will provide a test of this potential new method.

Nanoscopic diffusion studies on III-V compound semiconductor structures: Experiment and theory

NASA Astrophysics Data System (ADS)

Gonzalez Debs, Mariam

The electronic structure of multilayer semiconductor heterostructures is affected by the detailed compositional profiles throughout the structure and at critical interfaces. The extent of interdiffusion across these interfaces places limits on both the processing time and temperatures for many applications based on the resultant compositional profile and associated electronic structure. Atomic and phenomenological methods were used in this work through the combination of experiment and theory to understand the nanoscopic mechanisms in complex heterostructures. Two principal studies were conducted. Tin diffusion in GaAs was studied by fitting complex experimental diffusion profiles to a phenomenological model which involved the diffusion of substitutional and interstitial dopant atoms. A methodology was developed combining both the atomistic model and the use of key features within these experimentally-obtained diffusion profiles to determine meaningful values of the transport and defect reaction rate parameters. Interdiffusion across AlSb/GaSb multi-quantum well interfaces was also studied. The chemical diffusion coefficient characterizing the AlSb/GaSb diffusion couple was quantitatively determined by fitting the observed photoluminescence (PL) peak shifts to the solution of the Schrodinger equation using a potential derived from the solution of the diffusion equation to quantify the interband transition energy shifts. First-principles calculations implementing Density Functional Theory were performed to study the thermochemistry of point defects as a function of local environment, allowing a direct comparison of interfacial and bulk diffusion phenomena within these nanoscopic structures. Significant differences were observed in the Ga and Al vacancy formation energies at the AlSb/GaSb interface when compared to bulk AlSb and GaSb with the largest change found for Al vacancies. The AlSb/GaSb structures were further studied using positron annihilation spectroscopy (PAS) to investigate the role of vacancies in the interdiffusion of Al and Ga in the superlattices. The PL and PAS experimental techniques together with the phenomenological and atomistic modeling allowed for the determination of the underlying mass transport mechanisms at the nanoscale.

A theory for fracture of polymeric gels

NASA Astrophysics Data System (ADS)

Mao, Yunwei; Anand, Lallit

2018-06-01

A polymeric gel is a cross-linked polymer network swollen with a solvent. If the concentration of the solvent or the deformation is increased to substantial levels, especially in the presence of flaws, then the gel may rupture. Although various theoretical aspects of coupling of fluid permeation with large deformation of polymeric gels are reasonably well-understood and modeled in the literature, the understanding and modeling of the effects of fluid diffusion on the damage and fracture of polymeric gels is still in its infancy. In this paper we formulate a thermodynamically-consistent theory for fracture of polymeric gels - a theory which accounts for the coupled effects of fluid diffusion, large deformations, damage, and also the gradient effects of damage. The particular constitutive equations for fracture of a gel proposed in our paper, contain two essential new ingredients: (i) Our constitutive equation for the change in free energy of a polymer network accounts for not only changes in the entropy, but also changes in the internal energy due the stretching of the Kuhn segments of the polymer chains in the network. (ii) The damage and failure of the polymer network is taken to occur by chain-scission, a process which is driven by the changes in the internal energy of the stretched polymer chains in the network, and not directly by changes in the configurational entropy of the polymer chains. The theory developed in this paper is numerically implemented in an open-source finite element code MOOSE, by writing our own application. Using this simulation capability we report on our study of the fracture of a polymeric gel, and some interesting phenomena which show the importance of the diffusion of the fluid on fracture response of the gel are highlighted.

Global dynamics of a nonlocal delayed reaction-diffusion equation on a half plane

NASA Astrophysics Data System (ADS)

Hu, Wenjie; Duan, Yueliang

2018-04-01

We consider a delayed reaction-diffusion equation with spatial nonlocality on a half plane that describes population dynamics of a two-stage species living in a semi-infinite environment. A Neumann boundary condition is imposed accounting for an isolated domain. To describe the global dynamics, we first establish some a priori estimate for nontrivial solutions after investigating asymptotic properties of the nonlocal delayed effect and the diffusion operator, which enables us to show the permanence of the equation with respect to the compact open topology. We then employ standard dynamical system arguments to establish the global attractivity of the nontrivial equilibrium. The main results are illustrated by the diffusive Nicholson's blowfly equation and the diffusive Mackey-Glass equation.

FRACTIONAL PEARSON DIFFUSIONS.

PubMed

Leonenko, Nikolai N; Meerschaert, Mark M; Sikorskii, Alla

2013-07-15

Pearson diffusions are governed by diffusion equations with polynomial coefficients. Fractional Pearson diffusions are governed by the corresponding time-fractional diffusion equation. They are useful for modeling sub-diffusive phenomena, caused by particle sticking and trapping. This paper provides explicit strong solutions for fractional Pearson diffusions, using spectral methods. It also presents stochastic solutions, using a non-Markovian inverse stable time change.

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

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

PubMed Central

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

2017-01-01

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

Light propagation from fluorescent probes in biological tissues by coupled time-dependent parabolic simplified spherical harmonics equations

PubMed Central

Domínguez, Jorge Bouza; Bérubé-Lauzière, Yves

2011-01-01

We introduce a system of coupled time-dependent parabolic simplified spherical harmonic equations to model the propagation of both excitation and fluorescence light in biological tissues. We resort to a finite element approach to obtain the time-dependent profile of the excitation and the fluorescence light fields in the medium. We present results for cases involving two geometries in three-dimensions: a homogeneous cylinder with an embedded fluorescent inclusion and a realistically-shaped rodent with an embedded inclusion alike an organ filled with a fluorescent probe. For the cylindrical geometry, we show the differences in the time-dependent fluorescence response for a point-like, a spherical, and a spherically Gaussian distributed fluorescent inclusion. From our results, we conclude that the model is able to describe the time-dependent excitation and fluorescent light transfer in small geometries with high absorption coefficients and in nondiffusive domains, as may be found in small animal diffuse optical tomography (DOT) and fluorescence DOT imaging. PMID:21483606

Bounding the solutions of parametric weakly coupled second-order semilinear parabolic partial differential equations

DOE PAGES

Azunre, P.

2016-09-21

Here in this paper, two novel techniques for bounding the solutions of parametric weakly coupled second-order semilinear parabolic partial differential equations are developed. The first provides a theorem to construct interval bounds, while the second provides a theorem to construct lower bounds convex and upper bounds concave in the parameter. The convex/concave bounds can be significantly tighter than the interval bounds because of the wrapping effect suffered by interval analysis in dynamical systems. Both types of bounds are computationally cheap to construct, requiring solving auxiliary systems twice and four times larger than the original system, respectively. An illustrative numerical examplemore » of bound construction and use for deterministic global optimization within a simple serial branch-and-bound algorithm, implemented numerically using interval arithmetic and a generalization of McCormick's relaxation technique, is presented. Finally, problems within the important class of reaction-diffusion systems may be optimized with these tools.« less

ECCD-induced tearing mode stabilization in coupled IPS/NIMROD/GENRAY HPC simulations

NASA Astrophysics Data System (ADS)

Jenkins, Thomas; Kruger, S. E.; Held, E. D.; Harvey, R. W.; Elwasif, W. R.

2012-03-01

We summarize ongoing developments toward an integrated, predictive model for determining optimal ECCD-based NTM stabilization strategies in ITER. We demonstrate the capability of the SWIM Project's Integrated Plasma Simulator (IPS) framework to choreograph multiple executions of, and data exchanges between, physics codes modeling various spatiotemporal scales of this coupled RF/MHD problem on several thousand HPC processors. As NIMROD evolves fluid equations to model bulk plasma behavior, self-consistent propagation/deposition of RF power in the ensuing plasma profiles is calculated by GENRAY. Data from both codes is then processed by computational geometry packages to construct the RF-induced quasilinear diffusion tensor; moments of this tensor (entering as additional terms in NIMROD's fluid equations due to the disparity in RF/MHD spatiotemporal scales) influence the dynamics of current, momentum, and energy evolution as well as the MHD closures. Initial results are shown to correctly capture the physics of magnetic island stabilization; we also discuss the development of a numerical plasma control system for active feedback stabilization of tearing modes.

One-dimensional time-dependent fluid model of a very high density low-pressure inductively coupled plasma

NASA Astrophysics Data System (ADS)

Chaplin, Vernon H.; Bellan, Paul M.

2015-12-01

A time-dependent two-fluid model has been developed to understand axial variations in the plasma parameters in a very high density (peak ne≳ 5 ×1019 m-3 ) argon inductively coupled discharge in a long 1.1 cm radius tube. The model equations are written in 1D with radial losses to the tube walls accounted for by the inclusion of effective particle and energy sink terms. The ambipolar diffusion equation and electron energy equation are solved to find the electron density ne(z ,t ) and temperature Te(z ,t ) , and the populations of the neutral argon 4s metastable, 4s resonant, and 4p excited state manifolds are calculated to determine the stepwise ionization rate and calculate radiative energy losses. The model has been validated through comparisons with Langmuir probe ion saturation current measurements; close agreement between the simulated and measured axial plasma density profiles and the initial density rise rate at each location was obtained at pA r=30 -60 mTorr . We present detailed results from calculations at 60 mTorr, including the time-dependent electron temperature, excited state populations, and energy budget within and downstream of the radiofrequency antenna.

Statistical Mechanical Theory of Penetrant Diffusion in Polymer Melts and Glasses

NASA Astrophysics Data System (ADS)

Zhang, Rui; Schweizer, Kenneth

We generalize our force-level, self-consistent nonlinear Langevin equation theory of activated diffusion of a dilute spherical penetrant in hard sphere fluids to predict the long-time diffusivity of molecular penetrants in supercooled polymer liquids and non-aging glasses. Chemical complexity is treated using an a priori mapping to a temperature-dependent hard sphere mixture model where polymers are disconnected into effective spheres based on the Kuhn length as the relevant coarse graining scale. A key parameter for mobility is the penetrant to polymer segment diameter ratio, R. Our calculations agree well with experimental measurements for a wide range of temperatures, penetrant sizes (from gas molecules with R ~0.3 to aromatic molecules with R ~1) and diverse amorphous polymers, over 10 decades variation of penetrant diffusivity. Structural parameter transferability is good. We have also formulated a theory at finite penetrant loading for the coupled penetrant-polymer dynamics in chemically (nearly) matched mixtures (e.g., toluene-polystyrene) which captures well the increase of penetrant diffusivity and decrease of polymer matrix vitrification temperature with increasing loading.

Quantum to classical transition in quantum field theory

NASA Astrophysics Data System (ADS)

Lombardo, Fernando C.

1998-12-01

We study the quatum to classical transition process in the context of quantum field theory. Extending the influence functional formalism of Feynman and Vernon, we study the decoherence process for self-interacting quantum fields in flat space. We also use this formalism for arbitrary geometries to analyze the quantum to classical transition in quantum gravity. After summarizing the main results known for the quantum Brownian motion, we consider a self-interacting field theory in Minkowski spacetime. We compute a coarse grained effective action by integrating out the field modes with wavelength shorter than a critical value. From this effective action we obtain the evolution equation for the reduced density matrix (master equation). We compute the diffusion coefficients for this equation and analyze the decoherence induced on the long-wavelength modes. We generalize the results to the case of a conformally coupled scalar field in de Sitter spacetime. We show that the decoherence is effective as long as the critical wavelength is taken to be not shorter than the Hubble radius. On the other hand, we study the classical limit for scalar-tensorial models in two dimensions. We consider different couplings between the dilaton and the scalar field. We discuss the Hawking radiation process and, from an exact evaluation of the influence functional, we study the conditions by which decoherence ensures the validity of the semiclassical approximation in cosmological metrics. Finally we consider four dimensional models with massive scalar fields, arbitrary coupled to the geometry. We compute the Einstein-Langevin equations in order to study the effect of the fluctuations induced by the quantum fields on the classical geometry.

Molecular motion in cell membranes: Analytic study of fence-hindered random walks

NASA Astrophysics Data System (ADS)

Kenkre, V. M.; Giuggioli, L.; Kalay, Z.

2008-05-01

A theoretical calculation is presented to describe the confined motion of transmembrane molecules in cell membranes. The study is analytic, based on Master equations for the probability of the molecules moving as random walkers, and leads to explicit usable solutions including expressions for the molecular mean square displacement and effective diffusion constants. One outcome is a detailed understanding of the dependence of the time variation of the mean square displacement on the initial placement of the molecule within the confined region. How to use the calculations is illustrated by extracting (confinement) compartment sizes from experimentally reported published observations from single particle tracking experiments on the diffusion of gold-tagged G -protein coupled μ -opioid receptors in the normal rat kidney cell membrane, and by further comparing the analytical results to observations on the diffusion of phospholipids, also in normal rat kidney cells.

Sedimentation dynamics and diffusion of suspensions of swimming E. coli

NASA Astrophysics Data System (ADS)

Arratia, Paulo; Patteson, Alison; Singh, Jaspreet; Purohit, Prashant

2017-11-01

Sedimentation in active fluids has come into focus due to the ubiquity of swimming micro-organisms in natural and man-made environments. Here, we experimentally investigate sedimentation of passive particles in water containing various concentrations of the bacterium E. coli. Results show that the presence of live bacteria reduces the velocity of the sedimentation front even in the dilute regime, where constant sedimentation velocity is expected to be independent of particle concentration. The presence of live bacteria increases the effective diffusion coefficient, which determines the width of the sedimentation front. For higher bacteria concentration, we find the development of two sedimentation fronts due to bacterial death. A model in which the advection-diffusion equation describing the settling of particles under gravity is coupled to the population dynamics of the bacteria captures the experimental trends relatively well. This work is supported by NSF-CBET-1437482.

Diffusion of hydrous species in model basaltic melt

NASA Astrophysics Data System (ADS)

Zhang, Li; Guo, Xuan; Wang, Qinxia; Ding, Jiale; Ni, Huaiwei

2017-10-01

Water diffusion in Fe-free model basaltic melt with up to 2 wt% H2O was investigated at 1658-1846 K and 1 GPa in piston-cylinder apparatus using both hydration and diffusion couple techniques. Diffusion profiles measured by FTIR are consistent with a model in which both molecular H2O (H2Om) and hydroxyl (OH) contribute to water diffusion. OH diffusivity is roughly 13% of H2Om diffusivity, showing little dependence on temperature or water concentration. Water diffusion is dominated by the motion of OH until total H2O (H2Ot) concentration reaches 1 wt%. The dependence of apparent H2Ot diffusivity on H2Ot concentration appears to be overestimated by a previous study on MORB melt, but H2Ot diffusivity at 1 wt% H2Ot in basaltic melt is still greater than those in rhyolitic to andesitic melts. The appreciable contribution of OH to water diffusion in basaltic melt can be explained by enhanced mobility of OH, probably associated with the development of free hydroxyl bonded with network-modifying cations, as well as higher OH concentration. Calculation based on the Nernst-Einstein equation demonstrates that OH may serve as an effective charge carrier in hydrous basaltic melt, which could partly account for the previously observed strong influence of water on electrical conductivity of basaltic melt.

Solutal separation in a binary nanofluid due to thermodiffusion

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

Saghir, M.Z.; Yousefi, T.; Farahbakhsh, B.

2015-03-10

Transport phenomena in porous media have received considerable attention due to an increasing interest in geothermal processes, chemical catalytic reactors, waste storage (especially geological or ocean storage of carbon dioxide), etc. Among others, oil industry has shown an increasing interest in studying diffusion phenomenon. Nanofluid is a term used to describe the suspension of low concentration of metallic and non-metallic nanoparticles in a base fluid. The size of a nanoparticle ranges from 10 to 100nm, and the conventional fluids used are water, ethylene glycol (C{sub 2}H{sub 6}O{sub 2}) or engine oil. Various studies have proven that nanoparticles improve the heatmore » transfer of a base fluid. However, using various nanofluids it has been shown that the results could vary depending on different initial concentrations. The main objective of this paper is to study the diffusion and the thermodiffusion effect in a nanofluid for different fluid/porous media configurations. In this configuration, a liquid layer surrounds a porous layer. The full Brinkman equation coupled with the heat and mass transfer equations have been solved numerically for the porous layer using the finite element technique. The full Navier stokes equation coupled with heat and mass transfer equations have been solved for the liquid layer using the finite element method. A constraint between the liquid and porous layer has been applied to ensure heat flow and mass transfer continuity is maintained. A square cavity filled with hydrocarbon nanofluid of a mixture of fullerene-toluene with varying concentration of fullerene has been subject to different heating conditions. The entire cavity has been considered to be fully wetted with nanofluid. Results have confirmed that in the presence of a nanofluid a heat transfer enhancement is present up to certain initial concentration of the fullerene. The heat convection coefficient has been found to be 16% higher when a nanofluid is used as the working fluid.« less

Diffusion equations and the time evolution of foreign exchange rates

NASA Astrophysics Data System (ADS)

Figueiredo, Annibal; de Castro, Marcio T.; da Fonseca, Regina C. B.; Gleria, Iram

2013-10-01

We investigate which type of diffusion equation is most appropriate to describe the time evolution of foreign exchange rates. We modify the geometric diffusion model assuming a non-exponential time evolution and the stochastic term is the sum of a Wiener noise and a jump process. We find the resulting diffusion equation to obey the Kramers-Moyal equation. Analytical solutions are obtained using the characteristic function formalism and compared with empirical data. The analysis focus on the first four central moments considering the returns of foreign exchange rate. It is shown that the proposed model offers a good improvement over the classical geometric diffusion model.

Thermal diffusion effect on MHD mixed convective flow along a vertically inclined plate: A casson fluid flow

NASA Astrophysics Data System (ADS)

Prasad, D. V. V. Krishna; Chaitanya, G. S. Krishna; Raju, R. Srinivasa

2018-05-01

The nature of Casson fluid on MHD free convective flow of over an impulsively started infinite vertically inclined plate in presence of thermal diffusion (Soret), thermal radiation, heat and mass transfer effects is studied. The basic governing nonlinear coupled partial differential equations are solved numerically using finite element method. The relevant physical parameters appearing in velocity, temperature and concentration profiles are analyzed and discussed through graphs. Finally, the results for velocity profiles and the reduced Nusselt and Sherwood numbers are obtained and compared with previous results in the literature and are found to be in excellent agreement. Applications of the present study would be useful in magnetic material processing and chemical engineering systems.

A 1D-2D coupled SPH-SWE model applied to open channel flow simulations in complicated geometries

NASA Astrophysics Data System (ADS)

Chang, Kao-Hua; Sheu, Tony Wen-Hann; Chang, Tsang-Jung

2018-05-01

In this study, a one- and two-dimensional (1D-2D) coupled model is developed to solve the shallow water equations (SWEs). The solutions are obtained using a Lagrangian meshless method called smoothed particle hydrodynamics (SPH) to simulate shallow water flows in converging, diverging and curved channels. A buffer zone is introduced to exchange information between the 1D and 2D SPH-SWE models. Interpolated water discharge values and water surface levels at the internal boundaries are prescribed as the inflow/outflow boundary conditions in the two SPH-SWE models. In addition, instead of using the SPH summation operator, we directly solve the continuity equation by introducing a diffusive term to suppress oscillations in the predicted water depth. The performance of the two approaches in calculating the water depth is comprehensively compared through a case study of a straight channel. Additionally, three benchmark cases involving converging, diverging and curved channels are adopted to demonstrate the ability of the proposed 1D and 2D coupled SPH-SWE model through comparisons with measured data and predicted mesh-based numerical results. The proposed model provides satisfactory accuracy and guaranteed convergence.

First results of coupled IPS/NIMROD/GENRAY simulations

NASA Astrophysics Data System (ADS)

Jenkins, Thomas; Kruger, S. E.; Held, E. D.; Harvey, R. W.; Elwasif, W. R.; Schnack, D. D.

2010-11-01

The Integrated Plasma Simulator (IPS) framework, developed by the SWIM Project Team, facilitates self-consistent simulations of complicated plasma behavior via the coupling of various codes modeling different spatial/temporal scales in the plasma. Here, we apply this capability to investigate the stabilization of tearing modes by ECCD. Under IPS control, the NIMROD code (MHD) evolves fluid equations to model bulk plasma behavior, while the GENRAY code (RF) calculates the self-consistent propagation and deposition of RF power in the resulting plasma profiles. GENRAY data is then used to construct moments of the quasilinear diffusion tensor (induced by the RF) which influence the dynamics of momentum/energy evolution in NIMROD's equations. We present initial results from these coupled simulations and demonstrate that they correctly capture the physics of magnetic island stabilization [Jenkins et al, PoP 17, 012502 (2010)] in the low-beta limit. We also discuss the process of code verification in these simulations, demonstrating good agreement between NIMROD and GENRAY predictions for the flux-surface-averaged, RF-induced currents. An overview of ongoing model development (synthetic diagnostics/plasma control systems; neoclassical effects; etc.) is also presented. Funded by US DoE.

Scaling theory of tunneling diffusion of a heavy particle interacting with phonons

NASA Astrophysics Data System (ADS)

Itai, K.

1988-05-01

The author discusses motion of a heavy particle in a d-dimensional lattice interacting with phonons by different couplings. The models discussed are characterized by the dimension (d) and the set of two indices (λ,ν) which specify the momentum dependence of the dispersion of phonon energy (ω~kν) and of the particle-phonon coupling (~kλ). Scaling equations are derived by eliminating the short-time behavior in a renormalization-group scheme using Feynman's path-integral method, and the technique developed by Anderson, Yuval, and Hamann for the Kondo problem. The scaling equations show that the particle is localized in the strict sense when (2λ+d+2)/ν<2 and is not localized when (2λ+d+2)/ν>2. In the marginal case, i.e., (2λ+d+2)/ν=2, localization occurs for couplings larger than a critical value. This marginal case shows Ohmic dissipation and is a close analogy to the Caldeira-Leggett model for macroscopic quantum tunneling and the hopping models of Schmid's type. For large-enough (2λ+d+2)/ν, the particle is considered practically localized, but the origin of the localization is quite different from that for (2λ+d+2)/ν<=2. .AE

Restoration of rhythmicity in diffusively coupled dynamical networks.

PubMed

Zou, Wei; Senthilkumar, D V; Nagao, Raphael; Kiss, István Z; Tang, Yang; Koseska, Aneta; Duan, Jinqiao; Kurths, Jürgen

2015-07-15

Oscillatory behaviour is essential for proper functioning of various physical and biological processes. However, diffusive coupling is capable of suppressing intrinsic oscillations due to the manifestation of the phenomena of amplitude and oscillation deaths. Here we present a scheme to revoke these quenching states in diffusively coupled dynamical networks, and demonstrate the approach in experiments with an oscillatory chemical reaction. By introducing a simple feedback factor in the diffusive coupling, we show that the stable (in)homogeneous steady states can be effectively destabilized to restore dynamic behaviours of coupled systems. Even a feeble deviation from the normal diffusive coupling drastically shrinks the death regions in the parameter space. The generality of our method is corroborated in diverse non-linear systems of diffusively coupled paradigmatic models with various death scenarios. Our study provides a general framework to strengthen the robustness of dynamic activity in diffusively coupled dynamical networks.

An efficient transport solver for tokamak plasmas

DOE PAGES

Park, Jin Myung; Murakami, Masanori; St. John, H. E.; ...

2017-01-03

A simple approach to efficiently solve a coupled set of 1-D diffusion-type transport equations with a stiff transport model for tokamak plasmas is presented based on the 4th order accurate Interpolated Differential Operator scheme along with a nonlinear iteration method derived from a root-finding algorithm. Here, numerical tests using the Trapped Gyro-Landau-Fluid model show that the presented high order method provides an accurate transport solution using a small number of grid points with robust nonlinear convergence.

Expectation-Based Control of Noise and Chaos

NASA Technical Reports Server (NTRS)

Zak, Michael

2006-01-01

A proposed approach to control of noise and chaos in dynamic systems would supplement conventional methods. The approach is based on fictitious forces composed of expectations governed by Fokker-Planck or Liouville equations that describe the evolution of the probability densities of the controlled parameters. These forces would be utilized as feedback control forces that would suppress the undesired diffusion of the controlled parameters. Examples of dynamic systems in which the approach is expected to prove beneficial include spacecraft, electronic systems, and coupled lasers.

Regular Wave Propagation Out of Noise in Chemical Active Media

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

Alonso, S.; Sendina-Nadal, I.; Perez-Munuzuri, V.

2001-08-13

A pacemaker, regularly emitting chemical waves, is created out of noise when an excitable photosensitive Belousov-Zhabotinsky medium, strictly unable to autonomously initiate autowaves, is forced with a spatiotemporal patterned random illumination. These experimental observations are also reproduced numerically by using a set of reaction-diffusion equations for an activator-inhibitor model, and further analytically interpreted in terms of genuine coupling effects arising from parametric fluctuations. Within the same framework we also address situations of noise-sustained propagation in subexcitable media.

One-electron propagation in Fermi, Pasta, Ulam disordered chains with Gaussian acoustic pulse pumping

NASA Astrophysics Data System (ADS)

Silva, L. D. Da; Dos Santos, J. L. L.; Ranciaro Neto, A.; Sales, M. O.; de Moura, F. A. B. F.

In this work, we consider a one-electron moving on a Fermi, Pasta, Ulam disordered chain under effect of electron-phonon interaction and a Gaussian acoustic pulse pumping. We describe electronic dynamics using quantum mechanics formalism and the nonlinear atomic vibrations using standard classical physics. Solving numerical equations related to coupled quantum/classical behavior of this system, we study electronic propagation properties. Our calculations suggest that the acoustic pumping associated with the electron-lattice interaction promote a sub-diffusive electronic dynamics.

The exit-time problem for a Markov jump process

NASA Astrophysics Data System (ADS)

Burch, N.; D'Elia, M.; Lehoucq, R. B.

2014-12-01

The purpose of this paper is to consider the exit-time problem for a finite-range Markov jump process, i.e, the distance the particle can jump is bounded independent of its location. Such jump diffusions are expedient models for anomalous transport exhibiting super-diffusion or nonstandard normal diffusion. We refer to the associated deterministic equation as a volume-constrained nonlocal diffusion equation. The volume constraint is the nonlocal analogue of a boundary condition necessary to demonstrate that the nonlocal diffusion equation is well-posed and is consistent with the jump process. A critical aspect of the analysis is a variational formulation and a recently developed nonlocal vector calculus. This calculus allows us to pose nonlocal backward and forward Kolmogorov equations, the former equation granting the various moments of the exit-time distribution.

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.

A parallel algorithm for nonlinear convection-diffusion equations

NASA Technical Reports Server (NTRS)

Scroggs, Jeffrey S.

1990-01-01

A parallel algorithm for the efficient solution of nonlinear time-dependent convection-diffusion equations with small parameter on the diffusion term is presented. The method is based on a physically motivated domain decomposition that is dictated by singular perturbation analysis. The analysis is used to determine regions where certain reduced equations may be solved in place of the full equation. The method is suitable for the solution of problems arising in the simulation of fluid dynamics. Experimental results for a nonlinear equation in two-dimensions are presented.

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

NASA Astrophysics Data System (ADS)

Machida, Manabu

2017-01-01

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

Generalized fractional diffusion equations for accelerating subdiffusion and truncated Lévy flights

NASA Astrophysics Data System (ADS)

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

2008-08-01

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

Cu-Zn binary phase diagram and diffusion couples

NASA Technical Reports Server (NTRS)

Mccoy, Robert A.

1992-01-01

The objectives of this paper are to learn: (1) what information a binary phase diagram can yield; (2) how to construct and heat treat a simple diffusion couple; (3) how to prepare a metallographic sample; (4) how to operate a metallograph; (5) how to correlate phases found in the diffusion couple with phases predicted by the phase diagram; (6) how diffusion couples held at various temperatures could be used to construct a phase diagram; (7) the relation between the thickness of an intermetallic phase layer and the diffusion time; and (8) the effect of one species of atoms diffusing faster than another species in a diffusion couple.

Numerical solution of special ultra-relativistic Euler equations using central upwind scheme

NASA Astrophysics Data System (ADS)

Ghaffar, Tayabia; Yousaf, Muhammad; Qamar, Shamsul

2018-06-01

This article is concerned with the numerical approximation of one and two-dimensional special ultra-relativistic Euler equations. The governing equations are coupled first-order nonlinear hyperbolic partial differential equations. These equations describe perfect fluid flow in terms of the particle density, the four-velocity and the pressure. A high-resolution shock-capturing central upwind scheme is employed to solve the model equations. To avoid excessive numerical diffusion, the considered scheme avails the specific information of local propagation speeds. By using Runge-Kutta time stepping method and MUSCL-type initial reconstruction, we have obtained 2nd order accuracy of the proposed scheme. After discussing the model equations and the numerical technique, several 1D and 2D test problems are investigated. For all the numerical test cases, our proposed scheme demonstrates very good agreement with the results obtained by well-established algorithms, even in the case of highly relativistic 2D test problems. For validation and comparison, the staggered central scheme and the kinetic flux-vector splitting (KFVS) method are also implemented to the same model. The robustness and efficiency of central upwind scheme is demonstrated by the numerical results.

Snow Micro-Structure Model

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

Micah Johnson, Andrew Slaughter

PIKA is a MOOSE-based application for modeling micro-structure evolution of seasonal snow. The model will be useful for environmental, atmospheric, and climate scientists. Possible applications include application to energy balance models, ice sheet modeling, and avalanche forecasting. The model implements physics from published, peer-reviewed articles. The main purpose is to foster university and laboratory collaboration to build a larger multi-scale snow model using MOOSE. The main feature of the code is that it is implemented using the MOOSE framework, thus making features such as multiphysics coupling, adaptive mesh refinement, and parallel scalability native to the application. PIKA implements three equations:more » the phase-field equation for tracking the evolution of the ice-air interface within seasonal snow at the grain-scale; the heat equation for computing the temperature of both the ice and air within the snow; and the mass transport equation for monitoring the diffusion of water vapor in the pore space of the snow.« less

Symmetry classification of time-fractional diffusion equation

NASA Astrophysics Data System (ADS)

Naeem, I.; Khan, M. D.

2017-01-01

In this article, a new approach is proposed to construct the symmetry groups for a class of fractional differential equations which are expressed in the modified Riemann-Liouville fractional derivative. We perform a complete group classification of a nonlinear fractional diffusion equation which arises in fractals, acoustics, control theory, signal processing and many other applications. Introducing the suitable transformations, the fractional derivatives are converted to integer order derivatives and in consequence the nonlinear fractional diffusion equation transforms to a partial differential equation (PDE). Then the Lie symmetries are computed for resulting PDE and using inverse transformations, we derive the symmetries for fractional diffusion equation. All cases are discussed in detail and results for symmetry properties are compared for different values of α. This study provides a new way of computing symmetries for a class of fractional differential equations.

WE-AB-204-07: Spatiotemporal Distribution of the FDG PET Tracer in Solid Tumors: Contributions of Diffusion and Convection Mechanisms

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

Soltani, M; Sefidgar, M; Bazmara, H

2015-06-15

Purpose: In this study, a mathematical model is utilized to simulate FDG distribution in tumor tissue. In contrast to conventional compartmental modeling, tracer distributions across space and time are directly linked together (i.e. moving beyond ordinary differential equations (ODEs) to utilizing partial differential equations (PDEs) coupling space and time). The diffusion and convection transport mechanisms are both incorporated to model tracer distribution. We aimed to investigate the contributions of these two mechanisms on FDG distribution for various tumor geometries obtained from PET/CT images. Methods: FDG transport was simulated via a spatiotemporal distribution model (SDM). The model is based on amore » 5K compartmental model. We model the fact that tracer concentration in the second compartment (extracellular space) is modulated via convection and diffusion. Data from n=45 patients with pancreatic tumors as imaged using clinical FDG PET/CT imaging were analyzed, and geometrical information from the tumors including size, shape, and aspect ratios were classified. Tumors with varying shapes and sizes were assessed in order to investigate the effects of convection and diffusion mechanisms on FDG transport. Numerical methods simulating interstitial flow and solute transport in tissue were utilized. Results: We have shown the convection mechanism to depend on the shape and size of tumors whereas diffusion mechanism is seen to exhibit low dependency on shape and size. Results show that concentration distribution of FDG is relatively similar for the considered tumors; and that the diffusion mechanism of FDG transport significantly dominates the convection mechanism. The Peclet number which shows the ratio of convection to diffusion rates was shown to be of the order of 10−{sup 3} for all considered tumors. Conclusion: We have demonstrated that even though convection leads to varying tracer distribution profiles depending on tumor shape and size, the domination of the diffusion phenomenon prevents these factors from modulating FDG distribution.« less

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

NASA Astrophysics Data System (ADS)

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

2010-12-01

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

Heavy-tailed fractional Pearson diffusions.

PubMed

Leonenko, N N; Papić, I; Sikorskii, A; Šuvak, N

2017-11-01

We define heavy-tailed fractional reciprocal gamma and Fisher-Snedecor diffusions by a non-Markovian time change in the corresponding Pearson diffusions. Pearson diffusions are governed by the backward Kolmogorov equations with space-varying polynomial coefficients and are widely used in applications. The corresponding fractional reciprocal gamma and Fisher-Snedecor diffusions are governed by the fractional backward Kolmogorov equations and have heavy-tailed marginal distributions in the steady state. We derive the explicit expressions for the transition densities of the fractional reciprocal gamma and Fisher-Snedecor diffusions and strong solutions of the associated Cauchy problems for the fractional backward Kolmogorov equation.

Numerical algorithms based on Galerkin methods for the modeling of reactive interfaces in photoelectrochemical (PEC) solar cells

NASA Astrophysics Data System (ADS)

Harmon, Michael; Gamba, Irene M.; Ren, Kui

2016-12-01

This work concerns the numerical solution of a coupled system of self-consistent reaction-drift-diffusion-Poisson equations that describes the macroscopic dynamics of charge transport in photoelectrochemical (PEC) solar cells with reactive semiconductor and electrolyte interfaces. We present three numerical algorithms, mainly based on a mixed finite element and a local discontinuous Galerkin method for spatial discretization, with carefully chosen numerical fluxes, and implicit-explicit time stepping techniques, for solving the time-dependent nonlinear systems of partial differential equations. We perform computational simulations under various model parameters to demonstrate the performance of the proposed numerical algorithms as well as the impact of these parameters on the solution to the model.

Double Diffusive Magnetohydrodynamic (MHD) Mixed Convective Slip Flow along a Radiating Moving Vertical Flat Plate with Convective Boundary Condition

PubMed Central

Rashidi, Mohammad M.; Kavyani, Neda; Abelman, Shirley; Uddin, Mohammed J.; Freidoonimehr, Navid

2014-01-01

In this study combined heat and mass transfer by mixed convective flow along a moving vertical flat plate with hydrodynamic slip and thermal convective boundary condition is investigated. Using similarity variables, the governing nonlinear partial differential equations are converted into a system of coupled nonlinear ordinary differential equations. The transformed equations are then solved using a semi-numerical/analytical method called the differential transform method and results are compared with numerical results. Close agreement is found between the present method and the numerical method. Effects of the controlling parameters, including convective heat transfer, magnetic field, buoyancy ratio, hydrodynamic slip, mixed convective, Prandtl number and Schmidt number are investigated on the dimensionless velocity, temperature and concentration profiles. In addition effects of different parameters on the skin friction factor, , local Nusselt number, , and local Sherwood number are shown and explained through tables. PMID:25343360

Examining the validity of Stoney-equation for in-situ stress measurements in thin film electrodes using a large-deformation finite-element procedure

NASA Astrophysics Data System (ADS)

Wen, Jici; Wei, Yujie; Cheng, Yang-Tse

2018-05-01

During the lithiation and delithiation of a thin film electrode, stress in the electrode is deduced from the curvature change of the film using the Stoney equation. The accuracy of such a measurement is conditioned on the assumptions that (a) the mechanical properties of the electrode remain unchanged during lithiation and (b) small deformation holds. Here, we demonstrate that the change in elastic properties can influence the measurement of the stress in thin film electrodes. We consider the coupling between diffusion and deformation during lithiation and delithiation of thin film electrodes and implement the constitutive behavior in a finite-deformation finite element procedure. We demonstrate that both the variation in elastic properties in thin film electrodes and finite-deformation during lithiation and delithiation would challenge the applicability of the Stoney-equation for in-situ stress measurements of thin film electrodes.

On a Multiphase Multicomponent Model of Biofilm Growth

NASA Astrophysics Data System (ADS)

Friedman, Avner; Hu, Bei; Xue, Chuan

2014-01-01

Biofilms are formed when free-floating bacteria attach to a surface and secrete polysaccharide to form an extracellular polymeric matrix (EPS). A general model of biofilm growth needs to include the bacteria, the EPS, and the solvent within the biofilm region Ω( t), and the solvent in the surrounding region D( t). The interface between the two regions, Γ( t), is a free boundary. In this paper, we consider a mathematical model that consists of a Stokes equation for the EPS with bacteria attached to it, a Stokes equation for the solvent in Ω( t) and another for the solvent in D( t). The volume fraction of the EPS is another unknown satisfying a reaction-diffusion equation. The entire system is coupled nonlinearly within Ω( t) and across the free surface Γ( t). We prove the existence and uniqueness of a solution, with a smooth surface Γ( t), for a small time interval.

Feynman-Kac equations for reaction and diffusion processes

NASA Astrophysics Data System (ADS)

Hou, Ru; Deng, Weihua

2018-04-01

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

Numerical approximations for fractional diffusion equations via a Chebyshev spectral-tau method

NASA Astrophysics Data System (ADS)

Doha, Eid H.; Bhrawy, Ali H.; Ezz-Eldien, Samer S.

2013-10-01

In this paper, a class of fractional diffusion equations with variable coefficients is considered. An accurate and efficient spectral tau technique for solving the fractional diffusion equations numerically is proposed. This method is based upon Chebyshev tau approximation together with Chebyshev operational matrix of Caputo fractional differentiation. Such approach has the advantage of reducing the problem to the solution of a system of algebraic equations, which may then be solved by any standard numerical technique. We apply this general method to solve four specific examples. In each of the examples considered, the numerical results show that the proposed method is of high accuracy and is efficient for solving the time-dependent fractional diffusion equations.

The exit-time problem for a Markov jump process

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

Burch, N.; D'Elia, Marta; Lehoucq, Richard B.

2014-12-15

The purpose of our paper is to consider the exit-time problem for a finite-range Markov jump process, i.e, the distance the particle can jump is bounded independent of its location. Such jump diffusions are expedient models for anomalous transport exhibiting super-diffusion or nonstandard normal diffusion. We refer to the associated deterministic equation as a volume-constrained nonlocal diffusion equation. The volume constraint is the nonlocal analogue of a boundary condition necessary to demonstrate that the nonlocal diffusion equation is well-posed and is consistent with the jump process. A critical aspect of the analysis is a variational formulation and a recently developedmore » nonlocal vector calculus. Furthermore, this calculus allows us to pose nonlocal backward and forward Kolmogorov equations, the former equation granting the various moments of the exit-time distribution.« less

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

PubMed

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

2002-04-01

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

Diffusion approximations to the chemical master equation only have a consistent stochastic thermodynamics at chemical equilibrium

NASA Astrophysics Data System (ADS)

Horowitz, Jordan M.

2015-07-01

The stochastic thermodynamics of a dilute, well-stirred mixture of chemically reacting species is built on the stochastic trajectories of reaction events obtained from the chemical master equation. However, when the molecular populations are large, the discrete chemical master equation can be approximated with a continuous diffusion process, like the chemical Langevin equation or low noise approximation. In this paper, we investigate to what extent these diffusion approximations inherit the stochastic thermodynamics of the chemical master equation. We find that a stochastic-thermodynamic description is only valid at a detailed-balanced, equilibrium steady state. Away from equilibrium, where there is no consistent stochastic thermodynamics, we show that one can still use the diffusive solutions to approximate the underlying thermodynamics of the chemical master equation.

Diffusion approximations to the chemical master equation only have a consistent stochastic thermodynamics at chemical equilibrium.

PubMed

Horowitz, Jordan M

2015-07-28

The stochastic thermodynamics of a dilute, well-stirred mixture of chemically reacting species is built on the stochastic trajectories of reaction events obtained from the chemical master equation. However, when the molecular populations are large, the discrete chemical master equation can be approximated with a continuous diffusion process, like the chemical Langevin equation or low noise approximation. In this paper, we investigate to what extent these diffusion approximations inherit the stochastic thermodynamics of the chemical master equation. We find that a stochastic-thermodynamic description is only valid at a detailed-balanced, equilibrium steady state. Away from equilibrium, where there is no consistent stochastic thermodynamics, we show that one can still use the diffusive solutions to approximate the underlying thermodynamics of the chemical master equation.

Green functions and Langevin equations for nonlinear diffusion equations: A comment on ‘Markov processes, Hurst exponents, and nonlinear diffusion equations’ by Bassler et al.

NASA Astrophysics Data System (ADS)

Frank, T. D.

2008-02-01

We discuss two central claims made in the study by Bassler et al. [K.E. Bassler, G.H. Gunaratne, J.L. McCauley, Physica A 369 (2006) 343]. Bassler et al. claimed that Green functions and Langevin equations cannot be defined for nonlinear diffusion equations. In addition, they claimed that nonlinear diffusion equations are linear partial differential equations disguised as nonlinear ones. We review bottom-up and top-down approaches that have been used in the literature to derive Green functions for nonlinear diffusion equations and, in doing so, show that the first claim needs to be revised. We show that the second claim as well needs to be revised. To this end, we point out similarities and differences between non-autonomous linear Fokker-Planck equations and autonomous nonlinear Fokker-Planck equations. In this context, we raise the question whether Bassler et al.’s approach to financial markets is physically plausible because it necessitates the introduction of external traders and causes. Such external entities can easily be eliminated when taking self-organization principles and concepts of nonextensive thermostatistics into account and modeling financial processes by means of nonlinear Fokker-Planck equations.

Evolution and Growth Competition of Salt Fingers in Saline Lake with Slight Wind Shear

NASA Astrophysics Data System (ADS)

Yang, Ray-Yeng; Hwung, Hwung-Hweng; Shugan, Igor

2010-05-01

Since the discover of double-diffusive convection by Stommel, Arons & Blanchard (1956), 'evidence has accumulated for the widespread presence of double-diffusion throughout the ocean' and for its 'significant effects on global water-mass structure and the thermohaline convection' (Schmitt, 1998). The salt-fingering form of double-diffusion has particularly attracted interest because of salt-finger convection being now widely recognized as an important mechanism for mixing heat and salt both vertically and laterally in the ocean and saline lake. In oceanographic situations or saline lake where salt fingers may be an important mechanism for the transport of heat and salt in the vertical, velocity shears may also be present. Salt finger convection is analogous to Bénard convection in that the kinetic energy of the motions is obtained from the potential energy stored in the unstable distribution of a stratifying component. On the basis of the thermal analogy it is of interest to discover whether salt fingers are converted into two-dimensional sheets by the wind shear, and how the vertical fluxes of heat and salt are changed by the wind shear. Salt finger convection under the effect of steady wind shear is theoretically examined in this paper. The evolution of developing in the presence of a vertical density gradient disturbance and the horizontal Couette flow is considered near the onset of salt fingers in the saline lake under a moderate rate of wind shear. We use velocity as the basic variable and solve the pressure Poisson equation in terms of the associated Green function. Growth competition between the longitudinal rolls (LR) and the transverse rolls (TR), whose axes are respectively in the direction parallel to and perpendicular to the Couette flow, is investigated by the weakly nonlinear analysis of coupled-mode equations. The results show that the TR mode is characterized in some range of the effective Rayleigh number, and that the stability is dominated by the LR mode in the system. KEY WORDS: evolution, saline lake, salt finger convection, wind shear, growth competition, longitudinal rolls, transverse rolls, coupled-mode equations.

Application of linear multifrequency-grey acceleration to preconditioned Krylov iterations for thermal radiation transport

DOE PAGES

Till, Andrew T.; Warsa, James S.; Morel, Jim E.

2018-06-15

The thermal radiative transfer (TRT) equations comprise a radiation equation coupled to the material internal energy equation. Linearization of these equations produces effective, thermally-redistributed scattering through absorption-reemission. In this paper, we investigate the effectiveness and efficiency of Linear-Multi-Frequency-Grey (LMFG) acceleration that has been reformulated for use as a preconditioner to Krylov iterative solution methods. We introduce two general frameworks, the scalar flux formulation (SFF) and the absorption rate formulation (ARF), and investigate their iterative properties in the absence and presence of true scattering. SFF has a group-dependent state size but may be formulated without inner iterations in the presence ofmore » scattering, while ARF has a group-independent state size but requires inner iterations when scattering is present. We compare and evaluate the computational cost and efficiency of LMFG applied to these two formulations using a direct solver for the preconditioners. Finally, this work is novel because the use of LMFG for the radiation transport equation, in conjunction with Krylov methods, involves special considerations not required for radiation diffusion.« less

Dynamical density functional theory for arbitrary-shape colloidal fluids including inertia and hydrodynamic interactions

NASA Astrophysics Data System (ADS)

Duran-Olivencia, Miguel A.; Goddard, Ben; Kalliadasis, Serafim

2015-11-01

Over the last few decades the classical density-functional theory (DFT) and its dynamic extensions (DDFTs) have become a remarkably powerful tool in the study of colloidal fluids. Recently there has been extensive research to generalise all previous DDFTs finally yielding a general DDFT equation (for spherical particles) which takes into account both inertia and hydrodynamic interactions (HI) which strongly influence non-equilibrium properties. The present work will be devoted to a further generalisation of such a framework to systems of anisotropic particles. To this end, the kinetic equation for the Brownian particle distribution function is derived starting from the Liouville equation and making use of Zwanzig's projection-operator techniques. By averaging over all but one particle, a DDFT equation is finally obtained with some similarities to that for spherical colloids. However, there is now an inevitable translational-rotational coupling which affects the diffusivity of asymmetric particles. Lastly, in the overdamped (high friction) limit the theory is notably simplified leading to a DDFT equation which agrees with previous derivations. We acknowledge financial support from European Research Council via Advanced Grant No. 247031.

Optimal distributed control of a diffuse interface model of tumor growth

NASA Astrophysics Data System (ADS)

Colli, Pierluigi; Gilardi, Gianni; Rocca, Elisabetta; Sprekels, Jürgen

2017-06-01

In this paper, a distributed optimal control problem is studied for a diffuse interface model of tumor growth which was proposed by Hawkins-Daruud et al in Hawkins-Daruud et al (2011 Int. J. Numer. Math. Biomed. Eng. 28 3-24). The model consists of a Cahn-Hilliard equation for the tumor cell fraction φ coupled to a reaction-diffusion equation for a function σ representing the nutrient-rich extracellular water volume fraction. The distributed control u monitors as a right-hand side of the equation for σ and can be interpreted as a nutrient supply or a medication, while the cost function, which is of standard tracking type, is meant to keep the tumor cell fraction under control during the evolution. We show that the control-to-state operator is Fréchet differentiable between appropriate Banach spaces and derive the first-order necessary optimality conditions in terms of a variational inequality involving the adjoint state variables. The financial support of the FP7-IDEAS-ERC-StG #256872 (EntroPhase) and of the project Fondazione Cariplo-Regione Lombardia MEGAsTAR ‘Matematica d’Eccellenza in biologia ed ingegneria come accelleratore di una nuona strateGia per l’ATtRattività dell’ateneo pavese’ is gratefully acknowledged. The paper also benefited from the support of the MIUR-PRIN Grant 2015PA5MP7 ‘Calculus of Variations’ for PC and GG, and the GNAMPA (Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni) of INdAM (Istituto Nazionale di Alta Matematica) for PC, GG and ER.

Poisson-Boltzmann-Nernst-Planck model

NASA Astrophysics Data System (ADS)

Zheng, Qiong; Wei, Guo-Wei

2011-05-01

The Poisson-Nernst-Planck (PNP) model is based on a mean-field approximation of ion interactions and continuum descriptions of concentration and electrostatic potential. It provides qualitative explanation and increasingly quantitative predictions of experimental measurements for the ion transport problems in many areas such as semiconductor devices, nanofluidic systems, and biological systems, despite many limitations. While the PNP model gives a good prediction of the ion transport phenomenon for chemical, physical, and biological systems, the number of equations to be solved and the number of diffusion coefficient profiles to be determined for the calculation directly depend on the number of ion species in the system, since each ion species corresponds to one Nernst-Planck equation and one position-dependent diffusion coefficient profile. In a complex system with multiple ion species, the PNP can be computationally expensive and parameter demanding, as experimental measurements of diffusion coefficient profiles are generally quite limited for most confined regions such as ion channels, nanostructures and nanopores. We propose an alternative model to reduce number of Nernst-Planck equations to be solved in complex chemical and biological systems with multiple ion species by substituting Nernst-Planck equations with Boltzmann distributions of ion concentrations. As such, we solve the coupled Poisson-Boltzmann and Nernst-Planck (PBNP) equations, instead of the PNP equations. The proposed PBNP equations are derived from a total energy functional by using the variational principle. We design a number of computational techniques, including the Dirichlet to Neumann mapping, the matched interface and boundary, and relaxation based iterative procedure, to ensure efficient solution of the proposed PBNP equations. Two protein molecules, cytochrome c551 and Gramicidin A, are employed to validate the proposed model under a wide range of bulk ion concentrations and external voltages. Extensive numerical experiments show that there is an excellent consistency between the results predicted from the present PBNP model and those obtained from the PNP model in terms of the electrostatic potentials, ion concentration profiles, and current-voltage (I-V) curves. The present PBNP model is further validated by a comparison with experimental measurements of I-V curves under various ion bulk concentrations. Numerical experiments indicate that the proposed PBNP model is more efficient than the original PNP model in terms of simulation time.

Poisson-Boltzmann-Nernst-Planck model

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

Zheng Qiong; Wei Guowei; Department of Electrical and Computer Engineering, Michigan State University, East Lansing, Michigan 48824

2011-05-21

The Poisson-Nernst-Planck (PNP) model is based on a mean-field approximation of ion interactions and continuum descriptions of concentration and electrostatic potential. It provides qualitative explanation and increasingly quantitative predictions of experimental measurements for the ion transport problems in many areas such as semiconductor devices, nanofluidic systems, and biological systems, despite many limitations. While the PNP model gives a good prediction of the ion transport phenomenon for chemical, physical, and biological systems, the number of equations to be solved and the number of diffusion coefficient profiles to be determined for the calculation directly depend on the number of ion species inmore » the system, since each ion species corresponds to one Nernst-Planck equation and one position-dependent diffusion coefficient profile. In a complex system with multiple ion species, the PNP can be computationally expensive and parameter demanding, as experimental measurements of diffusion coefficient profiles are generally quite limited for most confined regions such as ion channels, nanostructures and nanopores. We propose an alternative model to reduce number of Nernst-Planck equations to be solved in complex chemical and biological systems with multiple ion species by substituting Nernst-Planck equations with Boltzmann distributions of ion concentrations. As such, we solve the coupled Poisson-Boltzmann and Nernst-Planck (PBNP) equations, instead of the PNP equations. The proposed PBNP equations are derived from a total energy functional by using the variational principle. We design a number of computational techniques, including the Dirichlet to Neumann mapping, the matched interface and boundary, and relaxation based iterative procedure, to ensure efficient solution of the proposed PBNP equations. Two protein molecules, cytochrome c551 and Gramicidin A, are employed to validate the proposed model under a wide range of bulk ion concentrations and external voltages. Extensive numerical experiments show that there is an excellent consistency between the results predicted from the present PBNP model and those obtained from the PNP model in terms of the electrostatic potentials, ion concentration profiles, and current-voltage (I-V) curves. The present PBNP model is further validated by a comparison with experimental measurements of I-V curves under various ion bulk concentrations. Numerical experiments indicate that the proposed PBNP model is more efficient than the original PNP model in terms of simulation time.« less

Poisson–Boltzmann–Nernst–Planck model

PubMed Central

Zheng, Qiong; Wei, Guo-Wei

2011-01-01

The Poisson–Nernst–Planck (PNP) model is based on a mean-field approximation of ion interactions and continuum descriptions of concentration and electrostatic potential. It provides qualitative explanation and increasingly quantitative predictions of experimental measurements for the ion transport problems in many areas such as semiconductor devices, nanofluidic systems, and biological systems, despite many limitations. While the PNP model gives a good prediction of the ion transport phenomenon for chemical, physical, and biological systems, the number of equations to be solved and the number of diffusion coefficient profiles to be determined for the calculation directly depend on the number of ion species in the system, since each ion species corresponds to one Nernst–Planck equation and one position-dependent diffusion coefficient profile. In a complex system with multiple ion species, the PNP can be computationally expensive and parameter demanding, as experimental measurements of diffusion coefficient profiles are generally quite limited for most confined regions such as ion channels, nanostructures and nanopores. We propose an alternative model to reduce number of Nernst–Planck equations to be solved in complex chemical and biological systems with multiple ion species by substituting Nernst–Planck equations with Boltzmann distributions of ion concentrations. As such, we solve the coupled Poisson–Boltzmann and Nernst–Planck (PBNP) equations, instead of the PNP equations. The proposed PBNP equations are derived from a total energy functional by using the variational principle. We design a number of computational techniques, including the Dirichlet to Neumann mapping, the matched interface and boundary, and relaxation based iterative procedure, to ensure efficient solution of the proposed PBNP equations. Two protein molecules, cytochrome c551 and Gramicidin A, are employed to validate the proposed model under a wide range of bulk ion concentrations and external voltages. Extensive numerical experiments show that there is an excellent consistency between the results predicted from the present PBNP model and those obtained from the PNP model in terms of the electrostatic potentials, ion concentration profiles, and current–voltage (I–V) curves. The present PBNP model is further validated by a comparison with experimental measurements of I–V curves under various ion bulk concentrations. Numerical experiments indicate that the proposed PBNP model is more efficient than the original PNP model in terms of simulation time. PMID:21599038

Poisson-Boltzmann-Nernst-Planck model.

PubMed

Zheng, Qiong; Wei, Guo-Wei

2011-05-21

The Poisson-Nernst-Planck (PNP) model is based on a mean-field approximation of ion interactions and continuum descriptions of concentration and electrostatic potential. It provides qualitative explanation and increasingly quantitative predictions of experimental measurements for the ion transport problems in many areas such as semiconductor devices, nanofluidic systems, and biological systems, despite many limitations. While the PNP model gives a good prediction of the ion transport phenomenon for chemical, physical, and biological systems, the number of equations to be solved and the number of diffusion coefficient profiles to be determined for the calculation directly depend on the number of ion species in the system, since each ion species corresponds to one Nernst-Planck equation and one position-dependent diffusion coefficient profile. In a complex system with multiple ion species, the PNP can be computationally expensive and parameter demanding, as experimental measurements of diffusion coefficient profiles are generally quite limited for most confined regions such as ion channels, nanostructures and nanopores. We propose an alternative model to reduce number of Nernst-Planck equations to be solved in complex chemical and biological systems with multiple ion species by substituting Nernst-Planck equations with Boltzmann distributions of ion concentrations. As such, we solve the coupled Poisson-Boltzmann and Nernst-Planck (PBNP) equations, instead of the PNP equations. The proposed PBNP equations are derived from a total energy functional by using the variational principle. We design a number of computational techniques, including the Dirichlet to Neumann mapping, the matched interface and boundary, and relaxation based iterative procedure, to ensure efficient solution of the proposed PBNP equations. Two protein molecules, cytochrome c551 and Gramicidin A, are employed to validate the proposed model under a wide range of bulk ion concentrations and external voltages. Extensive numerical experiments show that there is an excellent consistency between the results predicted from the present PBNP model and those obtained from the PNP model in terms of the electrostatic potentials, ion concentration profiles, and current-voltage (I-V) curves. The present PBNP model is further validated by a comparison with experimental measurements of I-V curves under various ion bulk concentrations. Numerical experiments indicate that the proposed PBNP model is more efficient than the original PNP model in terms of simulation time. © 2011 American Institute of Physics.

Effects of microwave electric fields on the translational diffusion of dipolar molecules in surface potential: A simulation study

NASA Astrophysics Data System (ADS)

Kapranov, Sergey V.; Kouzaev, Guennadi A.

2018-01-01

Variations of effective diffusion coefficient of polar molecules exposed to microwave electric fields in a surface potential are studied by solving coupled stochastic differential equations of motion with a deterministic component of the surface force. Being an essential tool for the simulation interpretation, a theoretical approach to effective diffusion in surface potential is first developed. The effective diffusion coefficient is represented as the product of the normal diffusion coefficient and potential-dependent correction function, whose temperature dependence is close to the Arrhenius form. The analytically found zero-diffusion condition defines the state of thermal equilibrium at the surface. The diffusion of a water-like dipole molecule in the potential of graphite surface is simulated in the field-free conditions and in the presence of the alternating electric fields of various magnitude intensities and frequencies. Temperature dependence of the correction function exhibits field-induced variations of the effective Lennard-Jones energy parameter. It demonstrates maximum departure from the zero-field value at certain frequencies and intensities, which is associated with variations in the rotational dynamics. A concept of the amplitude-frequency resonance put forward to interpret the simulation results is explained using a heuristic reasoning and is corroborated by semi-quantitative considerations in terms of the Dissado-Hill cluster theory of dielectric relaxation.

Diffusion Influenced Adsorption Kinetics.

PubMed

Miura, Toshiaki; Seki, Kazuhiko

2015-08-27

When the kinetics of adsorption is influenced by the diffusive flow of solutes, the solute concentration at the surface is influenced by the surface coverage of solutes, which is given by the Langmuir-Hinshelwood adsorption equation. The diffusion equation with the boundary condition given by the Langmuir-Hinshelwood adsorption equation leads to the nonlinear integro-differential equation for the surface coverage. In this paper, we solved the nonlinear integro-differential equation using the Grünwald-Letnikov formula developed to solve fractional kinetics. Guided by the numerical results, analytical expressions for the upper and lower bounds of the exact numerical results were obtained. The upper and lower bounds were close to the exact numerical results in the diffusion- and reaction-controlled limits, respectively. We examined the validity of the two simple analytical expressions obtained in the diffusion-controlled limit. The results were generalized to include the effect of dispersive diffusion. We also investigated the effect of molecular rearrangement of anisotropic molecules on surface coverage.

Diffusion and related transport mechanisms in brain tissue

NASA Astrophysics Data System (ADS)

Nicholson, Charles

2001-07-01

Diffusion plays a crucial role in brain function. The spaces between cells can be likened to the water phase of a foam and many substances move within this complicated region. Diffusion in this interstitial space can be accurately modelled with appropriate modifications of classical equations and quantified from measurements based on novel micro-techniques. Besides delivering glucose and oxygen from the vascular system to brain cells, diffusion also moves informational substances between cells, a process known as volume transmission. Deviations from expected results reveal how local uptake, degradation or bulk flow may modify the transport of molecules. Diffusion is also essential to many therapies that deliver drugs to the brain. The diffusion-generated concentration distributions of well-chosen molecules also reveal the structure of brain tissue. This structure is represented by the volume fraction (void space) and the tortuosity (hindrance to diffusion imposed by local boundaries or local viscosity). Analysis of these parameters also reveals how the local geometry of the brain changes with time or under pathological conditions. Theoretical and experimental approaches borrow from classical diffusion theory and from porous media concepts. Earlier studies were based on radiotracers but the recent methods use a point-source paradigm coupled with micro-sensors or optical imaging of macromolecules labelled with fluorescent tags. These concepts and methods are likely to be applicable elsewhere to measure diffusion properties in very small volumes of highly structured but delicate material.

Microscopic and macroscopic models for the onset and progression of Alzheimer's disease

NASA Astrophysics Data System (ADS)

Bertsch, Michiel; Franchi, Bruno; Carla Tesi, Maria; Tosin, Andrea

2017-10-01

In the first part of this paper we review a mathematical model for the onset and progression of Alzheimer’s disease (AD) that was developed in subsequent steps over several years. The model is meant to describe the evolution of AD in vivo. In Achdou et al (2013 J. Math. Biol. 67 1369-92) we treated the problem at a microscopic scale, where the typical length scale is a multiple of the size of the soma of a single neuron. Subsequently, in Bertsch et al (2017 Math. Med. Biol. 34 193-214) we concentrated on the macroscopic scale, where brain neurons are regarded as a continuous medium, structured by their degree of malfunctioning. In the second part of the paper we consider the relation between the microscopic and the macroscopic models. In particular we show under which assumptions the kinetic transport equation, which in the macroscopic model governs the evolution of the probability measure for the degree of malfunctioning of neurons, can be derived from a particle-based setting. The models are based on aggregation and diffusion equations for β-Amyloid (Aβ from now on), a protein fragment that healthy brains regularly produce and eliminate. In case of dementia Aβ monomers are no longer properly washed out and begin to coalesce forming eventually plaques. Two different mechanisms are assumed to be relevant for the temporal evolution of the disease: (i) diffusion and agglomeration of soluble polymers of amyloid, produced by damaged neurons; (ii) neuron-to-neuron prion-like transmission. In the microscopic model we consider mechanism (i), modelling it by a system of Smoluchowski equations for the amyloid concentration (describing the agglomeration phenomenon), with the addition of a diffusion term as well as of a source term on the neuronal membrane. At the macroscopic level instead we model processes (i) and (ii) by a system of Smoluchowski equations for the amyloid concentration, coupled to a kinetic-type transport equation for the distribution function of the degree of malfunctioning of the neurons. The transport equation contains an integral term describing the random onset of the disease as a jump process localized in particularly sensitive areas of the brain.

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

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

Boundary value problems for multi-term fractional differential equations

NASA Astrophysics Data System (ADS)

Daftardar-Gejji, Varsha; Bhalekar, Sachin

2008-09-01

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

A finite element formulation preserving symmetric and banded diffusion stiffness matrix characteristics for fractional differential equations

NASA Astrophysics Data System (ADS)

Lin, Zeng; Wang, Dongdong

2017-10-01

Due to the nonlocal property of the fractional derivative, the finite element analysis of fractional diffusion equation often leads to a dense and non-symmetric stiffness matrix, in contrast to the conventional finite element formulation with a particularly desirable symmetric and banded stiffness matrix structure for the typical diffusion equation. This work first proposes a finite element formulation that preserves the symmetry and banded stiffness matrix characteristics for the fractional diffusion equation. The key point of the proposed formulation is the symmetric weak form construction through introducing a fractional weight function. It turns out that the stiffness part of the present formulation is identical to its counterpart of the finite element method for the conventional diffusion equation and thus the stiffness matrix formulation becomes trivial. Meanwhile, the fractional derivative effect in the discrete formulation is completely transferred to the force vector, which is obviously much easier and efficient to compute than the dense fractional derivative stiffness matrix. Subsequently, it is further shown that for the general fractional advection-diffusion-reaction equation, the symmetric and banded structure can also be maintained for the diffusion stiffness matrix, although the total stiffness matrix is not symmetric in this case. More importantly, it is demonstrated that under certain conditions this symmetric diffusion stiffness matrix formulation is capable of producing very favorable numerical solutions in comparison with the conventional non-symmetric diffusion stiffness matrix finite element formulation. The effectiveness of the proposed methodology is illustrated through a series of numerical examples.

The pseudo-compartment method for coupling partial differential equation and compartment-based models of diffusion.

PubMed

Yates, Christian A; Flegg, Mark B

2015-05-06

Spatial reaction-diffusion models have been employed to describe many emergent phenomena in biological systems. The modelling technique most commonly adopted in the literature implements systems of partial differential equations (PDEs), which assumes there are sufficient densities of particles that a continuum approximation is valid. However, owing to recent advances in computational power, the simulation and therefore postulation, of computationally intensive individual-based models has become a popular way to investigate the effects of noise in reaction-diffusion systems in which regions of low copy numbers exist. The specific stochastic models with which we shall be concerned in this manuscript are referred to as 'compartment-based' or 'on-lattice'. These models are characterized by a discretization of the computational domain into a grid/lattice of 'compartments'. Within each compartment, particles are assumed to be well mixed and are permitted to react with other particles within their compartment or to transfer between neighbouring compartments. Stochastic models provide accuracy, but at the cost of significant computational resources. For models that have regions of both low and high concentrations, it is often desirable, for reasons of efficiency, to employ coupled multi-scale modelling paradigms. In this work, we develop two hybrid algorithms in which a PDE in one region of the domain is coupled to a compartment-based model in the other. Rather than attempting to balance average fluxes, our algorithms answer a more fundamental question: 'how are individual particles transported between the vastly different model descriptions?' First, we present an algorithm derived by carefully redefining the continuous PDE concentration as a probability distribution. While this first algorithm shows very strong convergence to analytical solutions of test problems, it can be cumbersome to simulate. Our second algorithm is a simplified and more efficient implementation of the first, it is derived in the continuum limit over the PDE region alone. We test our hybrid methods for functionality and accuracy in a variety of different scenarios by comparing the averaged simulations with analytical solutions of PDEs for mean concentrations. © 2015 The Author(s) Published by the Royal Society. All rights reserved.

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.

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

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

Diffusion approximations to the chemical master equation only have a consistent stochastic thermodynamics at chemical equilibrium

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

Horowitz, Jordan M., E-mail: jordan.horowitz@umb.edu

The stochastic thermodynamics of a dilute, well-stirred mixture of chemically reacting species is built on the stochastic trajectories of reaction events obtained from the chemical master equation. However, when the molecular populations are large, the discrete chemical master equation can be approximated with a continuous diffusion process, like the chemical Langevin equation or low noise approximation. In this paper, we investigate to what extent these diffusion approximations inherit the stochastic thermodynamics of the chemical master equation. We find that a stochastic-thermodynamic description is only valid at a detailed-balanced, equilibrium steady state. Away from equilibrium, where there is no consistent stochasticmore » thermodynamics, we show that one can still use the diffusive solutions to approximate the underlying thermodynamics of the chemical master equation.« less

S{sub 2}SA preconditioning for the S{sub n} equations with strictly non negative spatial discretization

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

Bruss, D. E.; Morel, J. E.; Ragusa, J. C.

2013-07-01

Preconditioners based upon sweeps and diffusion-synthetic acceleration have been constructed and applied to the zeroth and first spatial moments of the 1-D S{sub n} transport equation using a strictly non negative nonlinear spatial closure. Linear and nonlinear preconditioners have been analyzed. The effectiveness of various combinations of these preconditioners are compared. In one dimension, nonlinear sweep preconditioning is shown to be superior to linear sweep preconditioning, and DSA preconditioning using nonlinear sweeps in conjunction with a linear diffusion equation is found to be essentially equivalent to nonlinear sweeps in conjunction with a nonlinear diffusion equation. The ability to use amore » linear diffusion equation has important implications for preconditioning the S{sub n} equations with a strictly non negative spatial discretization in multiple dimensions. (authors)« less

Proteus two-dimensional Navier-Stokes computer code, version 2.0. Volume 1: Analysis description

NASA Technical Reports Server (NTRS)

Towne, Charles E.; Schwab, John R.; Bui, Trong T.

1993-01-01

A computer code called Proteus 2D was developed to solve the two-dimensional planar or axisymmetric, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort was to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The governing equations are solved in generalized nonorthogonal body-fitted coordinates, by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. This is the Analysis Description, and presents the equations and solution procedure. The governing equations, the turbulence model, the linearization of the equations and boundary conditions, the time and space differencing formulas, the ADI solution procedure, and the artificial viscosity models are described in detail.

Proteus three-dimensional Navier-Stokes computer code, version 1.0. Volume 1: Analysis description

NASA Technical Reports Server (NTRS)

Towne, Charles E.; Schwab, John R.; Bui, Trong T.

1993-01-01

A computer code called Proteus 3D has been developed to solve the three dimensional, Reynolds averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort has been to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation have been emphasized. The governing equations are solved in generalized non-orthogonal body-fitted coordinates by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. This is the Analysis Description, and presents the equations and solution procedure. It describes in detail the governing equations, the turbulence model, the linearization of the equations and boundary conditions, the time and space differencing formulas, the ADI solution procedure, and the artificial viscosity models.

MODFLOW-based coupled surface water routing and groundwater-flow simulation

USGS Publications Warehouse

Hughes, Joseph D.; Langevin, Christian D.; White, Jeremy T.

2015-01-01

In this paper, we present a flexible approach for simulating one- and two-dimensional routing of surface water using a numerical surface water routing (SWR) code implicitly coupled to the groundwater-flow process in MODFLOW. Surface water routing in SWR can be simulated using a diffusive-wave approximation of the Saint-Venant equations and/or a simplified level-pool approach. SWR can account for surface water flow controlled by backwater conditions caused by small water-surface gradients or surface water control structures. A number of typical surface water control structures, such as culverts, weirs, and gates, can be represented, and it is possible to implement operational rules to manage surface water stages and streamflow. The nonlinear system of surface water flow equations formulated in SWR is solved by using Newton methods and direct or iterative solvers. SWR was tested by simulating the (1) Lal axisymmetric overland flow, (2) V-catchment, and (3) modified Pinder-Sauer problems. Simulated results for these problems compare well with other published results and indicate that SWR provides accurate results for surface water-only and coupled surface water/groundwater problems. Results for an application of SWR and MODFLOW to the Snapper Creek area of Miami-Dade County, Florida, USA are also presented and demonstrate the value of coupled surface water and groundwater simulation in managed, low-relief coastal settings.

Stochastic theory of polarized light in nonlinear birefringent media: An application to optical rotation

NASA Astrophysics Data System (ADS)

Tsuchida, Satoshi; Kuratsuji, Hiroshi

2018-05-01

A stochastic theory is developed for the light transmitting the optical media exhibiting linear and nonlinear birefringence. The starting point is the two-component nonlinear Schrödinger equation (NLSE). On the basis of the ansatz of “soliton” solution for the NLSE, the evolution equation for the Stokes parameters is derived, which turns out to be the Langevin equation by taking account of randomness and dissipation inherent in the birefringent media. The Langevin equation is converted to the Fokker-Planck (FP) equation for the probability distribution by employing the technique of functional integral on the assumption of the Gaussian white noise for the random fluctuation. The specific application is considered for the optical rotation, which is described by the ellipticity (third component of the Stokes parameters) alone: (i) The asymptotic analysis is given for the functional integral, which leads to the transition rate on the Poincaré sphere. (ii) The FP equation is analyzed in the strong coupling approximation, by which the diffusive behavior is obtained for the linear and nonlinear birefringence. These would provide with a basis of statistical analysis for the polarization phenomena in nonlinear birefringent media.

SEAWAT Version 4: A Computer Program for Simulation of Multi-Species Solute and Heat Transport

USGS Publications Warehouse

Langevin, Christian D.; Thorne, Daniel T.; Dausman, Alyssa M.; Sukop, Michael C.; Guo, Weixing

2008-01-01

The SEAWAT program is a coupled version of MODFLOW and MT3DMS designed to simulate three-dimensional, variable-density, saturated ground-water flow. Flexible equations were added to the program to allow fluid density to be calculated as a function of one or more MT3DMS species. Fluid density may also be calculated as a function of fluid pressure. The effect of fluid viscosity variations on ground-water flow was included as an option. Fluid viscosity can be calculated as a function of one or more MT3DMS species, and the program includes additional functions for representing the dependence on temperature. Although MT3DMS and SEAWAT are not explicitly designed to simulate heat transport, temperature can be simulated as one of the species by entering appropriate transport coefficients. For example, the process of heat conduction is mathematically analogous to Fickian diffusion. Heat conduction can be represented in SEAWAT by assigning a thermal diffusivity for the temperature species (instead of a molecular diffusion coefficient for a solute species). Heat exchange with the solid matrix can be treated in a similar manner by using the mathematically equivalent process of solute sorption. By combining flexible equations for fluid density and viscosity with multi-species transport, SEAWAT Version 4 represents variable-density ground-water flow coupled with multi-species solute and heat transport. SEAWAT Version 4 is based on MODFLOW-2000 and MT3DMS and retains all of the functionality of SEAWAT-2000. SEAWAT Version 4 also supports new simulation options for coupling flow and transport, and for representing constant-head boundaries. In previous versions of SEAWAT, the flow equation was solved for every transport timestep, regardless of whether or not there was a large change in fluid density. A new option was implemented in SEAWAT Version 4 that allows users to control how often the flow field is updated. New options were also implemented for representing constant-head boundaries with the Time-Variant Constant-Head (CHD) Package. These options allow for increased flexibility when using CHD flow boundaries with the zero-dispersive flux solute boundaries implemented by MT3DMS at constant-head cells. This report contains revised input instructions for the MT3DMS Dispersion (DSP) Package, Variable-Density Flow (VDF) Package, Viscosity (VSC) Package, and CHD Package. The report concludes with seven cases of an example problem designed to highlight many of the new features.

Cooperative Activated Transport of Dilute Penetrants in Viscous Molecular and Polymer Liquids

NASA Astrophysics Data System (ADS)

Schweizer, Kenneth; Zhang, Rui

We generalize the force-level Elastically Collective Nonlinear Langevin Equation theory of activated relaxation in one-component supercooled liquids to treat the hopping transport of a dilute penetrant in a dense hard sphere fluid. The new idea is to explicitly account for the coupling between penetrant displacement and a local matrix cage re-arrangement which facilitates its hopping. A temporal casuality condition is employed to self-consistently determine a dimensionless degree of matrix distortion relative to the penetrant jump distance using the dynamic free energy concept. Penetrant diffusion becomes increasingly coupled to the correlated matrix displacements for larger penetrant to matrix particle size ratio (R) and/or attraction strength (physical bonds), but depends weakly on matrix packing fraction. In the absence of attractions, a nearly exponential dependence of penetrant diffusivity on R is predicted in the intermediate range of 0.2

A stable and accurate partitioned algorithm for conjugate heat transfer

NASA Astrophysics Data System (ADS)

Meng, F.; Banks, J. W.; Henshaw, W. D.; Schwendeman, D. W.

2017-09-01

We describe a new partitioned approach for solving conjugate heat transfer (CHT) problems where the governing temperature equations in different material domains are time-stepped in an implicit manner, but where the interface coupling is explicit. The new approach, called the CHAMP scheme (Conjugate Heat transfer Advanced Multi-domain Partitioned), is based on a discretization of the interface coupling conditions using a generalized Robin (mixed) condition. The weights in the Robin condition are determined from the optimization of a condition derived from a local stability analysis of the coupling scheme. The interface treatment combines ideas from optimized-Schwarz methods for domain-decomposition problems together with the interface jump conditions and additional compatibility jump conditions derived from the governing equations. For many problems (i.e. for a wide range of material properties, grid-spacings and time-steps) the CHAMP algorithm is stable and second-order accurate using no sub-time-step iterations (i.e. a single implicit solve of the temperature equation in each domain). In extreme cases (e.g. very fine grids with very large time-steps) it may be necessary to perform one or more sub-iterations. Each sub-iteration generally increases the range of stability substantially and thus one sub-iteration is likely sufficient for the vast majority of practical problems. The CHAMP algorithm is developed first for a model problem and analyzed using normal-mode theory. The theory provides a mechanism for choosing optimal parameters in the mixed interface condition. A comparison is made to the classical Dirichlet-Neumann (DN) method and, where applicable, to the optimized-Schwarz (OS) domain-decomposition method. For problems with different thermal conductivities and diffusivities, the CHAMP algorithm outperforms the DN scheme. For domain-decomposition problems with uniform conductivities and diffusivities, the CHAMP algorithm performs better than the typical OS scheme with one grid-cell overlap. The CHAMP scheme is also developed for general curvilinear grids and CHT examples are presented using composite overset grids that confirm the theory and demonstrate the effectiveness of the approach.

Effective Dynamics of Microorganisms That Interact with Their Own Trail

NASA Astrophysics Data System (ADS)

Kranz, W. Till; Gelimson, Anatolij; Zhao, Kun; Wong, Gerard C. L.; Golestanian, Ramin

2016-07-01

Like ants, some microorganisms are known to leave trails on surfaces to communicate. We explore how trail-mediated self-interaction could affect the behavior of individual microorganisms when diffusive spreading of the trail is negligible on the time scale of the microorganism using a simple phenomenological model for an actively moving particle and a finite-width trail. The effective dynamics of each microorganism takes on the form of a stochastic integral equation with the trail interaction appearing in the form of short-term memory. For a moderate coupling strength below an emergent critical value, the dynamics exhibits effective diffusion in both orientation and position after a phase of superdiffusive reorientation. We report experimental verification of a seemingly counterintuitive perpendicular alignment mechanism that emerges from the model.

Non-Markovian Quantum State Diffusion for temperature-dependent linear spectra of light harvesting aggregates

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

Ritschel, Gerhard; Möbius, Sebastian; Eisfeld, Alexander, E-mail: eisfeld@mpipks-dresden.mpg.de

2015-01-21

Non-Markovian Quantum State Diffusion (NMQSD) has turned out to be an efficient method to calculate excitonic properties of aggregates composed of organic chromophores, taking into account the coupling of electronic transitions to vibrational modes of the chromophores. NMQSD is an open quantum system approach that incorporates environmental degrees of freedom (the vibrations in our case) in a stochastic way. We show in this paper that for linear optical spectra (absorption, circular dichroism), no stochastics is needed, even for finite temperatures. Thus, the spectra can be obtained by propagating a single trajectory. To this end, we map a finite temperature environmentmore » to the zero temperature case using the so-called thermofield method. The resulting equations can then be solved efficiently by standard integrators.« less

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.

On the anisotropic advection-diffusion equation with time dependent coefficients

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

Hernandez-Coronado, Hector; Coronado, Manuel; Del-Castillo-Negrete, Diego B.

The advection-diffusion equation with time dependent velocity and anisotropic time dependent diffusion tensor is examined in regard to its non-classical transport features and to the use of a non-orthogonal coordinate system. Although this equation appears in diverse physical problems, particularly in particle transport in stochastic velocity fields and in underground porous media, a detailed analysis of its solutions is lacking. In order to study the effects of the time-dependent coefficients and the anisotropic diffusion on transport, we solve analytically the equation for an initial Dirac delta pulse. Here, we discuss the solutions to three cases: one based on power-law correlationmore » functions where the pulse diffuses faster than the classical rate ~t, a second case specically designed to display slower rate of diffusion than the classical one, and a third case to describe hydrodynamic dispersion in porous media« less

On the anisotropic advection-diffusion equation with time dependent coefficients

DOE PAGES

Hernandez-Coronado, Hector; Coronado, Manuel; Del-Castillo-Negrete, Diego B.

2017-02-01

The advection-diffusion equation with time dependent velocity and anisotropic time dependent diffusion tensor is examined in regard to its non-classical transport features and to the use of a non-orthogonal coordinate system. Although this equation appears in diverse physical problems, particularly in particle transport in stochastic velocity fields and in underground porous media, a detailed analysis of its solutions is lacking. In order to study the effects of the time-dependent coefficients and the anisotropic diffusion on transport, we solve analytically the equation for an initial Dirac delta pulse. Here, we discuss the solutions to three cases: one based on power-law correlationmore » functions where the pulse diffuses faster than the classical rate ~t, a second case specically designed to display slower rate of diffusion than the classical one, and a third case to describe hydrodynamic dispersion in porous media« less

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

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

Shurygin, V. A.

2006-08-15

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

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

NASA Astrophysics Data System (ADS)

Lin, Guoxing

2018-10-01

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

One-dimensional time-dependent fluid model of a very high density low-pressure inductively coupled plasma

DOE PAGES

Chaplin, Vernon H.; Bellan, Paul M.

2015-12-28

A time-dependent two-fluid model has been developed to understand axial variations in the plasma parameters in a very high density (peak n e~ > 5x10 19 m –3) argon inductively coupled discharge in a long 1.1 cm radius tube. The model equations are written in 1D, with radial losses to the tube walls accounted for by the inclusion of effective particle and energy sink terms. The ambipolar diffusion equation and electron energy equation are solved to find the electron density n e(z,t) and temperature T e(z,t), and the populations of the neutral argon 4s metastable, 4s resonant, and 4p excitedmore » state manifolds are calculated in order to determine the stepwise ionization rate and calculate radiative energy losses. The model has been validated through comparisons with Langmuir probe ion saturation current measurements; close agreement between the simulated and measured axial plasma density profiles and the initial density rise rate at each location was obtained at p Ar = 30-60 mTorr. Lastly, we present detailed results from calculations at 60 mTorr, including the time-dependent electron temperature, excited state populations, and energy budget within and downstream of the radiofrequency (RF) antenna.« less

Raman Spectroscopy of Isotopic Water Diffusion in Ultraviscous, Glassy, and Gel States in Aerosol by Use of Optical Tweezers.

PubMed

Davies, James F; Wilson, Kevin R

2016-02-16

The formation of ultraviscous, glassy, and amorphous gel states in aqueous aerosol following the loss of water results in nonequilibrium dynamics due to the extended time scales for diffusive mixing. Existing techniques for measuring water diffusion by isotopic exchange are limited by contact of samples with the substrate, and methods applied to infer diffusion coefficients from mass transport in levitated droplets requires analysis by complex coupled differential equations to derive diffusion coefficients. We present a new technique that combines contactless levitation with aerosol optical tweezers with isotopic exchange (D2O/H2O) to measure the water diffusion coefficient over a broad range (Dw ≈ 10(-12)-10(-17) m(2)·s(-1)) in viscous organic liquids (citric acid, sucrose, and shikimic acid) and inorganic gels (magnesium sulfate, MgSO4). For the organic liquids in binary and ternary mixtures, Dw depends on relative humidity and follows a simple compositional Vignes relationship. In MgSO4 droplets, water diffusivity decreases sharply with water activity and is consistent with predictions from percolation theory. These measurements show that, by combining micrometer-sized particle levitation (a contactless measurement with rapid mixing times) with an established probe of water diffusion, Dw can be simply and directly quantified for amorphous and glassy states that are inaccessible to existing methods.

Raman Spectroscopy of Isotopic Water Diffusion in Ultraviscous, Glassy, and Gel States in Aerosol by Use of Optical Tweezers

DOE PAGES

Davies, James F.; Wilson, Kevin R.

2016-01-11

The formation of ultraviscous, glassy, and amorphous gel states in aqueous aerosol following the loss of water results in nonequilibrium dynamics due to the extended time scales for diffusive mixing. Existing techniques for measuring water diffusion by isotopic exchange are limited by contact of samples with the substrate, and methods applied to infer diffusion coefficients from mass transport in levitated droplets requires analysis by complex coupled differential equations to derive diffusion coefficients. Here, we present a new technique that combines contactless levitation with aerosol optical tweezers with isotopic exchange (D 2O/H 2O) to measure the water diffusion coefficient over amore » broad range (D w ≈ 10 -12-10 -17 m 2s -1) in viscous organic liquids (citric acid, sucrose, and shikimic acid) and inorganic gels (magnesium sulfate, MgSO 4). For the organic liquids in binary and ternary mixtures, D w depends on relative humidity and follows a simple compositional Vignes relationship. In MgSO 4 droplets, water diffusivity decreases sharply with water activity and is consistent with predictions from percolation theory. These measurements show that, by combining micrometer-sized particle levitation (a contactless measurement with rapid mixing times) with an established probe of water diffusion, D w can be simply and directly quantified for amorphous and glassy states that are inaccessible to existing methods.« less

A class of exact solutions for biomacromolecule diffusion-reaction in live cells.

PubMed

Sadegh Zadeh, Kouroush; Montas, Hubert J

2010-06-07

A class of novel explicit analytic solutions for a system of n+1 coupled partial differential equations governing biomolecular mass transfer and reaction in living organisms are proposed, evaluated, and analyzed. The solution process uses Laplace and Hankel transforms and results in a recursive convolution of an exponentially scaled Gaussian with modified Bessel functions. The solution is developed for wide range of biomolecular binding kinetics from pure diffusion to multiple binding reactions. The proposed approach provides solutions for both Dirac and Gaussian laser beam (or fluorescence-labeled biomacromolecule) profiles during the course of a Fluorescence Recovery After Photobleaching (FRAP) experiment. We demonstrate that previous models are simplified forms of our theory for special cases. Model analysis indicates that at the early stages of the transport process, biomolecular dynamics is governed by pure diffusion. At large times, the dominant mass transfer process is effective diffusion. Analysis of the sensitivity equations, derived analytically and verified by finite difference differentiation, indicates that experimental biologists should use full space-time profile (instead of the averaged time series) obtained at the early stages of the fluorescence microscopy experiments to extract meaningful physiological information from the protocol. Such a small time frame requires improved bioinstrumentation relative to that in use today. Our mathematical analysis highlights several limitations of the FRAP protocol and provides strategies to improve it. The proposed model can be used to study biomolecular dynamics in molecular biology, targeted drug delivery in normal and cancerous tissues, motor-driven axonal transport in normal and abnormal nervous systems, kinetics of diffusion-controlled reactions between enzyme and substrate, and to validate numerical simulators of biological mass transport processes in vivo. Copyright (c) 2010 Elsevier Ltd. All rights reserved.

ANALYTICAL SOLUTIONS OF THE ATMOSPHERIC DIFFUSION EQUATION WITH MULTIPLE SOURCES AND HEIGHT-DEPENDENT WIND SPEED AND EDDY DIFFUSIVITIES. (R825689C072)

EPA Science Inventory

Abstract

Three-dimensional analytical solutions of the atmospheric diffusion equation with multiple sources and height-dependent wind speed and eddy diffusivities are derived in a systematic fashion. For homogeneous Neumann (total reflection), Dirichlet (total adsorpti...

ANALYTICAL SOLUTIONS OF THE ATMOSPHERIC DIFFUSION EQUATION WITH MULTIPLE SOURCES AND HEIGHT-DEPENDENT WIND SPEED AND EDDY DIFFUSIVITIES. (R825689C048)

EPA Science Inventory

Abstract

Three-dimensional analytical solutions of the atmospheric diffusion equation with multiple sources and height-dependent wind speed and eddy diffusivities are derived in a systematic fashion. For homogeneous Neumann (total reflection), Dirichlet (total adsorpti...

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

NASA Astrophysics Data System (ADS)

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

2014-09-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-09-01

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

Existence and Stability of Traveling Waves for Degenerate Reaction-Diffusion Equation with Time Delay

NASA Astrophysics Data System (ADS)

Huang, Rui; Jin, Chunhua; Mei, Ming; Yin, Jingxue

2018-01-01

This paper deals with the existence and stability of traveling wave solutions for a degenerate reaction-diffusion equation with time delay. The degeneracy of spatial diffusion together with the effect of time delay causes us the essential difficulty for the existence of the traveling waves and their stabilities. In order to treat this case, we first show the existence of smooth- and sharp-type traveling wave solutions in the case of c≥c^* for the degenerate reaction-diffusion equation without delay, where c^*>0 is the critical wave speed of smooth traveling waves. Then, as a small perturbation, we obtain the existence of the smooth non-critical traveling waves for the degenerate diffusion equation with small time delay τ >0 . Furthermore, we prove the global existence and uniqueness of C^{α ,β } -solution to the time-delayed degenerate reaction-diffusion equation via compactness analysis. Finally, by the weighted energy method, we prove that the smooth non-critical traveling wave is globally stable in the weighted L^1 -space. The exponential convergence rate is also derived.

Existence and Stability of Traveling Waves for Degenerate Reaction-Diffusion Equation with Time Delay

NASA Astrophysics Data System (ADS)

Huang, Rui; Jin, Chunhua; Mei, Ming; Yin, Jingxue

2018-06-01

This paper deals with the existence and stability of traveling wave solutions for a degenerate reaction-diffusion equation with time delay. The degeneracy of spatial diffusion together with the effect of time delay causes us the essential difficulty for the existence of the traveling waves and their stabilities. In order to treat this case, we first show the existence of smooth- and sharp-type traveling wave solutions in the case of c≥c^* for the degenerate reaction-diffusion equation without delay, where c^*>0 is the critical wave speed of smooth traveling waves. Then, as a small perturbation, we obtain the existence of the smooth non-critical traveling waves for the degenerate diffusion equation with small time delay τ >0. Furthermore, we prove the global existence and uniqueness of C^{α ,β }-solution to the time-delayed degenerate reaction-diffusion equation via compactness analysis. Finally, by the weighted energy method, we prove that the smooth non-critical traveling wave is globally stable in the weighted L^1-space. The exponential convergence rate is also derived.

Diffusion phenomenon for linear dissipative wave equations in an exterior domain

NASA Astrophysics Data System (ADS)

Ikehata, Ryo

Under the general condition of the initial data, we will derive the crucial estimates which imply the diffusion phenomenon for the dissipative linear wave equations in an exterior domain. In order to derive the diffusion phenomenon for dissipative wave equations, the time integral method which was developed by Ikehata and Matsuyama (Sci. Math. Japon. 55 (2002) 33) plays an effective role.

Charge and energy dynamics in photo-excited poly(para-phenylenevinylene) systems

NASA Astrophysics Data System (ADS)

Gisslén, L.; Johansson, A.˚.; Stafström, S.

2004-07-01

We report results from simulations of charge and energy dynamics in poly(para-phenylenevinylene) (PPV) and PPV interacting with C60. The simulations were performed by solving the time-dependent Schrödinger equation and the lattice equation of motion simultaneously and nonadiabatically. The electronic system and the coupling of the electrons to the lattice were described by an extended three-dimensional version of the Su-Schrieffer-Heeger model, which also included an external electric field. Electron and lattice dynamics following electronic excitations at different energies have been simulated. The effect of additional lattice energy was also included in the simulations. Our results show that both exciton diffusion and transitions from high to lower lying excitations are stimulated by increasing the lattice energy. Also field induced charge separation occurs faster if the lattice energy is increased. This separation process is highly nonadiabatic and involves a significant rearrangement of the electron distribution. In the case of PPV coupled to C60, we observe a spontaneous charge separation. The separation time is in this case limited by the local concentration of C60 molecules close to the PPV chain.

ECCD-induced tearing mode stabilization in coupled IPS/NIMROD/GENRAY HPC simulations

NASA Astrophysics Data System (ADS)

Jenkins, Thomas; Kruger, S. E.; Held, E. D.; Harvey, R. W.; Elwasif, W. R.; Schnack, D. D.; SWIM Project Team

2011-10-01

We present developments toward an integrated, predictive model for determining optimal ECCD-based NTM stabilization strategies in ITER. We demonstrate the capability of the SWIM Project's Integrated Plasma Simulator (IPS) framework to choreograph multiple executions of, and data exchanges between, physics codes modeling various spatiotemporal scales of this coupled RF/MHD problem on several thousand HPC processors. As NIMROD evolves fluid equations to model bulk plasma behavior, self-consistent propagation/deposition of RF power in the ensuing plasma profiles is calculated by GENRAY. A third code (QLCALC) then interfaces with computational geometry packages to construct the RF-induced quasilinear diffusion tensor from NIMROD/GENRAY data, and the moments of this tensor (entering as additional terms in NIMROD's fluid equations due to the disparity in RF/MHD spatiotemporal scales) influence the dynamics of current, momentum, and energy evolution. Initial results are shown to correctly capture the physics of magnetic island stabilization [Jenkins et al., PoP 17, 012502 (2010)]; we also discuss the development of a numerical plasma control system for active feedback stabilization of tearing modes. Funded by USDoE SciDAC.

Transport properties and equation of state for HCNO mixtures in and beyond the warm dense matter regime

DOE PAGES

Ticknor, Christopher; Collins, Lee A.; Kress, Joel D.

2015-08-04

We present simulations of a four component mixture of HCNO with orbital free molecular dynamics (OFMD). These simulations were conducted for 5–200 eV with densities ranging between 0.184 and 36.8 g/cm 3. We extract the equation of state from the simulations and compare to average atom models. We found that we only need to add a cold curve model to find excellent agreement. In addition, we studied mass transport properties. We present fits to the self-diffusion and shear viscosity that are able to reproduce the transport properties over the parameter range studied. We compare these OFMD results to models basedmore » on the Coulomb coupling parameter and one-component plasmas.« less

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.

A moving mesh finite difference method for equilibrium radiation diffusion equations

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

Yang, Xiaobo, E-mail: xwindyb@126.com; Huang, Weizhang, E-mail: whuang@ku.edu; Qiu, Jianxian, E-mail: jxqiu@xmu.edu.cn

2015-10-01

An efficient moving mesh finite difference method is developed for the numerical solution of equilibrium radiation diffusion equations in two dimensions. The method is based on the moving mesh partial differential equation approach and moves the mesh continuously in time using a system of meshing partial differential equations. The mesh adaptation is controlled through a Hessian-based monitor function and the so-called equidistribution and alignment principles. Several challenging issues in the numerical solution are addressed. Particularly, the radiation diffusion coefficient depends on the energy density highly nonlinearly. This nonlinearity is treated using a predictor–corrector and lagged diffusion strategy. Moreover, the nonnegativitymore » of the energy density is maintained using a cutoff method which has been known in literature to retain the accuracy and convergence order of finite difference approximation for parabolic equations. Numerical examples with multi-material, multiple spot concentration situations are presented. Numerical results show that the method works well for radiation diffusion equations and can produce numerical solutions of good accuracy. It is also shown that a two-level mesh movement strategy can significantly improve the efficiency of the computation.« less

Monte Carlo analysis of uncertainty propagation in a stratospheric model. 1: Development of a concise stratospheric model

NASA Technical Reports Server (NTRS)

Rundel, R. D.; Butler, D. M.; Stolarski, R. S.

1977-01-01

A concise model has been developed to analyze uncertainties in stratospheric perturbations, yet uses a minimum of computer time and is complete enough to represent the results of more complex models. The steady state model applies iteration to achieve coupling between interacting species. The species are determined from diffusion equations with appropriate sources and sinks. Diurnal effects due to chlorine nitrate formation are accounted for by analytic approximation. The model has been used to evaluate steady state perturbations due to injections of chlorine and NO(X).

Non-equilibrium radiation from viscous chemically reacting two-phase exhaust plumes

NASA Technical Reports Server (NTRS)

Penny, M. M.; Smith, S. D.; Mikatarian, R. R.; Ring, L. R.; Anderson, P. G.

1976-01-01

A knowledge of the structure of the rocket exhaust plumes is necessary to solve problems involving plume signatures, base heating, plume/surface interactions, etc. An algorithm is presented which treats the viscous flow of multiphase chemically reacting fluids in a two-dimensional or axisymmetric supersonic flow field. The gas-particle flow solution is fully coupled with the chemical kinetics calculated using an implicit scheme to calculate chemical production rates. Viscous effects include chemical species diffusion with the viscosity coefficient calculated using a two-equation turbulent kinetic energy model.

The equilibrium-diffusion limit for radiation hydrodynamics

DOE PAGES

Ferguson, J. M.; Morel, J. E.; Lowrie, R.

2017-07-27

The equilibrium-diffusion approximation (EDA) is used to describe certain radiation-hydrodynamic (RH) environments. When this is done the RH equations reduce to a simplified set of equations. The EDA can be derived by asymptotically analyzing the full set of RH equations in the equilibrium-diffusion limit. Here, we derive the EDA this way and show that it and the associated set of simplified equations are both first-order accurate with transport corrections occurring at second order. Having established the EDA’s first-order accuracy we then analyze the grey nonequilibrium-diffusion approximation and the grey Eddington approximation and show that they both preserve this first-order accuracy.more » Further, these approximations preserve the EDA’s first-order accuracy when made in either the comoving-frame (CMF) or the lab-frame (LF). And while analyzing the Eddington approximation, we found that the CMF and LF radiation-source equations are equivalent when neglecting O(β 2) terms and compared in the LF. Of course, the radiation pressures are not equivalent. It is expected that simplified physical models and numerical discretizations of the RH equations that do not preserve this first-order accuracy will not retain the correct equilibrium-diffusion solutions. As a practical example, we show that nonequilibrium-diffusion radiative-shock solutions devolve to equilibrium-diffusion solutions when the asymptotic parameter is small.« less

A Robust and Efficient Method for Steady State Patterns in Reaction-Diffusion Systems

PubMed Central

Lo, Wing-Cheong; Chen, Long; Wang, Ming; Nie, Qing

2012-01-01

An inhomogeneous steady state pattern of nonlinear reaction-diffusion equations with no-flux boundary conditions is usually computed by solving the corresponding time-dependent reaction-diffusion equations using temporal schemes. Nonlinear solvers (e.g., Newton’s method) take less CPU time in direct computation for the steady state; however, their convergence is sensitive to the initial guess, often leading to divergence or convergence to spatially homogeneous solution. Systematically numerical exploration of spatial patterns of reaction-diffusion equations under different parameter regimes requires that the numerical method be efficient and robust to initial condition or initial guess, with better likelihood of convergence to an inhomogeneous pattern. Here, a new approach that combines the advantages of temporal schemes in robustness and Newton’s method in fast convergence in solving steady states of reaction-diffusion equations is proposed. In particular, an adaptive implicit Euler with inexact solver (AIIE) method is found to be much more efficient than temporal schemes and more robust in convergence than typical nonlinear solvers (e.g., Newton’s method) in finding the inhomogeneous pattern. Application of this new approach to two reaction-diffusion equations in one, two, and three spatial dimensions, along with direct comparisons to several other existing methods, demonstrates that AIIE is a more desirable method for searching inhomogeneous spatial patterns of reaction-diffusion equations in a large parameter space. PMID:22773849

A model for interpretation of brine-dependent spontaneous imbibition experiments

NASA Astrophysics Data System (ADS)

Evje, S.; Hiorth, A.

2011-12-01

Previous experimental results for spontaneous imbibition experiments in the context of chalk cores have revealed a rather puzzling behavior: the oil recovery curves, both the shape as well as the steady state level which is reached, depend strongly on the brine composition. In particular, it has been demonstrated that Mg,SO42-, and Ca 2+ play a central role in this physico-chemical system. A good theoretical understanding of these experimental results, in terms of mathematical models that can suggest possible explanations of the lab experiments as well as predict behavior not yet tested in the lab, seems to still be lacking. The purpose of this paper is to try to shed light on some important modeling aspects. The model we propose is an extended version of the classical Buckley-Leverett (BL) equation for two-phase spontaneous imbibition where the water saturation equation has been coupled to a system of reaction-diffusion (RD) equations describing water-rock chemistry relevant for chalk core plugs. As far as water-rock chemistry is concerned we focus in this work on the combined effect of transport and dissolution/precipitation of calcite, magnesite, and anhydrite. The line we pursue is to couple changes of the wetting state, expressed in terms of the relative permeability and capillary pressure functions, to the water-rock chemistry behavior. More precisely, we build into the model the mechanism that the rock surface will become more water-wet at the places where dissolution of calcite takes place. In particular, we illustrate and analyze how different compositions of the imbibing brine then lead to different water-rock interaction scenarios which in turn gives qualitative and quantitative differences in the solution of the saturation equation describing spontaneous imbibition. Comparison with relevant experimental behavior is included as well as illustration of some possible interesting and non-trivial characteristic features of the model reflecting the nonlinear coupling mechanisms between the RD model for the water-rock chemistry and the BL equation for the water-oil transport.

Multiscale models and stochastic simulation methods for computing rare but key binding events in cell biology

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

Guerrier, C.; Holcman, D., E-mail: david.holcman@ens.fr; Mathematical Institute, Oxford OX2 6GG, Newton Institute

The main difficulty in simulating diffusion processes at a molecular level in cell microdomains is due to the multiple scales involving nano- to micrometers. Few to many particles have to be simulated and simultaneously tracked while there are exploring a large portion of the space for binding small targets, such as buffers or active sites. Bridging the small and large spatial scales is achieved by rare events representing Brownian particles finding small targets and characterized by long-time distribution. These rare events are the bottleneck of numerical simulations. A naive stochastic simulation requires running many Brownian particles together, which is computationallymore » greedy and inefficient. Solving the associated partial differential equations is also difficult due to the time dependent boundary conditions, narrow passages and mixed boundary conditions at small windows. We present here two reduced modeling approaches for a fast computation of diffusing fluxes in microdomains. The first approach is based on a Markov mass-action law equations coupled to a Markov chain. The second is a Gillespie's method based on the narrow escape theory for coarse-graining the geometry of the domain into Poissonian rates. The main application concerns diffusion in cellular biology, where we compute as an example the distribution of arrival times of calcium ions to small hidden targets to trigger vesicular release.« less

Nonlinear dynamics of capacitive charging and desalination by porous electrodes.

PubMed

Biesheuvel, P M; Bazant, M Z

2010-03-01

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

Nonlinear dynamics of capacitive charging and desalination by porous electrodes

NASA Astrophysics Data System (ADS)

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

2010-03-01

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

Coupling continuum dislocation transport with crystal plasticity for application to shock loading conditions

DOE PAGES

Luscher, Darby Jon; Mayeur, Jason Rhea; Mourad, Hashem Mohamed; ...

2015-08-05

Here, we have developed a multi-physics modeling approach that couples continuum dislocation transport, nonlinear thermoelasticity, crystal plasticity, and consistent internal stress and deformation fields to simulate the single-crystal response of materials under extreme dynamic conditions. Dislocation transport is modeled by enforcing dislocation conservation at a slip-system level through the solution of advection-diffusion equations. Nonlinear thermoelasticity provides a thermodynamically consistent equation of state to relate stress (including pressure), temperature, energy densities, and dissipation. Crystal plasticity is coupled to dislocation transport via Orowan's expression where the constitutive description makes use of recent advances in dislocation velocity theories applicable under extreme loading conditions.more » The configuration of geometrically necessary dislocation density gives rise to an internal stress field that can either inhibit or accentuate the flow of dislocations. An internal strain field associated with the internal stress field contributes to the kinematic decomposition of the overall deformation. The paper describes each theoretical component of the framework, key aspects of the constitutive theory, and some details of a one-dimensional implementation. Results from single-crystal copper plate impact simulations are discussed in order to highlight the role of dislocation transport and pile-up in shock loading regimes. The main conclusions of the paper reinforce the utility of the modeling approach to shock problems.« less

Approximate Solution Methods for Spectral Radiative Transfer in High Refractive Index Layers

NASA Technical Reports Server (NTRS)

Siegel, R.; Spuckler, C. M.

1994-01-01

Some ceramic materials for high temperature applications are partially transparent for radiative transfer. The refractive indices of these materials can be substantially greater than one which influences internal radiative emission and reflections. Heat transfer behavior of single and laminated layers has been obtained in the literature by numerical solutions of the radiative transfer equations coupled with heat conduction and heating at the boundaries by convection and radiation. Two-flux and diffusion methods are investigated here to obtain approximate solutions using a simpler formulation than required for exact numerical solutions. Isotropic scattering is included. The two-flux method for a single layer yields excellent results for gray and two band spectral calculations. The diffusion method yields a good approximation for spectral behavior in laminated multiple layers if the overall optical thickness is larger than about ten. A hybrid spectral model is developed using the two-flux method in the optically thin bands, and radiative diffusion in bands that are optically thick.

Mathematical modelling of the uptake and transport of salt in plant roots.

PubMed

Foster, Kylie J; Miklavcic, Stanley J

2013-11-07

In this paper, we present and discuss a mathematical model of ion uptake and transport in roots of plants. The underlying physical model of transport is based on the mechanisms of forced diffusion and convection. The model can take account of local variations in effective ion and water permeabilities across the major tissue regions of plant roots, represented through a discretized coupled system of governing equations including mass balance, forced diffusion, convection and electric potential. We present simulation results of an exploration of the consequent enormous parameter space. Among our findings we identify the electric potential as a major factor affecting ion transport across, and accumulation in, root tissues. We also find that under conditions of a constant but realistic level of bulk soil salt concentration and plant-soil hydraulic pressure, diffusion plays a significant role even when convection by the water transpiration stream is operating. Crown Copyright © 2013 Published by Elsevier Ltd. All rights reserved.

Solution of the nonlinear Poisson-Boltzmann equation: Application to ionic diffusion in cementitious materials

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

Arnold, J.; Kosson, D.S., E-mail: david.s.kosson@vanderbilt.edu; Garrabrants, A.

2013-02-15

A robust numerical solution of the nonlinear Poisson-Boltzmann equation for asymmetric polyelectrolyte solutions in discrete pore geometries is presented. Comparisons to the linearized approximation of the Poisson-Boltzmann equation reveal that the assumptions leading to linearization may not be appropriate for the electrochemical regime in many cementitious materials. Implications of the electric double layer on both partitioning of species and on diffusive release are discussed. The influence of the electric double layer on anion diffusion relative to cation diffusion is examined.

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

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

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

2015-08-15

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

Feedback coupling in dynamical systems

NASA Astrophysics Data System (ADS)

Trimper, Steffen; Zabrocki, Knud

2003-05-01

Different evolution models are considered with feedback-couplings. In particular, we study the Lotka-Volterra system under the influence of a cumulative term, the Ginzburg-Landau model with a convolution memory term and chemical rate equations with time delay. The memory leads to a modified dynamical behavior. In case of a positive coupling the generalized Lotka-Volterra system exhibits a maximum gain achieved after a finite time, but the population will die out in the long time limit. In the opposite case, the time evolution is terminated in a crash. Due to the nonlinear feedback coupling the two branches of a bistable model are controlled by the the strength and the sign of the memory. For a negative coupling the system is able to switch over between both branches of the stationary solution. The dynamics of the system is further controlled by the initial condition. The diffusion-limited reaction is likewise studied in case the reacting entities are not available simultaneously. Whereas for an external feedback the dynamics is altered, but the stationary solution remain unchanged, a self-organized internal feedback leads to a time persistent solution.

Radial Distribution Functions of Strongly Coupled Two-Temperature Plasmas

NASA Astrophysics Data System (ADS)

Shaffer, Nathaniel R.; Tiwari, Sanat Kumar; Baalrud, Scott D.

2017-10-01

We present tests of three theoretical models for the radial distribution functions (RDFs) in two-temperature strongly coupled plasmas. RDFs are useful in extending plasma thermodynamics and kinetic theory to strong coupling, but they are usually known only for thermal equilibrium or for approximate one-component model plasmas. Accurate two-component modeling is necessary to understand the impact of strong coupling on inter-species transport, e.g., ambipolar diffusion and electron-ion temperature relaxation. We demonstrate that the Seuferling-Vogel-Toeppfer (SVT) extension of the hypernetted chain equations not only gives accurate RDFs (as compared with classical molecular dynamics simulations), but also has a simple connection with the Yukawa OCP model. This connection gives a practical means to recover the structure of the electron background from knowledge of the ion-ion RDF alone. Using the model RDFs in Effective Potential Theory, we report the first predictions of inter-species transport coefficients of strongly coupled plasmas far from equilibrium. This work is supported by NSF Grant No. PHY-1453736, AFSOR Award No. FA9550-16-1-0221, and used XSEDE computational resources.

A Numerical and Experimental Study of Coflow Laminar Diffusion Flames: Effects of Gravity and Inlet Velocity

NASA Technical Reports Server (NTRS)

Cao, S.; Bennett, B. A. V.; Ma, B.; Giassi, D.; Stocker, D. P.; Takahashi, F.; Long, M. B.; Smooke, M. D.

2015-01-01

In this work, the influence of gravity, fuel dilution, and inlet velocity on the structure, stabilization, and sooting behavior of laminar coflow methane-air diffusion flames was investigated both computationally and experimentally. A series of flames measured in the Structure and Liftoff in Combustion Experiment (SLICE) was assessed numerically under microgravity and normal gravity conditions with the fuel stream CH4 mole fraction ranging from 0.4 to 1.0. Computationally, the MC-Smooth vorticity-velocity formulation of the governing equations was employed to describe the reactive gaseous mixture; the soot evolution process was considered as a classical aerosol dynamics problem and was represented by the sectional aerosol equations. Since each flame is axisymmetric, a two-dimensional computational domain was employed, where the grid on the axisymmetric domain was a nonuniform tensor product mesh. The governing equations and boundary conditions were discretized on the mesh by a nine-point finite difference stencil, with the convective terms approximated by a monotonic upwind scheme and all other derivatives approximated by centered differences. The resulting set of fully coupled, strongly nonlinear equations was solved simultaneously using a damped, modified Newton's method and a nested Bi-CGSTAB linear algebra solver. Experimentally, the flame shape, size, lift-off height, and soot temperature were determined by flame emission images recorded by a digital camera, and the soot volume fraction was quantified through an absolute light calibration using a thermocouple. For a broad spectrum of flames in microgravity and normal gravity, the computed and measured flame quantities (e.g., temperature profile, flame shape, lift-off height, and soot volume fraction) were first compared to assess the accuracy of the numerical model. After its validity was established, the influence of gravity, fuel dilution, and inlet velocity on the structure, stabilization, and sooting tendency of laminar coflow methane-air diffusion flames was explored further by examining quantities derived from the computational results.

The Influence of Preferential Flow on Pressure Propagation and Landslide Triggering of the Rocca Pitigliana Landslide

NASA Astrophysics Data System (ADS)

Shao, W.; Bogaard, T.; Bakker, M.; Berti, M.; Savenije, H. H. G.

2016-12-01

The fast pore water pressure response to rain events is an important triggering factor for slope instability. The fast pressure response may be caused by preferential flow that bypasses the soil matrix. Currently, most of the hydro-mechanical models simulate pore water pressure using a single-permeability model, which cannot quantify the effects of preferential flow on pressure propagation and landslide triggering. Previous studies showed that a model based on the linear-diffusion equation can simulate the fast pressure propagation in near-saturated landslides such as the Rocca Pitigliana landslide. In such a model, the diffusion coefficient depends on the degree of saturation, which makes it difficult to use the model for predictions. In this study, the influence of preferential flow on pressure propagation and slope stability is investigated with a 1D dual-permeability model coupled with an infinite-slope stability approach. The dual-permeability model uses two modified Darcy-Richards equations to simultaneously simulate the matrix flow and preferential flow in hillslopes. The simulated pressure head is used in an infinite-slope stability analysis to identify the influence of preferential flow on the fast pressure response and landslide triggering. The dual-permeability model simulates the height and arrival of the pressure peak reasonably well. Performance of the dual-permeability model is as good as or better than the linear-diffusion model even though the dual-permeability model is calibrated for two single pulse rain events only, while the linear-diffusion model is calibrated for each rain event separately.

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.

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.

Predicting diffusion paths and interface motion in gamma/gamma + beta, Ni-Cr-Al diffusion couples

NASA Technical Reports Server (NTRS)

Nesbitt, J. A.; Heckel, R. W.

1987-01-01

A simplified model has been developed to predict Beta recession and diffusion paths in ternary gamma/gamma + beta diffusion couples (gamma:fcc, beta: NiAl structure). The model was tested by predicting beta recession and diffusion paths for four gamma/gamma + beta, Ni-Cr-Al couples annealed for 100 hours at 1200 C. The model predicted beta recession within 20 percent of that measured for each of the couples. The model also predicted shifts in the concentration of the gamma phase at the gamma/gamma + beta interface within 2 at. pct Al and 6 at. pct Cr of that measured in each of the couples. A qualitative explanation based on simple kinetic and mass balance arguments has been given which demonstrates the necessity for diffusion in the two-phase region of certain gamma/gamma + beta, Ni-Cr-Al couples.

Effect of breathing-hole size on the electrochemical species in a free-breathing cathode of a DMFC

NASA Astrophysics Data System (ADS)

Hwang, J. J.; Wu, S. D.; Lai, L. K.; Chen, C. K.; Lai, D. Y.

A three-dimensional numerical model is developed to study the electrochemical species characteristics in a free-breathing cathode of a direct methanol fuel cell (DMFC). A perforated current collector is attached to the porous cathode that breathes the fresh air through an array of orifices. The radius of the orifice is varied to examine its effect on the electrochemical performance. Gas flow in the porous cathode is governed by the Darcy equation with constant porosity and permeability. The multi-species diffusive transports in the porous cathode are described using the Stefan-Maxwell equation. Electrochemical reaction on the surfaces of the porous matrices is depicted via the Butler-Volmer equation. The charge transports in the porous matrices are dealt with by Ohm's law. The coupled equations are solved by a finite-element-based CFD technique. Detailed distributions of electrochemical species characteristics such as flow velocities, species mass fractions, species fluxes, and current densities are presented. The optimal breathing-hole radius is derived from the current drawn out of the porous cathode under a fixed overpotential.

Fractional diffusion on bounded domains

DOE PAGES

Defterli, Ozlem; D'Elia, Marta; Du, Qiang; ...

2015-03-13

We found that the mathematically correct specification of a fractional differential equation on a bounded domain requires specification of appropriate boundary conditions, or their fractional analogue. In this paper we discuss the application of nonlocal diffusion theory to specify well-posed fractional diffusion equations on bounded domains.

Measurements and Modeling of Soot Formation and Radiation in Microgravity Jet Diffusion Flames. Volume 4

NASA Technical Reports Server (NTRS)

Ku, Jerry C.; Tong, Li; Greenberg, Paul S.

1996-01-01

This is a computational and experimental study for soot formation and radiative heat transfer in jet diffusion flames under normal gravity (1-g) and microgravity (0-g) conditions. Instantaneous soot volume fraction maps are measured using a full-field imaging absorption technique developed by the authors. A compact, self-contained drop rig is used for microgravity experiments in the 2.2-second drop tower facility at NASA Lewis Research Center. On modeling, we have coupled flame structure and soot formation models with detailed radiation transfer calculations. Favre-averaged boundary layer equations with a k-e-g turbulence model are used to predict the flow field, and a conserved scalar approach with an assumed Beta-pdf are used to predict gaseous species mole fraction. Scalar transport equations are used to describe soot volume fraction and number density distributions, with formation and oxidation terms modeled by one-step rate equations and thermophoretic effects included. An energy equation is included to couple flame structure and radiation analyses through iterations, neglecting turbulence-radiation interactions. The YIX solution for a finite cylindrical enclosure is used for radiative heat transfer calculations. The spectral absorption coefficient for soot aggregates is calculated from the Rayleigh solution using complex refractive index data from a Drude- Lorentz model. The exponential-wide-band model is used to calculate the spectral absorption coefficient for H20 and C02. It is shown that when compared to results from true spectral integration, the Rosseland mean absorption coefficient can provide reasonably accurate predictions for the type of flames studied. The soot formation model proposed by Moss, Syed, and Stewart seems to produce better fits to experimental data and more physically sound than the simpler model by Khan et al. Predicted soot volume fraction and temperature results agree well with published data for a normal gravity co-flow laminar flames and turbulent jet flames. Predicted soot volume fraction results also agree with our data for 1-g and 0-g laminar jet names as well as 1-g turbulent jet flames.

Proteus two-dimensional Navier-Stokes computer code, version 2.0. Volume 3: Programmer's reference

NASA Technical Reports Server (NTRS)

Towne, Charles E.; Schwab, John R.; Bui, Trong T.

1993-01-01

A computer code called Proteus 2D was developed to solve the two-dimensional planar or axisymmetric, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort was to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The governing equations are solved in generalized nonorthogonal body-fitted coordinates, by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. The Programmer's Reference contains detailed information useful when modifying the program. The program structure, the Fortran variables stored in common blocks, and the details of each subprogram are described.

Proteus three-dimensional Navier-Stokes computer code, version 1.0. Volume 3: Programmer's reference

NASA Technical Reports Server (NTRS)

Towne, Charles E.; Schwab, John R.; Bui, Trong T.

1993-01-01

A computer code called Proteus 3D was developed to solve the three-dimensional, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort was to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The governing equations are solved in generalized nonorthogonal body fitted coordinates, by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. The Programmer's Reference contains detailed information useful when modifying the program. The program structure, the Fortran variables stored in common blocks, and the details of each subprogram are described.

Proteus three-dimensional Navier-Stokes computer code, version 1.0. Volume 2: User's guide

NASA Technical Reports Server (NTRS)

Towne, Charles E.; Schwab, John R.; Bui, Trong T.

1993-01-01

A computer code called Proteus 3D was developed to solve the three-dimensional, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort was to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The governing equations are solved in generalized nonorthogonal body-fitted coordinates, by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. This User's Guide describes the program's features, the input and output, the procedure for setting up initial conditions, the computer resource requirements, the diagnostic messages that may be generated, the job control language used to run the program, and several test cases.

Cross-diffusion-driven hydrodynamic instabilities in a double-layer system: General classification and nonlinear simulations

NASA Astrophysics Data System (ADS)

Budroni, M. A.

2015-12-01

Cross diffusion, whereby a flux of a given species entrains the diffusive transport of another species, can trigger buoyancy-driven hydrodynamic instabilities at the interface of initially stable stratifications. Starting from a simple three-component case, we introduce a theoretical framework to classify cross-diffusion-induced hydrodynamic phenomena in two-layer stratifications under the action of the gravitational field. A cross-diffusion-convection (CDC) model is derived by coupling the fickian diffusion formalism to Stokes equations. In order to isolate the effect of cross-diffusion in the convective destabilization of a double-layer system, we impose a starting concentration jump of one species in the bottom layer while the other one is homogeneously distributed over the spatial domain. This initial configuration avoids the concurrence of classic Rayleigh-Taylor or differential-diffusion convective instabilities, and it also allows us to activate selectively the cross-diffusion feedback by which the heterogeneously distributed species influences the diffusive transport of the other species. We identify two types of hydrodynamic modes [the negative cross-diffusion-driven convection (NCC) and the positive cross-diffusion-driven convection (PCC)], corresponding to the sign of this operational cross-diffusion term. By studying the space-time density profiles along the gravitational axis we obtain analytical conditions for the onset of convection in terms of two important parameters only: the operational cross-diffusivity and the buoyancy ratio, giving the relative contribution of the two species to the global density. The general classification of the NCC and PCC scenarios in such parameter space is supported by numerical simulations of the fully nonlinear CDC problem. The resulting convective patterns compare favorably with recent experimental results found in microemulsion systems.

Mathematics of thermal diffusion in an exponential temperature field

NASA Astrophysics Data System (ADS)

Zhang, Yaqi; Bai, Wenyu; Diebold, Gerald J.

2018-04-01

The Ludwig-Soret effect, also known as thermal diffusion, refers to the separation of gas, liquid, or solid mixtures in a temperature gradient. The motion of the components of the mixture is governed by a nonlinear, partial differential equation for the density fractions. Here solutions to the nonlinear differential equation for a binary mixture are discussed for an externally imposed, exponential temperature field. The equation of motion for the separation without the effects of mass diffusion is reduced to a Hamiltonian pair from which spatial distributions of the components of the mixture are found. Analytical calculations with boundary effects included show shock formation. The results of numerical calculations of the equation of motion that include both thermal and mass diffusion are given.

Mathematical modelling of surface water-groundwater flow and salinity interactions in the coastal zone

NASA Astrophysics Data System (ADS)

Spanoudaki, Katerina; Kampanis, Nikolaos A.

2014-05-01

Coastal areas are the most densely-populated areas in the world. Consequently water demand is high, posing great pressure on fresh water resources. Climatic change and its direct impacts on meteorological variables (e.g. precipitation) and indirect impact on sea level rise, as well as anthropogenic pressures (e.g. groundwater abstraction), are strong drivers causing groundwater salinisation and subsequently affecting coastal wetlands salinity with adverse effects on the corresponding ecosystems. Coastal zones are a difficult hydrologic environment to represent with a mathematical model due to the large number of contributing hydrologic processes and variable-density flow conditions. Simulation of sea level rise and tidal effects on aquifer salinisation and accurate prediction of interactions between coastal waters, groundwater and neighbouring wetlands requires the use of integrated surface water-groundwater models. In the past few decades several computer codes have been developed to simulate coupled surface and groundwater flow. In these numerical models surface water flow is usually described by the 1-D Saint Venant equations (e.g. Swain and Wexler, 1996) or the 2D shallow water equations (e.g. Liang et al., 2007). Further simplified equations, such as the diffusion and kinematic wave approximations to the Saint Venant equations, are also employed for the description of 2D overland flow and 1D stream flow (e.g. Gunduz and Aral, 2005). However, for coastal bays, estuaries and wetlands it is often desirable to solve the 3D shallow water equations to simulate surface water flow. This is the case e.g. for wind-driven flows or density-stratified flows. Furthermore, most integrated models are based on the assumption of constant fluid density and therefore their applicability to coastal regions is questionable. Thus, most of the existing codes are not well-suited to represent surface water-groundwater interactions in coastal areas. To this end, the 3D integrated surface water-groundwater model IRENE (Spanoudaki et al., 2009; Spanoudaki, 2010) has been modified in order to simulate surface water-groundwater flow and salinity interactions in the coastal zone. IRENE, in its original form, couples the 3D, non-steady state Navier-Stokes equations, after Reynolds averaging and with the assumption of hydrostatic pressure distribution, to the equations describing 3D saturated groundwater flow of constant density. A semi-implicit finite difference scheme is used to solve the surface water flow equations, while a fully implicit finite difference scheme is used for the groundwater equations. Pollution interactions are simulated by coupling the advection-diffusion equation describing the fate and transport of contaminants introduced in a 3D turbulent flow field to the partial differential equation describing the fate and transport of contaminants in 3D transient groundwater flow systems. The model has been further developed to include the effects of density variations on surface water and groundwater flow, while the already built-in solute transport capabilities are used to simulate salinity interactions. Initial results show that IRENE can accurately predict surface water-groundwater flow and salinity interactions in coastal areas. Important research issues that can be investigated using IRENE include: (a) sea level rise and tidal effects on aquifer salinisation and the configuration of the saltwater wedge, (b) the effects of surface water-groundwater interaction on salinity increase of coastal wetlands and (c) the estimation of the location and magnitude of groundwater discharge to coasts. Acknowledgement The work presented in this paper has been funded by the Greek State Scholarships Foundation (IKY), Fellowships of Excellence for Postdoctoral Studies (Siemens Program), 'A simulation-optimization model for assessing the best practices for the protection of surface water and groundwater in the coastal zone', (2013 - 2015). References Gunduz, O. and Aral, M.M. (2005). River networks and groundwater flow: a simultaneous solution of a coupled system. Journal of Hydrology 301 (1-4), 216-234. Liang, D., Falconer, R.A. and Lin, B. (2007). Coupling surface and subsurface flows in a depth-averaged flood wave model. Journal of Hydrology 337, 147-158. Spanoudaki, K., Stamou, A.I. and Nanou-Giannarou, A. (2009). Development and verification of a 3-D integrated surface water-groundwater model. Journal of Hydrology, 375 (3-4), 410-427. Spanoudaki, K. (2010). Integrated numerical modelling of surface water groundwater systems (in Greek). Ph.D. Thesis, National Technical University of Athens, Greece. Swain, E.D. and Wexler, E.J. (1996). A coupled surface water and groundwater flow model (Modbranch) for simulation of stream-aquifer interaction. United States Geological Survey, Techniques of Water Resources Investigations (Book 6, Chapter A6).

a Cell Vertex Algorithm for the Incompressible Navier-Stokes Equations on Non-Orthogonal Grids

NASA Astrophysics Data System (ADS)

Jessee, J. P.; Fiveland, W. A.

1996-08-01

The steady, incompressible Navier-Stokes (N-S) equations are discretized using a cell vertex, finite volume method. Quadrilateral and hexahedral meshes are used to represent two- and three-dimensional geometries respectively. The dependent variables include the Cartesian components of velocity and pressure. Advective fluxes are calculated using bounded, high-resolution schemes with a deferred correction procedure to maintain a compact stencil. This treatment insures bounded, non-oscillatory solutions while maintaining low numerical diffusion. The mass and momentum equations are solved with the projection method on a non-staggered grid. The coupling of the pressure and velocity fields is achieved using the Rhie and Chow interpolation scheme modified to provide solutions independent of time steps or relaxation factors. An algebraic multigrid solver is used for the solution of the implicit, linearized equations.A number of test cases are anlaysed and presented. The standard benchmark cases include a lid-driven cavity, flow through a gradual expansion and laminar flow in a three-dimensional curved duct. Predictions are compared with data, results of other workers and with predictions from a structured, cell-centred, control volume algorithm whenever applicable. Sensitivity of results to the advection differencing scheme is investigated by applying a number of higher-order flux limiters: the MINMOD, MUSCL, OSHER, CLAM and SMART schemes. As expected, studies indicate that higher-order schemes largely mitigate the diffusion effects of first-order schemes but also shown no clear preference among the higher-order schemes themselves with respect to accuracy. The effect of the deferred correction procedure on global convergence is discussed.

The spin-temperature theory of dynamic nuclear polarization and nuclear spin-lattice relaxation

NASA Technical Reports Server (NTRS)

Byvik, C. E.; Wollan, D. S.

1974-01-01

A detailed derivation of the equations governing dynamic nuclear polarization (DNP) and nuclear spin lattice relaxation by use of the spin temperature theory has been carried to second order in a perturbation expansion of the density matrix. Nuclear spin diffusion in the rapid diffusion limit and the effects of the coupling of the electron dipole-dipole reservoir (EDDR) with the nuclear spins are incorporated. The complete expression for the dynamic nuclear polarization has been derived and then examined in detail for the limit of well resolved solid effect transitions. Exactly at the solid effect transition peaks, the conventional solid-effect DNP results are obtained, but with EDDR effects on the nuclear relaxation and DNP leakage factor included. Explicit EDDR contributions to DNP are discussed, and a new DNP effect is predicted.

Rarefied gas flows through a curved channel: Application of a diffusion-type equation

NASA Astrophysics Data System (ADS)

Aoki, Kazuo; Takata, Shigeru; Tatsumi, Eri; Yoshida, Hiroaki

2010-11-01

Rarefied gas flows through a curved two-dimensional channel, caused by a pressure or a temperature gradient, are investigated numerically by using a macroscopic equation of convection-diffusion type. The equation, which was derived systematically from the Bhatnagar-Gross-Krook model of the Boltzmann equation and diffuse-reflection boundary condition in a previous paper [K. Aoki et al., "A diffusion model for rarefied flows in curved channels," Multiscale Model. Simul. 6, 1281 (2008)], is valid irrespective of the degree of gas rarefaction when the channel width is much shorter than the scale of variations of physical quantities and curvature along the channel. Attention is also paid to a variant of the Knudsen compressor that can produce a pressure raise by the effect of the change of channel curvature and periodic temperature distributions without any help of moving parts. In the process of analysis, the macroscopic equation is (partially) extended to the case of the ellipsoidal-statistical model of the Boltzmann equation.

Numerical applications of the advective-diffusive codes for the inner magnetosphere

NASA Astrophysics Data System (ADS)

Aseev, N. A.; Shprits, Y. Y.; Drozdov, A. Y.; Kellerman, A. C.

2016-11-01

In this study we present analytical solutions for convection and diffusion equations. We gather here the analytical solutions for the one-dimensional convection equation, the two-dimensional convection problem, and the one- and two-dimensional diffusion equations. Using obtained analytical solutions, we test the four-dimensional Versatile Electron Radiation Belt code (the VERB-4D code), which solves the modified Fokker-Planck equation with additional convection terms. The ninth-order upwind numerical scheme for the one-dimensional convection equation shows much more accurate results than the results obtained with the third-order scheme. The universal limiter eliminates unphysical oscillations generated by high-order linear upwind schemes. Decrease in the space step leads to convergence of a numerical solution of the two-dimensional diffusion equation with mixed terms to the analytical solution. We compare the results of the third- and ninth-order schemes applied to magnetospheric convection modeling. The results show significant differences in electron fluxes near geostationary orbit when different numerical schemes are used.

Fractional-calculus diffusion equation

PubMed Central

2010-01-01

Background Sequel to the work on the quantization of nonconservative systems using fractional calculus and quantization of a system with Brownian motion, which aims to consider the dissipation effects in quantum-mechanical description of microscale systems. Results The canonical quantization of a system represented classically by one-dimensional Fick's law, and the diffusion equation is carried out according to the Dirac method. A suitable Lagrangian, and Hamiltonian, describing the diffusive system, are constructed and the Hamiltonian is transformed to Schrodinger's equation which is solved. An application regarding implementation of the developed mathematical method to the analysis of diffusion, osmosis, which is a biological application of the diffusion process, is carried out. Schrödinger's equation is solved. Conclusions The plot of the probability function represents clearly the dissipative and drift forces and hence the osmosis, which agrees totally with the macro-scale view, or the classical-version osmosis. PMID:20492677

Simulations of reactive transport and precipitation with smoothed particle hydrodynamics

NASA Astrophysics Data System (ADS)

Tartakovsky, Alexandre M.; Meakin, Paul; Scheibe, Timothy D.; Eichler West, Rogene M.

2007-03-01

A numerical model based on smoothed particle hydrodynamics (SPH) was developed for reactive transport and mineral precipitation in fractured and porous materials. Because of its Lagrangian particle nature, SPH has several advantages for modeling Navier-Stokes flow and reactive transport including: (1) in a Lagrangian framework there is no non-linear term in the momentum conservation equation, so that accurate solutions can be obtained for momentum dominated flows and; (2) complicated physical and chemical processes such as surface growth due to precipitation/dissolution and chemical reactions are easy to implement. In addition, SPH simulations explicitly conserve mass and linear momentum. The SPH solution of the diffusion equation with fixed and moving reactive solid-fluid boundaries was compared with analytical solutions, Lattice Boltzmann [Q. Kang, D. Zhang, P. Lichtner, I. Tsimpanogiannis, Lattice Boltzmann model for crystal growth from supersaturated solution, Geophysical Research Letters, 31 (2004) L21604] simulations and diffusion limited aggregation (DLA) [P. Meakin, Fractals, scaling and far from equilibrium. Cambridge University Press, Cambridge, UK, 1998] model simulations. To illustrate the capabilities of the model, coupled three-dimensional flow, reactive transport and precipitation in a fracture aperture with a complex geometry were simulated.

2D Lattice Boltzmann Simulation Of Chemical Reactions Within Rayleigh-Bénard And Poiseuille-Bénard Convection Systems

NASA Astrophysics Data System (ADS)

Amaya-Ventura, Gilberto; Rodríguez-Romo, Suemi

2011-09-01

This paper deals with the computational simulation of the reaction-diffusion-advection phenomena emerging in Rayleigh-Bénard (RB) and Poiseuille-Bénard reactive convection systems. We use the Boussinesq's approximation for buoyancy forces and the Lattice Boltzmann method (LBM). The first kinetic mesoscopic model proposed here is based on the discrete Boltzmann equation needed to solve the momentum balance coupled with buoyancy forces. Then, a second lattice Boltzmann algorithm is applied to solve the reaction-diffusion-advection equation to calculate the evolution of the chemical species concentration. We use a reactive system composed by nitrous oxide (so call laughing gas) in air as an example; its spatio-temporal decomposition is calculated. Two cases are considered, a rectangular enclosed cavity and an open channel. The simulations are performed at low Reynolds numbers and in a steady state between the first and second thermo-hydrodynamic instabilities. The results presented here, for the thermo-hydrodynamic behavior, are in good agreement with experimental data; while our| chemical kinetics simulation yields expected results. Some applications of our approach are related to chemical reactors and atmospheric phenomena, among others.

Multifield analysis of a piezoelectric valveless micropump: effects of actuation frequency and electric potential

NASA Astrophysics Data System (ADS)

Sayar, Ersin; Farouk, Bakhtier

2012-07-01

Coupled multifield analysis of a piezoelectrically actuated valveless micropump device is carried out for liquid (water) transport applications. The valveless micropump consists of two diffuser/nozzle elements; the pump chamber, a thin structural layer (silicon), and a piezoelectric layer, PZT-5A as the actuator. We consider two-way coupling of forces between solid and liquid domains in the systems where actuator deflection causes fluid flow and vice versa. Flow contraction and expansion (through the nozzle and the diffuser respectively) generate net fluid flow. Both structural and flow field analysis of the microfluidic device are considered. The effect of the driving power (voltage) and actuation frequency on silicon-PZT-5A bi-layer membrane deflection and flow rate is investigated. For the compressible flow formulation, an isothermal equation of state for the working fluid is employed. The governing equations for the flow fields and the silicon-PZT-5A bi-layer membrane motions are solved numerically. At frequencies below 5000 Hz, the predicted flow rate increases with actuation frequency. The fluid-solid system shows a resonance at 5000 Hz due to the combined effect of mechanical and fluidic capacitances, inductances, and damping. Time-averaged flow rate starts to drop with increase of actuation frequency above (5000 Hz). The velocity profile in the pump chamber becomes relatively flat or plug-like, if the frequency of pulsations is sufficiently large (high Womersley number). The pressure, velocity, and flow rate prediction models developed in the present study can be utilized to optimize the design of MEMS based micropumps.

Double diffusive magnetohydrodynamic (MHD) mixed convective slip flow along a radiating moving vertical flat plate with convective boundary condition.

PubMed

Rashidi, Mohammad M; Kavyani, Neda; Abelman, Shirley; Uddin, Mohammed J; Freidoonimehr, Navid

2014-01-01

In this study combined heat and mass transfer by mixed convective flow along a moving vertical flat plate with hydrodynamic slip and thermal convective boundary condition is investigated. Using similarity variables, the governing nonlinear partial differential equations are converted into a system of coupled nonlinear ordinary differential equations. The transformed equations are then solved using a semi-numerical/analytical method called the differential transform method and results are compared with numerical results. Close agreement is found between the present method and the numerical method. Effects of the controlling parameters, including convective heat transfer, magnetic field, buoyancy ratio, hydrodynamic slip, mixed convective, Prandtl number and Schmidt number are investigated on the dimensionless velocity, temperature and concentration profiles. In addition effects of different parameters on the skin friction factor, [Formula: see text], local Nusselt number, [Formula: see text], and local Sherwood number [Formula: see text] are shown and explained through tables.

On long-time instabilities in staggered finite difference simulations of the seismic acoustic wave equations on discontinuous grids

NASA Astrophysics Data System (ADS)

Gao, Longfei; Ketcheson, David; Keyes, David

2018-02-01

We consider the long-time instability issue associated with finite difference simulation of seismic acoustic wave equations on discontinuous grids. This issue is exhibited by a prototype algebraic problem abstracted from practical application settings. Analysis of this algebraic problem leads to better understanding of the cause of the instability and provides guidance for its treatment. Specifically, we use the concept of discrete energy to derive the proper solution transfer operators and design an effective way to damp the unstable solution modes. Our investigation shows that the interpolation operators need to be matched with their companion restriction operators in order to properly couple the coarse and fine grids. Moreover, to provide effective damping, specially designed diffusive terms are introduced to the equations at designated locations and discretized with specially designed schemes. These techniques are applied to simulations in practical settings and are shown to lead to superior results in terms of both stability and accuracy.

Simulation of the effects of sub-breakdown electric fields on the chemical kinetics in nonpremixed counterflow methane/air flames

NASA Astrophysics Data System (ADS)

Belhi, Memdouh; Im, Hong; Computational Reacting Flows Laboratory, Clean Combustion Research Center Team

2017-11-01

The effects of an electric field on the combustion kinetics in nonpremixed counterflow methane/air flames were investigated via one-dimensional numerical simulations. A classical fluid model coupling Poison's equation with transport equations for combustion species and electric field-induced particles was used. A methane-air reaction mechanism accounting for the natural ionization in flames was combined with a set of reactions that describe the formation of active particles induced by the electric field. Kinetic parameters for electron-impact reactions and transport coefficients of electrons were modeled as functions of reduced electric field via solutions to the Boltzmann kinetic equation using the BOLSIG code. Mobility of ions was computed based on the (n,6,4) and coulomb interaction potentials, while the diffusion coefficient was approximated from the mobility using Einstein relation. Contributions of electron dissociation, excitation and ionization processes were characterized quantitatively. An analysis to identify the plasma regime where the electric field can alter the combustion kinetic was proposed.

1/f Noise Inside a Faraday Cage

NASA Astrophysics Data System (ADS)

Handel, Peter H.; George, Thomas F.

2009-04-01

We show that quantum 1/f noise does not have a lower frequency limit given by the lowest free electromagnetic field mode in a Faraday cage, even in an ideal cage. Indeed, quantum 1/f noise comes from the infrared-divergent coupling of the field with the charges, in their joint nonlinear system, where the charges cause the field that reacts back on the charges, and so on. This low-frequency limitation is thus not applicable for the nonlinear system of matter and field in interaction. Indeed, this nonlinear system is governed by Newton's laws, Maxwell's equations, in general also by the diffusion equations for particles and heat, or reaction kinetics given by quantum matrix elements. Nevertheless, all the other quantities can be eliminated in principle, resulting in highly nonlinear integro-differential equations for the electromagnetic field only, which no longer yield a fundamental frequency. Alternatively, we may describe this through the presence of an infinite system of subharmonics. We show how this was proven early in the classical and quantum domains, adding new insight.

Numerical simulation of rarefied gas flow through a slit

NASA Technical Reports Server (NTRS)

Keith, Theo G., Jr.; Jeng, Duen-Ren; De Witt, Kenneth J.; Chung, Chan-Hong

1990-01-01

Two different approaches, the finite-difference method coupled with the discrete-ordinate method (FDDO), and the direct-simulation Monte Carlo (DSMC) method, are used in the analysis of the flow of a rarefied gas from one reservoir to another through a two-dimensional slit. The cases considered are for hard vacuum downstream pressure, finite pressure ratios, and isobaric pressure with thermal diffusion, which are not well established in spite of the simplicity of the flow field. In the FDDO analysis, by employing the discrete-ordinate method, the Boltzmann equation simplified by a model collision integral is transformed to a set of partial differential equations which are continuous in physical space but are point functions in molecular velocity space. The set of partial differential equations are solved by means of a finite-difference approximation. In the DSMC analysis, three kinds of collision sampling techniques, the time counter (TC) method, the null collision (NC) method, and the no time counter (NTC) method, are used.

EFFECT OF Mg AND TEMPERATURE ON Fe-Al ALLOY LAYER IN Fe/(Zn-6%Al-x%Mg) SOLID-LIQUID DIFFUSION COUPLES

NASA Astrophysics Data System (ADS)

Liang, Liu; Liu, Ya-Ling; Liu, Ya; Peng, Hao-Ping; Wang, Jian-Hua; Su, Xu-Ping

Fe/(Zn-6%Al-x%Mg) solid-liquid diffusion couples were kept at various temperatures for different periods of time to investigate the formation and growth of the Fe-Al alloy layer. Scanning electron microscopy (SEM), energy dispersive spectrometry (EDS) and X-ray diffraction (XRD) were used to study the constituents and morphology of the Fe-Al alloy layer. It was found that the Fe2Al5Znx phase layer forms close to the iron sheet and the FeAl3Znx phase layer forms near the side of the melted Zn-6%Al-3%Mg in diffusion couples. When the Fe/(Zn-6%Al-3%Mg) diffusion couple is kept at 510∘C for more than 15min, a continuous Fe-Al alloy layer is formed on the interface of the diffusion couple. Among all Fe/(Zn-6%Al-x%Mg) solid-liquid diffusion couples, the Fe-Al alloy layer on the interface of the Fe/(Zn-6% Al-3% Mg) diffusion couple is the thinnest. The Fe-Al alloy layer forms only when the diffusion temperature is above 475∘. These results show that the Fe-Al alloy layer in Fe/(Zn-6%Al-x%Mg) solid-liquid diffusion couples is composed of Fe2Al5Znx and FeAl3Znx phase layers. Increasing the diffusing temperature and time period would promote the formation and growth of the Fe-Al alloy layer. When the Mg content in the Fe/(Zn-6%Al-x%Mg) diffusion couples is 3%, the growth of the Fe-Al alloy layer is inhibited. These results may explain why there is no obvious Fe-Al alloy layer formed on the interface of steel with a Zn-6%Al-3%Mg coating.

An asymptotic induced numerical method for the convection-diffusion-reaction equation

NASA Technical Reports Server (NTRS)

Scroggs, Jeffrey S.; Sorensen, Danny C.

1988-01-01

A parallel algorithm for the efficient solution of a time dependent reaction convection diffusion equation with small parameter on the diffusion term is presented. The method is based on a domain decomposition that is dictated by singular perturbation analysis. The analysis is used to determine regions where certain reduced equations may be solved in place of the full equation. Parallelism is evident at two levels. Domain decomposition provides parallelism at the highest level, and within each domain there is ample opportunity to exploit parallelism. Run time results demonstrate the viability of the method.

A new Eulerian model for viscous and heat conducting compressible flows

NASA Astrophysics Data System (ADS)

Svärd, Magnus

2018-09-01

In this article, a suite of physically inconsistent properties of the Navier-Stokes equations, associated with the lack of mass diffusion and the definition of velocity, is presented. We show that these inconsistencies are consequences of the Lagrangian derivation that models viscous stresses rather than diffusion. A new model for compressible and diffusive (viscous and heat conducting) flows of an ideal gas, is derived in a purely Eulerian framework. We propose that these equations supersede the Navier-Stokes equations. A few numerical experiments demonstrate some differences and similarities between the new system and the Navier-Stokes equations.

MODFLOW-Based Coupled Surface Water Routing and Groundwater-Flow Simulation.

PubMed

Hughes, J D; Langevin, C D; White, J T

2015-01-01

In this paper, we present a flexible approach for simulating one- and two-dimensional routing of surface water using a numerical surface water routing (SWR) code implicitly coupled to the groundwater-flow process in MODFLOW. Surface water routing in SWR can be simulated using a diffusive-wave approximation of the Saint-Venant equations and/or a simplified level-pool approach. SWR can account for surface water flow controlled by backwater conditions caused by small water-surface gradients or surface water control structures. A number of typical surface water control structures, such as culverts, weirs, and gates, can be represented, and it is possible to implement operational rules to manage surface water stages and streamflow. The nonlinear system of surface water flow equations formulated in SWR is solved by using Newton methods and direct or iterative solvers. SWR was tested by simulating the (1) Lal axisymmetric overland flow, (2) V-catchment, and (3) modified Pinder-Sauer problems. Simulated results for these problems compare well with other published results and indicate that SWR provides accurate results for surface water-only and coupled surface water/groundwater problems. Results for an application of SWR and MODFLOW to the Snapper Creek area of Miami-Dade County, Florida, USA are also presented and demonstrate the value of coupled surface water and groundwater simulation in managed, low-relief coastal settings. Published 2014. This article is a U.S. Government work and is in the public domain in the USA.

Analytical solution of the nonlinear diffusion equation

NASA Astrophysics Data System (ADS)

Shanker Dubey, Ravi; Goswami, Pranay

2018-05-01

In the present paper, we derive the solution of the nonlinear fractional partial differential equations using an efficient approach based on the q -homotopy analysis transform method ( q -HATM). The fractional diffusion equations derivatives are considered in Caputo sense. The derived results are graphically demonstrated as well.

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

PubMed

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

2017-06-13

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

A flexible nonlinear diffusion acceleration method for the S N transport equations discretized with discontinuous finite elements

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

Schunert, Sebastian; Wang, Yaqi; Gleicher, Frederick

This paper presents a flexible nonlinear diffusion acceleration (NDA) method that discretizes both the S N transport equation and the diffusion equation using the discontinuous finite element method (DFEM). The method is flexible in that the diffusion equation can be discretized on a coarser mesh with the only restriction that it is nested within the transport mesh and the FEM shape function orders of the two equations can be different. The consistency of the transport and diffusion solutions at convergence is defined by using a projection operator mapping the transport into the diffusion FEM space. The diffusion weak form ismore » based on the modified incomplete interior penalty (MIP) diffusion DFEM discretization that is extended by volumetric drift, interior face, and boundary closure terms. In contrast to commonly used coarse mesh finite difference (CMFD) methods, the presented NDA method uses a full FEM discretized diffusion equation for acceleration. Suitable projection and prolongation operators arise naturally from the FEM framework. Via Fourier analysis and numerical experiments for a one-group, fixed source problem the following properties of the NDA method are established for structured quadrilateral meshes: (1) the presented method is unconditionally stable and effective in the presence of mild material heterogeneities if the same mesh and identical shape functions either of the bilinear or biquadratic type are used, (2) the NDA method remains unconditionally stable in the presence of strong heterogeneities, (3) the NDA method with bilinear elements extends the range of effectiveness and stability by a factor of two when compared to CMFD if a coarser diffusion mesh is selected. In addition, the method is tested for solving the C5G7 multigroup, eigenvalue problem using coarse and fine mesh acceleration. Finally, while NDA does not offer an advantage over CMFD for fine mesh acceleration, it reduces the iteration count required for convergence by almost a factor of two in the case of coarse mesh acceleration.« less

A flexible nonlinear diffusion acceleration method for the S N transport equations discretized with discontinuous finite elements

DOE PAGES

Schunert, Sebastian; Wang, Yaqi; Gleicher, Frederick; ...

2017-02-21

This paper presents a flexible nonlinear diffusion acceleration (NDA) method that discretizes both the S N transport equation and the diffusion equation using the discontinuous finite element method (DFEM). The method is flexible in that the diffusion equation can be discretized on a coarser mesh with the only restriction that it is nested within the transport mesh and the FEM shape function orders of the two equations can be different. The consistency of the transport and diffusion solutions at convergence is defined by using a projection operator mapping the transport into the diffusion FEM space. The diffusion weak form ismore » based on the modified incomplete interior penalty (MIP) diffusion DFEM discretization that is extended by volumetric drift, interior face, and boundary closure terms. In contrast to commonly used coarse mesh finite difference (CMFD) methods, the presented NDA method uses a full FEM discretized diffusion equation for acceleration. Suitable projection and prolongation operators arise naturally from the FEM framework. Via Fourier analysis and numerical experiments for a one-group, fixed source problem the following properties of the NDA method are established for structured quadrilateral meshes: (1) the presented method is unconditionally stable and effective in the presence of mild material heterogeneities if the same mesh and identical shape functions either of the bilinear or biquadratic type are used, (2) the NDA method remains unconditionally stable in the presence of strong heterogeneities, (3) the NDA method with bilinear elements extends the range of effectiveness and stability by a factor of two when compared to CMFD if a coarser diffusion mesh is selected. In addition, the method is tested for solving the C5G7 multigroup, eigenvalue problem using coarse and fine mesh acceleration. Finally, while NDA does not offer an advantage over CMFD for fine mesh acceleration, it reduces the iteration count required for convergence by almost a factor of two in the case of coarse mesh acceleration.« less

The effective boundary conditions and their lifespan of the logistic diffusion equation on a coated body

NASA Astrophysics Data System (ADS)

Li, Huicong; Wang, Xuefeng; Wu, Yanxia

2014-11-01

We consider the logistic diffusion equation on a bounded domain, which has two components with a thin coating surrounding a body. The diffusion tensor is isotropic on the body, and anisotropic on the coating. The size of the diffusion tensor on these components may be very different; within the coating, the diffusion rates in the normal and tangent directions may be in different scales. We find effective boundary conditions (EBCs) that are approximately satisfied by the solution of the diffusion equation on the boundary of the body. We also prove that the lifespan of each EBC, which measures how long the EBC remains effective, is infinite. The EBCs enable us to see clearly the effect of the coating and ease the difficult task of solving the PDE in a thin region with a small diffusion tensor. The motivation of the mathematics includes a nature reserve surrounded by a buffer zone.

Worst case prediction of additives migration from polystyrene for food safety purposes: a model update.

PubMed

Martínez-López, Brais; Gontard, Nathalie; Peyron, Stéphane

2018-03-01

A reliable prediction of migration levels of plastic additives into food requires a robust estimation of diffusivity. Predictive modelling of diffusivity as recommended by the EU commission is carried out using a semi-empirical equation that relies on two polymer-dependent parameters. These parameters were determined for the polymers most used by packaging industry (LLDPE, HDPE, PP, PET, PS, HIPS) from the diffusivity data available at that time. In the specific case of general purpose polystyrene, the diffusivity data published since then shows that the use of the equation with the original parameters results in systematic underestimation of diffusivity. The goal of this study was therefore, to propose an update of the aforementioned parameters for PS on the basis of up to date diffusivity data, so the equation can be used for a reasoned overestimation of diffusivity.

Kramers turnover: From energy diffusion to spatial diffusion using metadynamics

PubMed Central

Tiwary, Pratyush; Berne, B. J.

2016-01-01

We consider the rate of transition for a particle between two metastable states coupled to a thermal environment for various magnitudes of the coupling strength using the recently proposed infrequent metadynamics approach [P. Tiwary and M. Parrinello, Phys. Rev. Lett. 111, 230602 (2013)]. We are interested in understanding how this approach for obtaining rate constants performs as the dynamics regime changes from energy diffusion to spatial diffusion. Reassuringly, we find that the approach works remarkably well for various coupling strengths in the strong coupling regime, and to some extent even in the weak coupling regime. PMID:27059558

Modeling Morphogenesis with Reaction-Diffusion Equations Using Galerkin Spectral Methods

DTIC Science & Technology

2002-05-06

reaction- diffusion equation is a difficult problem in analysis that will not be addressed here. Errors will also arise from numerically approx solutions to...the ODEs. When comparing the approximate solution to actual reaction- diffusion systems found in nature, we must also take into account errors that...

A boundary integral approach in primitive variables for free surface flows

NASA Astrophysics Data System (ADS)

Casciola, C.; Piva, R.

The boundary integral formulation, very efficient for free surface potential flows, was considered for its possible extension to rotational flows either inviscid or viscous. We first analyze a general formulation for unsteady Navier-Stokes equations in primitive variables, which reduces to a representation for the Euler equations in the limiting case of Reynolds infinity. A first simplified model for rotational flows, obtained by decoupling kinematics and dynamics, reduces the integral equations to a known kinematical form whose mathematical and numerical properties have been studied. The dynamics equations to complete the model are obtained for the free surface and the wake. A simple and efficient scheme for the study of the non linear evolution of the wave system and its interaction with the body wake is presented. A steady state version for the calculation of the wave resistance is also reported. A second model was proposed for the simulation of rotational separated regions, by coupling the integral equations in velocity with an integral equation for the vorticity at the body boundary. The same procedure may be extended to include the diffusion of the vorticity in the flowfield. The vortex shedding from a cylindrical body in unsteady motion is discussed, as a first application of the model.

Correction of spin diffusion during iterative automated NOE assignment

NASA Astrophysics Data System (ADS)

Linge, Jens P.; Habeck, Michael; Rieping, Wolfgang; Nilges, Michael

2004-04-01

Indirect magnetization transfer increases the observed nuclear Overhauser enhancement (NOE) between two protons in many cases, leading to an underestimation of target distances. Wider distance bounds are necessary to account for this error. However, this leads to a loss of information and may reduce the quality of the structures generated from the inter-proton distances. Although several methods for spin diffusion correction have been published, they are often not employed to derive distance restraints. This prompted us to write a user-friendly and CPU-efficient method to correct for spin diffusion that is fully integrated in our program ambiguous restraints for iterative assignment (ARIA). ARIA thus allows automated iterative NOE assignment and structure calculation with spin diffusion corrected distances. The method relies on numerical integration of the coupled differential equations which govern relaxation by matrix squaring and sparse matrix techniques. We derive a correction factor for the distance restraints from calculated NOE volumes and inter-proton distances. To evaluate the impact of our spin diffusion correction, we tested the new calibration process extensively with data from the Pleckstrin homology (PH) domain of Mus musculus β-spectrin. By comparing structures refined with and without spin diffusion correction, we show that spin diffusion corrected distance restraints give rise to structures of higher quality (notably fewer NOE violations and a more regular Ramachandran map). Furthermore, spin diffusion correction permits the use of tighter error bounds which improves the distinction between signal and noise in an automated NOE assignment scheme.

Heat Transfer to a Thin Solid Combustible in Flame Spreading at Microgravity

NASA Technical Reports Server (NTRS)

Bhattacharjee, S.; Altenkirch, R. A.; Olson, S. L.; Sotos, R. G.

1991-01-01

The heat transfer rate to a thin solid combustible from an attached diffusion flame, spreading across the surface of the combustible in a quiescent, microgravity environment, was determined from measurements made in the drop tower facility at NASA-Lewis Research Center. With first-order Arrhenius pyrolysis kinetics, the solid-phase mass and energy equations along with the measured spread rate and surface temperature profiles were used to calculate the net heat flux to the surface. Results of the measurements are compared to the numerical solution of the complete set of coupled differential equations that describes the temperature, species, and velocity fields in the gas and solid phases. The theory and experiment agree on the major qualitative features of the heat transfer. Some fundamental differences are attributed to the neglect of radiation in the theoretical model.

Structural and functional networks in complex systems with delay.

PubMed

Eguíluz, Víctor M; Pérez, Toni; Borge-Holthoefer, Javier; Arenas, Alex

2011-05-01

Functional networks of complex systems are obtained from the analysis of the temporal activity of their components, and are often used to infer their unknown underlying connectivity. We obtain the equations relating topology and function in a system of diffusively delay-coupled elements in complex networks. We solve exactly the resulting equations in motifs (directed structures of three nodes) and in directed networks. The mean-field solution for directed uncorrelated networks shows that the clusterization of the activity is dominated by the in-degree of the nodes, and that the locking frequency decreases with increasing average degree. We find that the exponent of a power law degree distribution of the structural topology γ is related to the exponent of the associated functional network as α=(2-γ)(-1) for γ<2. © 2011 American Physical Society

An accurate computational method for the diffusion regime verification

NASA Astrophysics Data System (ADS)

Zhokh, Alexey A.; Strizhak, Peter E.

2018-04-01

The diffusion regime (sub-diffusive, standard, or super-diffusive) is defined by the order of the derivative in the corresponding transport equation. We develop an accurate computational method for the direct estimation of the diffusion regime. The method is based on the derivative order estimation using the asymptotic analytic solutions of the diffusion equation with the integer order and the time-fractional derivatives. The robustness and the computational cheapness of the proposed method are verified using the experimental methane and methyl alcohol transport kinetics through the catalyst pellet.

Heat transfer in suspensions of rigid particles

NASA Astrophysics Data System (ADS)

Brandt, Luca; Niazi Ardekani, Mehdi; Abouali, Omid

2016-11-01

We study the heat transfer in laminar Couette flow of suspensions of rigid neutrally buoyant particles by means of numerical simulations. An Immersed Boundary Method is coupled with a VOF approach to simulate the heat transfer in the fluid and solid phase, enabling us to fully resolve the heat diffusion. First, we consider spherical particles and show that the proposed algorithm is able to reproduce the correlations between heat flux across the channel, the particle volume fraction and the heat diffusivity obtained in laboratory experiments and recently proposed in the literature, results valid in the limit of vanishing inertia. We then investigate the role of inertia on the heat transfer and show an increase of the suspension diffusivity at finite particle Reynolds numbers. Finally, we vary the relativity diffusivity of the fluid and solid phase and investigate its effect on the effective heat flux across the channel. The data are analyzed by considering the ensemble averaged energy equation and decomposing the heat flux in 4 different contributions, related to diffusion in the solid and fluid phase, and the correlations between wall-normal velocity and temperature fluctuations. Results for non-spherical particles will be examined before the meeting. Supported by the European Research Council Grant No. ERC-2013- CoG-616186, TRITOS. The authors acknowledge computer time provided by SNIC (Swedish National Infrastructure for Computing).

Macroscopic modeling for heat and water vapor transfer in dry snow by homogenization.

PubMed

Calonne, Neige; Geindreau, Christian; Flin, Frédéric

2014-11-26

Dry snow metamorphism, involved in several topics related to cryospheric sciences, is mainly linked to heat and water vapor transfers through snow including sublimation and deposition at the ice-pore interface. In this paper, the macroscopic equivalent modeling of heat and water vapor transfers through a snow layer was derived from the physics at the pore scale using the homogenization of multiple scale expansions. The microscopic phenomena under consideration are heat conduction, vapor diffusion, sublimation, and deposition. The obtained macroscopic equivalent model is described by two coupled transient diffusion equations including a source term arising from phase change at the pore scale. By dimensional analysis, it was shown that the influence of such source terms on the overall transfers can generally not be neglected, except typically under small temperature gradients. The precision and the robustness of the proposed macroscopic modeling were illustrated through 2D numerical simulations. Finally, the effective vapor diffusion tensor arising in the macroscopic modeling was computed on 3D images of snow. The self-consistent formula offers a good estimate of the effective diffusion coefficient with respect to the snow density, within an average relative error of 10%. Our results confirm recent work that the effective vapor diffusion is not enhanced in snow.

Solid-state diffusion-controlled growth of the phases in the Au-Sn system

NASA Astrophysics Data System (ADS)

Baheti, Varun A.; Kashyap, Sanjay; Kumar, Praveen; Chattopadhyay, Kamanio; Paul, Aloke

2018-01-01

The solid state diffusion-controlled growth of the phases is studied for the Au-Sn system in the range of room temperature to 200 °C using bulk and electroplated diffusion couples. The number of product phases in the interdiffusion zone decreases with the decrease in annealing temperature. These phases grow with significantly high rates even at the room temperature. The growth rate of the AuSn4 phase is observed to be higher in the case of electroplated diffusion couple because of the relatively small grains and hence high contribution of the grain boundary diffusion when compared to the bulk diffusion couple. The diffraction pattern analysis indicates the same equilibrium crystal structure of the phases in these two types of diffusion couples. The analysis in the AuSn4 phase relating the estimated tracer diffusion coefficients with grain size, crystal structure, the homologous temperature of experiments and the concept of the sublattice diffusion mechanism in the intermetallic compounds indicate that Au diffuses mainly via the grain boundaries, whereas Sn diffuses via both the grain boundaries and the lattice.

Inter-diffusion analysis of joint interface of tungsten-rhenium couple

NASA Astrophysics Data System (ADS)

Hua, Y. F.; Li, Z. X.; Zhang, X.; Du, J. H.; Huang, C. L.; Du, M. H.

2011-09-01

The tungsten-rhenium couple was prepared by using glow plasma physical vapor deposition (PVD) on the isotropic fine grained graphite (IG) substrates. Diffusion anneals of the tungsten-rhenium couple were conducted at the temperature from 1100 °C to 1400 °C to investigate the inter-diffusion behaviors. The results showed that the thickness of the inter-diffusion zone increased with increasing annealing temperature. The relationship between the inter-diffusion coefficient and the annealing temperature accorded with the Arrhenius manner. The value of inter-diffusion activation energies was 189 kJ/mole (1.96 eV). The service time of tungsten-rhenium multilayer diffusion barrier was limited by the inter-diffusion for rhenium and tungsten rather than the diffusion of carbon in rhenium.

Fractional Number Operator and Associated Fractional Diffusion Equations

NASA Astrophysics Data System (ADS)

Rguigui, Hafedh

2018-03-01

In this paper, we study the fractional number operator as an analog of the finite-dimensional fractional Laplacian. An important relation with the Ornstein-Uhlenbeck process is given. Using a semigroup approach, the solution of the Cauchy problem associated to the fractional number operator is presented. By means of the Mittag-Leffler function and the Laplace transform, we give the solution of the Caputo time fractional diffusion equation and Riemann-Liouville time fractional diffusion equation in infinite dimensions associated to the fractional number operator.

Sharp rates of decay of solutions to the nonlinear fast diffusion equation via functional inequalities

PubMed Central

Vázquez, J. L.

2010-01-01

The goal of this paper is to state the optimal decay rate for solutions of the nonlinear fast diffusion equation and, in self-similar variables, the optimal convergence rates to Barenblatt self-similar profiles and their generalizations. It relies on the identification of the optimal constants in some related Hardy–Poincaré inequalities and concludes a long series of papers devoted to generalized entropies, functional inequalities, and rates for nonlinear diffusion equations. PMID:20823259

Note on coefficient matrices from stochastic Galerkin methods for random diffusion equations

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

Zhou Tao, E-mail: tzhou@lsec.cc.ac.c; Tang Tao, E-mail: ttang@hkbu.edu.h

2010-11-01

In a recent work by Xiu and Shen [D. Xiu, J. Shen, Efficient stochastic Galerkin methods for random diffusion equations, J. Comput. Phys. 228 (2009) 266-281], the Galerkin methods are used to solve stochastic diffusion equations in random media, where some properties for the coefficient matrix of the resulting system are provided. They also posed an open question on the properties of the coefficient matrix. In this work, we will provide some results related to the open question.

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

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

Lattice continuum and diffusional creep.

PubMed

Mesarovic, Sinisa Dj

2016-04-01

Diffusional creep is characterized by growth/disappearance of lattice planes at the crystal boundaries that serve as sources/sinks of vacancies, and by diffusion of vacancies. The lattice continuum theory developed here represents a natural and intuitive framework for the analysis of diffusion in crystals and lattice growth/loss at the boundaries. The formulation includes the definition of the Lagrangian reference configuration for the newly created lattice, the transport theorem and the definition of the creep rate tensor for a polycrystal as a piecewise uniform, discontinuous field. The values associated with each crystalline grain are related to the normal diffusional flux at grain boundaries. The governing equations for Nabarro-Herring creep are derived with coupled diffusion and elasticity with compositional eigenstrain. Both, bulk diffusional dissipation and boundary dissipation accompanying vacancy nucleation and absorption, are considered, but the latter is found to be negligible. For periodic arrangements of grains, diffusion formally decouples from elasticity but at the cost of a complicated boundary condition. The equilibrium of deviatorically stressed polycrystals is impossible without inclusion of interface energies. The secondary creep rate estimates correspond to the standard Nabarro-Herring model, and the volumetric creep is small. The initial (primary) creep rate is estimated to be much larger than the secondary creep rate.

Lattice continuum and diffusional creep

NASA Astrophysics Data System (ADS)

Mesarovic, Sinisa Dj.

2016-04-01

Diffusional creep is characterized by growth/disappearance of lattice planes at the crystal boundaries that serve as sources/sinks of vacancies, and by diffusion of vacancies. The lattice continuum theory developed here represents a natural and intuitive framework for the analysis of diffusion in crystals and lattice growth/loss at the boundaries. The formulation includes the definition of the Lagrangian reference configuration for the newly created lattice, the transport theorem and the definition of the creep rate tensor for a polycrystal as a piecewise uniform, discontinuous field. The values associated with each crystalline grain are related to the normal diffusional flux at grain boundaries. The governing equations for Nabarro-Herring creep are derived with coupled diffusion and elasticity with compositional eigenstrain. Both, bulk diffusional dissipation and boundary dissipation accompanying vacancy nucleation and absorption, are considered, but the latter is found to be negligible. For periodic arrangements of grains, diffusion formally decouples from elasticity but at the cost of a complicated boundary condition. The equilibrium of deviatorically stressed polycrystals is impossible without inclusion of interface energies. The secondary creep rate estimates correspond to the standard Nabarro-Herring model, and the volumetric creep is small. The initial (primary) creep rate is estimated to be much larger than the secondary creep rate.

Diffusion in the special theory of relativity.

PubMed

Herrmann, Joachim

2009-11-01

The Markovian diffusion theory is generalized within the framework of the special theory of relativity. Since the velocity space in relativity is a hyperboloid, the mathematical stochastic calculus on Riemanian manifolds can be applied but adopted here to the velocity space. A generalized Langevin equation in the fiber space of position, velocity, and orthonormal velocity frames is defined from which the generalized relativistic Kramers equation in the phase space in external force fields is derived. The obtained diffusion equation is invariant under Lorentz transformations and its stationary solution is given by the Jüttner distribution. Besides, a nonstationary analytical solution is derived for the example of force-free relativistic diffusion.

Group theoretic approach for solving the problem of diffusion of a drug through a thin membrane

NASA Astrophysics Data System (ADS)

Abd-El-Malek, Mina B.; Kassem, Magda M.; Meky, Mohammed L. M.

2002-03-01

The transformation group theoretic approach is applied to study the diffusion process of a drug through a skin-like membrane which tends to partially absorb the drug. Two cases are considered for the diffusion coefficient. The application of one parameter group reduces the number of independent variables by one, and consequently the partial differential equation governing the diffusion process with the boundary and initial conditions is transformed into an ordinary differential equation with the corresponding conditions. The obtained differential equation is solved numerically using the shooting method, and the results are illustrated graphically and in tables.

Dissipative solitons with energy and matter flows: Fundamental building blocks for the world of living organisms

NASA Astrophysics Data System (ADS)

Akhmediev, N.; Soto-Crespo, J. M.; Brand, H. R.

2013-05-01

We consider a combined model of dissipative solitons that are generated due to the balance between gain and loss of energy as well as to the balance between input and output of matter. The system is governed by the generic complex Ginzburg-Landau equation, which is coupled to a common reaction-diffusion (RD) system. Such a composite dynamical system may describe nerve pulses with a significant part of electromagnetic energy involved. We present examples of such composite dissipative solitons and analyse their internal balances between energy and matter generation and dissipation.

Ionic conduction and self-diffusion near infinitesimal concentration in lithium salt-organic solvent electrolytes

NASA Astrophysics Data System (ADS)

Aihara, Yuichi; Sugimoto, Kyoko; Price, William S.; Hayamizu, Kikuko

2000-08-01

The Debye-Hückel-Onsager and Nernst-Einstein equations, which are based on two different conceptual approaches, constitute the most widely used equations for relating ionic conduction to ionic mobility. However, both of these classical (simple) equations are predictive of ionic conductivity only at very low salt concentrations. In the present work the ionic conductivity of four organic solvent-lithium salt-based electrolytes were measured. These experimental conductivity values were then contrasted with theoretical values calculated using the translational diffusion (also known as self-diffusion or intradiffusion) coefficients of all of the species present obtained using pulsed-gradient spin-echo (1H, 19F and 7Li) nuclear magnetic resonance self-diffusion measurements. The experimental results verified the applicability of both theoretical approaches at very low salt concentrations for these particular systems as well as helping to clarify the reasons for the divergence between theory and experiment. In particular, it was found that the correspondence between the Debye-Hückel-Onsager equation and experimental values could be improved by using the measured solvent self-diffusion values to correct for salt-induced changes in the solution viscosity. The concentration dependence of the self-diffusion coefficients is discussed in terms of the Jones-Dole equation.

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

Coupled rotor and fuselage equations of motion

NASA Technical Reports Server (NTRS)

Warmbrodt, W.

1979-01-01

The governing equations of motion of a helicopter rotor coupled to a rigid body fuselage are derived. A consistent formulation is used to derive nonlinear periodic coefficient equations of motion which are used to study coupled rotor/fuselage dynamics in forward flight. Rotor/fuselage coupling is documented and the importance of an ordering scheme in deriving nonlinear equations of motion is reviewed. The nature of the final equations and the use of multiblade coordinates are discussed.

Derivation of Poisson and Nernst-Planck equations in a bath and channel from a molecular model.

PubMed

Schuss, Z; Nadler, B; Eisenberg, R S

2001-09-01

Permeation of ions from one electrolytic solution to another, through a protein channel, is a biological process of considerable importance. Permeation occurs on a time scale of micro- to milliseconds, far longer than the femtosecond time scales of atomic motion. Direct simulations of atomic dynamics are not yet possible for such long-time scales; thus, averaging is unavoidable. The question is what and how to average. In this paper, we average a Langevin model of ionic motion in a bulk solution and protein channel. The main result is a coupled system of averaged Poisson and Nernst-Planck equations (CPNP) involving conditional and unconditional charge densities and conditional potentials. The resulting NP equations contain the averaged force on a single ion, which is the sum of two components. The first component is the gradient of a conditional electric potential that is the solution of Poisson's equation with conditional and permanent charge densities and boundary conditions of the applied voltage. The second component is the self-induced force on an ion due to surface charges induced only by that ion at dielectric interfaces. The ion induces surface polarization charge that exerts a significant force on the ion itself, not present in earlier PNP equations. The proposed CPNP system is not complete, however, because the electric potential satisfies Poisson's equation with conditional charge densities, conditioned on the location of an ion, while the NP equations contain unconditional densities. The conditional densities are closely related to the well-studied pair-correlation functions of equilibrium statistical mechanics. We examine a specific closure relation, which on the one hand replaces the conditional charge densities by the unconditional ones in the Poisson equation, and on the other hand replaces the self-induced force in the NP equation by an effective self-induced force. This effective self-induced force is nearly zero in the baths but is approximately equal to the self-induced force in and near the channel. The charge densities in the NP equations are interpreted as time averages over long times of the motion of a quasiparticle that diffuses with the same diffusion coefficient as that of a real ion, but is driven by the averaged force. In this way, continuum equations with averaged charge densities and mean-fields can be used to describe permeation through a protein channel.

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

PubMed

Singh, Brajesh K; Srivastava, Vineet K

2015-04-01

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

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

PubMed Central

Singh, Brajesh K.; Srivastava, Vineet K.

2015-01-01

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

Obstructions to Existence in Fast-Diffusion Equations

NASA Astrophysics Data System (ADS)

Rodriguez, Ana; Vazquez, Juan L.

The study of nonlinear diffusion equations produces a number of peculiar phenomena not present in the standard linear theory. Thus, in the sub-field of very fast diffusion it is known that the Cauchy problem can be ill-posed, either because of non-uniqueness, or because of non-existence of solutions with small data. The equations we consider take the general form ut=( D( u, ux) ux) x or its several-dimension analogue. Fast diffusion means that D→∞ at some values of the arguments, typically as u→0 or ux→0. Here, we describe two different types of non-existence phenomena. Some fast-diffusion equations with very singular D do not allow for solutions with sign changes, while other equations admit only monotone solutions, no oscillations being allowed. The examples we give for both types of anomaly are closely related. The most typical examples are vt=( vx/∣ v∣) x and ut= uxx/∣ ux∣. For these equations, we investigate what happens to the Cauchy problem when we take incompatible initial data and perform a standard regularization. It is shown that the limit gives rise to an initial layer where the data become admissible (positive or monotone, respectively), followed by a standard evolution for all t>0, once the obstruction has been removed.

Poisson-Nernst-Planck equations for simulating biomolecular diffusion-reaction processes I: Finite element solutions

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

Lu Benzhuo; Holst, Michael J.; Center for Theoretical Biological Physics, University of California San Diego, La Jolla, CA 92093

2010-09-20

In this paper we developed accurate finite element methods for solving 3-D Poisson-Nernst-Planck (PNP) equations with singular permanent charges for simulating electrodiffusion in solvated biomolecular systems. The electrostatic Poisson equation was defined in the biomolecules and in the solvent, while the Nernst-Planck equation was defined only in the solvent. We applied a stable regularization scheme to remove the singular component of the electrostatic potential induced by the permanent charges inside biomolecules, and formulated regular, well-posed PNP equations. An inexact-Newton method was used to solve the coupled nonlinear elliptic equations for the steady problems; while an Adams-Bashforth-Crank-Nicolson method was devised formore » time integration for the unsteady electrodiffusion. We numerically investigated the conditioning of the stiffness matrices for the finite element approximations of the two formulations of the Nernst-Planck equation, and theoretically proved that the transformed formulation is always associated with an ill-conditioned stiffness matrix. We also studied the electroneutrality of the solution and its relation with the boundary conditions on the molecular surface, and concluded that a large net charge concentration is always present near the molecular surface due to the presence of multiple species of charged particles in the solution. The numerical methods are shown to be accurate and stable by various test problems, and are applicable to real large-scale biophysical electrodiffusion problems.« less

Poisson-Nernst-Planck Equations for Simulating Biomolecular Diffusion-Reaction Processes I: Finite Element Solutions

PubMed Central

Lu, Benzhuo; Holst, Michael J.; McCammon, J. Andrew; Zhou, Y. C.

2010-01-01

In this paper we developed accurate finite element methods for solving 3-D Poisson-Nernst-Planck (PNP) equations with singular permanent charges for electrodiffusion in solvated biomolecular systems. The electrostatic Poisson equation was defined in the biomolecules and in the solvent, while the Nernst-Planck equation was defined only in the solvent. We applied a stable regularization scheme to remove the singular component of the electrostatic potential induced by the permanent charges inside biomolecules, and formulated regular, well-posed PNP equations. An inexact-Newton method was used to solve the coupled nonlinear elliptic equations for the steady problems; while an Adams-Bashforth-Crank-Nicolson method was devised for time integration for the unsteady electrodiffusion. We numerically investigated the conditioning of the stiffness matrices for the finite element approximations of the two formulations of the Nernst-Planck equation, and theoretically proved that the transformed formulation is always associated with an ill-conditioned stiffness matrix. We also studied the electroneutrality of the solution and its relation with the boundary conditions on the molecular surface, and concluded that a large net charge concentration is always present near the molecular surface due to the presence of multiple species of charged particles in the solution. The numerical methods are shown to be accurate and stable by various test problems, and are applicable to real large-scale biophysical electrodiffusion problems. PMID:21709855

Poisson-Nernst-Planck Equations for Simulating Biomolecular Diffusion-Reaction Processes I: Finite Element Solutions.

PubMed

Lu, Benzhuo; Holst, Michael J; McCammon, J Andrew; Zhou, Y C

2010-09-20

In this paper we developed accurate finite element methods for solving 3-D Poisson-Nernst-Planck (PNP) equations with singular permanent charges for electrodiffusion in solvated biomolecular systems. The electrostatic Poisson equation was defined in the biomolecules and in the solvent, while the Nernst-Planck equation was defined only in the solvent. We applied a stable regularization scheme to remove the singular component of the electrostatic potential induced by the permanent charges inside biomolecules, and formulated regular, well-posed PNP equations. An inexact-Newton method was used to solve the coupled nonlinear elliptic equations for the steady problems; while an Adams-Bashforth-Crank-Nicolson method was devised for time integration for the unsteady electrodiffusion. We numerically investigated the conditioning of the stiffness matrices for the finite element approximations of the two formulations of the Nernst-Planck equation, and theoretically proved that the transformed formulation is always associated with an ill-conditioned stiffness matrix. We also studied the electroneutrality of the solution and its relation with the boundary conditions on the molecular surface, and concluded that a large net charge concentration is always present near the molecular surface due to the presence of multiple species of charged particles in the solution. The numerical methods are shown to be accurate and stable by various test problems, and are applicable to real large-scale biophysical electrodiffusion problems.

A Comparative Analysis of Reynolds-Averaged Navier-Stokes Model Predictions for Rayleigh-Taylor Instability and Mixing with Constant and Complex Accelerations

NASA Astrophysics Data System (ADS)

Schilling, Oleg

2016-11-01

Two-, three- and four-equation, single-velocity, multicomponent Reynolds-averaged Navier-Stokes (RANS) models, based on the turbulent kinetic energy dissipation rate or lengthscale, are used to simulate At = 0 . 5 Rayleigh-Taylor turbulent mixing with constant and complex accelerations. The constant acceleration case is inspired by the Cabot and Cook (2006) DNS, and the complex acceleration cases are inspired by the unstable/stable and unstable/neutral cases simulated using DNS (Livescu, Wei & Petersen 2011) and the unstable/stable/unstable case simulated using ILES (Ramaprabhu, Karkhanis & Lawrie 2013). The four-equation models couple equations for the mass flux a and negative density-specific volume correlation b to the K- ɛ or K- L equations, while the three-equation models use a two-fluid algebraic closure for b. The lengthscale-based models are also applied with no buoyancy production in the L equation to explore the consequences of neglecting this term. Predicted mixing widths, turbulence statistics, fields, and turbulent transport equation budgets are compared among these models to identify similarities and differences in the turbulence production, dissipation and diffusion physics represented by the closures used in these models. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.

Multi-Component Diffusion with Application To Computational Aerothermodynamics

NASA Technical Reports Server (NTRS)

Sutton, Kenneth; Gnoffo, Peter A.

1998-01-01

The accuracy and complexity of solving multicomponent gaseous diffusion using the detailed multicomponent equations, the Stefan-Maxwell equations, and two commonly used approximate equations have been examined in a two part study. Part I examined the equations in a basic study with specified inputs in which the results are applicable for many applications. Part II addressed the application of the equations in the Langley Aerothermodynamic Upwind Relaxation Algorithm (LAURA) computational code for high-speed entries in Earth's atmosphere. The results showed that the presented iterative scheme for solving the Stefan-Maxwell equations is an accurate and effective method as compared with solutions of the detailed equations. In general, good accuracy with the approximate equations cannot be guaranteed for a species or all species in a multi-component mixture. 'Corrected' forms of the approximate equations that ensured the diffusion mass fluxes sum to zero, as required, were more accurate than the uncorrected forms. Good accuracy, as compared with the Stefan- Maxwell results, were obtained with the 'corrected' approximate equations in defining the heating rates for the three Earth entries considered in Part II.

A Three-Fold Approach to the Heat Equation: Data, Modeling, Numerics

ERIC Educational Resources Information Center

Spayd, Kimberly; Puckett, James

2016-01-01

This article describes our modeling approach to teaching the one-dimensional heat (diffusion) equation in a one-semester undergraduate partial differential equations course. We constructed the apparatus for a demonstration of heat diffusion through a long, thin metal rod with prescribed temperatures at each end. The students observed the physical…

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.

Symmetry, Hopf bifurcation, and the emergence of cluster solutions in time delayed neural networks.

PubMed

Wang, Zhen; Campbell, Sue Ann

2017-11-01

We consider the networks of N identical oscillators with time delayed, global circulant coupling, modeled by a system of delay differential equations with Z N symmetry. We first study the existence of Hopf bifurcations induced by the coupling time delay and then use symmetric Hopf bifurcation theory to determine how these bifurcations lead to different patterns of symmetric cluster oscillations. We apply our results to a case study: a network of FitzHugh-Nagumo neurons with diffusive coupling. For this model, we derive the asymptotic stability, global asymptotic stability, absolute instability, and stability switches of the equilibrium point in the plane of coupling time delay (τ) and excitability parameter (a). We investigate the patterns of cluster oscillations induced by the time delay and determine the direction and stability of the bifurcating periodic orbits by employing the multiple timescales method and normal form theory. We find that in the region where stability switching occurs, the dynamics of the system can be switched from the equilibrium point to any symmetric cluster oscillation, and back to equilibrium point as the time delay is increased.

Stochastic theory of non-Markovian open quantum system

NASA Astrophysics Data System (ADS)

Zhao, Xinyu

In this thesis, a stochastic approach to solving non-Markovian open quantum system called "non-Markovian quantum state diffusion" (NMQSD) approach is discussed in details. The NMQSD approach can serve as an analytical and numerical tool to study the dynamics of the open quantum systems. We explore three main topics of the NMQSD approach. First, we extend the NMQSD approach to many-body open systems such as two-qubit system and coupled N-cavity system. Based on the exact NMQSD equations and the corresponding master equations, we investigate several interesting non-Markovian features due to the memory effect of the environment such as the entanglement generation in two-qubit system and the coherence and entanglement transfer between cavities. Second, we extend the original NMQSD approach to the case that system is coupled to a fermionic bath or a spin bath. By introducing the anti-commutative Grassmann noise and the fermionic coherent state, we derive a fermionic NMQSD equation and the corresponding master equation. The fermionic NMQSD is illustrated by several examples. In a single qubit dissipative example, we have explicitly demonstrated that the NMQSD approach and the ordinary quantum mechanics give rise to the exactly same results. We also show the difference between fermionic bath and bosonic bath. Third, we combine the bosonic and fermionic NMQSD approach to develop a unified NMQSD approach to study the case that an open system is coupled to a bosonic bath and a fermionic bath simultaneously. For all practical purposes, we develop a set of useful computer programs (NMQSD Toolbox) to implement the NMQSD equation in realistic computations. In particular, we develop an algorithm to calculate the exact O operator involved in the NMQSD equation. The NMQSD toolbox is designed to be user friendly, so it will be especially valuable for a non-expert who has interest to employ the NMQSD equation to solve a practical problem. Apart from the central topics on the NMQSD approach, we also study the environment-assisted error correction (EAEC) scheme. We have proposed two new schemes beyond the original EAEC scheme. Our schemes can be used to recover an unknown entangled initial state for a dephasing channel and recover an arbitrary unknown initial state for a dissipative channel using a generalized quantum measurement.

Good coupling for the multiscale patch scheme on systems with microscale heterogeneity

NASA Astrophysics Data System (ADS)

Bunder, J. E.; Roberts, A. J.; Kevrekidis, I. G.

2017-05-01

Computational simulation of microscale detailed systems is frequently only feasible over spatial domains much smaller than the macroscale of interest. The 'equation-free' methodology couples many small patches of microscale computations across space to empower efficient computational simulation over macroscale domains of interest. Motivated by molecular or agent simulations, we analyse the performance of various coupling schemes for patches when the microscale is inherently 'rough'. As a canonical problem in this universality class, we systematically analyse the case of heterogeneous diffusion on a lattice. Computer algebra explores how the dynamics of coupled patches predict the large scale emergent macroscale dynamics of the computational scheme. We determine good design for the coupling of patches by comparing the macroscale predictions from patch dynamics with the emergent macroscale on the entire domain, thus minimising the computational error of the multiscale modelling. The minimal error on the macroscale is obtained when the coupling utilises averaging regions which are between a third and a half of the patch. Moreover, when the symmetry of the inter-patch coupling matches that of the underlying microscale structure, patch dynamics predicts the desired macroscale dynamics to any specified order of error. The results confirm that the patch scheme is useful for macroscale computational simulation of a range of systems with microscale heterogeneity.

The influence of preferential flow on pressure propagation and landslide triggering of the Rocca Pitigliana landslide

NASA Astrophysics Data System (ADS)

Shao, Wei; Bogaard, Thom; Bakker, Mark; Berti, Matteo

2016-12-01

The fast pore water pressure response to rain events is an important triggering factor for slope instability. The fast pressure response may be caused by preferential flow that bypasses the soil matrix. Currently, most of the hydro-mechanical models simulate pore water pressure using a single-permeability model, which cannot quantify the effects of preferential flow on pressure propagation and landslide triggering. Previous studies showed that a model based on the linear-diffusion equation can simulate the fast pressure propagation in near-saturated landslides such as the Rocca Pitigliana landslide. In such a model, the diffusion coefficient depends on the degree of saturation, which makes it difficult to use the model for predictions. In this study, the influence of preferential flow on pressure propagation and slope stability is investigated with a 1D dual-permeability model coupled with an infinite-slope stability approach. The dual-permeability model uses two modified Darcy-Richards equations to simultaneously simulate the matrix flow and preferential flow in hillslopes. The simulated pressure head is used in an infinite-slope stability analysis to identify the influence of preferential flow on the fast pressure response and landslide triggering. The dual-permeability model simulates the height and arrival of the pressure peak reasonably well. Performance of the dual-permeability model is as good as or better than the linear-diffusion model even though the dual-permeability model is calibrated for two single pulse rain events only, while the linear-diffusion model is calibrated for each rain event separately. In conclusion, the 1D dual-permeability model is a promising tool for landslides under similar conditions.

Global Regularity and Time Decay for the 2D Magnetohydrodynamic Equations with Fractional Dissipation and Partial Magnetic Diffusion

NASA Astrophysics Data System (ADS)

Dong, Bo-Qing; Jia, Yan; Li, Jingna; Wu, Jiahong

2018-05-01

This paper focuses on a system of the 2D magnetohydrodynamic (MHD) equations with the kinematic dissipation given by the fractional operator (-Δ )^α and the magnetic diffusion by partial Laplacian. We are able to show that this system with any α >0 always possesses a unique global smooth solution when the initial data is sufficiently smooth. In addition, we make a detailed study on the large-time behavior of these smooth solutions and obtain optimal large-time decay rates. Since the magnetic diffusion is only partial here, some classical tools such as the maximal regularity property for the 2D heat operator can no longer be applied. A key observation on the structure of the MHD equations allows us to get around the difficulties due to the lack of full Laplacian magnetic diffusion. The results presented here are the sharpest on the global regularity problem for the 2D MHD equations with only partial magnetic diffusion.

Particle Filter-Based Recursive Data Fusion With Sensor Indexing for Large Core Neutron Flux Estimation

NASA Astrophysics Data System (ADS)

Tamboli, Prakash Kumar; Duttagupta, Siddhartha P.; Roy, Kallol

2017-06-01

We introduce a sequential importance sampling particle filter (PF)-based multisensor multivariate nonlinear estimator for estimating the in-core neutron flux distribution for pressurized heavy water reactor core. Many critical applications such as reactor protection and control rely upon neutron flux information, and thus their reliability is of utmost importance. The point kinetic model based on neutron transport conveniently explains the dynamics of nuclear reactor. The neutron flux in the large core loosely coupled reactor is sensed by multiple sensors measuring point fluxes located at various locations inside the reactor core. The flux values are coupled to each other through diffusion equation. The coupling facilitates redundancy in the information. It is shown that multiple independent data about the localized flux can be fused together to enhance the estimation accuracy to a great extent. We also propose the sensor anomaly handling feature in multisensor PF to maintain the estimation process even when the sensor is faulty or generates data anomaly.

A framework for discrete stochastic simulation on 3D moving boundary domains

DOE PAGES

Drawert, Brian; Hellander, Stefan; Trogdon, Michael; ...

2016-11-14

We have developed a method for modeling spatial stochastic biochemical reactions in complex, three-dimensional, and time-dependent domains using the reaction-diffusion master equation formalism. In particular, we look to address the fully coupled problems that arise in systems biology where the shape and mechanical properties of a cell are determined by the state of the biochemistry and vice versa. To validate our method and characterize the error involved, we compare our results for a carefully constructed test problem to those of a microscale implementation. Finally, we demonstrate the effectiveness of our method by simulating a model of polarization and shmoo formationmore » during the mating of yeast. The method is generally applicable to problems in systems biology where biochemistry and mechanics are coupled, and spatial stochastic effects are critical.« less

Multidimensional Fuel Performance Code: BISON

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

BISON is a finite element based nuclear fuel performance code applicable to a variety of fuel forms including light water reactor fuel rods, TRISO fuel particles, and metallic rod and plate fuel (Refs. [a, b, c]). It solves the fully-coupled equations of thermomechanics and species diffusion and includes important fuel physics such as fission gas release and material property degradation with burnup. BISON is based on the MOOSE framework (Ref. [d]) and can therefore efficiently solve problems on 1-, 2- or 3-D meshes using standard workstations or large high performance computers. BISON is also coupled to a MOOSE-based mesoscale phasemore » field material property simulation capability (Refs. [e, f]). As described here, BISON includes the code library named FOX, which was developed concurrent with BISON. FOX contains material and behavioral models that are specific to oxide fuels.« less

Combination of microscopic model and VoF-multiphase approach for numerical simulation of nodular cast iron solidification

NASA Astrophysics Data System (ADS)

Subasic, E.; Huang, C.; Jakumeit, J.; Hediger, F.

2015-06-01

The ongoing increase in the size and capacity of state-of-the-art wind power plants is highlighting the need to reduce the weight of critical components, such as hubs, main shaft bearing housings, gear box housings and support bases. These components are manufactured as nodular iron castings (spheroid graphite iron, or SGI). A weight reduction of up to 20% is achievable by optimizing the geometry to minimize volume, thus enabling significant downsizing of wind power plants. One method for enhancing quality control in the production of thick-walled SGI castings, and thus reducing tolerances and, consequently, enabling castings of smaller volume is via a casting simulation of mould filling and solidification based on a combination of microscopic model and VoF-multiphase approach. Coupled fluid flow with heat transport and phase transformation kinetics during solidification is described by partial differential equations and solved using the finite volume method. The flow of multiple phases is described using a volume of fluid approach. Mass conservation equations are solved separately for both liquid and solid phases. At the micro-level, the diffusion-controlled growth model for grey iron eutectic grains by Wetterfall et al. is combined with a growth model for white iron eutectic grains. The micro-solidification model is coupled with macro-transport equations via source terms in the energy and continuity equations. As a first step the methodology was applied to a simple geometry to investigate the impact of mould-filling on the grey-to-white transition prediction in nodular cast iron.

Fisher equation for anisotropic diffusion: simulating South American human dispersals.

PubMed

Martino, Luis A; Osella, Ana; Dorso, Claudio; Lanata, José L

2007-09-01

The Fisher equation is commonly used to model population dynamics. This equation allows describing reaction-diffusion processes, considering both population growth and diffusion mechanism. Some results have been reported about modeling human dispersion, always assuming isotropic diffusion. Nevertheless, it is well-known that dispersion depends not only on the characteristics of the habitats where individuals are but also on the properties of the places where they intend to move, then isotropic approaches cannot adequately reproduce the evolution of the wave of advance of populations. Solutions to a Fisher equation are difficult to obtain for complex geometries, moreover, when anisotropy has to be considered and so few studies have been conducted in this direction. With this scope in mind, we present in this paper a solution for a Fisher equation, introducing anisotropy. We apply a finite difference method using the Crank-Nicholson approximation and analyze the results as a function of the characteristic parameters. Finally, this methodology is applied to model South American human dispersal.

Viscous regularization of the full set of nonequilibrium-diffusion Grey Radiation-Hydrodynamic equations

DOE PAGES

Delchini, Marc O.; Ragusa, Jean C.; Ferguson, Jim

2017-02-17

A viscous regularization technique, based on the local entropy residual, was proposed by Delchini et al. (2015) to stabilize the nonequilibrium-diffusion Grey Radiation-Hydrodynamic equations using an artificial viscosity technique. This viscous regularization is modulated by the local entropy production and is consistent with the entropy minimum principle. However, Delchini et al. (2015) only based their work on the hyperbolic parts of the Grey Radiation-Hydrodynamic equations and thus omitted the relaxation and diffusion terms present in the material energy and radiation energy equations. Here in this paper, we extend the theoretical grounds for the method and derive an entropy minimum principlemore » for the full set of nonequilibrium-diffusion Grey Radiation-Hydrodynamic equations. This further strengthens the applicability of the entropy viscosity method as a stabilization technique for radiation-hydrodynamic shock simulations. Radiative shock calculations using constant and temperature-dependent opacities are compared against semi-analytical reference solutions, and we present a procedure to perform spatial convergence studies of such simulations.« less

Localization and Ballistic Diffusion for the Tempered Fractional Brownian-Langevin Motion

NASA Astrophysics Data System (ADS)

Chen, Yao; Wang, Xudong; Deng, Weihua

2017-10-01

This paper discusses the tempered fractional Brownian motion (tfBm), its ergodicity, and the derivation of the corresponding Fokker-Planck equation. Then we introduce the generalized Langevin equation with the tempered fractional Gaussian noise for a free particle, called tempered fractional Langevin equation (tfLe). While the tfBm displays localization diffusion for the long time limit and for the short time its mean squared displacement (MSD) has the asymptotic form t^{2H}, we show that the asymptotic form of the MSD of the tfLe transits from t^2 (ballistic diffusion for short time) to t^{2-2H}, and then to t^2 (again ballistic diffusion for long time). On the other hand, the overdamped tfLe has the transition of the diffusion type from t^{2-2H} to t^2 (ballistic diffusion). The tfLe with harmonic potential is also considered.

A Nonlinear Diffusion Equation-Based Model for Ultrasound Speckle Noise Removal

NASA Astrophysics Data System (ADS)

Zhou, Zhenyu; Guo, Zhichang; Zhang, Dazhi; Wu, Boying

2018-04-01

Ultrasound images are contaminated by speckle noise, which brings difficulties in further image analysis and clinical diagnosis. In this paper, we address this problem in the view of nonlinear diffusion equation theories. We develop a nonlinear diffusion equation-based model by taking into account not only the gradient information of the image, but also the information of the gray levels of the image. By utilizing the region indicator as the variable exponent, we can adaptively control the diffusion type which alternates between the Perona-Malik diffusion and the Charbonnier diffusion according to the image gray levels. Furthermore, we analyze the proposed model with respect to the theoretical and numerical properties. Experiments show that the proposed method achieves much better speckle suppression and edge preservation when compared with the traditional despeckling methods, especially in the low gray level and low-contrast regions.

Nature of self-diffusion in two-dimensional fluids

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

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.

Recovery Discontinuous Galerkin Jacobian-Free Newton-Krylov Method for All-Speed Flows

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

HyeongKae Park; Robert Nourgaliev; Vincent Mousseau

2008-07-01

A novel numerical algorithm (rDG-JFNK) for all-speed fluid flows with heat conduction and viscosity is introduced. The rDG-JFNK combines the Discontinuous Galerkin spatial discretization with the implicit Runge-Kutta time integration under the Jacobian-free Newton-Krylov framework. We solve fully-compressible Navier-Stokes equations without operator-splitting of hyperbolic, diffusion and reaction terms, which enables fully-coupled high-order temporal discretization. The stability constraint is removed due to the L-stable Explicit, Singly Diagonal Implicit Runge-Kutta (ESDIRK) scheme. The governing equations are solved in the conservative form, which allows one to accurately compute shock dynamics, as well as low-speed flows. For spatial discretization, we develop a “recovery” familymore » of DG, exhibiting nearly-spectral accuracy. To precondition the Krylov-based linear solver (GMRES), we developed an “Operator-Split”-(OS) Physics Based Preconditioner (PBP), in which we transform/simplify the fully-coupled system to a sequence of segregated scalar problems, each can be solved efficiently with Multigrid method. Each scalar problem is designed to target/cluster eigenvalues of the Jacobian matrix associated with a specific physics.« less

MPSalsa Version 1.5: A Finite Element Computer Program for Reacting Flow Problems: Part 1 - Theoretical Development

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

Devine, K.D.; Hennigan, G.L.; Hutchinson, S.A.

1999-01-01

The theoretical background for the finite element computer program, MPSalsa Version 1.5, is presented in detail. MPSalsa is designed to solve laminar or turbulent low Mach number, two- or three-dimensional incompressible and variable density reacting fluid flows on massively parallel computers, using a Petrov-Galerkin finite element formulation. The code has the capability to solve coupled fluid flow (with auxiliary turbulence equations), heat transport, multicomponent species transport, and finite-rate chemical reactions, and to solve coupled multiple Poisson or advection-diffusion-reaction equations. The program employs the CHEMKIN library to provide a rigorous treatment of multicomponent ideal gas kinetics and transport. Chemical reactions occurringmore » in the gas phase and on surfaces are treated by calls to CHEMKIN and SURFACE CHEMK3N, respectively. The code employs unstructured meshes, using the EXODUS II finite element database suite of programs for its input and output files. MPSalsa solves both transient and steady flows by using fully implicit time integration, an inexact Newton method and iterative solvers based on preconditioned Krylov methods as implemented in the Aztec. solver library.« less

Multi-physics transient simulation of monolithic niobium dioxide-tantalum dioxide memristor-selector structures

NASA Astrophysics Data System (ADS)

Sevic, John F.; Kobayashi, Nobuhiko P.

2017-10-01

Self-assembled niobium dioxide (NbO2) thin-film selectors self-aligned to tantalum dioxide (TaO2) memristive memory cells are studied by a multi-physics transient solution of the heat equation coupled to the nonlinear current continuity equation. While a compact model can resolve the quasi-static bulk negative differential resistance (NDR), a self-consistent coupled transport formulation provides a non-equilibrium picture of NbO2-TaO2 selector-memristor operation ab initio. By employing the drift-diffusion transport approximation, a finite element method is used to study the dynamic electrothermal behavior of our experimentally obtained selector-memristor devices, showing that existing conditions are suitable for electroformation of NbO2 selector thin-films. Both transient and steady-state simulations support our theory, suggesting that the phase change due to insulator-metal transition is responsible for NbO2 selector NDR in our as-fabricated selector-memristor devices. Simulation results further suggest that TiN nano-via may play a central role in electroforming, as its dimensions and material properties establish the mutual electrothermal interaction between TiN nano-via and the selector-memristor.

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

NASA Astrophysics Data System (ADS)

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

2013-03-01

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

Generic reactive transport codes as flexible tools to integrate soil organic matter degradation models with water, transport and geochemistry in soils

NASA Astrophysics Data System (ADS)

Jacques, Diederik; Gérard, Fréderic; Mayer, Uli; Simunek, Jirka; Leterme, Bertrand

2016-04-01

A large number of organic matter degradation, CO2 transport and dissolved organic matter models have been developed during the last decades. However, organic matter degradation models are in many cases strictly hard-coded in terms of organic pools, degradation kinetics and dependency on environmental variables. The scientific input of the model user is typically limited to the adjustment of input parameters. In addition, the coupling with geochemical soil processes including aqueous speciation, pH-dependent sorption and colloid-facilitated transport are not incorporated in many of these models, strongly limiting the scope of their application. Furthermore, the most comprehensive organic matter degradation models are combined with simplified representations of flow and transport processes in the soil system. We illustrate the capability of generic reactive transport codes to overcome these shortcomings. The formulations of reactive transport codes include a physics-based continuum representation of flow and transport processes, while biogeochemical reactions can be described as equilibrium processes constrained by thermodynamic principles and/or kinetic reaction networks. The flexibility of these type of codes allows for straight-forward extension of reaction networks, permits the inclusion of new model components (e.g.: organic matter pools, rate equations, parameter dependency on environmental conditions) and in such a way facilitates an application-tailored implementation of organic matter degradation models and related processes. A numerical benchmark involving two reactive transport codes (HPx and MIN3P) demonstrates how the process-based simulation of transient variably saturated water flow (Richards equation), solute transport (advection-dispersion equation), heat transfer and diffusion in the gas phase can be combined with a flexible implementation of a soil organic matter degradation model. The benchmark includes the production of leachable organic matter and inorganic carbon in the aqueous and gaseous phases, as well as different decomposition functions with first-order, linear dependence or nonlinear dependence on a biomass pool. In addition, we show how processes such as local bioturbation (bio-diffusion) can be included implicitly through a Fickian formulation of transport of soil organic matter. Coupling soil organic matter models with generic and flexible reactive transport codes offers a valuable tool to enhance insights into coupled physico-chemical processes at different scales within the scope of C-biogeochemical cycles, possibly linked with other chemical elements such as plant nutrients and pollutants.

Vapor Transport Within the Thermal Diffusion Cloud Chamber

NASA Technical Reports Server (NTRS)

Ferguson, Frank T.; Heist, Richard H.; Nuth, Joseph A., III

2000-01-01

A review of the equations used to determine the 1-D vapor transport in the thermal diffusion cloud chamber (TDCC) is presented. These equations closely follow those of the classical Stefan tube problem in which there is transport of a volatile species through a noncondensible, carrier gas. In both cases, the very plausible assumption is made that the background gas is stagnant. Unfortunately, this assumption results in a convective flux which is inconsistent with the momentum and continuity equations for both systems. The approximation permits derivation of an analytical solution for the concentration profile in the Stefan tube, but there is no computational advantage in the case of the TDCC. Furthermore, the degree of supersaturation is a sensitive function of the concentration profile in the TD CC and the stagnant background gas approximation can make a dramatic difference in the calculated supersaturation. In this work, the equations typically used with a TDCC are compared with very general transport equations describing the 1-D diffusion of the volatile species. Whereas no pressure dependence is predicted with the typical equations, a strong pressure dependence is present with the more general equations given in this work. The predicted behavior is consistent with observations in diffusion cloud experiments. It appears that the new equations may account for much of the pressure dependence noted in TDCC experiments, but a comparison between the new equations and previously obtained experimental data are needed for verification.

Analysis of Mathematical Modelling on Potentiometric Biosensors

PubMed Central

Mehala, N.; Rajendran, L.

2014-01-01

A mathematical model of potentiometric enzyme electrodes for a nonsteady condition has been developed. The model is based on the system of two coupled nonlinear time-dependent reaction diffusion equations for Michaelis-Menten formalism that describes the concentrations of substrate and product within the enzymatic layer. Analytical expressions for the concentration of substrate and product and the corresponding flux response have been derived for all values of parameters using the new homotopy perturbation method. Furthermore, the complex inversion formula is employed in this work to solve the boundary value problem. The analytical solutions obtained allow a full description of the response curves for only two kinetic parameters (unsaturation/saturation parameter and reaction/diffusion parameter). Theoretical descriptions are given for the two limiting cases (zero and first order kinetics) and relatively simple approaches for general cases are presented. All the analytical results are compared with simulation results using Scilab/Matlab program. The numerical results agree with the appropriate theories. PMID:25969765

Analysis of mathematical modelling on potentiometric biosensors.

PubMed

Mehala, N; Rajendran, L

2014-01-01

A mathematical model of potentiometric enzyme electrodes for a nonsteady condition has been developed. The model is based on the system of two coupled nonlinear time-dependent reaction diffusion equations for Michaelis-Menten formalism that describes the concentrations of substrate and product within the enzymatic layer. Analytical expressions for the concentration of substrate and product and the corresponding flux response have been derived for all values of parameters using the new homotopy perturbation method. Furthermore, the complex inversion formula is employed in this work to solve the boundary value problem. The analytical solutions obtained allow a full description of the response curves for only two kinetic parameters (unsaturation/saturation parameter and reaction/diffusion parameter). Theoretical descriptions are given for the two limiting cases (zero and first order kinetics) and relatively simple approaches for general cases are presented. All the analytical results are compared with simulation results using Scilab/Matlab program. The numerical results agree with the appropriate theories.

The role of intraluminal thrombus on oxygen transport in abdominal aortic aneurysms

NASA Astrophysics Data System (ADS)

Madhavan, Sudharsan; Cherry Kemmerling, Erica

2017-11-01

Abdominal aortic aneurysm is ranked as the 13th leading cause of death in the United States. The presence of intraluminal thrombus is thought to cause hypoxia in the vessel wall eventually aggravating the condition. Our work investigates oxygen transport and consumption in a patient-specific model of an abdominal aortic aneurysm. The model includes intraluminal thrombus and consists of the abdominal aorta, renal arteries, and iliac arteries. Oxygen transport to and within the aortic wall layer was modeled, accounting for oxygen consumption and diffusion. Flow and transport in the lumen layer were modeled using coupled Navier-Stokes and scalar transport equations. The thrombus layer was assumed to be biomechanically inactive but permeable to oxygen transport in accordance with previously-measured diffusion coefficients. Plots of oxygen concentration through the layers illustrating reduced oxygen supply to the vessel walls in parts of the model that include thrombus will be presented.

Mathematical Modeling of Decarburization in Levitated Fe-Cr-C Droplets

NASA Astrophysics Data System (ADS)

Gao, Lei; Shi, Zhe; Yang, Yindong; Li, Donghui; Zhang, Guifang; McLean, Alexander; Chattopadhyay, Kinnor

2018-04-01

Using carbon dioxide to replace oxygen as an alternative oxidant gas has proven to be a viable solution in the decarburization process, with potential for industrial applications. In a recent study, the transport phenomena governing the carbon dioxide decarburization process through the use of electromagnetic levitation (EML) was examined. CO2/CO mass transfer was found to be the principal reaction rate control step, as a result gas diffusion has gained significant attention. In the present study, gas diffusion during decarburization process was investigated using computational fluid dynamics (CFD) modeling coupled with chemical reactions. The resulting model was verified through experimental data in a published paper, and employed to provide insights on phenomena typically unobservable through experiments. Based on the results, a new correction of the Frössling equation was presented which better represents the mass transfer phenomena at the metal-gas interface within the range of this research.

Stochastic fire-diffuse-fire model with realistic cluster dynamics.

PubMed

Calabrese, Ana; Fraiman, Daniel; Zysman, Daniel; Ponce Dawson, Silvina

2010-09-01

Living organisms use waves that propagate through excitable media to transport information. Ca2+ waves are a paradigmatic example of this type of processes. A large hierarchy of Ca2+ signals that range from localized release events to global waves has been observed in Xenopus laevis oocytes. In these cells, Ca2+ release occurs trough inositol 1,4,5-trisphosphate receptors (IP3Rs) which are organized in clusters of channels located on the membrane of the endoplasmic reticulum. In this article we construct a stochastic model for a cluster of IP3R 's that replicates the experimental observations reported in [D. Fraiman, Biophys. J. 90, 3897 (2006)]. We then couple this phenomenological cluster model with a reaction-diffusion equation, so as to have a discrete stochastic model for calcium dynamics. The model we propose describes the transition regimes between isolated release and steadily propagating waves as the IP3 concentration is increased.

Boundary particle method for Laplace transformed time fractional diffusion equations

NASA Astrophysics Data System (ADS)

Fu, Zhuo-Jia; Chen, Wen; Yang, Hai-Tian

2013-02-01

This paper develops a novel boundary meshless approach, Laplace transformed boundary particle method (LTBPM), for numerical modeling of time fractional diffusion equations. It implements Laplace transform technique to obtain the corresponding time-independent inhomogeneous equation in Laplace space and then employs a truly boundary-only meshless boundary particle method (BPM) to solve this Laplace-transformed problem. Unlike the other boundary discretization methods, the BPM does not require any inner nodes, since the recursive composite multiple reciprocity technique (RC-MRM) is used to convert the inhomogeneous problem into the higher-order homogeneous problem. Finally, the Stehfest numerical inverse Laplace transform (NILT) is implemented to retrieve the numerical solutions of time fractional diffusion equations from the corresponding BPM solutions. In comparison with finite difference discretization, the LTBPM introduces Laplace transform and Stehfest NILT algorithm to deal with time fractional derivative term, which evades costly convolution integral calculation in time fractional derivation approximation and avoids the effect of time step on numerical accuracy and stability. Consequently, it can effectively simulate long time-history fractional diffusion systems. Error analysis and numerical experiments demonstrate that the present LTBPM is highly accurate and computationally efficient for 2D and 3D time fractional diffusion equations.

Large-scale optimization-based non-negative computational framework for diffusion equations: Parallel implementation and performance studies

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

Chang, Justin; Karra, Satish; Nakshatrala, Kalyana B.

It is well-known that the standard Galerkin formulation, which is often the formulation of choice under the finite element method for solving self-adjoint diffusion equations, does not meet maximum principles and the non-negative constraint for anisotropic diffusion equations. Recently, optimization-based methodologies that satisfy maximum principles and the non-negative constraint for steady-state and transient diffusion-type equations have been proposed. To date, these methodologies have been tested only on small-scale academic problems. The purpose of this paper is to systematically study the performance of the non-negative methodology in the context of high performance computing (HPC). PETSc and TAO libraries are, respectively, usedmore » for the parallel environment and optimization solvers. For large-scale problems, it is important for computational scientists to understand the computational performance of current algorithms available in these scientific libraries. The numerical experiments are conducted on the state-of-the-art HPC systems, and a single-core performance model is used to better characterize the efficiency of the solvers. Furthermore, our studies indicate that the proposed non-negative computational framework for diffusion-type equations exhibits excellent strong scaling for real-world large-scale problems.« less