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

Pre-Darcy flow in tight and shale formations

NASA Astrophysics Data System (ADS)

Dejam, Morteza; Hassanzadeh, Hassan; Chen, Zhangxin

2017-11-01

There are evidences that the fluid flow in tight and shale formations does not follow Darcy law, which is identified as pre-Darcy flow. Here, the unsteady linear flow of a slightly compressible fluid under the action of pre-Darcy flow is modeled and a generalized Boltzmann transformation technique is used to solve the corresponding highly nonlinear diffusivity equation analytically. The effect of pre-Darcy flow on the pressure diffusion in a homogenous formation is studied in terms of the nonlinear exponent, m, and the threshold pressure gradient, G1. In addition, the pressure gradient, flux, and cumulative production per unit area for different m and G1 are compared with the classical solution of the diffusivity equation based on Darcy flow. Department of Petroleum Engineering in College of Engineering and Applied Science at University of Wyoming and NSERC/AI-EES(AERI)/Foundation CMG and AITF (iCORE) Chairs in Department of Chemical and Petroleum Engineering at University of Calgary.

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.

Formulation, Implementation and Validation of a Two-Fluid model in a Fuel Cell CFD Code

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

Jain, Kunal; Cole, J. Vernon; Kumar, Sanjiv

2008-12-01

Water management is one of the main challenges in PEM Fuel Cells. While water is essential for membrane electrical conductivity, excess liquid water leads to flooding of catalyst layers. Despite the fact that accurate prediction of two-phase transport is key for optimal water management, understanding of the two-phase transport in fuel cells is relatively poor. Wang et. al. have studied the two-phase transport in the channel and diffusion layer separately using a multiphase mixture model. The model fails to accurately predict saturation values for high humidity inlet streams. Nguyen et. al. developed a two-dimensional, two-phase, isothermal, isobaric, steady state modelmore » of the catalyst and gas diffusion layers. The model neglects any liquid in the channel. Djilali et. al. developed a three-dimensional two-phase multicomponent model. The model is an improvement over previous models, but neglects drag between the liquid and the gas phases in the channel. In this work, we present a comprehensive two-fluid model relevant to fuel cells. Models for two-phase transport through Channel, Gas Diffusion Layer (GDL) and Channel-GDL interface, are discussed. In the channel, the gas and liquid pressures are assumed to be same. The surface tension effects in the channel are incorporated using the continuum surface force (CSF) model. The force at the surface is expressed as a volumetric body force and added as a source to the momentum equation. In the GDL, the gas and liquid are assumed to be at different pressures. The difference in the pressures (capillary pressure) is calculated using an empirical correlations. At the Channel-GDL interface, the wall adhesion affects need to be taken into account. SIMPLE-type methods recast the continuity equation into a pressure-correction equation, the solution of which then provides corrections for velocities and pressures. However, in the two-fluid model, the presence of two phasic continuity equations gives more freedom and more complications. A general approach would be to form a mixture continuity equation by linearly combining the phasic continuity equations using appropriate weighting factors. Analogous to mixture equation for pressure correction, a difference equation is used for the volume/phase fraction by taking the difference between the phasic continuity equations. The relative advantages of the above mentioned algorithmic variants for computing pressure correction and volume fractions are discussed and quantitatively assessed. Preliminary model validation is done for each component of the fuel cell. The two-phase transport in the channel is validated using empirical correlations. Transport in the GDL is validated against results obtained from LBM and VOF simulation techniques. The Channel-GDL interface transport will be validated against experiment and empirical correlation of droplet detachment at the interface.« less

Pore-scale modeling of phase change in porous media

NASA Astrophysics Data System (ADS)

Juanes, Ruben; Cueto-Felgueroso, Luis; Fu, Xiaojing

2017-11-01

One of the main open challenges in pore-scale modeling is the direct simulation of flows involving multicomponent mixtures with complex phase behavior. Reservoir fluid mixtures are often described through cubic equations of state, which makes diffuse interface, or phase field theories, particularly appealing as a modeling framework. What is still unclear is whether equation-of-state-driven diffuse-interface models can adequately describe processes where surface tension and wetting phenomena play an important role. Here we present a diffuse interface model of single-component, two-phase flow (a van der Waals fluid) in a porous medium under different wetting conditions. We propose a simplified Darcy-Korteweg model that is appropriate to describe flow in a Hele-Shaw cell or a micromodel, with a gap-averaged velocity. We study the ability of the diffuse-interface model to capture capillary pressure and the dynamics of vaporization/condensation fronts, and show that the model reproduces pressure fluctuations that emerge from abrupt interface displacements (Haines jumps) and from the break-up of wetting films.

Self-diffusivity and interdiffusivity of molten aluminum-copper alloys under pressure, derived from molecular dynamics.

PubMed

Rudd, Robert E; Cabot, William H; Caspersen, Kyle J; Greenough, Jeffrey A; Richards, David F; Streitz, Frederick H; Miller, Paul L

2012-03-01

We use molecular dynamics (MD) to simulate diffusion in molten aluminum-copper (AlCu) alloys. The self-diffusivities and Maxwell-Stefan diffusivities are calculated for AlCu mixtures using the Green-Kubo formulas at temperatures from 1000 to 4000 K and pressures from 0 to 25 GPa, along with additional points at higher temperatures and pressures. The diffusivities are corrected for finite-size effects. The Maxwell-Stefan diffusivity is compared to the diffusivity calculated from the self-diffusivities using a generalization of the Darken equation. We find that the effects of cross-correlation are small. Using the calculated self-diffusivities, we have assessed whether dilute hard-sphere and dilute Lennard-Jones models apply to the molten mixture. Neither of the two dilute gas diffusivities describes the diffusivity in molten Al and Cu. We report generalized analytic models for the self-diffusivities and interdiffusivity (mutual diffusivity) that fit the MD results well. The MD-derived transport coefficients are in good agreement with the available experimental data. We also report MD calculations of the viscosity and an analytic fit to those results. The ionic thermal conductivity is discussed briefly.

Self-diffusivity and interdiffusivity of molten aluminum-copper alloys under pressure, derived from molecular dynamics

NASA Astrophysics Data System (ADS)

Rudd, Robert E.; Cabot, William H.; Caspersen, Kyle J.; Greenough, Jeffrey A.; Richards, David F.; Streitz, Frederick H.; Miller, Paul L.

2012-03-01

We use molecular dynamics (MD) to simulate diffusion in molten aluminum-copper (AlCu) alloys. The self-diffusivities and Maxwell-Stefan diffusivities are calculated for AlCu mixtures using the Green-Kubo formulas at temperatures from 1000 to 4000 K and pressures from 0 to 25 GPa, along with additional points at higher temperatures and pressures. The diffusivities are corrected for finite-size effects. The Maxwell-Stefan diffusivity is compared to the diffusivity calculated from the self-diffusivities using a generalization of the Darken equation. We find that the effects of cross-correlation are small. Using the calculated self-diffusivities, we have assessed whether dilute hard-sphere and dilute Lennard-Jones models apply to the molten mixture. Neither of the two dilute gas diffusivities describes the diffusivity in molten Al and Cu. We report generalized analytic models for the self-diffusivities and interdiffusivity (mutual diffusivity) that fit the MD results well. The MD-derived transport coefficients are in good agreement with the available experimental data. We also report MD calculations of the viscosity and an analytic fit to those results. The ionic thermal conductivity is discussed briefly.

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

NASA Astrophysics Data System (ADS)

Hsieh, T.

1986-10-01

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

On Thermodiffusion and Gauge Transformations for Thermodynamic Fluxes and Driving Forces

NASA Astrophysics Data System (ADS)

Goldobin, D. S.

2017-12-01

We discuss the molecular diffusion transport in infinitely dilute liquid solutions under nonisothermal conditions. This discussion is motivated by an occurring misinterpretation of thermodynamic transport equations written in terms of chemical potential in the presence of temperature gradient. The transport equations contain the contributions owned by a gauge transformation related to the fact that chemical potential is determined up to the summand of form ( AT + B) with arbitrary constants A and B, where constant A is owned by the entropy invariance with respect to shifts by a constant value and B is owned by the potential energy invariance with respect to shifts by a constant value. The coefficients of the cross-effect terms in thermodynamic fluxes are contributed by this gauge transformation and, generally, are not the actual cross-effect physical transport coefficients. Our treatment is based on consideration of the entropy balance and suggests a promising hint for attempts of evaluation of the thermal diffusion constant from the first principles. We also discuss the impossibility of the "barodiffusion" for dilute solutions, understood in a sense of diffusion flux driven by the pressure gradient itself. When one speaks of "barodiffusion" terms in literature, these terms typically represent the drift in external potential force field (e.g., electric or gravitational fields), where in the final equations the specific force on molecules is substituted with an expression with the hydrostatic pressure gradient this external force field produces. Obviously, the interpretation of the latter as barodiffusion is fragile and may hinder the accounting for the diffusion fluxes produced by the pressure gradient itself.

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

NASA Astrophysics Data System (ADS)

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

2013-08-01

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

Finite Element Analysis of Poroelastic Composites Undergoing Thermal and Gas Diffusion

NASA Technical Reports Server (NTRS)

Salamon, N. J. (Principal Investigator); Sullivan, Roy M.; Lee, Sunpyo

1995-01-01

A theory for time-dependent thermal and gas diffusion in mechanically time-rate-independent anisotropic poroelastic composites has been developed. This theory advances previous work by the latter two authors by providing for critical transverse shear through a three-dimensional axisymmetric formulation and using it in a new hypothesis for determining the Biot fluid pressure-solid stress coupling factor. The derived governing equations couple material deformation with temperature and internal pore pressure and more strongly couple gas diffusion and heat transfer than the previous theory. Hence the theory accounts for the interactions between conductive heat transfer in the porous body and convective heat carried by the mass flux through the pores. The Bubnov Galerkin finite element method is applied to the governing equations to transform them into a semidiscrete finite element system. A numerical procedure is developed to solve the coupled equations in the space and time domains. The method is used to simulate two high temperature tests involving thermal-chemical decomposition of carbon-phenolic composites. In comparison with measured data, the results are accurate. Moreover unlike previous work, for a single set of poroelastic parameters, they are consistent with two measurements in a restrained thermal growth test.

Large Eddy Simulation of a Supercritical Turbulent Mixing Layer

NASA Astrophysics Data System (ADS)

Sheikhi, Reza; Hadi, Fatemeh; Safari, Mehdi

2017-11-01

Supercritical turbulent flows are relevant to a wide range of applications such as supercritical power cycles, gas turbine combustors, rocket propulsion and internal combustion engines. Large eddy simulation (LES) analysis of such flows involves solving mass, momentum, energy and scalar transport equations with inclusion of generalized diffusion fluxes. These equations are combined with a real gas equation of state and the corresponding thermodynamic mixture variables. Subgrid scale models are needed for not only the conventional convective terms but also the additional high pressure effects arising due to the nonlinearity associated with generalized diffusion fluxes and real gas equation of state. In this study, LES is carried out to study the high pressure turbulent mixing of methane with carbon dioxide in a temporally developing mixing layer under supercritical condition. LES results are assessed by comparing with data obtained from direct numerical simulation (DNS) of the same layer. LES predictions agree favorably with DNS data and represent several key supercritical turbulent flow features such as high density gradient regions. Supported by DOE Grant SC0017097; computational support is provided by DOE National Energy Research Scientific Computing Center.

Simulations of surface winds at the Viking Lander sites using a one-level model

NASA Technical Reports Server (NTRS)

Bridger, Alison F. C.; Haberle, Robert M.

1992-01-01

The one-level model developed by Mass and Dempsey for use in predicting surface flows in regions of complex terrain was adapted to simulate surface flows at the Viking lander sites on Mars. In the one-level model, prediction equations for surface winds and temperatures are formulated and solved. Surface temperatures change with time in response to diabatic heating, horizontal advection, adiabatic heating and cooling effects, and horizontal diffusion. Surface winds can change in response to horizontal advection, pressure gradient forces, Coriolis forces, surface drag, and horizontal diffusion. Surface pressures are determined by integration of the hydrostatic equation from the surface to some reference level. The model has successfully simulated surface flows under a variety of conditions in complex-terrain regions on Earth.

Effect of Static Strains on Diffusion

NASA Technical Reports Server (NTRS)

Girifalco, L. A.; Grimes, H. H.

1961-01-01

A theory is developed that gives the diffusion coefficient in strained systems as an exponential function of the strain. This theory starts with the statistical theory of the atomic jump frequency as developed by Vineyard. The parameter determining the effect of strain on diffusion is related to the changes in the inter-atomic forces with strain. Comparison of the theory with published experimental results for the effect of pressure on diffusion shows that the experiments agree with the form of the theoretical equation in all cases within experimental error.

Effects of pressure and fuel dilution on coflow laminar methane-air diffusion flames: A computational and experimental study

NASA Astrophysics Data System (ADS)

Cao, Su; Ma, Bin; Giassi, Davide; Bennett, Beth Anne V.; Long, Marshall B.; Smooke, Mitchell D.

2018-03-01

In this study, the influence of pressure and fuel dilution on the structure and geometry of coflow laminar methane-air diffusion flames is examined. A series of methane-fuelled, nitrogen-diluted flames has been investigated both computationally and experimentally, with pressure ranging from 1.0 to 2.7 atm and CH4 mole fraction ranging from 0.50 to 0.65. Computationally, the MC-Smooth vorticity-velocity formulation was employed to describe the reactive gaseous mixture, and soot evolution was modelled by sectional aerosol equations. The governing equations and boundary conditions were discretised on a two-dimensional computational domain by finite differences, and the resulting set of fully coupled, strongly nonlinear equations was solved simultaneously at all points using a damped, modified Newton's method. Experimentally, chemiluminescence measurements of CH* were taken to determine its relative concentration profile and the structure of the flame front. A thin-filament ratio pyrometry method using a colour digital camera was employed to determine the temperature profiles of the non-sooty, atmospheric pressure flames, while soot volume fraction was quantified, after evaluation of soot temperature, through an absolute light calibration using a thermocouple. For a broad spectrum of flames in atmospheric and elevated pressures, the computed and measured flame quantities were examined to characterise the influence of pressure and fuel dilution, and the major conclusions were as follows: (1) maximum temperature increases with increasing pressure or CH4 concentration; (2) lift-off height decreases significantly with increasing pressure, modified flame length is roughly independent of pressure, and flame radius decreases with pressure approximately as P-1/2; and (3) pressure and fuel stream dilution significantly affect the spatial distribution and the peak value of the soot volume fraction.

Translational and Rotational Diffusion in Water in the Gigapascal Range

NASA Astrophysics Data System (ADS)

Bove, L. E.; Klotz, S.; Strässle, Th.; Koza, M.; Teixeira, J.; Saitta, A. M.

2013-11-01

First measurements of the self-dynamics of liquid water in the GPa range are reported. The GPa range has here become accessible through a new setup for the Paris-Edinburgh press specially conceived for quasielastic neutron scattering studies. A direct measurement of both the translational and rotational diffusion coefficients of water along the 400 K isotherm up to 3 GPa, corresponding to the melting point of ice VII, is provided and compared with molecular dynamics simulations. The translational diffusion is observed to strongly decrease with pressure, though its variation slows down for pressures higher than 1 GPa and decouples from that of the shear viscosity. The rotational diffusion turns out to be insensitive to pressure. Through comparison with structural data and molecular dynamics simulations, we show that this is a consequence of the rigidity of the first neighbors shell and of the invariance of the number of hydrogen bonds of a water molecule under high pressure. These results show the inadequacy of the Stokes-Einstein-Debye equations to predict the self-diffusive behavior of water at high temperature and high pressure, and challenge the usual description of hot dense water behaving as a simple liquid.

Possibility of increasing the fire-suppression efficiency of the foam in automatic extinguishing installations

NASA Astrophysics Data System (ADS)

Kachanov, I. V.; Veremenyuk, V. V.; Karpenchuk, I. V.; Pavlyukov, S. Yu.

2013-05-01

The mechanics of movement of a liquid in the diffuser of the injector of an automatic extinguishing installation with preaeration of the fire-fighting substance was theoretically investigated. An integral solution of the equation for movement of the preaerated fire-fighting gas-liquid mixture in the indicated diffuser has been obtained. A mathematical model of two-phase liquid flow in this diffuser, which allows one to calculate the distribution of the average pressure in the diffuser along its length and to determine the loss in this pressure, has been developed. This model can be used for designing the output region of a hydraulic system with a hydrodynamic drag providing the operation of its injector in a definite regime.

Pre-Darcy Flow in Porous Media

NASA Astrophysics Data System (ADS)

Dejam, Morteza; Hassanzadeh, Hassan; Chen, Zhangxin

2017-10-01

Fluid flow in porous media is very important in a wide range of science and engineering applications. The entire establishment of fluid flow application in porous media is based on the use of an experimental law proposed by Darcy (1856). There are evidences in the literature that the flow of a fluid in consolidated and unconsolidated porous media does not follow Darcy law at very low fluxes, which is called pre-Darcy flow. In this paper, the unsteady flow regimes of a slightly compressible fluid under the linear and radial pre-Darcy flow conditions are modeled and the corresponding highly nonlinear diffusivity equations are solved analytically by aid of a generalized Boltzmann transformation technique. The influence of pre-Darcy flow on the pressure diffusion for homogeneous porous media is studied in terms of the nonlinear exponent and the threshold pressure gradient. In addition, the pressure gradient, flux, and cumulative production per unit area are compared with the classical solution of the diffusivity equation based on Darcy flow. The presented results advance our understanding of fluid flow in low-permeability media such as shale and tight formations, where pre-Darcy is the dominant flow regime.

Prediction of heat release effects on a mixing layer

NASA Technical Reports Server (NTRS)

Farshchi, M.

1986-01-01

A fully second-order closure model for turbulent reacting flows is suggested based on Favre statistics. For diffusion flames the local thermodynamic state is related to single conserved scalar. The properties of pressure fluctuations are analyzed for turbulent flows with fluctuating density. Closure models for pressure correlations are discussed and modeled transport equations for Reynolds stresses, turbulent kinetic energy dissipation, density-velocity correlations, scalar moments and dissipation are presented and solved, together with the mean equations for momentum and mixture fraction. Solutions of these equations are compared with the experimental data for high heat release free mixing layers of fluorine and hydrogen in a nitrogen diluent.

Initiation and propagation of a PKN hydraulic fracture in permeable rock: Toughness dominated regime

NASA Astrophysics Data System (ADS)

Sarvaramini, E.; Garagash, D.

2011-12-01

The present work investigates the injection of a low-viscosity fluid into a pre-existing fracture with constrained height (PKN), as in waterflooding or supercritical CO2 injection. Contrary to conventional hydraulic fracturing, where 'cake build up' limits diffusion to a small zone, the low viscosity fluid allows for diffusion over a wider range of scales. Over large injection times the pattern becomes 2 or 3-D, necessitating a full-space diffusion modeling. In addition, the dissipation of energy associated with fracturing of rock dominates the energy needed for the low-viscosity fluid flow into the propagating crack. As a result, the fracture toughness is important in evaluating both the initiation and the ensuing propagation of these fractures. Classical PKN hydraulic fracturing model, amended to account for full-space leak-off and the toughness [Garagash, unpublished 2009], is used to evaluate the pressure history and fluid leak-off volume during the injection of low viscosity fluid into a pre-existing and initially stationary. In order to find the pressure history, the stationary crack is first subject to a step pressure increase. The response of the porous medium to the step pressure increase in terms of fluid leak-off volume provides the fundamental solution, which then can be used to find the transient pressurization using Duhamel theorem [Detournay & Cheng, IJSS 1991]. For the step pressure increase an integral equation technique is used to find the leak-off rate history. For small time the solution must converge to short time asymptote, which corresponds to 1-D diffusion pattern. However, as the diffusion length in the zone around the fracture increases the assumption of a 1-D pattern is no longer valid and the diffusion follows a 2-D pattern. The solution to the corresponding integral equation gives the leak-off rate history, which is used to find the cumulative leak-off volume. The transient pressurization solution is obtained using global conservation of fluid injected into the fracture. With increasing pressure in the fracture due to the fluid injection, the energy release rate eventually becomes equal to the toughness and fracture propagates. The evolution of the fracture length is established using the method similar to the one employed for the stationary crack.

Simulation of propagation of the HPM in the low-pressure argon plasma

NASA Astrophysics Data System (ADS)

Zhigang, LI; Zhongcai, YUAN; Jiachun, WANG; Jiaming, SHI

2018-02-01

The propagation of the high-power microwave (HPM) with a frequency of 6 GHz in the low-pressure argon plasma was studied by the method of fluid approximation. The two-dimensional transmission model was built based on the wave equation, the electron drift-diffusion equations and the heavy species transport equations, which were solved by means of COMSOL Multiphysics software. The simulation results showed that the propagation characteristic of the HPM was closely related to the average electron density of the plasma. The attenuation of the transmitted wave increased nonlinearly with the electron density. Specifically, the growth of the attenuation slowed down as the electron density increased uniformly. In addition, the concrete transmission process of the HPM wave in the low-pressure argon plasma was given.

Modeling Disturbance Dynamics in Transitional and Turbulent Boundary Layers

NASA Technical Reports Server (NTRS)

Grosch, C. E.; Gatski, T. B. (Technical Monitor)

2002-01-01

The dynamics of an ensemble of linear disturbances in boundary-layer flows at various Reynolds numbers is studied through an analysis of the transport equations for the mean disturbance kinetic energy and energy dissipation rate. Effects of adverse and favorable pressure-gradients on the disturbance dynamics are also included in the analysis. Unlike the fully turbulent regime where nonlinear phase scrambling of the fluctuations affects the flow field even in proximity to the wall, the early stage transition regime fluctuations studied here are influenced across the boundary layer by the solid boundary. In addition, the dominating dynamics in the disturbance kinetic energy equation is governed by the energy production, pressure-transport and viscous diffusion - also in contrast to the fully turbulent regime. For the disturbance dissipation rate, a dynamic balance exists between the destruction and diffusion of dissipation.

Galactic cosmic-ray mediation of a spherical solar wind flow. 1: The steady state cold gas hydrodynamical approximation

NASA Technical Reports Server (NTRS)

Le Roux, J. A.; Ptuskin, V. S.

1995-01-01

Realistic models of the outer heliosphere should consider that the interstellar cosmic-ray pressure becomes comparable to pressures in the solar wind at distances more than 100 AU from the Sun. The cosmic-ray pressure dynamically affects solar wind flow through deceleration. This effect, which occurs over a scale length of the order of the effective diffusion length at large radial distances, has important implications for cosmic-ray modulation and acceleration. As a first step toward solution of this nonlinear problem, a steady state numerical model was developed for a relatively cold spherical solar wind flow which encounters the confining isotropic pressure of the surrounding Galactic medium. This pressure is assumed to be dominated by energetic particles (Galactic cosmic rays). The system of equations, which are solved self-consistently, includes the relevant hydrodynamical equations for the solar wind flow and the spherical cosmic-ray transport equation. To avoid the closure parameter problem of the two-fluid model, the latter equation is solved for the energy-dependent cosmic-ray distribution function.

Modeling fluid injection induced microseismicity in shales

NASA Astrophysics Data System (ADS)

Carcione, José M.; Currenti, Gilda; Johann, Lisa; Shapiro, Serge

2018-02-01

Hydraulic fracturing in shales generates a cloud of seismic—tensile and shear—events that can be used to evaluate the extent of the fracturing (event clouds) and obtain the hydraulic properties of the medium, such as the degree of anisotropy and the permeability. Firstly, we investigate the suitability of novel semi-analytical reference solutions for pore pressure evolution around a well after fluid injection in anisotropic media. To do so, we use cylindrical coordinates in the presence of a formation (a layer) and spherical coordinates for a homogeneous and unbounded medium. The involved differential equations are transformed to an isotropic diffusion equation by means of pseudo-spatial coordinates obtained from the spatial variables re-scaled by the permeability components. We consider pressure-dependent permeability components, which are independent of the spatial direction. The analytical solutions are compared to numerical solutions to verify their applicability. The comparison shows that the solutions are suitable for a limited permeability range and moderate to minor pressure dependences of the permeability. Once the pressure evolution around the well has been established, we can model the microseismic events. Induced seismicity by failure due to fluid injection in a porous rock depends on the properties of the hydraulic and elastic medium and in situ stress conditions. Here, we define a tensile threshold pressure above which there is tensile emission, while the shear threshold is obtained by using the octahedral stress criterion and the in situ rock properties and conditions. Subsequently, we generate event clouds for both cases and study the spatio-temporal features. The model considers anisotropic permeability and the results are spatially re-scaled to obtain an effective isotropic medium representation. For a 3D diffusion in spherical coordinates and exponential pressure dependence of the permeability, the results differ from those of the classical diffusion equation. Use of the classical front to fit cloud events spatially, provides good results but with a re-scaled value of these components. Modeling is required to evaluate the scaling constant in real cases.

Correlation transfer and diffusion of ultrasound-modulated multiply scattered light.

PubMed

Sakadzić, Sava; Wang, Lihong V

2006-04-28

We develop a temporal correlation transfer equation (CTE) and a temporal correlation diffusion equation (CDE) for ultrasound-modulated multiply scattered light. These equations can be applied to an optically scattering medium with embedded optically scattering and absorbing objects to calculate the power spectrum of light modulated by a nonuniform ultrasound field. We present an analytical solution based on the CDE and Monte Carlo simulation results for light modulated by a cylinder of ultrasound in an optically scattering slab. We further validate with experimental measurements the numerical calculations for an actual ultrasound field. The CTE and CDE are valid for moderate ultrasound pressures and on a length scale comparable with the optical transport mean-free path. These equations should be applicable to a wide spectrum of conditions for ultrasound-modulated optical tomography of soft biological tissues.

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

NASA Astrophysics Data System (ADS)

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

2016-09-01

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

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

NASA Astrophysics Data System (ADS)

Afzali, R.; Pashaee, F.

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

Evolution of Edge Pedestal Profiles Over the L-H Transition

NASA Astrophysics Data System (ADS)

Sayer, M. S.; Stacey, W. M.; Floyd, J. P.; Groebner, R. J.

2012-10-01

The detailed time evolution of thermal diffusivities, electromagnetic forces, pressure gradients, particle pinch and momentum transport frequencies (which determine the diffusion coefficient) have been analyzed during the L-H transition in a DIII-D discharge. Density, temperature, rotation velocity and electric field profiles at times just before and after the L-H transition are analyzed in terms of these quantities. The analysis is based on the fluid particle balance, energy balance, force balance and heat conduction equations, as in Ref. [1], but with much greater time resolution and with account for thermal ion orbit loss. The variation of diffusive and non-diffusive transport over the L-H transition is determined from the variation in the radial force balance (radial electric field, VxB force, and pressure gradient) and the variation in the interpreted diffusive transport coefficients. 6pt [1] W.M. Stacey and R.J. Groebner, Phys. Plasmas 17, 112512 (2010).

Diffuse interface immersed boundary method for multi-fluid flows with arbitrarily moving rigid bodies

NASA Astrophysics Data System (ADS)

Patel, Jitendra Kumar; Natarajan, Ganesh

2018-05-01

We present an interpolation-free diffuse interface immersed boundary method for multiphase flows with moving bodies. A single fluid formalism using the volume-of-fluid approach is adopted to handle multiple immiscible fluids which are distinguished using the volume fractions, while the rigid bodies are tracked using an analogous volume-of-solid approach that solves for the solid fractions. The solution to the fluid flow equations are carried out using a finite volume-immersed boundary method, with the latter based on a diffuse interface philosophy. In the present work, we assume that the solids are filled with a "virtual" fluid with density and viscosity equal to the largest among all fluids in the domain. The solids are assumed to be rigid and their motion is solved using Newton's second law of motion. The immersed boundary methodology constructs a modified momentum equation that reduces to the Navier-Stokes equations in the fully fluid region and recovers the no-slip boundary condition inside the solids. An implicit incremental fractional-step methodology in conjunction with a novel hybrid staggered/non-staggered approach is employed, wherein a single equation for normal momentum at the cell faces is solved everywhere in the domain, independent of the number of spatial dimensions. The scalars are all solved for at the cell centres, with the transport equations for solid and fluid volume fractions solved using a high-resolution scheme. The pressure is determined everywhere in the domain (including inside the solids) using a variable coefficient Poisson equation. The solution to momentum, pressure, solid and fluid volume fraction equations everywhere in the domain circumvents the issue of pressure and velocity interpolation, which is a source of spurious oscillations in sharp interface immersed boundary methods. A well-balanced algorithm with consistent mass/momentum transport ensures robust simulations of high density ratio flows with strong body forces. The proposed diffuse interface immersed boundary method is shown to be discretely mass-preserving while being temporally second-order accurate and exhibits nominal second-order accuracy in space. We examine the efficacy of the proposed approach through extensive numerical experiments involving one or more fluids and solids, that include two-particle sedimentation in homogeneous and stratified environment. The results from the numerical simulations show that the proposed methodology results in reduced spurious force oscillations in case of moving bodies while accurately resolving complex flow phenomena in multiphase flows with moving solids. These studies demonstrate that the proposed diffuse interface immersed boundary method, which could be related to a class of penalisation approaches, is a robust and promising alternative to computationally expensive conformal moving mesh algorithms as well as the class of sharp interface immersed boundary methods for multibody problems in multi-phase flows.

Nonlinear theory of nonstationary low Mach number channel flows of freely cooling nearly elastic granular gases.

PubMed

Meerson, Baruch; Fouxon, Itzhak; Vilenkin, Arkady

2008-02-01

We employ hydrodynamic equations to investigate nonstationary channel flows of freely cooling dilute gases of hard and smooth spheres with nearly elastic particle collisions. This work focuses on the regime where the sound travel time through the channel is much shorter than the characteristic cooling time of the gas. As a result, the gas pressure rapidly becomes almost homogeneous, while the typical Mach number of the flow drops well below unity. Eliminating the acoustic modes and employing Lagrangian coordinates, we reduce the hydrodynamic equations to a single nonlinear and nonlocal equation of a reaction-diffusion type. This equation describes a broad class of channel flows and, in particular, can follow the development of the clustering instability from a weakly perturbed homogeneous cooling state to strongly nonlinear states. If the heat diffusion is neglected, the reduced equation becomes exactly soluble, and the solution develops a finite-time density blowup. The blowup has the same local features at singularity as those exhibited by the recently found family of exact solutions of the full set of ideal hydrodynamic equations [I. Fouxon, Phys. Rev. E 75, 050301(R) (2007); I. Fouxon,Phys. Fluids 19, 093303 (2007)]. The heat diffusion, however, always becomes important near the attempted singularity. It arrests the density blowup and brings about previously unknown inhomogeneous cooling states (ICSs) of the gas, where the pressure continues to decay with time, while the density profile becomes time-independent. The ICSs represent exact solutions of the full set of granular hydrodynamic equations. Both the density profile of an ICS and the characteristic relaxation time toward it are determined by a single dimensionless parameter L that describes the relative role of the inelastic energy loss and heat diffusion. At L>1 the intermediate cooling dynamics proceeds as a competition between "holes": low-density regions of the gas. This competition resembles Ostwald ripening (only one hole survives at the end), and we report a particular regime where the "hole ripening" statistics exhibits a simple dynamic scaling behavior.

Modeling growth kinetics of thin films made by atomic layer deposition in lateral high-aspect-ratio structures

NASA Astrophysics Data System (ADS)

Ylilammi, Markku; Ylivaara, Oili M. E.; Puurunen, Riikka L.

2018-05-01

The conformality of thin films grown by atomic layer deposition (ALD) is studied using all-silicon test structures with long narrow lateral channels. A diffusion model, developed in this work, is used for studying the propagation of ALD growth in narrow channels. The diffusion model takes into account the gas transportation at low pressures, the dynamic Langmuir adsorption model for the film growth and the effect of channel narrowing due to film growth. The film growth is calculated by solving the diffusion equation with surface reactions. An efficient analytic approximate solution of the diffusion equation is developed for fitting the model to the measured thickness profile. The fitting gives the equilibrium constant of adsorption and the sticking coefficient. This model and Gordon's plug flow model are compared. The simulations predict the experimental measurement results quite well for Al2O3 and TiO2 ALD processes.

Dynamics of gas bubble growth in a supersaturated solution with Sievert's solubility law.

PubMed

Gor, G Yu; Kuchma, A E

2009-07-21

This paper presents a theoretical description of diffusion growth of a gas bubble after its nucleation in supersaturated liquid solution. We study systems where gas molecules completely dissociate in the solvent into two parts, thus making Sievert's solubility law valid. We show that the difference between Henry's and Sievert's laws for chemical equilibrium conditions causes the difference in bubble growth dynamics. Assuming that diffusion flux is steady we obtain a differential equation on bubble radius. Bubble dynamics equation is solved analytically for the case of homogeneous nucleation of a bubble, which takes place at a significant pressure drop. We also obtain conditions of diffusion flux steadiness. The fulfillment of these conditions is studied for the case of nucleation of water vapor bubbles in magmatic melts.

On the Stability of Shocks with Particle Pressure

NASA Astrophysics Data System (ADS)

Finazzi, Stefano; Vietri, Mario

2008-11-01

We perform a linear stability analysis for corrugations of a Newtonian shock, with particle pressure included, for an arbitrary diffusion coefficient. We study first the dispersion relation for homogeneous media, showing that, besides the conventional pressure waves and entropy/vorticity disturbances, two new perturbation modes exist, dominated by the particles' pressure and damped by diffusion. We show that, due to particle diffusion into the upstream region, the fluid will be perturbed also upstream; we treat these perturbation in the short-wavelength (WKBJ) regime. We then show how to construct a corrugational mode for the shock itself, one, that is, where the shock executes free oscillations (possibly damped or growing) and sheds perturbations away from itself; this global mode requires the new modes. Then, using the perturbed Rankine-Hugoniot conditions, we show that this leads to the determination of the corrugational eigenfrequency. We solve numerically the equations for the eigenfrequency in the WKBJ regime for the models of Amato & Blasi, showing that they are stable. We then discuss the differences between our treatment and previous work.

Diffusional limits to the consumption of atmospheric methane by soils

USGS Publications Warehouse

Striegl, Robert G.

1993-01-01

Net transport of atmospheric gases into and out of soil systems is primarily controlled by diffusion along gas partial pressure gradients. Gas fluxes between soil and the atmosphere can therefore be estimated by a generalization of the equation for ordinary gaseous diffusion in porous unsaturated media. Consumption of CH4 by methylotrophic bacteria in the top several centimeters of soil causes the uptake of atmospheric CH4 by aerated soils. The capacity of the methylotrophs to consume CH4 commonly exceeds the potential of CH4 to diffuse from the atmosphere to the consumers. The maximum rate of uptake of atmospheric CH4 by soil is, therefore, limited by diffusion and can be calculated from soil physical properties and the CH4 concentration gradient. The CH4 concentration versus depth profile is theoretically described by the equation for gaseous diffusion with homogeneous chemical reaction in porous unsaturated media. This allows for calculation of the in situ rate of CH4 consumption within specified depth intervals.

Creeping gaseous flows through elastic tube and annulus micro-configurations

NASA Astrophysics Data System (ADS)

Elbaz, Shai; Jacob, Hila; Gat, Amir

2016-11-01

Gaseous flows in elastic micro-configurations is relevant to biological systems (e.g. alveolar ducts in the lungs) as well as to applications such as gas actuated soft micro-robots. We here examine the effect of low-Mach-number compressibility on creeping gaseous axial flows through linearly elastic tube and annulus micro-configurations. For steady flows, the leading-order effects of elasticity on the pressure distribution and mass-flux are obtained. For transient flow in a tube with small deformations, elastic effects are shown to be negligible in leading order due to compressibility. We then examine transient flows in annular configurations where the deformation is significant compared with the gap between the inner and outer cylinders defining the annulus. Both compressibility and elasticity are obtained as dominant terms interacting with viscosity. For a sudden flux impulse, the governing non-linear leading order diffusion equation is initially approximated by a porous-medium-equation of order 2.5 for the pressure square. However, as the fluid expand and the pressure decreases, the governing equation degenerates to a porous-medium-equation of order 2 for the pressure.

Fractional calculus phenomenology in two-dimensional plasma models

NASA Astrophysics Data System (ADS)

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

2006-10-01

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

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.

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.

Fundamental Flux Equations for Fracture-Matrix Interactions with Linear Diffusion

NASA Astrophysics Data System (ADS)

Oldenburg, C. M.; Zhou, Q.; Rutqvist, J.; Birkholzer, J. T.

2017-12-01

The conventional dual-continuum models are only applicable for late-time behavior of pressure propagation in fractured rock, while discrete-fracture-network models may explicitly deal with matrix blocks at high computational expense. To address these issues, we developed a unified-form diffusive flux equation for 1D isotropic (spheres, cylinders, slabs) and 2D/3D rectangular matrix blocks (squares, cubes, rectangles, and rectangular parallelepipeds) by partitioning the entire dimensionless-time domain (Zhou et al., 2017a, b). For each matrix block, this flux equation consists of the early-time solution up until a switch-over time after which the late-time solution is applied to create continuity from early to late time. The early-time solutions are based on three-term polynomial functions in terms of square root of dimensionless time, with the coefficients dependent on dimensionless area-to-volume ratio and aspect ratios for rectangular blocks. For the late-time solutions, one exponential term is needed for isotropic blocks, while a few additional exponential terms are needed for highly anisotropic blocks. The time-partitioning method was also used for calculating pressure/concentration/temperature distribution within a matrix block. The approximate solution contains an error-function solution for early times and an exponential solution for late times, with relative errors less than 0.003. These solutions form the kernel of multirate and multidimensional hydraulic, solute and thermal diffusion in fractured reservoirs.

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

PubMed Central

Song, Hongjun; Wang, Yi; Pant, Kapil

2011-01-01

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

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

PubMed

Song, Hongjun; Wang, Yi; Pant, Kapil

2012-01-01

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

Modeling High-Pressure Gas-Polymer Sorpion Behavior Using the Sanchez-Lacombe Equation of State.

DTIC Science & Technology

1987-06-01

The solubility of a gas in an amorphous or molten polymer is an important consideration in membrane and polymer processes . For instance, the efficacy...to a supercritical fluid during the impregnation process . Swelling the polymer effectively increases the diffusion coefficient of the heavy dopant by...dissolve the impurity, and then diffuse out of the swollen matrix thus removing the impurity. This supercritical fluid extraction process is somewhat

Modeling of outgassing and matrix decomposition in carbon-phenolic composites

NASA Technical Reports Server (NTRS)

Mcmanus, Hugh L.

1993-01-01

A new release rate equation to model the phase change of water to steam in composite materials was derived from the theory of molecular diffusion and equilibrium moisture concentration. The new model is dependent on internal pressure, the microstructure of the voids and channels in the composite materials, and the diffusion properties of the matrix material. Hence, it is more fundamental and accurate than the empirical Arrhenius rate equation currently in use. The model was mathematically formalized and integrated into the thermostructural analysis code CHAR. Parametric studies on variation of several parameters have been done. Comparisons to Arrhenius and straight-line models show that the new model produces physically realistic results under all conditions.

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

NASA Technical Reports Server (NTRS)

Jameson, Antony

1994-01-01

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

Technical basis for inner container leak detection sensitivity goals in 3013 DE surveillance

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

Berg, John M.

Helium leak checking of 3013 inner container lids is under consideration for addition to DE Surveillance tasks as an improved means to detect any through-wall flaws that may have formed during storage. This white paper evaluates whether leak checking at DE could replace and improve upon the current method of comparing gas compositions and pressures within the inner and outer containers. We have used viscous and molecular flow equations in ANSI N14.5 to calculate what the measured standard helium leak rate would be for hypothetical leaks of three different sizes. For comparison, we have also calculated the effects on gasmore » composition and pressure differences as a function of pre-DE storage time for the same three leak sizes, using molecular and viscous flow equations as well as diffusion equations to predict the relevant gas transport. For a hypothetical leak that would be measured at 1x10 -7 std cc/sec, likely an achievable sensitivity using helium leak checking at DE, the calculations predict no measurable effect on pressure difference or gas composition as measured by DE gas analysis. We also calculate that it would take over 200 years for water vapor to diffuse through a 10 -7 std cc/sec leak enough to raise the RH outer container to half the RH value in the inner container. A leak 100 times larger, which would be measured at 1x10 -5 std cc/sec, the same water vapor diffusion would take at least 14 years. Our conclusion is that helium leak checking will be useful even at a sensitivity of 1x10 -5 std cc/sec, and a significant improvement over current DE methods at a sensitivity of 1x10 -7 std cc/sec.« less

The entrance of water into beef and dog red cells.

PubMed

VILLEGAS, R; BARTON, T C; SOLOMON, A K

1958-11-20

The rate constants for diffusion of THO across the red cell membrane of beef and dog, and the rate of entrance of water into the erythrocytes of these species under an osmotic pressure gradient have been measured. For water entrance into the erythrocyte by diffusion the rate constants are 0.10 +/- 0.02 msec.(-1) (beef) and 0.14 +/- 0.03 msec.(-1) (dog); the permeability coefficients for water entrance under a pressure gradient of 1 osmol./cm(3) are 0.28 See PDF for Equation These values permit the calculation of an equivalent pore radius for the erythrocyte membrane of 4.1 A for beef and 7.4 A for dog. In the beef red cell the change in THO diffusion due to osmotically produced cell volume shifts has been studied. The resistance to THO diffusion increases as the cell volume increases. At the maximum volume, (1.06 times normal), THO diffusion is decreased to 0.84 times the normal rate. This change in diffusion is attributed to swelling of the cellular membrane.

Solutions for Reacting and Nonreacting Viscous Shock Layers with Multicomponent Diffusion and Mass Injection. Ph.D. Thesis - Virginia Polytechnic Inst. and State Univ.

NASA Technical Reports Server (NTRS)

Moss, J. N.

1971-01-01

Numerical solutions are presented for the viscous shocklayer equations where the chemistry is treated as being either frozen, equilibrium, or nonequilibrium. Also the effects of the diffusion model, surface catalyticity, and mass injection on surface transport and flow parameters are considered. The equilibrium calculations for air species using multicomponent: diffusion provide solutions previously unavailable. The viscous shock-layer equations are solved by using an implicit finite-difference scheme. The flow is treated as a mixture of inert and thermally perfect species. Also the flow is assumed to be in vibrational equilibrium. All calculations are for a 45 deg hyperboloid. The flight conditions are those for various altitudes and velocities in the earth's atmosphere. Data are presented showing the effects of the chemical models; diffusion models; surface catalyticity; and mass injection of air, water, and ablation products on heat transfer; skin friction; shock stand-off distance; wall pressure distribution; and tangential velocity, temperature, and species profiles.

New Models for Velocity/Pressure-Gradient Correlations in Turbulent Boundary Layers

NASA Astrophysics Data System (ADS)

Poroseva, Svetlana; Murman, Scott

2014-11-01

To improve the performance of Reynolds-Averaged Navier-Stokes (RANS) turbulence models, one has to improve the accuracy of models for three physical processes: turbulent diffusion, interaction of turbulent pressure and velocity fluctuation fields, and dissipative processes. The accuracy of modeling the turbulent diffusion depends on the order of a statistical closure chosen as a basis for a RANS model. When the Gram-Charlier series expansions for the velocity correlations are used to close the set of RANS equations, no assumption on Gaussian turbulence is invoked and no unknown model coefficients are introduced into the modeled equations. In such a way, this closure procedure reduces the modeling uncertainty of fourth-order RANS (FORANS) closures. Experimental and direct numerical simulation data confirmed the validity of using the Gram-Charlier series expansions in various flows including boundary layers. We will address modeling the velocity/pressure-gradient correlations. New linear models will be introduced for the second- and higher-order correlations applicable to two-dimensional incompressible wall-bounded flows. Results of models' validation with DNS data in a channel flow and in a zero-pressure gradient boundary layer over a flat plate will be demonstrated. A part of the material is based upon work supported by NASA under award NNX12AJ61A.

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 projection hybrid high order finite volume/finite element method for incompressible turbulent flows

NASA Astrophysics Data System (ADS)

Busto, S.; Ferrín, J. L.; Toro, E. F.; Vázquez-Cendón, M. E.

2018-01-01

In this paper the projection hybrid FV/FE method presented in [1] is extended to account for species transport equations. Furthermore, turbulent regimes are also considered thanks to the k-ε model. Regarding the transport diffusion stage new schemes of high order of accuracy are developed. The CVC Kolgan-type scheme and ADER methodology are extended to 3D. The latter is modified in order to profit from the dual mesh employed by the projection algorithm and the derivatives involved in the diffusion term are discretized using a Galerkin approach. The accuracy and stability analysis of the new method are carried out for the advection-diffusion-reaction equation. Within the projection stage the pressure correction is computed by a piecewise linear finite element method. Numerical results are presented, aimed at verifying the formal order of accuracy of the scheme and to assess the performance of the method on several realistic test problems.

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.

Numerical solutions of Navier-Stokes equations for compressible turbulent two/three dimensional flows in terminal shock region of an inlet/diffuser

NASA Technical Reports Server (NTRS)

Liu, N. S.; Shamroth, S. J.; Mcdonald, H.

1983-01-01

The multidimensional ensemble averaged compressible time dependent Navier Stokes equations in conjunction with mixing length turbulence model and shock capturing technique were used to study the terminal shock type of flows in various flight regimes occurring in a diffuser/inlet model. The numerical scheme for solving the governing equations is based on a linearized block implicit approach and the following high Reynolds number calculations were carried out: (1) 2 D, steady, subsonic; (2) 2 D, steady, transonic with normal shock; (3) 2 D, steady, supersonic with terminal shock; (4) 2 D, transient process of shock development and (5) 3 D, steady, transonic with normal shock. The numerical results obtained for the 2 D and 3 D transonic shocked flows were compared with corresponding experimental data; the calculated wall static pressure distributions agree well with the measured data.

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.

Effect of tumor shape, size, and tissue transport properties on drug delivery to solid tumors

PubMed Central

2014-01-01

Background The computational methods provide condition for investigation related to the process of drug delivery, such as convection and diffusion of drug in extracellular matrices, drug extravasation from microvessels or to lymphatic vessels. The information of this process clarifies the mechanisms of drug delivery from the injection site to absorption by a solid tumor. In this study, an advanced numerical method is used to solve fluid flow and solute transport equations simultaneously to investigate the effect of tumor shape and size on drug delivery to solid tumor. Methods The advanced mathematical model used in our previous work is further developed by adding solute transport equation to the governing equations. After applying appropriate boundary and initial conditions on tumor and surrounding tissue geometry, the element-based finite volume method is used for solving governing equations of drug delivery in solid tumor. Also, the effects of size and shape of tumor and some of tissue transport parameters such as effective pressure and hydraulic conductivity on interstitial fluid flow and drug delivery are investigated. Results Sensitivity analysis shows that drug delivery in prolate shape is significantly better than other tumor shapes. Considering size effect, increasing tumor size decreases drug concentration in interstitial fluid. This study shows that dependency of drug concentration in interstitial fluid to osmotic and intravascular pressure is negligible. Conclusions This study shows that among diffusion and convection mechanisms of drug transport, diffusion is dominant in most different tumor shapes and sizes. In tumors in which the convection has considerable effect, the drug concentration is larger than that of other tumors at the same time post injection. PMID:24987457

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.

Diffuse interfacelets in transcritical flows of propellants into high-pressure combustors

NASA Astrophysics Data System (ADS)

Urzay, Javier; Jofre, Lluis

2017-11-01

Rocket engines and new generations of high-power jet engines and diesel engines oftentimes involve the injection of one or more reactants at subcritical temperatures into combustor environments at high pressures, and more particularly, at pressures higher than those corresponding to the critical points of the individual components of the mixture, which typically range from 13 to 50 bars for most propellants. This class of trajectories in the thermodynamic space has been traditionally referred to as transcritical. Under particular conditions often found in hydrocarbon-fueled chemical propulsion systems, and despite the prevailing high pressures, the flow in the combustor may contain regions close to the injector where a diffuse interface is formed in between the fuel and oxidizer streams that is sustained by surface-tension forces as a result of the elevation of the critical pressure of the mixture. This talk describes progress towards modeling these effects in the conservation equations. Funded by the US Department of Energy.

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.

A proposal for the experimental detection of CSL induced random walk

PubMed Central

Bera, Sayantani; Motwani, Bhawna; Singh, Tejinder P.; Ulbricht, Hendrik

2015-01-01

Continuous Spontaneous Localization (CSL) is one possible explanation for dynamically induced collapse of the wave-function during a quantum measurement. The collapse is mediated by a stochastic non-linear modification of the Schrödinger equation. A consequence of the CSL mechanism is an extremely tiny violation of energy-momentum conservation, which can, in principle, be detected in the laboratory via the random diffusion of a particle induced by the stochastic collapse mechanism. In a paper in 2003, Collett and Pearle investigated the translational CSL diffusion of a sphere, and the rotational CSL diffusion of a disc, and showed that this effect dominates over the ambient environmental noise at low temperatures and extremely low pressures (about ten-thousandth of a pico-Torr). In the present paper, we revisit their analysis and argue that this stringent condition on pressure can be relaxed, and that the CSL effect can be seen at the pressure of about a pico-Torr. A similar analysis is provided for diffusion produced by gravity-induced decoherence, where the effect is typically much weaker than CSL. We also discuss the CSL induced random displacement of a quantum oscillator. Lastly, we propose possible experimental set-ups justifying that CSL diffusion is indeed measurable with the current technology. PMID:25563619

Transport Coefficients in weakly compressible turbulence

NASA Technical Reports Server (NTRS)

Rubinstein, Robert; Erlebacher, Gordon

1996-01-01

A theory of transport coefficients in weakly compressible turbulence is derived by applying Yoshizawa's two-scale direct interaction approximation to the compressible equations of motion linearized about a state of incompressible turbulence. The result is a generalization of the eddy viscosity representation of incompressible turbulence. In addition to the usual incompressible eddy viscosity, the calculation generates eddy diffusivities for entropy and pressure, and an effective bulk viscosity acting on the mean flow. The compressible fluctuations also generate an effective turbulent mean pressure and corrections to the speed of sound. Finally, a prediction unique to Yoshizawa's two-scale approximation is that terms containing gradients of incompressible turbulence quantities also appear in the mean flow equations. The form these terms take is described.

Mathematical Development of the Spill Assessment Model (SAM) for Hydrazine and Similar Acting Materials in Water Bodies.

DTIC Science & Technology

1980-02-01

migration of the chemical mass in the fluid volume according to two entirely different means, yet governed by the same form of the equation: molecular ...pressure or temperature gradients, gravitational or other body forces, or bulk fluid motion, is observed as molecular diffusion. In general, the...need be made at this stage as to whether the diffusion of a released mass in the fluid is molecular or turbulent in nature. The general form of the one

The Reynolds-stress tensor in diffusion flames; An experimental and theoretical investigation

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

Schneider, F.; Janicka, J.

1990-07-01

The authors present measurements and predictions of Reynolds-stress components and mean velocities in a CH{sub 4}-air diffusion flame. A reference beam LDA technique is applied for measuring all Reynolds-stress components. A hologram with dichromated gelatine as recording medium generates strictly coherent reference beams. The theoretical part describes a Reynolds-stress model based on Favre-averaged quantities, paying special attention to modeling the pressure-shear correlation and the dissipation equation in flames. Finally, measurement/prediction comparisons are presented.

Design and Implementation of a Numerical Technique to Inform Anisotropic Hyperelastic Finite Element Models using Diffusion-Weighted Imaging

DTIC Science & Technology

2011-10-01

the deviatoric part of a tensor in the reference configuration and p = −∂Ψ ∂J is the hydrostatic pressure. Using the chain 4 rule, equation 13 can be...Kirchoff stress tensor S to the current configuration, and a scaling with the inverse of the volume ratio, transforms equation 16 to the Cauchy stress ...a characteristic of most soft tissues. Then, similar to equation 13, the second Piola-Kirchoff stress is given by: S = 2J−2/3DEV [ ∂Ψisoc ( C ) ∂C

The role of facilitated diffusion in oxygen transport by cell-free hemoglobins: implications for the design of hemoglobin-based oxygen carriers.

PubMed

McCarthy, M R; Vandegriff, K D; Winslow, R M

2001-08-30

We compared rates of oxygen transport in an in vitro capillary system using red blood cells (RBCs) and cell-free hemoglobins. The axial PO(2) drop down the capillary was calculated using finite-element analysis. RBCs, unmodified hemoglobin (HbA(0)), cross-linked hemoglobin (alpha alpha-Hb) and hemoglobin conjugated to polyethylene-glycol (PEG-Hb) were evaluated. According to their fractional saturation curves, PEG-Hb showed the least desaturation down the capillary, which most closely matched the RBCs; HbA(0) and alpha alpha-Hb showed much greater desaturation. A lumped diffusion parameter, K*, was calculated based on the Fick diffusion equation with a term for facilitated diffusion. The overall rates of oxygen transfer are consistent with hemoglobin diffusion rates according to the Stokes-Einstein Law and with previously measured blood pressure responses in rats. This study provides a conceptual framework for the design of a 'blood substitute' based on mimicking O(2) transport by RBCs to prevent autoregulatory changes in blood flow and pressure.

Movement of Landslide Triggered by Bedrock Exfiltration with Nonuniform Pore Pressure Distribution

NASA Astrophysics Data System (ADS)

Jan, C. D.; Jian, Z. K.

2014-12-01

Landslides are common phenomena of sediment movement in mountain areas and usually pose severe risks to people and infrastructure around those areas. The occurrence of landslides is influenced by groundwater dynamics and bedrock characteristics as well as by rainfall and soil-mass properties. The bedrock may drain or contribute to groundwater in the overlying soil mass, depending on the hydraulic conductivity, degree of fracturing, saturation, and hydraulic head. Our study here is based on the model proposed by Iverson (2005). The model describes the relation between landslide displacement and the shear-zone dilation/contraction of pore water pressure. To study landslide initiation and movement, a block soil mass sliding down an inclined beck-rock plane is governed by Newton's equation of motion, while both the bedrock exfiltration and excess pore pressure induced by dilatation or contraction of basal shear zone are described by diffusion equations. The Chebyshev collocation method was used to transform the governing equations to a system of first-order ordinary differential equations, without the need of iteration. Then a fourth-order Runge-Kutta scheme was used to solve these ordinary differential equations. The effects of nonuniform bedrock exfiltration pressure distributions, such as the delayed peak, central peak, and advanced peak distributions, on the time of landslide initiation and the speed of landslide movement were compared and discussed.

A thermodynamically consistent model for granular-fluid mixtures considering pore pressure evolution and hypoplastic behavior

NASA Astrophysics Data System (ADS)

Hess, Julian; Wang, Yongqi

2016-11-01

A new mixture model for granular-fluid flows, which is thermodynamically consistent with the entropy principle, is presented. The extra pore pressure described by a pressure diffusion equation and the hypoplastic material behavior obeying a transport equation are taken into account. The model is applied to granular-fluid flows, using a closing assumption in conjunction with the dynamic fluid pressure to describe the pressure-like residual unknowns, hereby overcoming previous uncertainties in the modeling process. Besides the thermodynamically consistent modeling, numerical simulations are carried out and demonstrate physically reasonable results, including simple shear flow in order to investigate the vertical distribution of the physical quantities, and a mixture flow down an inclined plane by means of the depth-integrated model. Results presented give insight in the ability of the deduced model to capture the key characteristics of granular-fluid flows. We acknowledge the support of the Deutsche Forschungsgemeinschaft (DFG) for this work within the Project Number WA 2610/3-1.

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

NASA Technical Reports Server (NTRS)

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

1989-01-01

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

Hydrodynamic theory of diffusion in two-temperature multicomponent plasmas

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

Ramshaw, J.D.; Chang, C.H.

Detailed numerical simulations of multicomponent plasmas require tractable expressions for species diffusion fluxes, which must be consistent with the given plasma current density J{sub q} to preserve local charge neutrality. The common situation in which J{sub q} = 0 is referred to as ambipolar diffusion. The use of formal kinetic theory in this context leads to results of formidable complexity. We derive simple tractable approximations for the diffusion fluxes in two-temperature multicomponent plasmas by means of a generalization of the hydrodynamical approach used by Maxwell, Stefan, Furry, and Williams. The resulting diffusion fluxes obey generalized Stefan-Maxwell equations that contain drivingmore » forces corresponding to ordinary, forced, pressure, and thermal diffusion. The ordinary diffusion fluxes are driven by gradients in pressure fractions rather than mole fractions. Simplifications due to the small electron mass are systematically exploited and lead to a general expression for the ambipolar electric field in the limit of infinite electrical conductivity. We present a self-consistent effective binary diffusion approximation for the diffusion fluxes. This approximation is well suited to numerical implementation and is currently in use in our LAVA computer code for simulating multicomponent thermal plasmas. Applications to date include a successful simulation of demixing effects in an argon-helium plasma jet, for which selected computational results are presented. Generalizations of the diffusion theory to finite electrical conductivity and nonzero magnetic field are currently in progress.« less

Electron kinetics dependence on gas pressure in laser-induced oxygen plasma experiment: Theoretical analysis

NASA Astrophysics Data System (ADS)

Gamal, Yosr E. E.-D.; Abdellatif, Galila

2017-08-01

A study is performed to investigate the dependency of threshold intensity on gas pressure observed in the measurements of the breakdown of molecular oxygen that carried out by Phuoc (2000) [1]. In this experiment, the breakdown was induced by 532 nm laser radiation of pulse width 5.5 ns and spot size of 8.5 μm, in oxygen over a wide pressure range (190-3000 Torr). The analysis aimed to explore the electron kinetic reliance on gas pressure for the separate contribution of each of the gain and loss processes encountered in this study. The investigation is based on an electron cascade model applied previously in Gamal and Omar (2001) [2] and Gaabour et al. (2013) [3]. This model solves numerically a differential equation designates the time evolution of the electron energy distribution, and a set of rate equations that describe the change of excited states population. The numerical examination of the electron energy distribution function and its parameters revealed that photo-ionization of the excited molecules plays a significant role in enhancing the electron density growth rate over the whole tested gas pressure range. This process is off set by diffusion of electrons out of the focal volume in the low-pressure regime. At atmospheric pressure electron, collisional processes dominate and act mainly to populate the excited states. Hence photo-ionization becomes efficient and compete with the encountered loss processes (electron diffusion, vibrational excitation of the ground state molecules as well as two body attachments). At high pressures ( 3000 Torr) three body attachments are found to be the primary cause of losses which deplete the electron density and hence results in the slow decrease of the threshold intensity.

Design of Capillary Flows with Spatially Graded Porous Films

NASA Astrophysics Data System (ADS)

Joung, Young Soo; Figliuzzi, Bruno Michel; Buie, Cullen

2013-11-01

We have developed a new capillary tube model, consisting of multi-layered capillary tubes oriented in the direction of flow, to predict capillary speeds on spatially graded porous films. Capillary flows through thin porous media have been widely utilized for small size liquid transport systems. However, for most media it is challenging to realize arbitrary shapes and spatially functionalized micro-structures with variable flow properties. Therefore, conventional media can only be used for capillary flows obeying Washburn's equation and the modifications thereof. Given this background, we recently developed a method called breakdown anodization (BDA) to produce highly wetting porous films. The resulting surfaces show nearly zero contact angles and fast water spreading speed. Furthermore, capillary pressure and spreading diffusivity can be expressed as functions of capillary height when customized electric fields are used in BDA. From the capillary tube model, we derived a general capillary flow equation of motion in terms of capillary pressure and spreading diffusivity. The theoretical model shows good agreement with experimental capillary flows. The study will provide novel design methodologies for paper-based microfluidic devices.

Hydrodynamics of steady state phloem transport with radial leakage of solute

PubMed Central

Cabrita, Paulo; Thorpe, Michael; Huber, Gregor

2013-01-01

Long-distance phloem transport occurs under a pressure gradient generated by the osmotic exchange of water associated with solute exchange in source and sink regions. But these exchanges also occur along the pathway, and yet their physiological role has almost been ignored in mathematical models of phloem transport. Here we present a steady state model for transport phloem which allows solute leakage, based on the Navier-Stokes and convection-diffusion equations which describe fluid motion rigorously. Sieve tube membrane permeability Ps for passive solute exchange (and correspondingly, membrane reflection coefficient) influenced model results strongly, and had to lie in the bottom range of the values reported for plant cells for the results to be realistic. This smaller permeability reflects the efficient specialization of sieve tube elements, minimizing any diffusive solute loss favored by the large concentration difference across the sieve tube membrane. We also found there can be a specific reflection coefficient for which pressure profiles and sap velocities can both be similar to those predicted by the Hagen-Poiseuille equation for a completely impermeable tube. PMID:24409189

A numerical method for osmotic water flow and solute diffusion with deformable membrane boundaries in two spatial dimension

NASA Astrophysics Data System (ADS)

Yao, Lingxing; Mori, Yoichiro

2017-12-01

Osmotic forces and solute diffusion are increasingly seen as playing a fundamental role in cell movement. Here, we present a numerical method that allows for studying the interplay between diffusive, osmotic and mechanical effects. An osmotically active solute obeys a advection-diffusion equation in a region demarcated by a deformable membrane. The interfacial membrane allows transmembrane water flow which is determined by osmotic and mechanical pressure differences across the membrane. The numerical method is based on an immersed boundary method for fluid-structure interaction and a Cartesian grid embedded boundary method for the solute. We demonstrate our numerical algorithm with the test case of an osmotic engine, a recently proposed mechanism for cell propulsion.

Environmental solid particle effects on compressor cascade performance

NASA Technical Reports Server (NTRS)

Tabakoff, W.; Balan, C.

1982-01-01

The effect of suspended solid particles on the performance of the compressor cascade was investigated experimentally in a specially built cascade tunnel, using quartz sand particles. The cascades were made of NACA 65(10)10 airfoils. Three cascades were tested, one accelerating cascade and two diffusing cascades. The theoretical analysis assumes inviscid and incompressible two dimensional flow. The momentum exchange between the fluid and the particle is accounted for by the interphase force terms in the fluid momentum equation. The modified fluid phase momentum equations and the continuity equation are reduced to the conventional stream function vorticity formulation. The method treats the fluid phase in the Eulerian system and the particle phase in Lagrangian system. The experimental results indicate a small increase in the blade surface static pressures, while the theoretical results indicate a small decrease. The theoretical analysis, also predicts the loss in total pressure associated with the particulate flow through the cascade.

The development of a three-dimensional partially elliptic flow computer program for combustor research

NASA Technical Reports Server (NTRS)

Pan, Y. S.

1978-01-01

A three dimensional, partially elliptic, computer program was developed. Without requiring three dimensional computer storage locations for all flow variables, the partially elliptic program is capable of predicting three dimensional combustor flow fields with large downstream effects. The program requires only slight increase of computer storage over the parabolic flow program from which it was developed. A finite difference formulation for a three dimensional, fully elliptic, turbulent, reacting, flow field was derived. Because of the negligible diffusion effects in the main flow direction in a supersonic combustor, the set of finite-difference equations can be reduced to a partially elliptic form. Only the pressure field was governed by an elliptic equation and requires three dimensional storage; all other dependent variables are governed by parabolic equations. A numerical procedure which combines a marching integration scheme with an iterative scheme for solving the elliptic pressure was adopted.

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.

The electron Boltzmann equation in a plasma generated by fission fragments

NASA Technical Reports Server (NTRS)

Hassan, H. A.; Deese, J. E.

1976-01-01

A Boltzmann equation formulation is presented for the determination of the electron distribution function in a plasma generated by fission fragments. The formulation takes into consideration ambipolar diffusion, elastic and inelastic collisions, recombination and ionization, and allows for the fact that the primary electrons are not monoenergetic. Calculations for He in a tube coated with fissionable material show that, over a wide pressure and neutron flux range, the distribution function is non-Maxwellian, but the electrons are essentially thermal. Moreover, about a third of the energy of the primary electrons is transferred into the inelastic levels of He. This fraction of energy transfer is almost independent of pressure and neutron flux but increases sharply in the presence of a sustainer electric field.

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.

Effect of particle- and specimen-level transport on product state in compacted-powder combustion synthesis and thermal debinding of polymers from molded powders

NASA Astrophysics Data System (ADS)

Oliveira, Amir Antonio Martins

The existence of large gradients within particles and fast temporal variations in the temperature and species concentration prevents the use of asymptotic approximations for the closure of the volume-averaged, specimen-level formulations. In this case a solution of the particle-level transport problem is needed to complement the specimen-level volume-averaged equations. Here, the use of combined specimen-level and particle-level models for transport in reactive porous media is demonstrated with two examples. For the gasless compacted-powder combustion synthesis, a three-scale model is developed. The specimen-level model is based on the volume-averaged equations for species and temperature. Local thermal equilibrium is assumed and the macroscopic mass diffusion and convection fluxes are neglected. The particle-level model accounts for the interparticle diffusion (i.e., the liquid migration from liquid-rich to liquid-lean regions) and the intraparticle diffusion (i.e., the species mass diffusion within the product layer formed at the surface of the high melting temperature component). It is found that the interparticle diffusion controls the extent of conversion to the final product, the maximum temperature, and to a smaller degree the propagation velocity. The intraparticle diffusion controls the propagation velocity and to a smaller degree the maximum temperature. The initial stages of thermal degradation of EVA from molded specimens is modeled using volume-averaged equations for the species and empirical models for the kinetics of the thermal degradation, the vapor-liquid equilibrium, and the diffusion coefficient of acetic acid in the molten polymer. It is assumed that a bubble forms when the partial pressure of acetic acid exceeds the external ambient pressure. It is found that the removal of acetic acid is characterized by two regimes, a pre-charge dominated regime and a generation dominated regime. For the development of an optimum debinding schedule, the heating rate is modulated to avoid bubbling, while the concentration and temperature follow the bubble-point line for the mixture. The results show a strong dependence on the presence of a pre-charge. It is shown that isolation of the pre-charge effect by using temporary lower heating rates results in an optimum schedule for which the process time is reduced by over 70% when compared to a constant heating rate schedule.

Preshock region acceleration of implanted cometary H(+) and O(+)

NASA Astrophysics Data System (ADS)

Gombosi, T. I.

1988-01-01

A self-consistent, three-fluid model of plasma transport and implanted ion acceleration in the unshocked solar wind is presented. The solar wind plasma is depleted by charge exchange with the expanding cometary exosphere, while implanted protons and heavy ions are produced by photoionization and charge transfer and lost by charge exchange. A generalized transport equation describing convection, adiabatic and diffusive velocity change, and the appropriate production terms is used to describe the evolution of the two cometary ion components, while the moments of the Boltzmann equation are used to calculate the solar wind density and pressure. The flow velocity is obtained self-consistently by combining the conservation equations of the three ion species. The results imply that second-order Fermi acceleration can explain the implanted spectra observed in the unshocked solar wind. Comparison of measured and calculated distribution indicates that spatial diffusion of implanted ions probably plays an important role in forming the energetic particle environment in the shock vicinity.

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

NASA Astrophysics Data System (ADS)

Stanislavsky, Aleksander; Weron, Karina

2008-03-01

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

Study on copper kinetics in processing sulphide ore mixed with copper and zinc with sulfuric acid leaching under pressure

NASA Astrophysics Data System (ADS)

Wen-bo, LUO; Ji-kun, WANG; Yin, GAN

2018-01-01

Sulphide ore mixed with copper and zinc is processed with pressure acid leaching. Research is conducted on the copper kinetic. The stirring rate is set at 600 rpm which could eliminate the influence of external diffusions. Research is conducted on the factors affecting the copper leaching kinetic are temperature, pressure, concentration of sulfuric acid, particle size. The result shows that the apparent activity energy is 50.7 KJ/mol. We could determine that the copper leaching process is shrinking core model of chemical reaction control and work out the leaching equation.

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

From the Highly Compressible Navier-Stokes Equations to Fast Diffusion and Porous Media Equations, Existence of Global Weak Solution for the Quasi-Solutions

NASA Astrophysics Data System (ADS)

Haspot, Boris

2016-06-01

We consider the compressible Navier-Stokes equations for viscous and barotropic fluids with density dependent viscosity. The aim is to investigate mathematical properties of solutions of the Navier-Stokes equations using solutions of the pressureless Navier-Stokes equations, that we call quasi solutions. This regime corresponds to the limit of highly compressible flows. In this paper we are interested in proving the announced result in Haspot (Proceedings of the 14th international conference on hyperbolic problems held in Padova, pp 667-674, 2014) concerning the existence of global weak solution for the quasi-solutions, we also observe that for some choice of initial data (irrotationnal) the quasi solutions verify the porous media, the heat equation or the fast diffusion equations in function of the structure of the viscosity coefficients. In particular it implies that it exists classical quasi-solutions in the sense that they are {C^{∞}} on {(0,T)× {R}N} for any {T > 0}. Finally we show the convergence of the global weak solution of compressible Navier-Stokes equations to the quasi solutions in the case of a vanishing pressure limit process. In particular for highly compressible equations the speed of propagation of the density is quasi finite when the viscosity corresponds to {μ(ρ)=ρ^{α}} with {α > 1}. Furthermore the density is not far from converging asymptotically in time to the Barrenblatt solution of mass the initial density {ρ0}.

Numerical simulation of the hydrodynamical combustion to strange quark matter in the trapped neutrino regime

NASA Astrophysics Data System (ADS)

Ouyed, Amir; Ouyed, Rachid; Jaikumar, Prashanth

2018-02-01

We simulate and study the microphysics of combustion (flame burning) of two flavored quark matter (u,d) to three flavored quark matter (u,d,s) in a trapped neutrino regime applicable to conditions prevailing in a hot proto-neutron star. The reaction-diffusion-advection equations for (u,d) to (u,d,s) combustion are coupled with neutrino transport, which is modeled through a flux-limited diffusion scheme. The flame speed is proportional to initial lepton fraction because of the release of electron chemical potential as heat, and reaches a steady-state burning speed of (0.001-0.008)c. We find that the burning speed is ultimately driven by the neutrino pressure gradient, given that the pressure gradient induced by quarks is opposed by the pressure gradients induced by electrons. This suggests, somewhat counter-intuitively, that the pressure gradients that drive the interface are controlled primarily by leptonic weak decays rather than by the quark Equation of State (EOS). In other words, the effects of the leptonic weak interaction, including the corresponding weak decay rates and the EOS of electrons and neutrinos, are at least as important as the uncertainties related to the EOS of high density matter. We find that for baryon number densities nB ≤ 0.35 fm-3, strong pressure gradients induced by leptonic weak decays drastically slow down the burning speed, which is thereafter controlled by the much slower burning process driven by backflowing downstream matter. We discuss the implications of our findings to proto-neutron stars.

On axisymmetric resistive magnetohydrodynamic equilibria with flow free of Pfirsch-Schlüter diffusion

NASA Astrophysics Data System (ADS)

Throumoulopoulos, G. N.; Tasso, H.

2003-06-01

The equilibrium of an axisymmetric magnetically confined plasma with anisotropic resistivity and incompressible flows parallel to the magnetic field is investigated within the framework of the magnetohydrodynamic (MHD) theory by keeping the convective flow term in the momentum equation. It turns out that the stationary states are determined by a second-order elliptic partial differential equation for the poloidal magnetic flux function ψ along with a decoupled Bernoulli equation for the pressure identical in form with the respective ideal MHD equations; equilibrium consistent expressions for the resistivities η∥ and η⊥ parallel and perpendicular to the magnetic field are also derived from Ohm's and Faraday's laws. Unlike in the case of stationary states with isotropic resistivity and parallel flows [G. N. Throumoulopoulos and H. Tasso, J. Plasma Phys. 64, 601 (2000)] the equilibrium is compatible with nonvanishing poloidal current densities. Also, although exactly Spitzer resistivities either η∥(ψ) or η⊥(ψ) are not allowed, exact solutions with vanishing poloidal electric fields can be constructed with η∥ and η⊥ profiles compatible with roughly collisional resistivity profiles, i.e., profiles having a minimum close to the magnetic axis, taking very large values on the boundary and such that η⊥>η∥. For equilibria with vanishing flows satisfying the relation (dP/dψ)(dI2/dψ)>0, where P and I are the pressure and the poloidal current functions, the difference η⊥-η∥ for the reversed-field pinch scaling, Bp≈Bt, is nearly two times larger than that for the tokamak scaling, Bp≈0.1Bt (Bp and Bt are the poloidal and toroidal magnetic-field components). The particular resistive equilibrium solutions obtained in the present work, inherently free of—but not inconsistent with—Pfirsch-Schlüter diffusion, indicate that parallel flows might result in a reduction of the diffusion observed in magnetically confined plasmas.

Pressure-based high-order TVD methodology for dynamic stall control

NASA Astrophysics Data System (ADS)

Yang, H. Q.; Przekwas, A. J.

1992-01-01

The quantitative prediction of the dynamics of separating unsteady flows, such as dynamic stall, is of crucial importance. This six-month SBIR Phase 1 study has developed several new pressure-based methodologies for solving 3D Navier-Stokes equations in both stationary and moving (body-comforting) coordinates. The present pressure-based algorithm is equally efficient for low speed incompressible flows and high speed compressible flows. The discretization of convective terms by the presently developed high-order TVD schemes requires no artificial dissipation and can properly resolve the concentrated vortices in the wing-body with minimum numerical diffusion. It is demonstrated that the proposed Newton's iteration technique not only increases the convergence rate but also strongly couples the iteration between pressure and velocities. The proposed hyperbolization of the pressure correction equation is shown to increase the solver's efficiency. The above proposed methodologies were implemented in an existing CFD code, REFLEQS. The modified code was used to simulate both static and dynamic stalls on two- and three-dimensional wing-body configurations. Three-dimensional effect and flow physics are discussed.

Reynolds-Stress Budgets in an Impinging Shock Wave/Boundary-Layer Interaction

NASA Technical Reports Server (NTRS)

Vyas, Manan A.; Yoder, Dennis A.; Gaitonde, Datta V.

2018-01-01

Implicit large-eddy simulation (ILES) of a shock wave/boundary-layer interaction (SBLI) was performed. Comparisons with experimental data showed a sensitivity of the current prediction to the modeling of the sidewalls. This was found to be common among various computational studies in the literature where periodic boundary conditions were used in the spanwise direction, as was the case in the present work. Thus, although the experiment was quasi-two-dimensional, the present simulation was determined to be two-dimensional. Quantities present in the exact equation of the Reynolds-stress transport, i.e., production, molecular diffusion, turbulent transport, pressure diffusion, pressure strain, dissipation, and turbulent mass flux were calculated. Reynolds-stress budgets were compared with past large-eddy simulation and direct numerical simulation datasets in the undisturbed portion of the turbulent boundary layer to validate the current approach. The budgets in SBLI showed the growth in the production term for the primary normal stress and energy transfer mechanism was led by the pressure strain term in the secondary normal stresses. The pressure diffusion term, commonly assumed as negligible by turbulence model developers, was shown to be small but non-zero in the normal stress budgets, however it played a key role in the primary shear stress budget.

The effect of water on thermal stresses in polymer composites

NASA Technical Reports Server (NTRS)

Sullivan, Roy M.

1994-01-01

The fundamentals of the thermodynamic theory of mixtures and continuum thermochemistry are reviewed for a mixture of condensed water and polymer. A specific mixture which is mechanically elastic with temperature and water concentration gradients present is considered. An expression for the partial pressure of water in the mixture is obtained based on certain assumptions regarding the thermodynamic state of the water in the mixture. Along with a simple diffusion equation, this partial pressure expression may be used to simulate the thermostructural behavior of polymer composite materials due to water in the free volumes of the polymer. These equations are applied to a specific polymer composite material during isothermal heating conditions. The thermal stresses obtained by the application of the theory are compared to measured results to verify the accuracy of the approach.

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.

Diffusion-driven fluid dynamics in ideal gases and plasmas

NASA Astrophysics Data System (ADS)

Vold, E. L.; Yin, L.; Taitano, W.; Molvig, K.; Albright, B. J.

2018-06-01

The classical transport theory based on Chapman-Enskog methods provides self-consistent approximations for the kinetic flux of mass, heat, and momentum in a fluid limit characterized with a small Knudsen number. The species mass fluxes relative to the center of mass, or "diffusive fluxes," are expressed as functions of known gradient quantities with kinetic coefficients evaluated using similar analyses for mixtures of gases or plasma components. The sum over species of the diffusive mass fluxes is constrained to be zero in the Lagrange frame, and thus results in a non-zero molar flux leading to a pressure perturbation. At an interface between two species initially in pressure equilibrium, the pressure perturbation driven by the diffusive molar flux induces a center of mass velocity directed from the species of greater atomic mass towards the lighter atomic mass species. As the ratio of the species particle masses increases, this center of mass velocity carries an increasingly greater portion of the mass across the interface and for a particle mass ratio greater than about two, the center of mass velocity carries more mass than the gradient driven diffusion flux. Early time transients across an interface between two species in a 1D plasma regime and initially in equilibrium are compared using three methods; a fluid code with closure in a classical transport approximation, a particle in cell simulation, and an implicit Fokker-Planck solver for the particle distribution functions. The early time transient phenomenology is shown to be similar in each of the computational simulation methods, including a pressure perturbation associated with the stationary "induced" component of the center of mass velocity which decays to pressure equilibrium during diffusion. At early times, the diffusive process generates pressure and velocity waves which propagate outward from the interface and are required to maintain momentum conservation. The energy in the outgoing waves dissipates as heat in viscous regions, and it is hypothesized that these diffusion driven waves may sustain fluctuations in less viscid finite domains after reflections from the boundaries. These fluid dynamic phenomena are similar in gases or plasmas and occur in flow transients with a moderate Knudsen number. The analysis and simulation results show how the kinetic flux, represented in the fluid transport closure, directly modifies the mass averaged flow described with the Euler equations.

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.

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.

Diffusive counter dispersion of mass in bubbly media.

PubMed

Goldobin, Denis S; Brilliantov, Nikolai V

2011-11-01

We consider a liquid bearing gas bubbles in a porous medium. When gas bubbles are immovably trapped in a porous matrix by surface-tension forces, the dominant mechanism of transfer of gas mass becomes the diffusion of gas molecules through the liquid. Essentially, the gas solution is in local thermodynamic equilibrium with vapor phase all over the system, i.e., the solute concentration equals the solubility. When temperature and/or pressure gradients are applied, diffusion fluxes appear and these fluxes are faithfully determined by the temperature and pressure fields, not by the local solute concentration, which is enslaved by the former. We derive the equations governing such systems, accounting for thermodiffusion and gravitational segregation effects, which are shown not to be neglected for geological systems-marine sediments, terrestrial aquifers, etc. The results are applied for the treatment of non-high-pressure systems and real geological systems bearing methane or carbon dioxide, where we find a potential possibility of the formation of gaseous horizons deep below a porous medium surface. The reported effects are of particular importance for natural methane hydrate deposits and the problem of burial of industrial production of carbon dioxide in deep aquifers.

Simulation of 2-dimensional viscous flow through cascades using a semi-elliptic analysis and hybrid C-H grids

NASA Technical Reports Server (NTRS)

Ramamurti, R.; Ghia, U.; Ghia, K. N.

1988-01-01

A semi-elliptic formulation, termed the interacting parabolized Navier-Stokes (IPNS) formulation, is developed for the analysis of a class of subsonic viscous flows for which streamwise diffusion is neglible but which are significantly influenced by upstream interactions. The IPNS equations are obtained from the Navier-Stokes equations by dropping the streamwise viscous-diffusion terms but retaining upstream influence via the streamwise pressure-gradient. A two-step alternating-direction-explicit numerical scheme is developed to solve these equations. The quasi-linearization and discretization of the equations are carefully examined so that no artificial viscosity is added externally to the scheme. Also, solutions to compressible as well as nearly compressible flows are obtained without any modification either in the analysis or in the solution process. The procedure is applied to constricted channels and cascade passages formed by airfoils of various shapes. These geometries are represented using numerically generated curilinear boundary-oriented coordinates forming an H-grid. A hybrid C-H grid, more appropriate for cascade of airfoils with rounded leading edges, was also developed. Satisfactory results are obtained for flows through cascades of Joukowski airfoils.

Surface Properties of PEMFC Gas Diffusion Layers

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

WoodIII, David L; Rulison, Christopher; Borup, Rodney

2010-01-01

The wetting properties of PEMFC Gas Diffusion Layers (GDLs) were quantified by surface characterization measurements and modeling of material properties. Single-fiber contact-angle and surface energy (both Zisman and Owens-Wendt) data of a wide spectrum of GDL types is presented to delineate the effects of hydrophobic post-processing treatments. Modeling of the basic sessile-drop contact angle demonstrates that this value only gives a fraction of the total picture of interfacial wetting physics. Polar forces are shown to contribute 10-20 less than dispersive forces to the composite wetting of GDLs. Internal water contact angles obtained from Owens-Wendt analysis were measured at 13-19 highermore » than their single-fiber counterparts. An inverse relationship was found between internal contact angle and both Owens-Wendt surface energy and % polarity of the GDL. The most sophisticated PEMFC mathematical models use either experimentally measured capillary pressures or the standard Young-Laplace capillary-pressure equation. Based on the results of the Owens-Wendt analysis, an advancement to the Young-Laplace equation is proposed for use in these mathematical models, which utilizes only solid surface energies and fractional surface coverage of fluoropolymer. Capillary constants for the spectrum of analyzed GDLs are presented for the same purpose.« less

Frequency Response of Pressure Sensitive Paints

NASA Technical Reports Server (NTRS)

Winslow, Neal A.; Carroll, Bruce F.; Setzer, Fred M.

1996-01-01

An experimental method for measuring the frequency response of Pressure Sensitive Paints (PSP) is presented. These results lead to the development of a dynamic correction technique for PSP measurements which is of great importance to the advancement of PSP as a measurement technique. The ability to design such a dynamic corrector is most easily formed from the frequency response of the given system. An example of this correction technique is shown. In addition to the experimental data, an analytical model for the frequency response is developed from the one dimensional mass diffusion equation.

An atmospheric pressure flow reactor: Gas phase kinetics and mechanism in tropospheric conditions without wall effects

NASA Technical Reports Server (NTRS)

Koontz, Steven L.; Davis, Dennis D.; Hansen, Merrill

1988-01-01

A new type of gas phase flow reactor, designed to permit the study of gas phase reactions near 1 atm of pressure, is described. A general solution to the flow/diffusion/reaction equations describing reactor performance under pseudo-first-order kinetic conditions is presented along with a discussion of critical reactor parameters and reactor limitations. The results of numerical simulations of the reactions of ozone with monomethylhydrazine and hydrazine are discussed, and performance data from a prototype flow reactor are presented.

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.

Plasma Equilibria With Stochastic Magnetic Fields

NASA Astrophysics Data System (ADS)

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

2009-05-01

Plasma equilibria that include regions of stochastic magnetic fields are of interest in a variety of applications, including tokamaks with ergodic limiters and high-pressure stellarators. Such equilibria are examined theoretically, and a numerical algorithm for their construction is described.^2,3 % The balance between stochastic diffusion of magnetic lines and small effects^2 omitted from the simplest MHD description can support pressure and current profiles that need not be flattened in stochastic regions. The diffusion can be described analytically by renormalizing stochastic Langevin equations for pressure and parallel current j, with particular attention being paid to the satisfaction of the periodicity constraints in toroidal configurations with sheared magnetic fields. The equilibrium field configuration can then be constructed by coupling the prediction for j to Amp'ere's law, which is solved numerically. A. Reiman et al., Pressure-induced breaking of equilibrium flux surfaces in the W7AS stellarator, Nucl. Fusion 47, 572--8 (2007). J. A. Krommes and A. H. Reiman, Plasma equilibrium in a magnetic field with stochastic regions, submitted to Phys. Plasmas. J. A. Krommes, Fundamental statistical theories of plasma turbulence in magnetic fields, Phys. Reports 360, 1--351.

Vortex Generators in a Streamline-Traced, External-Compression Supersonic Inlet

NASA Technical Reports Server (NTRS)

Baydar, Ezgihan; Lu, Frank K.; Slater, John W.; Trefny, Charles J.

2017-01-01

Vortex generators within a streamline-traced, external-compression supersonic inlet for Mach 1.66 were investigated to determine their ability to increase total pressure recovery and reduce total pressure distortion. The vortex generators studied were rectangular vanes arranged in counter-rotating and co-rotating arrays. The vane geometric factors of interest included height, length, spacing, angle-of-incidence, and positions upstream and downstream of the inlet terminal shock. The flow through the inlet was simulated numerically through the solution of the steady-state, Reynolds-averaged Navier-Stokes equations on multi-block, structured grids using the Wind-US flow solver. The vanes were simulated using a vortex generator model. The inlet performance was characterized by the inlet total pressure recovery and the radial and circumferential total pressure distortion indices at the engine face. Design of experiments and statistical analysis methods were applied to quantify the effect of the geometric factors of the vanes and search for optimal vane arrays. Co-rotating vane arrays with negative angles-of-incidence positioned on the supersonic diffuser were effective in sweeping low-momentum flow from the top toward the sides of the subsonic diffuser. This distributed the low-momentum flow more evenly about the circumference of the subsonic diffuser and reduced distortion. Co-rotating vane arrays with negative angles-of-incidence or counter-rotating vane arrays positioned downstream of the terminal shock were effective in mixing higher-momentum flow with lower-momentum flow to increase recovery and decrease distortion. A strategy of combining a co-rotating vane array on the supersonic diffuser with a counter-rotating vane array on the subsonic diffuser was effective in increasing recovery and reducing distortion.

Raetrad model extensions for radon entry into multi-level buildings with basements or crawl spaces.

PubMed

Nielson, K K; Rogers, V C; Rogers, V; Holt, R B

1997-10-01

The RAETRAD model was generalized to characterize radon generation and movement from soils and building materials into multi-level buildings with basements or crawl spaces. With the generalization, the model retains its original simplicity and ease of use. The model calculates radon entry rates that are consistent with measurements published for basement test structures at Colorado State University, confirming approximately equal contributions from diffusion and pressure-driven air flow at indoor-outdoor air pressure differences of deltaP(i-o) = -3.5 Pa. About one-fourth of the diffusive radon entry comes from concrete slabs and three-fourths comes from the surrounding soils. Calculated radon entry rates with and without a barrier over floor-wall shrinkage cracks generally agree with Colorado State University measurements when a sustained pressure of deltaP(i-o) = -2 Pa is used to represent calm wind (<1 m s(-1)) conditions. Calculated radon distributions in a 2-level house also are consistent with published measurements and equations.

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.

Evaporation in Capillary Porous Media at the Perfect Piston-Like Invasion Limit: Evidence of Nonlocal Equilibrium Effects

NASA Astrophysics Data System (ADS)

Attari Moghaddam, Alireza; Prat, Marc; Tsotsas, Evangelos; Kharaghani, Abdolreza

2017-12-01

The classical continuum modeling of evaporation in capillary porous media is revisited from pore network simulations of the evaporation process. The computed moisture diffusivity is characterized by a minimum corresponding to the transition between liquid and vapor transport mechanisms confirming previous interpretations. Also the study suggests an explanation for the scattering generally observed in the moisture diffusivity obtained from experimental data. The pore network simulations indicate a noticeable nonlocal equilibrium effect leading to a new interpretation of the vapor pressure-saturation relationship classically introduced to obtain the one-equation continuum model of evaporation. The latter should not be understood as a desorption isotherm as classically considered but rather as a signature of a nonlocal equilibrium effect. The main outcome of this study is therefore that nonlocal equilibrium two-equation model must be considered for improving the continuum modeling of evaporation.

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.

An investigation of the information propagation and entropy transport aspects of Stirling machine numerical simulation

NASA Technical Reports Server (NTRS)

Goldberg, Louis F.

1992-01-01

Aspects of the information propagation modeling behavior of integral machine computer simulation programs are investigated in terms of a transmission line. In particular, the effects of pressure-linking and temporal integration algorithms on the amplitude ratio and phase angle predictions are compared against experimental and closed-form analytic data. It is concluded that the discretized, first order conservation balances may not be adequate for modeling information propagation effects at characteristic numbers less than about 24. An entropy transport equation suitable for generalized use in Stirling machine simulation is developed. The equation is evaluated by including it in a simulation of an incompressible oscillating flow apparatus designed to demonstrate the effect of flow oscillations on the enhancement of thermal diffusion. Numerical false diffusion is found to be a major factor inhibiting validation of the simulation predictions with experimental and closed-form analytic data. A generalized false diffusion correction algorithm is developed which allows the numerical results to match their analytic counterparts. Under these conditions, the simulation yields entropy predictions which satisfy Clausius' inequality.

Communication: On the diffusion tensor in macroscopic theory of cavitation

NASA Astrophysics Data System (ADS)

Shneidman, Vitaly A.

2017-08-01

The classical description of nucleation of cavities in a stretched fluid relies on a one-dimensional Fokker-Planck equation (FPE) in the space of their sizes r, with the diffusion coefficient D(r) constructed for all r from macroscopic hydrodynamics and thermodynamics, as shown by Zeldovich. When additional variables (e.g., vapor pressure) are required to describe the state of a bubble, a similar approach to construct a diffusion tensor D ^ generally works only in the direct vicinity of the thermodynamic saddle point corresponding to the critical nucleus. It is shown, nevertheless, that "proper" kinetic variables to describe a cavity can be selected, allowing to introduce D ^ in the entire domain of parameters. In this way, for the first time, complete FPE's are constructed for viscous volatile and inertial fluids. In the former case, the FPE with symmetric D ^ is solved numerically. Alternatively, in the case of an inertial fluid, an equivalent Langevin equation is considered; results are compared with analytics. The suggested approach is quite general and can be applied beyond the cavitation problem.

Effective diffusion coefficients of gas mixture in heavy oil under constant-pressure conditions

NASA Astrophysics Data System (ADS)

Li, Huazhou Andy; Sun, Huijuan; Yang, Daoyong

2017-05-01

We develop a method to determine the effective diffusion coefficient for each individual component of a gas mixture in a non-volatile liquid (e.g., heavy oil) at high pressures with compositional analysis. Theoretically, a multi-component one-way diffusion model is coupled with the volume-translated Peng-Robinson equation of state to quantify the mass transfer between gas and liquid (e.g., heavy oil). Experimentally, the diffusion tests have been conducted with a PVT setup for one pure CO2-heavy oil system and one C3H8-CO2-heavy oil system under constant temperature and pressure, respectively. Both the gas-phase volume and liquid-phase swelling effect are simultaneously recorded during the measurement. As for the C3H8-CO2-heavy oil system, the gas chromatography method is employed to measure compositions of the gas phase at the beginning and end of the diffusion measurement, respectively. The effective diffusion coefficients are then determined by minimizing the discrepancy between the measured and calculated gas-phase composition at the end of diffusion measurement. The newly developed technique can quantify the contributions of each component of mixture to the bulk mass transfer from gas into liquid. The effective diffusion coefficient of C3H8 in the C3H8-CO2 mixture at 3945 ± 20 kPa and 293.85 K, i.e., 18.19 × 10^{ - 10} {{m}}^{ 2} / {{s}}, is found to be much higher than CO2 at 3950 ± 18 kPa and 293.85 K, i.e., 8.68 × 10^{ - 10} {{m}}^{ 2} / {{s}}. In comparison with pure CO2, the presence of C3H8 in the C3H8-CO2 mixture contributes to a faster diffusion of CO2 from the gas phase into heavy oil and consequently a larger swelling factor of heavy oil.

Pinning and gas oversaturation imply stable single surface nanobubbles.

PubMed

Lohse, Detlef; Zhang, Xuehua

2015-03-01

Surface nanobubbles are experimentally known to survive for days at hydrophobic surfaces immersed in gas-oversaturated water. This is different from bulk nanobubbles, which are pressed out by the Laplace pressure against any gas oversaturation and dissolve in submilliseconds, as derived by Epstein and Plesset [J. Chem. Phys. 18, 1505 (1950)]. Pinning of the contact line has been speculated to be the reason for the stability of the surface nanobubbles. Building on an exact result by Popov [Phys. Rev. E 71, 036313 (2005)] on coffee stain evaporation, here we confirm this speculation by an exact calculation for single surface nanobubbles. It is based only on (i) the diffusion equation, (ii) Laplace pressure, and (iii) Henry's equation, i.e., fluid dynamical equations which are all known to be valid down to the nanometer scale. The crucial parameter is the gas oversaturation ζ of the liquid. At the stable equilibrium, the gas overpressures due to this oversaturation and the Laplace pressure balance. The theory predicts how the contact angle of the pinned bubble depends on ζ and the surface nanobubble's footprint lateral extension L. It also predicts an upper lateral extension threshold for stable surface nanobubbles to exist.

An Extended Trajectory Mechanics Approach for Calculating the Path of a Pressure Transient: Derivation and Illustration

NASA Astrophysics Data System (ADS)

Vasco, D. W.

2018-04-01

Following an approach used in quantum dynamics, an exponential representation of the hydraulic head transforms the diffusion equation governing pressure propagation into an equivalent set of ordinary differential equations. Using a reservoir simulator to determine one set of dependent variables leaves a reduced set of equations for the path of a pressure transient. Unlike the current approach for computing the path of a transient, based on a high-frequency asymptotic solution, the trajectories resulting from this new formulation are valid for arbitrary spatial variations in aquifer properties. For a medium containing interfaces and layers with sharp boundaries, the trajectory mechanics approach produces paths that are compatible with travel time fields produced by a numerical simulator, while the asymptotic solution produces paths that bend too strongly into high permeability regions. The breakdown of the conventional asymptotic solution, due to the presence of sharp boundaries, has implications for model parameter sensitivity calculations and the solution of the inverse problem. For example, near an abrupt boundary, trajectories based on the asymptotic approach deviate significantly from regions of high sensitivity observed in numerical computations. In contrast, paths based on the new trajectory mechanics approach coincide with regions of maximum sensitivity to permeability changes.

Determination of diffusion coefficients of hydrogen and deuterium in Zr-2.5%Nb pressure tube material using hot vacuum extraction-quadrupole mass spectrometry

NASA Astrophysics Data System (ADS)

Shrivastava, Komal Chandra; Kulkarni, A. S.; Ramanjaneyulu, P. S.; Sunil, Saurav; Saxena, M. K.; Singh, R. N.; Tomar, B. S.; Ramakumar, K. L.

2015-06-01

The diffusion coefficients of hydrogen and deuterium in Zr-2.5%Nb alloy were measured in the temperature range 523 to 673 K, employing hot vacuum extraction-quadrupole mass spectrometry (HVE-QMS). One end of the Zr-2.5%Nb alloy specimens was charged electrolytically with the desired hydrogen isotope. After annealing at different temperatures for a predetermined time, the specimens were cut into thin slices, which were analyzed for their H2/D2 content using the HVE-QMS technique. The depth profile data were fitted into the equation representing the solution of Fick's second law of diffusion. The activation energy of hydrogen/deuterium diffusion was obtained from the Arrhenius relation between the diffusion coefficient and temperature. The temperature dependent diffusion coefficient can be represented as DH = 1.41 × 10-7 exp(-36,000/RT) and DD = 6.16 × 10-8 exp(-35,262/RT) for hydrogen and deuterium, respectively.

Summer Work Experience: Determining Methane Combustion Mechanisms and Sub-Scale Diffuser Properties for Space Transporation System Engine Testing

NASA Technical Reports Server (NTRS)

Williams, Powtawche N.

1998-01-01

To assess engine performance during the testing of Space Shuttle Main Engines (SSMEs), the design of an optimal altitude diffuser is studied for future Space Transportation Systems (STS). For other Space Transportation Systems, rocket propellant using kerosene is also studied. Methane and dodecane have similar reaction schemes as kerosene, and are used to simulate kerosene combustion processes at various temperatures. The equations for the methane combustion mechanism at high temperature are given, and engine combustion is simulated on the General Aerodynamic Simulation Program (GASP). The successful design of an altitude diffuser depends on the study of a sub-scaled diffuser model tested through two-dimensional (2-D) flow-techniques. Subroutines given calculate the static temperature and pressure at each Mach number within the diffuser flow. Implementing these subroutines into program code for the properties of 2-D compressible fluid flow determines all fluid characteristics, and will be used in the development of an optimal diffuser design.

The specific diffusion behaviour in paper and migration modelling from recycled board into dry foodstuffs.

PubMed

Hauder, J; Benz, H; Rüter, M; Piringer, O-G

2013-01-01

Recycled board plays an important role in food packaging, but the great variety of organic impurities must be considered as potential food contaminants. The diffusion behaviour of the impurities is significantly different from that in plastic materials. The two-layer concept for paper and board introduced recently is now treated in more detail. In the rate-determining surface region the diffusion coefficients of the n-alkanes in the homologous series with 15-35 carbon atoms decrease proportionally as their vapour pressures. This leads to a different equation of the diffusion coefficients in comparison with that for the core layer. Different polarities of the migrants have additional influences on the diffusion due to their interactions with the fibre matrix. A new analytical method for the quantification of aromatic impurities has previously been developed. Based on this method and on the described diffusion behaviour, a migration model for specific and global mass transfer of impurities from recycled board into dry food and food simulants is given.

The Martian climate and energy balance models with CO2/H2O atmospheres

NASA Technical Reports Server (NTRS)

Hoffert, M. I.

1986-01-01

The analysis begins with a seasonal energy balance model (EBM) for Mars. This is used to compute surface temperature versus x = sin(latitude) and time over the seasonal cycle. The core model also computes the evolving boundaries of the CO2 icecaps, net sublimational/condensation rates, and the resulting seasonal pressure wave. Model results are compared with surface temperature and pressure history data at Viking lander sites, indicating fairly good agreement when meridional heat transport is represented by a thermal diffusion coefficient D approx. 0.015 W/sq. m/K. Condensational wind distributions are also computed. An analytic model of Martian wind circulation is then proposed, as an extension of the EMB, which incorporates vertical wind profiles containing an x-dependent function evaluated by substitution in the equation defining the diffusion coefficient. This leads to a parameterization of D(x) and of the meridional circulation which recovers the high surface winds predicted by dynamic Mars atmosphere models (approx. 10 m/sec). Peak diffusion coefficients, D approx. 0.6 w/sq m/K, are found over strong Hadley zones - some 40 times larger than those of high-latitude baroclinic eddies. When the wind parameterization is used to find streamline patterns over Martian seasons, the resulting picture shows overturning hemispheric Hadley cells crossing the equator during solstices, and attaining peak intensities during the south summer dust storm season, while condensational winds are most important near the polar caps.

Group invariant solution for a pre-existing fluid-driven fracture in impermeable rock

NASA Astrophysics Data System (ADS)

Fitt, A. D.; Mason, D. P.; Moss, E. A.

2007-11-01

The propagation of a two-dimensional fluid-driven fracture in impermeable rock is considered. The fluid flow in the fracture is laminar. By applying lubrication theory a partial differential equation relating the half-width of the fracture to the fluid pressure is derived. To close the model the PKN formulation is adopted in which the fluid pressure is proportional to the half-width of the fracture. By considering a linear combination of the Lie point symmetries of the resulting non-linear diffusion equation the boundary value problem is expressed in a form appropriate for a similarity solution. The boundary value problem is reformulated as two initial value problems which are readily solved numerically. The similarity solution describes a preexisting fracture since both the total volume and length of the fracture are initially finite and non-zero. Applications in which the rate of fluid injection into the fracture and the pressure at the fracture entry are independent of time are considered.

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.

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.

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.

Instability of turing patterns in reaction-diffusion-ODE systems.

PubMed

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

2017-02-01

The aim of this paper is to contribute to the understanding of the pattern formation phenomenon in reaction-diffusion equations coupled with ordinary differential equations. Such systems of equations arise, for example, from modeling of interactions between cellular processes such as cell growth, differentiation or transformation and diffusing signaling factors. We focus on stability analysis of solutions of a prototype model consisting of a single reaction-diffusion equation coupled to an ordinary differential equation. We show that such systems are very different from classical reaction-diffusion models. They exhibit diffusion-driven instability (turing instability) under a condition of autocatalysis of non-diffusing component. However, the same mechanism which destabilizes constant solutions of such models, destabilizes also all continuous spatially heterogeneous stationary solutions, and consequently, there exist no stable Turing patterns in such reaction-diffusion-ODE systems. We provide a rigorous result on the nonlinear instability, which involves the analysis of a continuous spectrum of a linear operator induced by the lack of diffusion in the destabilizing equation. These results are extended to discontinuous patterns for a class of nonlinearities.

Effects of High-energy Particles on Accretion Flows onto a Supermassive Black Hole

NASA Astrophysics Data System (ADS)

Kimura, Shigeo S.; Toma, Kenji; Takahara, Fumio

2014-08-01

We study the effects of high-energy particles (HEPs) on the accretion flows onto a supermassive black hole and luminosities of escaping particles such as protons, neutrons, gamma rays, and neutrinos. We formulate a one-dimensional model of the two-component accretion flow consisting of thermal particles and HEPs, supposing that some fraction of the released energy is converted to the acceleration of HEPs. The thermal component is governed by fluid dynamics while the HEPs obey the moment equations of the diffusion-convection equation. By solving the time evolution of these equations, we obtain advection-dominated flows as the steady state solutions. The effects of the HEPs on the flow structures turn out to be small even if the pressure of the HEPs dominates over the thermal pressure. For a model in which the escaping protons take away almost all the energy released, the HEPs have a large enough influence to make the flow have a Keplerian angular velocity at the inner region. We calculate the luminosities of the escaping particles for these steady solutions. The escaping particles can extract the energy from about 10^{-4}\\dot{M} c^2 to 10^{-2}\\dot{M} c^2, where \\dot{M} is the mass accretion rate. The luminosities of the escaping particles depend on parameters such as the injection Lorentz factors, the mass accretion rates, and the diffusion coefficients. We also discuss some implications on the relativistic jet production by the escaping particles.

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.

Combustion of liquid-fuel droplets in supercritical conditions

NASA Technical Reports Server (NTRS)

Shuen, J. S.; Yang, Vigor; Hsaio, C. C.

1992-01-01

A comprehensive analysis of liquid-fuel droplet combustion in both subcritical and supercritical environments has been conducted. The formulation is based on the complete conservation equations for both gas and liquid phases, and accommodates variable thermophysical properties, finite-rate chemical kinetics, and a full treatment of liquid-vapor phase equilibrium at the drop surface. The governing equations and associated interfacial boundary conditions are solved numerically using a fully coupled, implicit scheme with the dual time-stepping integration technique. The model is capable of treating the entire droplet history, including the transition from the subcritical to supercritical state. As a specific example, the combustion of n-pentane fuel droplets in air is studied for pressures in the range of 5-140 atm. Results indicate that the ambient gas pressure exerts significant control of droplet gasification and burning processes through its influence on fluid transport, gas-liquid interfacial thermodynamics, and chemical reactions. The droplet gasification rate increases progressively with pressure. However, the data for the overall burnout time exhibit a considerable change in the combustion mechanism at the critical pressure, mainly as a result of reduced mass diffusivity and latent heat of vaporization with increased pressure.

Combustion of liquid fuel droplets in supercritical conditions

NASA Technical Reports Server (NTRS)

Shuen, J. S.; Yang, Vigor

1991-01-01

A comprehensive analysis of liquid-fuel droplet combustion in both sub- and super-critical environments has been conducted. The formulation is based on the complete conservation equations for both gas and liquid phases, and accommodates finite-rate chemical kinetics and a full treatment of liquid-vapor phase equilibrium at the droplet surface. The governing equations and the associated interface boundary conditions are solved numerically using a fully coupled, implicit scheme with the dual time-stepping integration technique. The model is capable of treating the entire droplet history, including the transition from the subcritical to the supercritical state. As a specific example, the combustion of n-pentane fuel droplets in air is studied for pressures of 5-140 atm. Results indicate that the ambient gas pressure exerts significant control of droplet gasification and burning processes through its influences on the fluid transport, gas/liquid interface thermodynamics, and chemical reactions. The droplet gasification rate increases progressively with pressure. However, the data for the overall burnout time exhibits a significant variation near the critical burning pressure, mainly as a result of reduced mass-diffusion rate and latent heat of vaporization with increased pressure. The influence of droplet size on the burning characteristics is also noted.

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

Oxygen potentials, oxygen diffusion coefficients and defect equilibria of nonstoichiometric (U,Pu)O2±x

NASA Astrophysics Data System (ADS)

Kato, Masato; Watanabe, Masashi; Matsumoto, Taku; Hirooka, Shun; Akashi, Masatoshi

2017-04-01

Oxygen potential of (U,Pu)O2±x was evaluated based on defect chemistry using an updated experimental data set. The relationship between oxygen partial pressure and deviation x in (U,Pu)O2±x was analyzed, and equilibrium constants of defect formation were determined as functions of Pu content and temperature. Brouwer's diagrams were constructed using the determined equilibrium constants, and a relational equation to determine O/M ratio was derived as functions of O/M ratio, Pu content and temperature. In addition, relationship between oxygen potential and oxygen diffusion coefficients were described.

A 2D model of axial symmetry for proximal tubule of an average human nephron: indicative results of diffusion, convection and absorption processes

NASA Astrophysics Data System (ADS)

Insfrán, J. F.; Ubal, S.; Di Paolo, y. J.

2016-04-01

A simplified model of a proximal convoluted tubule of an average human nephron is presented. The model considers the 2D axisymmetric flow of the luminal solution exchanging matter with the tubule walls and the peritubular fluid by means of 0D models for the epithelial cells. The tubule radius is considered to vary along the conduit due to the trans-epithelial pressure difference. The fate of more than ten typical solutes is tracked down by the model. The Navier-Stokes and Reaction-Diffusion-Advection equations (considering the electro-neutrality principle) are solved in the lumen, giving a detailed picture of the velocity, pressure and concentration fields, along with trans-membrane fluxes and tubule deformation, via coupling with the 0D model for the tubule wall. The calculations are carried out numerically by means of the finite element method. The results obtained show good agreement with those published by other authors using models that ignore the diffusive transport and disregard a detailed calculation of velocity, pressure and concentrations. This work should be seen as a first approach towards the development of a more comprehensive model of the filtration process taking place in the kidneys, which ultimately helps in devising a device that can mimic/complement the renal function.

Comparison between results of solution of Burgers' equation and Laplace's equation by Galerkin and least-square finite element methods

NASA Astrophysics Data System (ADS)

Adib, Arash; Poorveis, Davood; Mehraban, Farid

2018-03-01

In this research, two equations are considered as examples of hyperbolic and elliptic equations. In addition, two finite element methods are applied for solving of these equations. The purpose of this research is the selection of suitable method for solving each of two equations. Burgers' equation is a hyperbolic equation. This equation is a pure advection (without diffusion) equation. This equation is one-dimensional and unsteady. A sudden shock wave is introduced to the model. This wave moves without deformation. In addition, Laplace's equation is an elliptical equation. This equation is steady and two-dimensional. The solution of Laplace's equation in an earth dam is considered. By solution of Laplace's equation, head pressure and the value of seepage in the directions X and Y are calculated in different points of earth dam. At the end, water table is shown in the earth dam. For Burgers' equation, least-square method can show movement of wave with oscillation but Galerkin method can not show it correctly (the best method for solving of the Burgers' equation is discrete space by least-square finite element method and discrete time by forward difference.). For Laplace's equation, Galerkin and least square methods can show water table correctly in earth dam.

A New Ghost Cell/Level Set Method for Moving Boundary Problems: Application to Tumor Growth

PubMed Central

Macklin, Paul

2011-01-01

In this paper, we present a ghost cell/level set method for the evolution of interfaces whose normal velocity depend upon the solutions of linear and nonlinear quasi-steady reaction-diffusion equations with curvature-dependent boundary conditions. Our technique includes a ghost cell method that accurately discretizes normal derivative jump boundary conditions without smearing jumps in the tangential derivative; a new iterative method for solving linear and nonlinear quasi-steady reaction-diffusion equations; an adaptive discretization to compute the curvature and normal vectors; and a new discrete approximation to the Heaviside function. We present numerical examples that demonstrate better than 1.5-order convergence for problems where traditional ghost cell methods either fail to converge or attain at best sub-linear accuracy. We apply our techniques to a model of tumor growth in complex, heterogeneous tissues that consists of a nonlinear nutrient equation and a pressure equation with geometry-dependent jump boundary conditions. We simulate the growth of glioblastoma (an aggressive brain tumor) into a large, 1 cm square of brain tissue that includes heterogeneous nutrient delivery and varied biomechanical characteristics (white matter, gray matter, cerebrospinal fluid, and bone), and we observe growth morphologies that are highly dependent upon the variations of the tissue characteristics—an effect observed in real tumor growth. PMID:21331304

Simulation of naturally fractured reservoirs

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

Saidi, A.M.

1983-11-01

A three-dimensional, three-phase reservoir simulator was developed to study the behavior of fully or partially fractured reservoirs. It is also demonstrated, that when a fractured reservoir is subject to a relatively large rate of pressure drop and/or it composed of relatively large blocks, the pseudo steady-state pressure concept gives large errors as compared with transient fromulation. In addition, when gravity drainage and imbibitum processes, which is the most important mechanism in the fractured reservoirs, are represented by a ''lumped parameter'' even larger errors can be produced in exchange flow between matrix and fractures. For these reasons, the matrix blocks aremore » gridded and the transfer between matrix and fractures are calculated using pressure and diffusion transient concept. In this way the gravity drainage is also calculated accurately. As the matrix-fracture exchange flow depends on the location of each matrix grid relative to the GOC and/or WOC in fracture, the exchange flow equation are derived and given for each possible case. The differential equation describing the flow of water, oil, and gas within the matrix and fracture system, each of which may contain six unknowns, are presented. The two sets of equations are solved implicitly for pressure water, and gas stauration in both matrix and fractures. The first twenty two years of the history of Haft Kel field was successfully matched with this model and the results are included.« less

Simulations of the stratocumulus-topped boundary layer with a third-order closure model

NASA Technical Reports Server (NTRS)

Moeng, C. H.; Randall, D. A.

1984-01-01

A third order closure model is proposed by Andre et al. (1982), in which the time rate of change terms, the relaxation and rapid effects for the pressure related terms, and the clipping approximation are included along with the quasi-normal closure, to study turbulence in a cloudy layer which is cooled radiatively from above. A spurious oscillation which is strongest near the inversion occurs. An analysis of the problem shows that the oscillation arises from the mean gradient and buoyancy terms of the triple moment equations; these terms are largest near the cloud top. The oscillation is physical, rather than computational. In nature the oscillation is effectively damped, by a mechanism which apparently is not included in our model. In the stably stratified layer just above the mixed layer top, turbulence can excite gravity waves, whose energy is radiated away. Because the closure assumption for the pressure terms does not take into account the transport of wave energy, the model generates spurious oscillations. Damping of the oscillations is possible by introducing diffusion terms into the triple moment equations. With a large enough choice for the diffusion coefficient, the oscillation is effectively eliminated. The results are quite sensitive to the ad hoc eddy coefficient.

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.

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.

Projection methods for incompressible flow problems with WENO finite difference schemes

NASA Astrophysics Data System (ADS)

de Frutos, Javier; John, Volker; Novo, Julia

2016-03-01

Weighted essentially non-oscillatory (WENO) finite difference schemes have been recommended in a competitive study of discretizations for scalar evolutionary convection-diffusion equations [20]. This paper explores the applicability of these schemes for the simulation of incompressible flows. To this end, WENO schemes are used in several non-incremental and incremental projection methods for the incompressible Navier-Stokes equations. Velocity and pressure are discretized on the same grid. A pressure stabilization Petrov-Galerkin (PSPG) type of stabilization is introduced in the incremental schemes to account for the violation of the discrete inf-sup condition. Algorithmic aspects of the proposed schemes are discussed. The schemes are studied on several examples with different features. It is shown that the WENO finite difference idea can be transferred to the simulation of incompressible flows. Some shortcomings of the methods, which are due to the splitting in projection schemes, become also obvious.

The cosmic-ray shock structure problem for relativistic shocks

NASA Technical Reports Server (NTRS)

Webb, G. M.

1985-01-01

The time asymptotic behaviour of a relativistic (parallel) shock wave significantly modified by the diffusive acceleration of cosmic-rays is investigated by means of relativistic hydrodynamical equations for both the cosmic-rays and thermal gas. The form of the shock structure equation and the dispersion relation for both long and short wavelength waves in the system are obtained. The dependence of the shock acceleration efficiency on the upstream fluid spped, long wavelength Mach number and the ratio N = P sub co/cP sub co+P sub go)(Psub co and P sub go are the upstream cosmic-ray and thermal gas pressures respectively) are studied.

Spatial model of convective solute transport in brain extracellular space does not support a “glymphatic” mechanism

PubMed Central

Jin, Byung-Ju; Smith, Alex J.

2016-01-01

A “glymphatic system,” which involves convective fluid transport from para-arterial to paravenous cerebrospinal fluid through brain extracellular space (ECS), has been proposed to account for solute clearance in brain, and aquaporin-4 water channels in astrocyte endfeet may have a role in this process. Here, we investigate the major predictions of the glymphatic mechanism by modeling diffusive and convective transport in brain ECS and by solving the Navier–Stokes and convection–diffusion equations, using realistic ECS geometry for short-range transport between para-arterial and paravenous spaces. Major model parameters include para-arterial and paravenous pressures, ECS volume fraction, solute diffusion coefficient, and astrocyte foot-process water permeability. The model predicts solute accumulation and clearance from the ECS after a step change in solute concentration in para-arterial fluid. The principal and robust conclusions of the model are as follows: (a) significant convective transport requires a sustained pressure difference of several mmHg between the para-arterial and paravenous fluid and is not affected by pulsatile pressure fluctuations; (b) astrocyte endfoot water permeability does not substantially alter the rate of convective transport in ECS as the resistance to flow across endfeet is far greater than in the gaps surrounding them; and (c) diffusion (without convection) in the ECS is adequate to account for experimental transport studies in brain parenchyma. Therefore, our modeling results do not support a physiologically important role for local parenchymal convective flow in solute transport through brain ECS. PMID:27836940

Spatial model of convective solute transport in brain extracellular space does not support a "glymphatic" mechanism.

PubMed

Jin, Byung-Ju; Smith, Alex J; Verkman, Alan S

2016-12-01

A "glymphatic system," which involves convective fluid transport from para-arterial to paravenous cerebrospinal fluid through brain extracellular space (ECS), has been proposed to account for solute clearance in brain, and aquaporin-4 water channels in astrocyte endfeet may have a role in this process. Here, we investigate the major predictions of the glymphatic mechanism by modeling diffusive and convective transport in brain ECS and by solving the Navier-Stokes and convection-diffusion equations, using realistic ECS geometry for short-range transport between para-arterial and paravenous spaces. Major model parameters include para-arterial and paravenous pressures, ECS volume fraction, solute diffusion coefficient, and astrocyte foot-process water permeability. The model predicts solute accumulation and clearance from the ECS after a step change in solute concentration in para-arterial fluid. The principal and robust conclusions of the model are as follows: (a) significant convective transport requires a sustained pressure difference of several mmHg between the para-arterial and paravenous fluid and is not affected by pulsatile pressure fluctuations; (b) astrocyte endfoot water permeability does not substantially alter the rate of convective transport in ECS as the resistance to flow across endfeet is far greater than in the gaps surrounding them; and (c) diffusion (without convection) in the ECS is adequate to account for experimental transport studies in brain parenchyma. Therefore, our modeling results do not support a physiologically important role for local parenchymal convective flow in solute transport through brain ECS. © 2016 Jin et al.

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

On the modelling of non-reactive and reactive turbulent combustor flows

NASA Technical Reports Server (NTRS)

Nikjooy, Mohammad; So, Ronald M. C.

1987-01-01

A study of non-reactive and reactive axisymmetric combustor flows with and without swirl is presented. Closure of the Reynolds equations is achieved by three models: kappa-epsilon, algebraic stress and Reynolds stress closure. Performance of two locally nonequilibrium and one equilibrium algebraic stress models is analyzed assuming four pressure strain models. A comparison is also made of the performance of a high and a low Reynolds number model for combustor flow calculations using Reynolds stress closures. Effects of diffusion and pressure-strain models on these closures are also investigated. Two models for the scalar transport are presented. One employs the second-moment closure which solves the transport equations for the scalar fluxes, while the other solves the algebraic equations for the scalar fluxes. In addition, two cases of non-premixed and one case of premixed combustion are considered. Fast- and finite-rate chemistry models are applied to non-premixed combustion. Both show promise for application in gas turbine combustors. However, finite rate chemistry models need to be examined to establish a suitable coupling of the heat release effects on turbulence field and rate constants.

Scaling of postinjection-induced seismicity: An approach to assess hydraulic fracturing related processes

NASA Astrophysics Data System (ADS)

Johann, Lisa; Dinske, Carsten; Shapiro, Serge

2017-04-01

Fluid injections into unconventional reservoirs have become a standard for the enhancement of fluid-mobility parameters. Microseismic activity during and after the injection can be frequently directly associated with subsurface fluid injections. Previous studies demonstrate that postinjection-induced seismicity has two important characteristics: On the one hand, the triggering front, which corresponds to early and distant events and envelops farthest induced events. On the other hand, the back front, which describes the lower boundary of the seismic cloud and envelops the aseismic domain evolving around the source after the injection stop. A lot of research has been conducted in recent years to understand seismicity-related processes. For this work, we follow the assumption that the diffusion of pore-fluid pressure is the dominant triggering mechanism. Based on Terzaghi's concept of an effective normal stress, the injection of fluids leads to increasing pressures which in turn reduce the effective normal stress and lead to sliding along pre-existing critically stressed and favourably oriented fractures and cracks. However, in many situations, spatio-temporal signatures of induced events are captured by a rather non-linear process of pore-fluid pressure diffusion, where the hydraulic diffusivity becomes pressure-dependent. This is for example the case during hydraulic fracturing where hydraulic transport properties are significantly enhanced. For a better understanding of processes related to postinjection-induced seismicity, we analytically describe the temporal behaviour of triggering and back fronts. We introduce a scaling law which shows that postinjection-induced events are sensitive to the degree of non-linearity and to the Euclidean dimension of the seismic cloud (see Johann et al., 2016, JGR). To validate the theory, we implement comprehensive modelling of non-linear pore-fluid pressure diffusion in 3D. We solve numerically for the non-linear equation of diffusion with a power-law dependent hydraulic diffusivity on pressure and generate catalogues of synthetic seismicity. We study spatio-temporal features of the seismic clouds and compare the results to theoretical values predicted by the novel scaling law. Subsequently, we apply the scaling relation to real hydraulic fracturing and Enhanced Geothermal System data. Our results show that the derived scaling relations well describe synthetic and real data. Thus, the methodology can be used to obtain hydraulic reservoir properties and can contribute significantly to a general understanding of injection related processes as well as to hazard assessment.

Effect of Structure on Transport Properties (Viscosity, Ionic Conductivity, and Self-Diffusion Coefficient) of Aprotic Heterocyclic Anion (AHA) Room-Temperature Ionic Liquids. 1. Variation of Anionic Species.

PubMed

Sun, Liyuan; Morales-Collazo, Oscar; Xia, Han; Brennecke, Joan F

2015-12-03

A series of room temperature ionic liquids (RTILs) based on 1-ethyl-3-methylimidazolium ([emim](+)) with different aprotic heterocyclic anions (AHAs) were synthesized and characterized as potential electrolyte candidates for lithium ion batteries. The density and transport properties of these ILs were measured over the temperature range between 283.15 and 343.15 K at ambient pressure. The temperature dependence of the transport properties (viscosity, ionic conductivity, self-diffusion coefficient, and molar conductivity) is fit well by the Vogel-Fulcher-Tamman (VFT) equation. The best-fit VFT parameters, as well as linear fits to the density, are reported. The ionicity of these ILs was quantified by the ratio of the molar conductivity obtained from the ionic conductivity and molar concentration to that calculated from the self-diffusion coefficients using the Nernst-Einstein equation. The results of this study, which is based on ILs composed of both a planar cation and planar anions, show that many of the [emim][AHA] ILs exhibit very good conductivity for their viscosities and provide insight into the design of ILs with enhanced dynamics that may be suitable for electrolyte applications.

Thermal engineering research. [Runge-Kutta investigation of gas flow inside multilayer insulation system for rocket booster fuel tanks

NASA Technical Reports Server (NTRS)

Shih, C. C.

1973-01-01

A theoretical investigation of gas flow inside a multilayer insulation system has been made for the case of the broadside pumping process. A set of simultaneous first-order differential equations for the temperature and pressure of the gas mixture was obtained by considering the diffusion mechanism of the gas molecules through the perforations on the insulation layers. A modified Runge-Kutta method was used for numerical experiment. The numerical stability problem was investigated. It has been shown that when the relaxation time is small compared with the time period over which the gas properties change appreciably, the set of differential equations can be replaced by a set of algebraic equations for solution. Numerical examples were given, and comparisons with experimental data were made.

Low Mach number fluctuating hydrodynamics of multispecies liquid mixtures

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

Donev, Aleksandar, E-mail: donev@courant.nyu.edu; Bhattacharjee, Amit Kumar; Nonaka, Andy

We develop a low Mach number formulation of the hydrodynamic equations describing transport of mass and momentum in a multispecies mixture of incompressible miscible liquids at specified temperature and pressure, which generalizes our prior work on ideal mixtures of ideal gases [Balakrishnan et al., “Fluctuating hydrodynamics of multispecies nonreactive mixtures,” Phys. Rev. E 89 013017 (2014)] and binary liquid mixtures [Donev et al., “Low mach number fluctuating hydrodynamics of diffusively mixing fluids,” Commun. Appl. Math. Comput. Sci. 9(1), 47-105 (2014)]. In this formulation, we combine and extend a number of existing descriptions of multispecies transport available in the literature. Themore » formulation applies to non-ideal mixtures of arbitrary number of species, without the need to single out a “solvent” species, and includes contributions to the diffusive mass flux due to gradients of composition, temperature, and pressure. Momentum transport and advective mass transport are handled using a low Mach number approach that eliminates fast sound waves (pressure fluctuations) from the full compressible system of equations and leads to a quasi-incompressible formulation. Thermal fluctuations are included in our fluctuating hydrodynamics description following the principles of nonequilibrium thermodynamics. We extend the semi-implicit staggered-grid finite-volume numerical method developed in our prior work on binary liquid mixtures [Nonaka et al., “Low mach number fluctuating hydrodynamics of binary liquid mixtures,” http://arxiv.org/abs/1410.2300 (2015)] and use it to study the development of giant nonequilibrium concentration fluctuations in a ternary mixture subjected to a steady concentration gradient. We also numerically study the development of diffusion-driven gravitational instabilities in a ternary mixture and compare our numerical results to recent experimental measurements [Carballido-Landeira et al., “Mixed-mode instability of a miscible interface due to coupling between Rayleigh–Taylor and double-diffusive convective modes,” Phys. Fluids 25, 024107 (2013)] in a Hele-Shaw cell. We find that giant nonequilibrium fluctuations can trigger the instability but are eventually dominated by the deterministic growth of the unstable mode, in both quasi-two-dimensional (Hele-Shaw) and fully three-dimensional geometries used in typical shadowgraph experiments.« less

Effects of pressure on the magnetic properties of FeO: A diffusion Monte Carlo study

NASA Astrophysics Data System (ADS)

Townsend, Joshua; Shulenburger, Luke; Mattsson, Thomas; Esler, Ken; Cohen, Ronald

While simple in terms of structure and composition, both experimental and computational investigations have demonstrated that FeO has a rich phase diagram of structural phase transformations, electronic spin transitions, insulator-metal transitions, and magnetic ordering transitions, due to the open-shell occupation of the Fe 3d electrons. We investigated the magnetic and electronic structures of FeO under ambient and high pressure conditions using diffusion Quantum Monte Carlo (QMC) within the fixed-node approximation. QMC techniques are especially well suited to the study of strongly correlated systems because they explicitly include correlation into the ground-state wave function. Here we report on the effects of the choice of trial wave function on the ambient pressure lattice distortion due to AFM ordering, as well as the equation of state, spin collapse, and metal-insulator transitions. Sandia National Laboratories is a multi-mission laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE.

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

Nanoscale simulation of shale transport properties using the lattice Boltzmann method: Permeability and diffusivity

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

Chen, Li; Zhang, Lei; Kang, Qinjun

Here, porous structures of shales are reconstructed using the markov chain monte carlo (MCMC) method based on scanning electron microscopy (SEM) images of shale samples from Sichuan Basin, China. Characterization analysis of the reconstructed shales is performed, including porosity, pore size distribution, specific surface area and pore connectivity. The lattice Boltzmann method (LBM) is adopted to simulate fluid flow and Knudsen diffusion within the reconstructed shales. Simulation results reveal that the tortuosity of the shales is much higher than that commonly employed in the Bruggeman equation, and such high tortuosity leads to extremely low intrinsic permeability. Correction of the intrinsicmore » permeability is performed based on the dusty gas model (DGM) by considering the contribution of Knudsen diffusion to the total flow flux, resulting in apparent permeability. The correction factor over a range of Knudsen number and pressure is estimated and compared with empirical correlations in the literature. We find that for the wide pressure range investigated, the correction factor is always greater than 1, indicating Knudsen diffusion always plays a role on shale gas transport mechanisms in the reconstructed shales. Specifically, we found that most of the values of correction factor fall in the slip and transition regime, with no Darcy flow regime observed.« less

Nanoscale simulation of shale transport properties using the lattice Boltzmann method: Permeability and diffusivity

DOE PAGES

Chen, Li; Zhang, Lei; Kang, Qinjun; ...

2015-01-28

Here, porous structures of shales are reconstructed using the markov chain monte carlo (MCMC) method based on scanning electron microscopy (SEM) images of shale samples from Sichuan Basin, China. Characterization analysis of the reconstructed shales is performed, including porosity, pore size distribution, specific surface area and pore connectivity. The lattice Boltzmann method (LBM) is adopted to simulate fluid flow and Knudsen diffusion within the reconstructed shales. Simulation results reveal that the tortuosity of the shales is much higher than that commonly employed in the Bruggeman equation, and such high tortuosity leads to extremely low intrinsic permeability. Correction of the intrinsicmore » permeability is performed based on the dusty gas model (DGM) by considering the contribution of Knudsen diffusion to the total flow flux, resulting in apparent permeability. The correction factor over a range of Knudsen number and pressure is estimated and compared with empirical correlations in the literature. We find that for the wide pressure range investigated, the correction factor is always greater than 1, indicating Knudsen diffusion always plays a role on shale gas transport mechanisms in the reconstructed shales. Specifically, we found that most of the values of correction factor fall in the slip and transition regime, with no Darcy flow regime observed.« less

Nanoscale simulation of shale transport properties using the lattice Boltzmann method: permeability and diffusivity

PubMed Central

Chen, Li; Zhang, Lei; Kang, Qinjun; Viswanathan, Hari S.; Yao, Jun; Tao, Wenquan

2015-01-01

Porous structures of shales are reconstructed using the markov chain monte carlo (MCMC) method based on scanning electron microscopy (SEM) images of shale samples from Sichuan Basin, China. Characterization analysis of the reconstructed shales is performed, including porosity, pore size distribution, specific surface area and pore connectivity. The lattice Boltzmann method (LBM) is adopted to simulate fluid flow and Knudsen diffusion within the reconstructed shales. Simulation results reveal that the tortuosity of the shales is much higher than that commonly employed in the Bruggeman equation, and such high tortuosity leads to extremely low intrinsic permeability. Correction of the intrinsic permeability is performed based on the dusty gas model (DGM) by considering the contribution of Knudsen diffusion to the total flow flux, resulting in apparent permeability. The correction factor over a range of Knudsen number and pressure is estimated and compared with empirical correlations in the literature. For the wide pressure range investigated, the correction factor is always greater than 1, indicating Knudsen diffusion always plays a role on shale gas transport mechanisms in the reconstructed shales. Specifically, we found that most of the values of correction factor fall in the slip and transition regime, with no Darcy flow regime observed. PMID:25627247

Numerical simulation of the generation of reactive oxygen and nitrogen species (RONS) in water by atmospheric-pressure plasmas and their effects on Escherichia coli (E. coli)

NASA Astrophysics Data System (ADS)

Ikuse, Kazumasa; Hamaguchi, Satoshi

2016-09-01

We have used two types of numerical simulations to examine biological effects of reactive oxygen and nitrogen species (RONS) generated in water by an atmospheric-pressure plasma (APP) that irradiates the water surface. One is numerical simulation for the generation and transport of RONS in water based on the reaction-diffusion-advection equations coupled with Poisson equation. The rate constants, mobilities, and diffusion coefficients used in the equations are obtained from the literature. The gaseous species are given as boundary conditions and time evolution of the concentrations of chemical species in pure water is solved numerically as functions of the depth in one dimension. Although it is not clear how living organisms respond to such exogenous RONS, we also use numerical simulation for metabolic reactions of Escherichia coli (E. coli) and examine possible effects of such RONS on an in-silico model organism. The computation model is based on the flux balance analysis (FBA), where the fluxes of the metabolites in a biological system are evaluated in steady state, i.e., under the assumption that the fluxes do not change in time. The fluxes are determined with liner programming to maximize the growth rate of the bacteria under the given conditions. Although FBA cannot be directly applied to dynamical responses of metabolic reactions, the simulation still gives insight into the biological reactions to exogenous chemical species generated by an APP. Partially supported by JSPS Grants-in-Aid for Scientific Research.

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.

Managing multiple diffuse pressures on water quality and ecological habitat: Spatially targeting effective mitigation actions at the landscape scale.

NASA Astrophysics Data System (ADS)

Joyce, Hannah; Reaney, Sim

2015-04-01

Catchment systems provide multiple benefits for society, including: land for agriculture, climate regulation and recreational space. Yet, these systems also have undesirable externalities, such as flooding, and the benefits they create can be compromised through societal use. For example, agriculture, forestry and urban land use practices can increase the export of fine sediment and faecal indicator organisms (FIO) delivered to river systems. These diffuse landscape pressures are coupled with pressures on the in stream temperature environment from projected climate change. Such pressures can have detrimental impacts on water quality and ecological habitat and consequently the benefits they provide for society. These diffuse and in-stream pressures can be reduced through actions at the landscape scale but are commonly tackled individually. Any intervention may have benefits for other pressures and hence the challenge is to consider all of the different pressures simultaneously to find solutions with high levels of cross-pressure benefits. This research presents (1) a simple but spatially distributed model to predict the pattern of multiple pressures at the landscape scale, and (2) a method for spatially targeting the optimum location for riparian woodland planting as mitigation action against these pressures. The model follows a minimal information requirement approach along the lines of SCIMAP (www.scimap.org.uk). This approach defines the critical source areas of fine sediment diffuse pollution, rapid overland flow and FIOs, based on the analysis of the pattern of the pressure in the landscape and the connectivity from source areas to rivers. River temperature was modeled using a simple energy balance equation; focusing on temperature of inflowing and outflowing water across a catchment. The model has been calibrated using a long term observed temperature record. The modelling outcomes enabled the identification of the severity of each pressure in relative rather than absolute sense at the landscape scale. Riparian woodland planting is proposed as one mitigation action to address these pressures. This planting disconnects the transfer of material from the landscape to the river channel by promoting increased infiltration and also provides river shading and hence decreases the rate of water heating. To identify the optimal locations for riparian woodland planting, a Monte Carlo based approach was used to identify multiple mitigation options and their influence on the pressures identified. These results were integrated into a decision support tool, which allows the user to explore the implications of individual and a set of pressures. This is achieved by allowing the user to change the importance of different pressures to identify the optimal locations for a custom combination of pressures. For example, reductions in flood risk can be prioritized over reductions in fine sediment. This approach provides an innovative way of identifying and targeting multiple diffuse pressures at the catchment scale simultaneously, which has presented a challenge in previous management efforts. The approach has been tested in the River Ribble Catchment, North West England.

The Effect of Hypertension on the Transport of LDL Across the Deformable Arterial Wall

NASA Astrophysics Data System (ADS)

Dabagh, Mahsa; Jalali, Payman

2010-05-01

The influences of increased endothelial cell turnover and deformation of the intima on the transport of low-density lipoprotein (LDL) under hypertension are investigated by applying a multilayered model of aortic wall. The thickness and properties of the endothelium, intima, internal elastic lamina (IEL), and media are affected by the transmural pressure. Navier-Stokes and Brinkman equations are applied for the transport of the transmural flow and the convective-diffusion equation is solved for LDL transport. LDL macromolecules enter the intima through leaky junctions, and then pass through the media layer where they permeate over the surface of smooth muscle cells (SMC). Uptake of LDL by cells is modeled through a uniform reaction evenly distributed in the macroscopically homogeneous media layer. The results show that transmural pressure significantly affects the LDL fluxes across the leaky junction, the intima, fenestral pores in the IEL, and the media layer. Many realistic predictions including the proper magnitudes for the permeability of endothelium and intimal layers, and the hydraulic conductivity of all layers as well as their trends with pressure are predicted by the present model.

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 Fast Vector Radiative Transfer Model for Atmospheric and Oceanic Remote Sensing

NASA Astrophysics Data System (ADS)

Ding, J.; Yang, P.; King, M. D.; Platnick, S. E.; Meyer, K.

2017-12-01

A fast vector radiative transfer model is developed in support of atmospheric and oceanic remote sensing. This model is capable of simulating the Stokes vector observed at the top of the atmosphere (TOA) and the terrestrial surface by considering absorption, scattering, and emission. The gas absorption is parameterized in terms of atmospheric gas concentrations, temperature, and pressure. The parameterization scheme combines a regression method and the correlated-K distribution method, and can easily integrate with multiple scattering computations. The approach is more than four orders of magnitude faster than a line-by-line radiative transfer model with errors less than 0.5% in terms of transmissivity. A two-component approach is utilized to solve the vector radiative transfer equation (VRTE). The VRTE solver separates the phase matrices of aerosol and cloud into forward and diffuse parts and thus the solution is also separated. The forward solution can be expressed by a semi-analytical equation based on the small-angle approximation, and serves as the source of the diffuse part. The diffuse part is solved by the adding-doubling method. The adding-doubling implementation is computationally efficient because the diffuse component needs much fewer spherical function expansion terms. The simulated Stokes vector at both the TOA and the surface have comparable accuracy compared with the counterparts based on numerically rigorous methods.

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.

Light radiation pressure upon an optically orthotropic surface

NASA Astrophysics Data System (ADS)

Nerovny, Nikolay A.; Lapina, Irina E.; Grigorjev, Anton S.

2017-11-01

In this paper, we discuss the problem of determination of light radiation pressure force upon an anisotropic surface. The optical parameters of such a surface are considered to have major and minor axes, so the model is called an orthotropic model. We derive the equations for force components from emission, absorption, and reflection, utilizing a modified Maxwell's specular-diffuse model. The proposed model can be used to model a flat solar sail with wrinkles. By performing Bayesian analysis for example of a wrinkled surface, we show that there are cases in which an orthotropic model of the optical parameters of a surface may be more accurate than an isotropic model.

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.

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.

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.

Flow of variably fluidized granular masses across three-dimensional terrain 2. Numerical predictions and experimental tests

USGS Publications Warehouse

Denlinger, R.P.; Iverson, R.M.

2001-01-01

Numerical solutions of the equations describing flow of variably fluidized Coulomb mixtures predict key features of dry granular avalanches and water-saturated debris flows measured in physical experiments. These features include time-dependent speeds, depths, and widths of flows as well as the geometry of resulting deposits. Threedimensional (3-D) boundary surfaces strongly influence flow dynamics because transverse shearing and cross-stream momentum transport occur where topography obstructs or redirects motion. Consequent energy dissipation can cause local deceleration and deposition, even on steep slopes. Velocities of surge fronts and other discontinuities that develop as flows cross 3-D terrain are predicted accurately by using a Riemann solution algorithm. The algorithm employs a gravity wave speed that accounts for different intensities of lateral stress transfer in regions of extending and compressing flow and in regions with different degrees of fluidization. Field observations and experiments indicate that flows in which fluid plays a significant role typically have high-friction margins with weaker interiors partly fluidized by pore pressure. Interaction of the strong perimeter and weak interior produces relatively steep-sided, flat-topped deposits. To simulate these effects, we compute pore pressure distributions using an advection-diffusion model with enhanced diffusivity near flow margins. Although challenges remain in evaluating pore pressure distributions in diverse geophysical flows, Riemann solutions of the depthaveraged 3-D Coulomb mixture equations provide a powerful tool for interpreting and predicting flow behavior. They provide a means of modeling debris flows, rock avalanches, pyroclastic flows, and related phenomena without invoking and calibrating Theological parameters that have questionable physical significance.

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.

Pressure and Chemical Potential: Effects Hydrophilic Soils Have on Adsorption and Transport

NASA Astrophysics Data System (ADS)

Bennethum, L. S.; Weinstein, T.

2003-12-01

Using the assumption that thermodynamic properties of fluid is affected by its proximity to the solid phase, a theoretical model has been developed based on upscaling and fundamental thermodynamic principles (termed Hybrid Mixture Theory). The theory indicates that Darcy's law and the Darcy-scale chemical potential (which determines the rate of adsorption and diffusion) need to be modified in order to apply to soils containing hydrophilic soils. In this talk we examine the Darcy-scale definition of pressure and chemical potential, especially as it applies to hydrophilic soils. To arrive at our model, we used hybrid mixture theory - first pioneered by Hassanizadeh and Gray in 1979. The technique involves averaging the field equations (i.e. conservation of mass, momentum balance, energy balance, etc.) to obtain macroscopic field equations, where each field variable is defined precisely in terms of its microscale counterpart. To close the system consistently with classical thermodynamics, the entropy inequality is exploited in the sense of Coleman and Noll. With the exceptions that the macroscale field variables are defined precisely in terms of their microscale counterparts and that microscopic interfacial equations can also be treated in a similar manner, the resulting system of equations is consistent with those derived using classical mixture theory. Hence the terminology, Hybrid Mixture Theory.

Methodes d'optimisation des parametres 2D du reflecteur dans un reacteur a eau pressurisee

NASA Astrophysics Data System (ADS)

Clerc, Thomas

With a third of the reactors in activity, the Pressurized Water Reactor (PWR) is today the most used reactor design in the world. This technology equips all the 19 EDF power plants. PWRs fit into the category of thermal reactors, because it is mainly the thermal neutrons that contribute to the fission reaction. The pressurized light water is both used as the moderator of the reaction and as the coolant. The active part of the core is composed of uranium, slightly enriched in uranium 235. The reflector is a region surrounding the active core, and containing mostly water and stainless steel. The purpose of the reflector is to protect the vessel from radiations, and also to slow down the neutrons and reflect them into the core. Given that the neutrons participate to the reaction of fission, the study of their behavior within the core is capital to understand the general functioning of how the reactor works. The neutrons behavior is ruled by the transport equation, which is very complex to solve numerically, and requires very long calculation. This is the reason why the core codes that will be used in this study solve simplified equations to approach the neutrons behavior in the core, in an acceptable calculation time. In particular, we will focus our study on the diffusion equation and approximated transport equations, such as SPN or S N equations. The physical properties of the reflector are radically different from those of the fissile core, and this structural change causes important tilt in the neutron flux at the core/reflector interface. This is why it is very important to accurately design the reflector, in order to precisely recover the neutrons behavior over the whole core. Existing reflector calculation techniques are based on the Lefebvre-Lebigot method. This method is only valid if the energy continuum of the neutrons is discretized in two energy groups, and if the diffusion equation is used. The method leads to the calculation of a homogeneous reflector. The aim of this study is to create a computational scheme able to compute the parameters of heterogeneous, multi-group reflectors, with both diffusion and SPN/SN operators. For this purpose, two computational schemes are designed to perform such a reflector calculation. The strategy used in both schemes is to minimize the discrepancies between a power distribution computed with a core code and a reference distribution, which will be obtained with an APOLLO2 calculation based on the method Method Of Characteristics (MOC). In both computational schemes, the optimization parameters, also called control variables, are the diffusion coefficients in each zone of the reflector, for diffusion calculations, and the P-1 corrected macroscopic total cross-sections in each zone of the reflector, for SPN/SN calculations (or correction factors on these parameters). After a first validation of our computational schemes, the results are computed, always by optimizing the fast diffusion coefficient for each zone of the reflector. All the tools of the data assimilation have been used to reflect the different behavior of the solvers in the different parts of the core. Moreover, the reflector is refined in six separated zones, corresponding to the physical structure of the reflector. There will be then six control variables for the optimization algorithms. [special characters omitted]. Our computational schemes are then able to compute heterogeneous, 2-group or multi-group reflectors, using diffusion or SPN/SN operators. The optimization performed reduces the discrepancies distribution between the power computed with the core codes and the reference power. However, there are two main limitations to this study: first the homogeneous modeling of the reflector assemblies doesn't allow to properly describe its physical structure near the core/reflector interface. Moreover, the fissile assemblies are modeled in infinite medium, and this model reaches its limit at the core/reflector interface. These two problems should be tackled in future studies. (Abstract shortened by UMI.).

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.

Calculating Pressure-Driven Current Near Magnetic Islands for 3D MHD Equilibria

NASA Astrophysics Data System (ADS)

Radhakrishnan, Dhanush; Reiman, Allan

2016-10-01

In general, 3D MHD equilibria in toroidal plasmas do not result in nested pressure surfaces. Instead, islands and chaotic regions appear in the equilibrium. Near small magnetic islands, the pressure varies within the flux surfaces, which has a significant effect on the pressure-driven current, introducing singularities. Previously, the MHD equilibrium current near a magnetic island was calculated, including the effect of ``stellarator symmetry,'' wherein the singular components of the pressure-driven current vanish [A. H. Reiman, Phys. Plasmas 23, 072502 (2016)]. Here we first solve for pressure in a cylindrical plasma from the heat diffusion equation, after adding a helical perturbation. We then numerically calculate the corresponding Pfirsch-Schluter current. At the small island limit, we compare the pressure-driven current with the previously calculated solution, and far from the island, we recover the solution for nested flux surfaces. Lastly, we compute the current for a toroidal plasma for symmetric and non-symmetric geometries.

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

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

Diffusion coefficients of phenylbutazone in supercritical CO2 and in ethanol.

PubMed

Kong, Chang Yi; Watanabe, Kou; Funazukuri, Toshitaka

2013-03-01

The diffusion coefficients D(12) of phenylbutazone at infinite dilution in supercritical CO(2) were measured by the chromatographic impulse response (CIR) method. The measurements were carried out over the temperature range from 308.2 to 343.2 K at pressures up to 40.0 MPa. In addition, the D(12) data of phenylbutazone at infinite dilution in ethanol were also measured by the Taylor dispersion method at 298.2-333.2K and at atmospheric pressure. The D(12) value of phenylbutazone increased from 4.45×10(-10) m(2) s(-1) at 298.2 K and 0.1 MPa in ethanol to about 1.43×10(-8) m(2) s(-1) at 343.2 K and 14.0 MPa in supercritical CO(2). It was found that all diffusion data of phenylbutazone measured in this study in supercritical CO(2) and in ethanol can be satisfactorily represented by the hydrodynamic equation over a wide range of fluid viscosity from supercritical state to liquid state with average absolute relative deviation of 5.4% for 112 data points. Copyright © 2013 Elsevier B.V. All rights reserved.

Border-Crossing Model for the Diffusive Coarsening of Wet Foams

NASA Astrophysics Data System (ADS)

Durian, Douglas; Schimming, Cody

For dry foams, the transport of gas from small high-pressure bubbles to large low-pressure bubbles is dominated by diffusion across the thin soap films separating neighboring bubbles. For wetter foams, the film areas become smaller as the Plateau borders and vertices inflate with liquid. So-called ``border-blocking'' models can explain some features of wet-foam coarsening based on the presumption that the inflated borders totally block the gas flux; however, this approximation dramatically fails in the wet/unjamming limit where the bubbles become close-packed spheres. Here, we account for the ever-present border-crossing flux by a new length scale defined by the average gradient of gas concentration inside the borders. We argue that it is proportional to the geometric average of film and border thicknesses, and we verify this scaling and the numerical prefactor by numerical solution of the diffusion equation. Then we show how the dA / dt =K0 (n - 6) von Neumann law is modified by the appearance of terms that depend on bubble size and shape as well as the concentration gradient length scale. Finally, we use the modified von Neumann law to compute the growth rate of the average bubble, which is not constant.

Imaging hydraulic fractures using temperature transients in the Belridge Diatomite

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

Shahin, G.T.; Johnston, R.M.

1995-12-31

Results of a temperature transient analysis of Shell`s Phase 1 and Phase 2 Diatomite Steamdrive Pilots are used to image hydraulic injection fracture lengths, angles, and heat injectivities into the low-permeability formation. The Phase 1 Pilot is a limited-interval injection test. In Phase 2, steam is injected into two 350 ft upper and lower zones through separate hydraulic fractures. Temperature response of both pilots is monitored with sixteen logging observation wells. A perturbation analysis of the non-linear pressure diffusion and heat transport equations indicates that at a permeability of about 0.1 md or less, heat transport in the Diatomite tendsmore » to be dominated by thermal diffusivity, and pressure diffusion is dominated by the ratio of thermal expansion to fluid compressibility. Under these conditions, the temperature observed at a logging observation well is governed by a dimensionless quantity that depends on the perpendicular distance between the observation well and the hydraulic fracture, divided by the square root of time. Using this dependence, a novel method is developed for imaging hydraulic fracture geometry and relative heat injectivity from the temperature history of the pilot.« 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

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.

Evaluation of a Multigrid Scheme for the Incompressible Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Swanson, R. C.

2004-01-01

A fast multigrid solver for the steady, incompressible Navier-Stokes equations is presented. The multigrid solver is based upon a factorizable discrete scheme for the velocity-pressure form of the Navier-Stokes equations. This scheme correctly distinguishes between the advection-diffusion and elliptic parts of the operator, allowing efficient smoothers to be constructed. To evaluate the multigrid algorithm, solutions are computed for flow over a flat plate, parabola, and a Karman-Trefftz airfoil. Both nonlifting and lifting airfoil flows are considered, with a Reynolds number range of 200 to 800. Convergence and accuracy of the algorithm are discussed. Using Gauss-Seidel line relaxation in alternating directions, multigrid convergence behavior approaching that of O(N) methods is achieved. The computational efficiency of the numerical scheme is compared with that of Runge-Kutta and implicit upwind based multigrid methods.

Development of monitoring system of helium leakage from canister

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

Toriu, D.; Ushijima, S.; Takeda, H.

2013-07-01

This paper presents a computational method for the helium leakage from a canister. The governing equations for compressible fluids consist of mass conservation equation in Eulerian description, momentum equations and energy equation. The numerical procedures are divided into three phases, advection, diffusion and acoustic phases, and the equations of compressible fluids are discretized with a finite volume method. Thus, the mass conservation law is sufficiently satisfied in the calculation region. In particular, our computational method enables us to predict the change of the temperature distributions around the canister boundaries by calculating the governing equations for the compressible gas flows, whichmore » are leaked out from a slight crack on the canister boundary. In order to confirm the validity of our method, it was applied to the basic problem, 2-dimensional natural convection flows in a rectangular cavity. As a result, it was shown that the naturally convected flows can be reasonably simulated by our method. Furthermore, numerical experiments were conducted for the helium leakage from canister and we derived a close relationship between the inner pressure and the boundary temperature distributions.« less

Simulating the Cranfield geological carbon sequestration project with high-resolution static models and an accurate equation of state

DOE PAGES

Soltanian, Mohamad Reza; Amooie, Mohammad Amin; Cole, David R.; ...

2016-10-11

In this study, a field-scale carbon dioxide (CO 2) injection pilot project was conducted as part of the Southeast Regional Sequestration Partnership (SECARB) at Cranfield, Mississippi. We present higher-order finite element simulations of the compositional two-phase CO 2-brine flow and transport during the experiment. High- resolution static models of the formation geology in the Detailed Area Study (DAS) located below the oil- water contact (brine saturated) are used to capture the impact of connected flow paths on breakthrough times in two observation wells. Phase behavior is described by the cubic-plus-association (CPA) equation of state, which takes into account the polarmore » nature of water molecules. Parameter studies are performed to investigate the importance of Fickian diffusion, permeability heterogeneity, relative permeabilities, and capillarity. Simulation results for the pressure response in the injection well and the CO 2 breakthrough times at the observation wells show good agreement with the field data. For the high injection rates and short duration of the experiment, diffusion is relatively unimportant (high P clet numbers), while relative permeabilities have a profound impact on the pressure response. High-permeability pathways, created by fluvial deposits, strongly affect the CO 2 transport and highlight the importance of properly characterizing the formation heterogeneity in future carbon sequestration projects.« less

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.

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.

Simulations of high Mach number perpendicular shocks with resistive electrons

NASA Technical Reports Server (NTRS)

Quest, K. B.

1986-01-01

A simulation code which models the ions as microparticles and the electrons as a resistive massless fluid is employed to study the structure of high Mach number perpendicular shocks. It is found that stable stationary shock solutions can be obtained for Alfven Mach numbers (M sub A) between 5 and 60 for upstream plasmas where the ratio of the plasma pressure to the magnetic pressure is 1, providing that the upstream resistive diffusion length is much smaller than the ion inertial length. For much larger resistive diffusion lengths, the magnetic field overshoot is damped, and the imbalance in the electron momentum equation results in a periodic fluctuation of the fraction of reflected ions. In the limit of M sub A of less than 10, the magnetic overshoot and the fraction of reflected ions increase with increasing M sub A, while at higher Mach numbers the fraction of reflected ions peaks at about 40 percent and the magnetic field overshoot increases at a much slower rate. Electron inertial effects are also considered.

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.

Effects of High Hydrostatic Pressure on Water Absorption of Adzuki Beans

PubMed Central

Ueno, Shigeaki; Shigematsu, Toru; Karo, Mineko; Hayashi, Mayumi; Fujii, Tomoyuki

2015-01-01

The effect of high hydrostatic pressure (HHP) treatment on dried soybean, adzuki bean, and kintoki kidney bean, which are low-moisture-content cellular biological materials, was investigated from the viewpoint of water absorption. The samples were vacuum-packed with distilled water and pressurized at 200 MPa and 25 °C for 10 min. After the HHP treatment, time courses of the moisture contents of the samples were measured, and the dimensionless moisture contents were estimated. Water absorption in the case of soybean could be fitted well by a simple water diffusion model. High pressures were found to have negligible effects on water absorption into the cotyledon of soybean and kintoki kidney bean. A non-linear least square method based on the Weibull equation was applied for the adzuki beans, and the effective water diffusion coefficient was found to increase significantly from 8.6 × 10−13 to 6.7 × 10−10 m2/s after HHP treatment. Approximately 30% of the testa of the adzuki bean was damaged upon HHP treatment, which was comparable to the surface area of the testa in the partially peeled adzuki bean sample. Thus, HHP was confirmed to promote mass transfer to the cotyledon of legumes with a tight testa. PMID:28231195

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

Effects of grain size evolution on mantle dynamics

NASA Astrophysics Data System (ADS)

Schulz, Falko; Tosi, Nicola; Plesa, Ana-Catalina; Breuer, Doris

2016-04-01

The rheology of planetary mantle materials is strongly dependent on temperature, pressure, strain-rate, and grain size. In particular, the rheology of olivine, the most abundant mineral of the Earth's upper mantle, has been extensively studied in the laboratory (e.g., Karato and Wu, 1993; Hirth and Kohlstedt, 2003). Two main mechanisms control olivine's deformation: dislocation and diffusion creep. While the former implies a power-law dependence of the viscosity on the strain-rate that leads to a non-Newtonian behaviour, the latter is sensitively dependent on the grain size. The dynamics of planetary interiors is locally controlled by the deformation mechanism that delivers the lowest viscosity. Models of the dynamics and evolution of planetary mantles should thus be capable to self-consistently distinguish which of the two mechanisms dominates at given conditions of temperature, pressure, strain-rate and grain size. As the grain size can affect the viscosity associated with diffusion creep by several orders of magnitude, it can strongly influence the dominant deformation mechanism. The vast majority of numerical, global-scale models of mantle convection, however, are based on the use of a linear diffusion-creep rheology with constant grain-size. Nevertheless, in recent studies, a new equation has been proposed to properly model the time-dependent evolution of the grain size (Austin and Evens, 2007; Rozel et al., 2010). We implemented this equation in our mantle convection code Gaia (Hüttig et al., 2013). In the framework of simple models of stagnant lid convection, we compared simulations based on the fully time-dependent equation of grain-size evolution with simulations based on its steady-state version. In addition, we tested a number of different parameters in order to identify those that affects the grain size to the first order and, in turn, control the conditions at which mantle deformation is dominated by diffusion or dislocation creep. References Austin, N. J. and Evans, B. (2007). Geology, 35(4):343. Hirth, G. and Kohlstedt, D. (2003). Geophysical Monograph Series, page 83105. Hüttig, C., Tosi, N., and Moore, W. B. (2013). Physics of the Earth and Planetary Interiors, 220:11-18. Karato, S.-i. and Wu, P. (1993). Science, 260(5109):771778. Rozel, A., Ricard, Y., and Bercovici, D. (2010). Geophysical Journal International, 184(2):719728.

Analysis of sound propagation in ducts using the wave envelope concept

NASA Technical Reports Server (NTRS)

Baumeister, K. J.

1974-01-01

A finite difference formulation is presented for sound propagation in a rectangular two-dimensional duct without steady flow for plane wave input. Before the difference equations are formulated, the governing Helmholtz equation is first transformed to a form whose solution does not oscillate along the length of the duct. This transformation reduces the required number of grid points by an order of magnitude, and the number of grid points becomes independent of the sound frequency. Physically, the transformed pressure represents the amplitude of the conventional sound wave. Example solutions are presented for sound propagation in a one-dimensional straight hard-wall duct and in a two-dimensional straight soft-wall duct without steady flow. The numerical solutions show evidence of the existence along the duct wall of a developing acoustic pressure diffusion boundary layer which is similar in nature to the conventional viscous flow boundary layer. In order to better illustrate this concept, the wave equation and boundary conditions are written such that the frequency no longer appears explicitly in them. The frequency effects in duct propagation can be visualized solely as an expansion and stretching of the suppressor duct.

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.

Thermodynamic properties and equations of state for Ag, Al, Au, Cu and MgO using a lattice vibrational method

NASA Astrophysics Data System (ADS)

Jacobs, M.; Schmid-Fetzer, R.

2012-04-01

A prerequisite for the determination of pressure in static high pressure measurements, such as in diamond anvil cells is the availability of accurate equations of state for reference materials. These materials serve as luminescence gauges or as X-ray gauges and equations of state for these materials serve as secondary pressure scales. Recently, successful progress has been made in the development of consistency between static, dynamic shock-wave and ultrasonic measurements of equations of state (e.g. Dewaele et al. Phys. Rev. B70, 094112, 2004, Dorogokupets and Oganov, Doklady Earth Sciences, 410, 1091-1095, 2006, Holzapfel, High Pressure Research 30, 372-394, 2010) allowing testing models to arrive at consistent thermodynamic descriptions for X-ray gauges. Apart from applications of metallic elements in high-pressure work, thermodynamic properties of metallic elements are also of mandatory interest in the field of metallurgy for studying phase equilibria of alloys, kinetics of phase transformation and diffusion related problems, requiring accurate thermodynamic properties in the low pressure regime. Our aim is to develop a thermodynamic data base for metallic alloy systems containing Ag, Al, Au, Cu, Fe, Ni, Pt, from which volume properties in P-T space can be predicted when it is coupled to vibrational models. This mandates the description of metallic elements as a first step aiming not only at consistency in the pressure scales for the elements, but also at accurate representations of thermodynamic properties in the low pressure regime commonly addressed in metallurgical applications. In previous works (e.g. Jacobs and de Jong, Geochim. Cosmochim. Acta, 71, 3630-3655, 2007, Jacobs and van den Berg, Phys. Earth Planet. Inter., 186, 36-48, 2011) it was demonstrated that a lattice vibrational framework based on Kieffer's model for the vibrational density of states, is suitable to construct a thermodynamic database for Earth mantle materials. Such a database aims at, when coupled to a thermodynamic computation program, the calculation and prediction of phase equilibria and thermo-physical properties of phase equilibrium assemblages in pressure-temperature-composition space. In Jacobs and van den Berg (2011) the vibrational method, together with a thermodynamic data base, was successfully applied to mantle convection of materials in the Earth. These works demonstrate that the vibrational method has the advantages of (1) computational speed, (2) coupling or making comparisons with ab initio methods and (3) making reliable extrapolations to extreme conditions. We present results of thermodynamic analyses, using lattice vibrational methods, of Ag, Al, Au, Cu and MgO covering the pressure and temperature regime of the Earth's interior. We show results on consistency of the pressure scales for these materials using different equations of state, under the constraint that thermodynamic properties in the low-pressure regime are accurately represented.

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

Chlorination of lanthanum oxide.

PubMed

Gaviría, Juan P; Navarro, Lucas G; Bohé, Ana E

2012-03-08

The reactive system La(2)O(3)(s)-Cl(2)(g) was studied in the temperature range 260-950 °C. The reaction course was followed by thermogravimetry, and the solids involved were characterized by X-ray diffraction, scanning electron microscopy, and energy dispersive spectroscopy. The results showed that the reaction leads to the formation of solid LaOCl, and for temperatures above 850 °C, the lanthanum oxychloride is chlorinated, producing LaCl(3)(l). The formation of the oxychloride progresses through a nucleation and growth mechanism, and the kinetic analysis showed that at temperatures below 325 °C the system is under chemical control. The influence of diffusive processes on the kinetics of production of LaOCl was evaluated by studying the effect of the reactive gas flow rate, the mass of the sample, and the chlorine diffusion through the boundary layer surrounding the solid sample. The conversion curves were analyzed and fitted according to the Johnson-Mehl-Avrami description, and the reaction order with respect to the chlorine partial pressure was obtained by varying this partial pressure between 10 and 70 kPa. The rate equation was obtained, which includes the influence of the temperature, chlorine partial pressure, and reaction degree.

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.

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.

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).

An innovation diffusion model of a local electricity network that is influenced by internal and external factors

NASA Astrophysics Data System (ADS)

Hattam, Laura; Greetham, Danica Vukadinović

2018-01-01

Haynes et al. (1977) derived a nonlinear differential equation to determine the spread of innovations within a social network across space and time. This model depends upon the imitators and the innovators within the social system, where the imitators respond to internal influences, whilst the innovators react to external factors. Here, this differential equation is applied to simulate the uptake of a low-carbon technology (LCT) within a real local electricity network that is situated in the UK. This network comprises of many households that are assigned to certain feeders. Firstly, travelling wave solutions of Haynes' model are used to predict adoption times as a function of the imitation and innovation influences. Then, the grid that represents the electricity network is created so that the finite element method (FEM) can be implemented. Next, innovation diffusion is modelled with Haynes' equation and the FEM, where varying magnitudes of the internal and external pressures are imposed. Consequently, the impact of these model parameters is investigated. Moreover, LCT adoption trajectories at fixed feeder locations are calculated, which give a macroscopic understanding of the uptake behaviour at specific network sites. Lastly, the adoption of LCTs at a household level is examined, where microscopic and macroscopic approaches are combined.

Heat Transfer Characteristics of Mixed Electroosmotic and Pressure Driven Micro-Flows

NASA Astrophysics Data System (ADS)

Horiuchi, Keisuke; Dutta, Prashanta

We analyze heat transfer characteristics of steady electroosmotic flows with an arbitrary pressure gradient in two-dimensional straight microchannels considering the effects of Joule heating in electroosmotic pumping. Both the temperature distribution and local Nusselt number are mathematically derived in this study. The thermal analysis takes into consideration of the interaction among advective, diffusive, and Joule heating terms to obtain the thermally developing behavior. Unlike macro-scale pipes, axial conduction in micro-scale cannot be negligible, and the governing energy equation is not separable. Thus, a method that considers an extended Graetz problem is introduced. Analytical results show that the Nusselt number of pure electrooosmotic flow is higher than that of plane Poiseulle flow. Moreover, when the electroosmotic flow and pressure driven flow coexist, it is found that adverse pressure gradient to the electroosmotic flow makes the thermal entrance length smaller and the heat transfer ability stronger than pure electroosmotic flow case.

A pressure-driven flow analysis of gas trapping behavior in nanocomposite thermite films

NASA Astrophysics Data System (ADS)

Sullivan, K. T.; Bastea, S.; Kuntz, J. D.; Gash, A. E.

2013-10-01

This article is in direct response to a recently published article entitled Electrophoretic deposition and mechanistic studies of nano-Al/CuO thermites (K. T. Sullivan et al., J. Appl. Phys., 112(2), 2012), in which we introduced a non-dimensional parameter as the ratio of gas production to gas escape within a thin porous thermite film. In our original analysis, we had treated the problem as Fickian diffusion of gases through the porous network. However, we believe a more physical representation of the problem is to treat this as pressure-driven flow of gases in a porous medium. We offer a new derivation of the non-dimensional parameter which calculates gas velocity using the well-known Poiseuille's Law for pressure-driven flow in a pipe. This updated analysis incorporates the porosity, gas viscosity, and pressure gradient into the equation.

Electron distribution function in a plasma generated by fission fragments

NASA Technical Reports Server (NTRS)

Hassan, H. A.; Deese, J. E.

1976-01-01

A Boltzmann equation formulation is presented for the determination of the electron distribution function in a plasma generated by fission fragments. The formulation takes into consideration ambipolar diffusion, elastic and inelastic collisions, recombination and ionization, and allows for the fact that the primary electrons are not monoenergetic. Calculations for He in a tube coated with fissionable material shows that, over a wide pressure and neutron flux range, the distribution function is non-Maxwellian, but the electrons are essentially thermal. Moreover, about a third of the energy of the primary electrons is transferred into the inelastic levels of He. This fraction of energy transfer is almost independent of pressure and neutron flux.

Direct numerical simulations of temporally developing hydrocarbon shear flames at elevated pressure: effects of the equation of state and the unity Lewis number assumption

NASA Astrophysics Data System (ADS)

Korucu, Ayse; Miller, Richard

2016-11-01

Direct numerical simulations (DNS) of temporally developing shear flames are used to investigate both equation of state (EOS) and unity-Lewis (Le) number assumption effects in hydrocarbon flames at elevated pressure. A reduced Kerosene / Air mechanism including a semi-global soot formation/oxidation model is used to study soot formation/oxidation processes in a temporarlly developing hydrocarbon shear flame operating at both atmospheric and elevated pressures for the cubic Peng-Robinson real fluid EOS. Results are compared to simulations using the ideal gas law (IGL). The results show that while the unity-Le number assumption with the IGL EOS under-predicts the flame temperature for all pressures, with the real fluid EOS it under-predicts the flame temperature for 1 and 35 atm and over-predicts the rest. The soot mass fraction, Ys, is only under-predicted for the 1 atm flame for both IGL and real gas fluid EOS models. While Ys is over-predicted for elevated pressures with IGL EOS, for the real gas EOS Ys's predictions are similar to results using a non-unity Le model derived from non-equilibrium thermodynamics and real diffusivities. Adopting the unity Le assumption is shown to cause misprediction of Ys, the flame temperature, and the mass fractions of CO, H and OH.

A transport equation for the scalar dissipation in reacting flows with variable density: First results

NASA Technical Reports Server (NTRS)

Mantel, T.

1993-01-01

Although the different regimes of premixed combustion are not well defined, most of the recent developments in turbulent combustion modeling are led in the so-called flamelet regime. The goal of these models is to give a realistic expression to the mean reaction rate (w). Several methods can be used to estimate (w). Bray and coworkers (Libby & Bray 1980, Bray 1985, Bray & Libby 1986) express the instantaneous reaction rate by means of a flamelet library and a frequency which describes the local interaction between the laminar flamelets and the turbulent flowfield. In another way, the mean reaction rate can be directly connected to the flame surface density (Sigma). This quantity can be given by the transport equation of the coherent flame model initially proposed by Marble & Broadwell 1977 and developed elsewhere. The mean reaction rate, (w), can also be estimated thanks to the evolution of an arbitrary scalar field G(x, t) = G(sub O) which represents the flame sheet. G(x, t) is obtained from the G-equation proposed by Williams 1985, Kerstein et al. 1988 and Peters 1993. Another possibility proposed in a recent study by Mantel & Borghi 1991, where a transport equation for the mean dissipation rate (epsilon(sub c)) of the progress variable c is used to determine (w). In their model, Mantel & Borghi 1991 considered a medium with constant density and constant diffusivity in the determination of the transport equation for (epsilon(sub c)). A comparison of different flamelet models made by Duclos et al. 1993 shows the realistic behavior of this model even in the case of constant density. Our objective in this present report is to present preliminary results on the study of this equation in the case of variable density and variable diffusivity. Assumptions of constant pressure and a Lewis number equal to unity allow us to significantly simplify the equation. A systematic order of magnitude analysis based on adequate scale relations is performed on each term of the equation. As in the case of constant density and constant diffusivity, the effects of stretching of the scalar field by the turbulent strain field, of local curvature, and of chemical reactions are predominant. In this preliminary work, we suggest closure models for certain terms, which will be validated after comparisons with DNS data.

Particle-size segregation and diffusive remixing in shallow granular avalanches

NASA Astrophysics Data System (ADS)

Gray, J. M. N. T.; Chugunov, V. A.

2006-12-01

Segregation and mixing of dissimilar grains is a problem in many industrial and pharmaceutical processes, as well as in hazardous geophysical flows, where the size-distribution can have a major impact on the local rheology and the overall run-out. In this paper, a simple binary mixture theory is used to formulate a model for particle-size segregation and diffusive remixing of large and small particles in shallow gravity-driven free-surface flows. This builds on a recent theory for the process of kinetic sieving, which is the dominant mechanism for segregation in granular avalanches provided the density-ratio and the size-ratio of the particles are not too large. The resulting nonlinear parabolic segregation remixing equation reduces to a quasi-linear hyperbolic equation in the no-remixing limit. It assumes that the bulk velocity is incompressible and that the bulk pressure is lithostatic, making it compatible with most theories used to compute the motion of shallow granular free-surface flows. In steady-state, the segregation remixing equation reduces to a logistic type equation and the ‘S’-shaped solutions are in very good agreement with existing particle dynamics simulations for both size and density segregation. Laterally uniform time-dependent solutions are constructed by mapping the segregation remixing equation to Burgers equation and using the Cole Hopf transformation to linearize the problem. It is then shown how solutions for arbitrary initial conditions can be constructed using standard methods. Three examples are investigated in which the initial concentration is (i) homogeneous, (ii) reverse graded with the coarse grains above the fines, and, (iii) normally graded with the fines above the coarse grains. Time-dependent two-dimensional solutions are also constructed for plug-flow in a semi-infinite chute.

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.

Optimization of post-column reactor radius in capillary high performance liquid chromatography Effect of chromatographic column diameter and particle diameter

PubMed Central

Xu, Hongjuan; Weber, Stephen G.

2006-01-01

A post-column reactor consisting of a simple open tube (Capillary Taylor Reactor) affects the performance of a capillary LC in two ways: stealing pressure from the column and adding band spreading. The former is a problem for very small radius reactors, while the latter shows itself for large reactor diameters. We derived an equation that defines the observed number of theoretical plates (Nobs) taking into account the two effects stated above. Making some assumptions and asserting certain conditions led to a final equation with a limited number of variables, namely chromatographic column radius, reactor radius and chromatographic particle diameter. The assumptions and conditions are that the van Deemter equation applies, the mass transfer limitation is for intraparticle diffusion in spherical particles, the velocity is at the optimum, the analyte’s retention factor, k′, is zero, the post-column reactor is only long enough to allow complete mixing of reagents and analytes and the maximum operating pressure of the pumping system is used. Optimal ranges of the reactor radius (ar) are obtained by comparing the number of observed theoretical plates (and theoretical plates per time) with and without a reactor. Results show that the acceptable reactor radii depend on column diameter, particle diameter, and maximum available pressure. Optimal ranges of ar become narrower as column diameter increases, particle diameter decreases or the maximum pressure is decreased. When the available pressure is 4000 psi, a Capillary Taylor Reactor with 12 μm radius is suitable for all columns smaller than 150 μm (radius) packed with 2–5 μm particles. For 1 μm packing particles, only columns smaller than 42.5 μm (radius) can be used and the reactor radius needs to be 5 μm. PMID:16494886

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.

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

Modeling of near-wall turbulence

NASA Technical Reports Server (NTRS)

Shih, T. H.; Mansour, N. N.

1990-01-01

An improved k-epsilon model and a second order closure model is presented for low Reynolds number turbulence near a wall. For the k-epsilon model, a modified form of the eddy viscosity having correct asymptotic near wall behavior is suggested, and a model for the pressure diffusion term in the turbulent kinetic energy equation is proposed. For the second order closure model, the existing models are modified for the Reynolds stress equations to have proper near wall behavior. A dissipation rate equation for the turbulent kinetic energy is also reformulated. The proposed models satisfy realizability and will not produce unphysical behavior. Fully developed channel flows are used for model testing. The calculations are compared with direct numerical simulations. It is shown that the present models, both the k-epsilon model and the second order closure model, perform well in predicting the behavior of the near wall turbulence. Significant improvements over previous models are obtained.

Grating formation by a high power radio wave in near-equator ionosphere

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

Singh, Rohtash; Sharma, A. K.; Tripathi, V. K.

2011-11-15

The formation of a volume grating in the near-equator regions of ionosphere due to a high power radio wave is investigated. The radio wave, launched from a ground based transmitter, forms a standing wave pattern below the critical layer, heating the electrons in a space periodic manner. The thermal conduction along the magnetic lines of force inhibits the rise in electron temperature, limiting the efficacy of heating to within a latitude of few degrees around the equator. The space periodic electron partial pressure leads to ambipolar diffusion creating a space periodic density ripple with wave vector along the vertical. Suchmore » a volume grating is effective to cause strong reflection of radio waves at a frequency one order of magnitude higher than the maximum plasma frequency in the ionosphere. Linearly mode converted plasma wave could scatter even higher frequency radio waves.« less

Quantum molecular dynamics simulation of shock-wave experiments in aluminum

NASA Astrophysics Data System (ADS)

Minakov, D. V.; Levashov, P. R.; Khishchenko, K. V.; Fortov, V. E.

2014-06-01

We present quantum molecular dynamics calculations of principal, porous, and double shock Hugoniots, release isentropes, and sound velocity behind the shock front for aluminum. A comprehensive analysis of available shock-wave data is performed; the agreement and discrepancies of simulation results with measurements are discussed. Special attention is paid to the melting region of aluminum along the principal Hugoniot; the boundaries of the melting zone are estimated using the self-diffusion coefficient. Also, we make a comparison with a high-quality multiphase equation of state for aluminum. Independent semiempirical and first-principle models are very close to each other in caloric variables (pressure, density, particle velocity, etc.) but the equation of state gives higher temperature on the principal Hugoniot and release isentropes than ab initio calculations. Thus, the quantum molecular dynamics method can be used for calibration of semiempirical equations of state in case of lack of experimental data.

Quantum molecular dynamics simulation of shock-wave experiments in aluminum

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

Minakov, D. V.; Khishchenko, K. V.; Fortov, V. E.

2014-06-14

We present quantum molecular dynamics calculations of principal, porous, and double shock Hugoniots, release isentropes, and sound velocity behind the shock front for aluminum. A comprehensive analysis of available shock-wave data is performed; the agreement and discrepancies of simulation results with measurements are discussed. Special attention is paid to the melting region of aluminum along the principal Hugoniot; the boundaries of the melting zone are estimated using the self-diffusion coefficient. Also, we make a comparison with a high-quality multiphase equation of state for aluminum. Independent semiempirical and first-principle models are very close to each other in caloric variables (pressure, density,more » particle velocity, etc.) but the equation of state gives higher temperature on the principal Hugoniot and release isentropes than ab initio calculations. Thus, the quantum molecular dynamics method can be used for calibration of semiempirical equations of state in case of lack of experimental data.« 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

Transition regime analytical solution to gas mass flow rate in a rectangular micro channel

NASA Astrophysics Data System (ADS)

Dadzie, S. Kokou; Dongari, Nishanth

2012-11-01

We present an analytical model predicting the experimentally observed gas mass flow rate in rectangular micro channels over slip and transition regimes without the use of any fitting parameter. Previously, Sone reported a class of pure continuum regime flows that requires terms of Burnett order in constitutive equations of shear stress to be predicted appropriately. The corrective terms to the conventional Navier-Stokes equation were named the ghost effect. We demonstrate in this paper similarity between Sone ghost effect model and newly so-called 'volume diffusion hydrodynamic model'. A generic analytical solution to gas mass flow rate in a rectangular micro channel is then obtained. It is shown that the volume diffusion hydrodynamics allows to accurately predict the gas mass flow rate up to Knudsen number of 5. This can be achieved without necessitating the use of adjustable parameters in boundary conditions or parametric scaling laws for constitutive relations. The present model predicts the non-linear variation of pressure profile along the axial direction and also captures the change in curvature with increase in rarefaction.

Asymptotic expansions for 2D symmetrical laminar wakes

NASA Astrophysics Data System (ADS)

Belan, Marco; Tordella, Daniela

1999-11-01

An extension of the well known asymptotic representation of the 2D laminar incompressible wake past a symmetrical body is presented. Using the thin free shear layer approximation we determined solutions in terms of infinite asymptotic expansions. These are power series of the streamwise space variable with fractional negative coefficients. The general n-th order term has been analytically established. Through analysis of the behaviour of the same expansions inserted into the Navier-Stokes equations, we verified the self-consistency of the approximation showing that at the third order the correction due to pressure variations identically vanishes while the contribution of the longitudinal diffusion is still two-three order of magnitude smaller than that of the transversal diffusion, depending on Re. When the procedure is applied to the Navier-Stokes equations, we showed that further mathematical difficulties do not arise. Where opportune one may thus easily shift to the complete model. Through a spatial multiscaling approach, a brief account on the stability properties of these expansions as representing the non parallel basic flow of 2D wakes will be given.

Causes of plasma column contraction in surface-wave-driven discharges in argon at atmospheric pressure

NASA Astrophysics Data System (ADS)

Ridenti, Marco Antonio; de Amorim, Jayr; Dal Pino, Arnaldo; Guerra, Vasco; Petrov, George

2018-01-01

In this work we compute the main features of a surface-wave-driven plasma in argon at atmospheric pressure in view of a better understanding of the contraction phenomenon. We include the detailed chemical kinetics dynamics of Ar and solve the mass conservation equations of the relevant neutral excited and charged species. The gas temperature radial profile is calculated by means of the thermal diffusion equation. The electric field radial profile is calculated directly from the numerical solution of the Maxwell equations assuming the surface wave to be propagating in the TM00 mode. The problem is considered to be radially symmetrical, the axial variations are neglected, and the equations are solved in a self-consistent fashion. We probe the model results considering three scenarios: (i) the electron energy distribution function (EEDF) is calculated by means of the Boltzmann equation; (ii) the EEDF is considered to be Maxwellian; (iii) the dissociative recombination is excluded from the chemical kinetics dynamics, but the nonequilibrium EEDF is preserved. From this analysis, the dissociative recombination is shown to be the leading mechanism in the constriction of surface-wave plasmas. The results are compared with mass spectrometry measurements of the radial density profile of the ions Ar+ and Ar2+. An explanation is proposed for the trends seen by Thomson scattering diagnostics that shows a substantial increase of electron temperature towards the plasma borders where the electron density is small.

High-temperature high-pressure properties of silica from Quantum Monte Carlo and Density Functional Perturbation Theory

NASA Astrophysics Data System (ADS)

Cohen, R. E.; Driver, K.; Wu, Z.; Militzer, B.; Rios, P. L.; Towler, M.; Needs, R.

2009-03-01

We have used diffusion quantum Monte Carlo (DMC) with the CASINO code with thermal free energies from phonons computed using density functional perturbation theory (DFPT) with the ABINIT code to obtain phase transition curves and thermal equations of state of silica phases under pressure. We obtain excellent agreement with experiments for the metastable phase transition from quartz to stishovite. The local density approximation (LDA) incorrectly gives stishovite as the ground state. The generalized gradient approximation (GGA) correctly gives quartz as the ground state, but does worse than LDA for the equations of state. DMC, variational quantum Monte Carlo (VMC), and DFT all give good results for the ferroelastic transition of stishovite to the CaCl2 structure, and LDA or the WC exchange correlation potentials give good results within a given silica phase. The δV and δH from the CaCl2 structure to α-PbO2 is small, giving uncertainly in the theoretical transition pressure. It is interesting that DFT has trouble with silica transitions, although the electronic structures of silica are insulating, simple closed-shell with ionic/covalent bonding. It seems like the errors in DFT are from not precisely giving the ion sizes.

An oscillation free shock-capturing method for compressible van der Waals supercritical fluid flows

DOE PAGES

Pantano, C.; Saurel, R.; Schmitt, T.

2017-02-01

Numerical solutions of the Euler equations using real gas equations of state (EOS) often exhibit serious inaccuracies. The focus here is the van der Waals EOS and its variants (often used in supercritical fluid computations). The problems are not related to a lack of convexity of the EOS since the EOS are considered in their domain of convexity at any mesh point and at any time. The difficulties appear as soon as a density discontinuity is present with the rest of the fluid in mechanical equilibrium and typically result in spurious pressure and velocity oscillations. This is reminiscent of well-knownmore » pressure oscillations occurring with ideal gas mixtures when a mass fraction discontinuity is present, which can be interpreted as a discontinuity in the EOS parameters. We are concerned with pressure oscillations that appear just for a single fluid each time a density discontinuity is present. As a result, the combination of density in a nonlinear fashion in the EOS with diffusion by the numerical method results in violation of mechanical equilibrium conditions which are not easy to eliminate, even under grid refinement.« less

An oscillation free shock-capturing method for compressible van der Waals supercritical fluid flows

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

Pantano, C.; Saurel, R.; Schmitt, T.

Numerical solutions of the Euler equations using real gas equations of state (EOS) often exhibit serious inaccuracies. The focus here is the van der Waals EOS and its variants (often used in supercritical fluid computations). The problems are not related to a lack of convexity of the EOS since the EOS are considered in their domain of convexity at any mesh point and at any time. The difficulties appear as soon as a density discontinuity is present with the rest of the fluid in mechanical equilibrium and typically result in spurious pressure and velocity oscillations. This is reminiscent of well-knownmore » pressure oscillations occurring with ideal gas mixtures when a mass fraction discontinuity is present, which can be interpreted as a discontinuity in the EOS parameters. We are concerned with pressure oscillations that appear just for a single fluid each time a density discontinuity is present. As a result, the combination of density in a nonlinear fashion in the EOS with diffusion by the numerical method results in violation of mechanical equilibrium conditions which are not easy to eliminate, even under grid refinement.« less

Towards a multi-physics modelling framework for thrombolysis under the influence of blood flow.

PubMed

Piebalgs, Andris; Xu, X Yun

2015-12-06

Thrombolytic therapy is an effective means of treating thromboembolic diseases but can also give rise to life-threatening side effects. The infusion of a high drug concentration can provoke internal bleeding while an insufficient dose can lead to artery reocclusion. It is hoped that mathematical modelling of the process of clot lysis can lead to a better understanding and improvement of thrombolytic therapy. To this end, a multi-physics continuum model has been developed to simulate the dissolution of clot over time upon the addition of tissue plasminogen activator (tPA). The transport of tPA and other lytic proteins is modelled by a set of reaction-diffusion-convection equations, while blood flow is described by volume-averaged continuity and momentum equations. The clot is modelled as a fibrous porous medium with its properties being determined as a function of the fibrin fibre radius and voidage of the clot. A unique feature of the model is that it is capable of simulating the entire lytic process from the initial phase of lysis of an occlusive thrombus (diffusion-limited transport), the process of recanalization, to post-canalization thrombolysis under the influence of convective blood flow. The model has been used to examine the dissolution of a fully occluding clot in a simplified artery at different pressure drops. Our predicted lytic front velocities during the initial stage of lysis agree well with experimental and computational results reported by others. Following canalization, clot lysis patterns are strongly influenced by local flow patterns, which are symmetric at low pressure drops, but asymmetric at higher pressure drops, which give rise to larger recirculation regions and extended areas of intense drug accumulation. © 2015 The Authors.

A Hydrodynamic Theory for Spatially Inhomogeneous Semiconductor Lasers: Microscopic Approach

NASA Technical Reports Server (NTRS)

Li, Jianzhong; Ning, C. Z.; Biegel, Bryan A. (Technical Monitor)

2001-01-01

Starting from the microscopic semiconductor Bloch equations (SBEs) including the Boltzmann transport terms in the distribution function equations for electrons and holes, we derived a closed set of diffusion equations for carrier densities and temperatures with self-consistent coupling to Maxwell's equation and to an effective optical polarization equation. The coherent many-body effects are included within the screened Hartree-Fock approximation, while scatterings are treated within the second Born approximation including both the in- and out-scatterings. Microscopic expressions for electron-hole (e-h) and carrier-LO (c-LO) phonon scatterings are directly used to derive the momentum and energy relaxation rates. These rates expressed as functions of temperatures and densities lead to microscopic expressions for self- and mutual-diffusion coefficients in the coupled density-temperature diffusion equations. Approximations for reducing the general two-component description of the electron-hole plasma (EHP) to a single-component one are discussed. In particular, we show that a special single-component reduction is possible when e-h scattering dominates over c-LO phonon scattering. The ambipolar diffusion approximation is also discussed and we show that the ambipolar diffusion coefficients are independent of e-h scattering, even though the diffusion coefficients of individual components depend sensitively on the e-h scattering rates. Our discussions lead to new perspectives into the roles played in the single-component reduction by the electron-hole correlation in momentum space induced by scatterings and the electron-hole correlation in real space via internal static electrical field. Finally, the theory is completed by coupling the diffusion equations to the lattice temperature equation and to the effective optical polarization which in turn couples to the laser field.

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

Three Dimensional Compressible Turbulent Flow Computations for a Diffusing S-Duct With/Without Vortex Generators

NASA Technical Reports Server (NTRS)

Cho, Soo-Yong; Greber, Isaac

1994-01-01

Numerical investigations on a diffusing S-duct with/without vortex generators and a straight duct with vortex generators are presented. The investigation consists of solving the full three-dimensional unsteady compressible mass averaged Navier-Stokes equations. An implicit finite volume lower-upper time marching code (RPLUS3D) has been employed and modified. A three-dimensional Baldwin-Lomax turbulence model has been modified in conjunction with the flow physics. A model for the analysis of vortex generators in a fully viscous subsonic internal flow is evaluated. A vortical structure for modeling the shed vortex is used as a source term in the computation domain. The injected vortex paths in the straight duct are compared with the analysis by two kinds of prediction models. The flow structure by the vortex generators are investigated along the duct. Computed results of the flow in a circular diffusing S-duct provide an understanding of the flow structure within a typical engine inlet system. These are compared with the experimental wall static-pressure, static- and total-pressure field, and secondary velocity profiles. Additionally, boundary layer thickness, skin friction values, and velocity profiles in wall coordinates are presented. In order to investigate the effect of vortex generators, various vortex strengths are examined in this study. The total-pressure recovery and distortion coefficients are obtained at the exit of the S-duct. The numerical results clearly depict the interaction between the low velocity flow by the flow separation and the injected vortices.

An iterative phase-space explicit discontinuous Galerkin method for stellar radiative transfer in extended atmospheres

NASA Astrophysics Data System (ADS)

de Almeida, Valmor F.

2017-07-01

A phase-space discontinuous Galerkin (PSDG) method is presented for the solution of stellar radiative transfer problems. It allows for greater adaptivity than competing methods without sacrificing generality. The method is extensively tested on a spherically symmetric, static, inverse-power-law scattering atmosphere. Results for different sizes of atmospheres and intensities of scattering agreed with asymptotic values. The exponentially decaying behavior of the radiative field in the diffusive-transparent transition region, and the forward peaking behavior at the surface of extended atmospheres were accurately captured. The integrodifferential equation of radiation transfer is solved iteratively by alternating between the radiative pressure equation and the original equation with the integral term treated as an energy density source term. In each iteration, the equations are solved via an explicit, flux-conserving, discontinuous Galerkin method. Finite elements are ordered in wave fronts perpendicular to the characteristic curves so that elemental linear algebraic systems are solved quickly by sweeping the phase space element by element. Two implementations of a diffusive boundary condition at the origin are demonstrated wherein the finite discontinuity in the radiation intensity is accurately captured by the proposed method. This allows for a consistent mechanism to preserve photon luminosity. The method was proved to be robust and fast, and a case is made for the adequacy of parallel processing. In addition to classical two-dimensional plots, results of normalized radiation intensity were mapped onto a log-polar surface exhibiting all distinguishing features of the problem studied.

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.

Kinetic bottlenecks to chemical exchange rates for deep-sea animals - Part 1: Oxygen

NASA Astrophysics Data System (ADS)

Hofmann, A. F.; Peltzer, E. T.; Brewer, P. G.

2012-10-01

Ocean warming will reduce dissolved oxygen concentrations which can pose challenges to marine life. Oxygen limits are traditionally reported simply as a static concentration thresholds with no temperature, pressure or flow rate dependency. Here we treat the oceanic oxygen supply potential for heterotrophic consumption as a dynamic molecular exchange problem analogous to familiar gas exchange processes at the sea surface. A combination of the purely physico-chemical oceanic properties temperature, hydrostatic pressure, and oxygen concentration defines the ability of the ocean to supply oxygen to any given animal. This general oceanic oxygen supply potential is modulated by animal specific properties such as the diffusive boundary layer thickness to define and limit maximal oxygen supply rates. Here we combine all these properties into formal, mechanistic equations defining novel oceanic properties that subsume various relevant classical oceanographic parameters to better visualize, map, comprehend, and predict the impact of ocean deoxygenation on aerobic life. By explicitly including temperature and hydrostatic pressure into our quantities, various ocean regions ranging from the cold deep-sea to warm, coastal seas can be compared. We define purely physico-chemical quantities to describe the oceanic oxygen supply potential, but also quantities that contain organism-specific properties which in a most generalized way describe general concepts and dependencies. We apply these novel quantities to example oceanic profiles around the world and find that temperature and pressure dependencies of diffusion and partial pressure create zones of greatest physical constriction on oxygen supply typically at around 1000 m depth, which coincides with oxygen concentration minimum zones. In these zones, which comprise the bulk of the world ocean, ocean warming and deoxygenation have a clear negative effect for aerobic life. In some shallow and warm waters the enhanced diffusion and higher partial pressure due to higher temperatures might slightly overcompensate for oxygen concentration decreases due to decreases in solubility.

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.

Application of the order-of-magnitude analysis to a fourth-order RANS closure for simulating a 2D boundary layer

NASA Astrophysics Data System (ADS)

Poroseva, Svetlana V.

2013-11-01

Simulations of turbulent boundary-layer flows are usually conducted using a set of the simplified Reynolds-Averaged Navier-Stokes (RANS) equations obtained by order-of-magnitude analysis (OMA) of the original RANS equations. The resultant equations for the mean-velocity components are closed using the Boussinesq approximation for the Reynolds stresses. In this study OMA is applied to the fourth-order RANS (FORANS) set of equations. The FORANS equations are chosen as they can be closed on the level of the 5th-order correlations without using unknown model coefficients, i.e. no turbulent diffusion modeling is required. New models for the 2nd-, 3rd- and 4th-order velocity-pressure gradient correlations are derived for the current FORANS equations. This set of FORANS equations and models are analyzed for the case of two-dimensional mean flow. The equations include familiar transport terms for the mean-velocity components along with algebraic expressions for velocity correlations of different orders specific to the FORANS approach. Flat plate DNS data (Spalart, 1988) are used to verify these expressions and the areas of the OMA applicability within the boundary layer. The material is based upon work supported by NASA under award NNX12AJ61A.

Effect of Geometric Parameters on the Performance of Second Throat Annular Steam Ejectors

DTIC Science & Technology

1991-07-01

Cell Pressure versus Rake Average Exit Pitot Pressure . . . . . . . . . . . 42 15. Baseline Wall Pressure Profiles...diffuser exit plane pitot pressure rake . 2.5.2 Alternate Configurations Six alternate ejector diffuser configurations were tested. A summary of...along the walls of the diffusers to help characterize the flow. The ejector diffuser exit pitot pressure was measured with a 6-probe pitot pressure rake

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.

Effects of inlet flow field conditions on the performance of centrifugal compressor diffusers: Part 1 -- Discrete-passage diffuser

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

Filipenco, V.G.; Deniz, S.; Johnston, J.M.

2000-01-01

This is Part 1 of a two-part paper considering the performance of radial diffusers for use in a high-performance centrifugal compressor. Part 1 reports on discrete-passage diffusers, while Part 2 describes a test of a straight-channel diffuser designed for equivalent duty. Two builds of discrete-passage diffuser were tested, with 30 and 38 separate passages. Both the 30 and 38 passage diffusers investigated showed comparable range of unstalled operation and similar level of overall diffuser pressure recovery. The paper concentrates on the influence of inlet flow conditions on the pressure recovery and operating range of radial diffusers for centrifugal compressor stages.more » The flow conditions examined include diffuser inlet Mach number, flow angle, blockage, and axial flow nonuniformity. The investigation was carried out in a specially built test facility, designed to provide a controlled inlet flow field to the test diffusers. The facility can provide a wide range of diffuser inlet velocity profile distortion and skew with Mach numbers up to unity and flow angles of 63 to 75 deg from the radical direction. The consequences of different averaging methods for the inlet total pressure distributions, which are needed in the definition of diffuser pressure recovery coefficient for nonuniform diffuser inlet conditions, were also assessed. The overall diffuser pressure recovery coefficient, based on suitably averaged inlet total pressure, was found to correlate well with the momentum-averaged flow angle into the diffuser. It is shown that the generally accepted sensitivity of diffuser pressure recovery performance to inlet flow distortion and boundary layer blockage can be largely attributed to inappropriate quantification of the average dynamic pressure at diffuser inlet. Use of an inlet dynamic pressure based on availability or mass-averaging in combination with definition of inlet flow angle based on mass average of the radial and tangential velocity at diffuser inlet removes this sensitivity.« less

COMPARISON OF IMPLICIT SCHEMES TO SOLVE EQUATIONS OF RADIATION HYDRODYNAMICS WITH A FLUX-LIMITED DIFFUSION APPROXIMATION: NEWTON–RAPHSON, OPERATOR SPLITTING, AND LINEARIZATION

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

Tetsu, Hiroyuki; Nakamoto, Taishi, E-mail: h.tetsu@geo.titech.ac.jp

Radiation is an important process of energy transport, a force, and a basis for synthetic observations, so radiation hydrodynamics (RHD) calculations have occupied an important place in astrophysics. However, although the progress in computational technology is remarkable, their high numerical cost is still a persistent problem. In this work, we compare the following schemes used to solve the nonlinear simultaneous equations of an RHD algorithm with the flux-limited diffusion approximation: the Newton–Raphson (NR) method, operator splitting, and linearization (LIN), from the perspective of the computational cost involved. For operator splitting, in addition to the traditional simple operator splitting (SOS) scheme,more » we examined the scheme developed by Douglas and Rachford (DROS). We solve three test problems (the thermal relaxation mode, the relaxation and the propagation of linear waves, and radiating shock) using these schemes and then compare their dependence on the time step size. As a result, we find the conditions of the time step size necessary for adopting each scheme. The LIN scheme is superior to other schemes if the ratio of radiation pressure to gas pressure is sufficiently low. On the other hand, DROS can be the most efficient scheme if the ratio is high. Although the NR scheme can be adopted independently of the regime, especially in a problem that involves optically thin regions, the convergence tends to be worse. In all cases, SOS is not practical.« less

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.

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.

The experimental study of matching between centrifugal compressor impeller and diffuser

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

Tamaki, H.; Nakao, H.; Saito, M.

1999-01-01

the centrifugal compressor for a marine use turbocharger with its design pressure ratio of 3.2 was tested with a vaneless diffuser and various vaned diffusers. Vaned diffusers were chosen to cover impeller operating range as broad as possible. The analysis of the static pressure ratio in the impeller and the diffusing system, consisting of the diffuser and scroll, showed that there were four possible combinations of characteristics of impeller pressure ratio and diffusing system pressure ratio. The flow rate, Q{sub P}, where the impeller achieved maximum static pressure ratio, was surge flow rate of the centrifugal compressor determined by themore » critical flow rate. In order to operate the compressor at a rate lower than Q{sub P}, the diffusing system, whose pressure recovery factor was steep negative slope near Q{sub P}, was needed. When the diffuser throat area was less than a certain value, the compressor efficiency deteriorated; however, the compressor stage pressure ratio was almost constant. In this study, by reducing the diffuser throat area, the compressor could be operated at a flow rate less than 40% of its design flow rate. Analysis of the pressure ratio in the impeller and diffusing systems at design and off-design speeds showed that the irregularities in surge line occurred when the component that controlled the negative slope on the compressor stage pressure ratio changed.« less

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

Modeling of FMISO [F18] nanoparticle PET tracer in normal-cancerous tissue based on real clinical image.

PubMed

Asgari, Hanie; Soltani, M; Sefidgar, Mostafa

2018-07-01

Hypoxia as one of the principal properties of tumor cells is a reaction to the deprivation of oxygen. The location of tumor cells could be identified by assessment of oxygen and nutrient level in human body. Positron emission tomography (PET) is a well-known non-invasive method that is able to measure hypoxia based on the FMISO (Fluoromisonidazole) tracer dynamic. This paper aims to study the PET tracer concentration through convection-diffusion-reaction equations in a real human capillary-like network. A non-uniform oxygen pressure along the capillary path and convection mechanism for FMISO transport are taken into account to accurately model the characteristics of the tracer. To this end, a multi-scale model consists of laminar blood flow through the capillary network, interstitial pressure, oxygen pressure, FMISO diffusion and FMISO convection transport in the extravascular region is developed. The present model considers both normal and tumor tissue regions in computational domain. The accuracy of numerical model is verified with the experimental results available in the literature. The convection and diffusion types of transport mechanism are employed in order to calculate the concentration of FMISO in the normal and tumor sub-domain. The influences of intravascular oxygen pressure, FMISO transport mechanisms, capillary density and different types of tissue on the FMISO concentration have been investigated. According to result (Table 4) the convection mechanism of FMISO molecules transportation is negligible, but it causes more accuracy of the proposed model. The approach of present study can be employed in order to investigate the effects of various parameters, such as tumor shape, on the dynamic behavior of different PET tracers, such as FDG, can be extended to different case study problems, such as drug delivery. Copyright © 2018 Elsevier Inc. All rights reserved.

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

NASA Astrophysics Data System (ADS)

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

2011-03-01

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

Role of shell diffusion area in incubating eggs at simulated high altitude.

PubMed

Weiss, H S

1978-10-01

Embryonic development is inhibited when eggs are incubated at 9,100 m (0.3 atm) despite a normoxic environment. The problem apparently relates to respiratory gas exchange occurring by diffusion through gas-filled pores in the shell. Gaseous flux is therefore inversely proportional to ambient pressure and is affected by the physical characteristics of the ambient gas (Chapman-Enskog equation). Excess loss of H2O and CO2 occurs in eggs incubating at altitude and could be detrimental. Such increased loss should be correctable by decreasing diffusion area. This was tested by progressively increasing coverage of the shell with paraffin and incubating at simulated 0.3 ATA (225 Torr) in 100% O2. Uncoated eggs failed to hatch, but numbers of chicks increased with increased coverage. Maximum hatch was an extrapolated 90% of controls at 69% shell coverage. With further coverage, hatch size decreased. Egg weight loss, and estimate of H2O diffusion, was around three times controls in uncoated eggs but decreased linearly with paraffin coverage, reaching near normal at maximum hatch. Reduction of diffusion area to 0.3 normal at maximum hatch generally balanced the increased flux predicted for 0.3 ATA.

Experimental and theoretical aspects of studying themodynamics and mass transport in polymer-solvent systems

NASA Astrophysics Data System (ADS)

Davis, Peter Kennedy

Mass transport and thermodynamics in polymer-solvent systems are two key areas of importance to the polymer industry. Numerous processes including polymerization reactors, membrane separations, foam production, devolatilization processes, film and coating drying, supercritical extractions, drug delivery, and even nano-technology require fundamental phase equilibria and diffusion information. Although such information is vital in equipment design and optimization, acquisition and modeling of these data are still in the research and development stages. This thesis is rather diverse as it addresses many realms of this broad research area. From high pressure to low pressure, experimental to theoretical, and infinite dilution to finite concentration, the thesis covers a wide range of topics that are of current importance to the industrial and academic polymer community. Chapter 1 discusses advances in the development of a new volumetric sorption pressure decay technique to make phase equilibrium and diffusion measurements in severe temperature-pressure environments. Chapter 2 provides the derivations and results of a new completely predictive Group Contribution Lattice Fluid Equation of State for multi-component polymer-solvent systems. The remaining four chapters demonstrate advances in the modeling of inverse gas chromatography (IGC) experiments. IGC has been used extensively of the last 50 years to make low pressure sorption and diffusion measurements at infinitely dilute and finite solvent concentrations. Chapter 3 proposes a new IGC experiment capable of obtaining ternary vapor-liquid equilibria in polymer-solvent-solvent systems. Also in that chapter, an extensive derivation is provided for a continuum model capable of describing the results of such an experiment. Chapter 4 presents new data collected on a packed column IGC experiment and a new model that can be used with those experimental data to obtain diffusion and partition coefficients. Chapter 5 addresses a rather controversial topic about IGC experiments near the polymer glass transition temperature. Using a new IGC model capable of describing both bulk absorption and surface adsorption, IGC behavior around the glass transition was able to be better understood. Finally, Chapter 6 presents an IGC model that can be used to separate bulk effects from surface effects in capillary column IGC experiments.

A PDF projection method: A pressure algorithm for stand-alone transported PDFs

NASA Astrophysics Data System (ADS)

Ghorbani, Asghar; Steinhilber, Gerd; Markus, Detlev; Maas, Ulrich

2015-03-01

In this paper, a new formulation of the projection approach is introduced for stand-alone probability density function (PDF) methods. The method is suitable for applications in low-Mach number transient turbulent reacting flows. The method is based on a fractional step method in which first the advection-diffusion-reaction equations are modelled and solved within a particle-based PDF method to predict an intermediate velocity field. Then the mean velocity field is projected onto a space where the continuity for the mean velocity is satisfied. In this approach, a Poisson equation is solved on the Eulerian grid to obtain the mean pressure field. Then the mean pressure is interpolated at the location of each stochastic Lagrangian particle. The formulation of the Poisson equation avoids the time derivatives of the density (due to convection) as well as second-order spatial derivatives. This in turn eliminates the major sources of instability in the presence of stochastic noise that are inherent in particle-based PDF methods. The convergence of the algorithm (in the non-turbulent case) is investigated first by the method of manufactured solutions. Then the algorithm is applied to a one-dimensional turbulent premixed flame in order to assess the accuracy and convergence of the method in the case of turbulent combustion. As a part of this work, we also apply the algorithm to a more realistic flow, namely a transient turbulent reacting jet, in order to assess the performance of the method.

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.

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.

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.

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 variable turbulent Prandtl and Schmidt number model study for scramjet applications

NASA Astrophysics Data System (ADS)

Keistler, Patrick

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

A controlled variation scheme for convection treatment in pressure-based algorithm

NASA Technical Reports Server (NTRS)

Shyy, Wei; Thakur, Siddharth; Tucker, Kevin

1993-01-01

Convection effect and source terms are two primary sources of difficulties in computing turbulent reacting flows typically encountered in propulsion devices. The present work intends to elucidate the individual as well as the collective roles of convection and source terms in the fluid flow equations, and to devise appropriate treatments and implementations to improve our current capability of predicting such flows. A controlled variation scheme (CVS) has been under development in the context of a pressure-based algorithm, which has the characteristics of adaptively regulating the amount of numerical diffusivity, relative to central difference scheme, according to the variation in local flow field. Both the basic concepts and a pragmatic assessment will be presented to highlight the status of this work.

Effect of Structure on Transport Properties (Viscosity, Ionic Conductivity, and Self-Diffusion Coefficient) of Aprotic Heterocyclic Anion (AHA) Room Temperature Ionic Liquids. 2. Variation of Alkyl Chain Length in the Phosphonium Cation.

PubMed

Sun, Liyuan; Morales-Collazo, Oscar; Xia, Han; Brennecke, Joan F

2016-06-30

A series of room-temperature ionic liquids (ILs) composed of triethyl(alkyl)phosphonium cations paired with three different aprotic heterocyclic anions (AHAs) (alkyl = butyl ([P2224](+)) and octyl ([P2228](+))) were prepared to investigate the effect of cationic alkyl chain length on transport properties. The transport properties and density of these ILs were measured from 283.15 to 343.15 K at ambient pressure. The dependence of the transport properties (viscosity, ionic conductivity, diffusivity, and molar conductivity) on temperature can be described by the Vogel-Fulcher-Tamman (VFT) equation. The ratio of the molar conductivity obtained from the molar concentration and ionic conductivity measurements to that calculated from self-diffusion coefficients (measured by pulsed gradient spin-echo nuclear magnetic resonance spectroscopy) using the Nernst-Einstein equation was used to quantify the ionicity of these ILs. The molar conductivity ratio decreases with increasing number of carbon atoms in the alkyl chain, indicating that the reduced Coulombic interactions resulting from lower density are more than balanced by the increased van der Waals interactions between the alkyl chains. The results of this study may provide insight into the design of ILs with enhanced dynamics that may be suitable as electrolytes in lithium ion batteries and other electrochemical applications.

Dissipative particle dynamics study of velocity autocorrelation function and self-diffusion coefficient in terms of interaction potential strength

NASA Astrophysics Data System (ADS)

Zohravi, Elnaz; Shirani, Ebrahim; Pishevar, Ahmadreza; Karimpour, Hossein

2018-07-01

This research focuses on numerically investigating the self-diffusion coefficient and velocity autocorrelation function (VACF) of a dissipative particle dynamics (DPD) fluid as a function of the conservative interaction strength. Analytic solutions to VACF and self-diffusion coefficients in DPD were obtained by many researchers in some restricted cases including ideal gases, without the account of conservative force. As departure from the ideal gas conditions are accentuated with increasing the relative proportion of conservative force, it is anticipated that the VACF should gradually deviate from its normally expected exponentially decay. This trend is confirmed through numerical simulations and an expression in terms of the conservative force parameter, density and temperature is proposed for the self-diffusion coefficient. As it concerned the VACF, the equivalent Langevin equation describing Brownian motion of particles with a harmonic potential is adapted to the problem and reveals an exponentially decaying oscillatory pattern influenced by the conservative force parameter, dissipative parameter and temperature. Although the proposed model for obtaining the self-diffusion coefficient with consideration of the conservative force could not be verified due to computational complexities, nonetheless the Arrhenius dependency of the self-diffusion coefficient to temperature and pressure permits to certify our model over a definite range of DPD parameters.

Exact Solutions of Coupled Multispecies Linear Reaction–Diffusion Equations on a Uniformly Growing Domain

PubMed Central

Simpson, Matthew J.; Sharp, Jesse A.; Morrow, Liam C.; Baker, Ruth E.

2015-01-01

Embryonic development involves diffusion and proliferation of cells, as well as diffusion and reaction of molecules, within growing tissues. Mathematical models of these processes often involve reaction–diffusion equations on growing domains that have been primarily studied using approximate numerical solutions. Recently, we have shown how to obtain an exact solution to a single, uncoupled, linear reaction–diffusion equation on a growing domain, 0 < x < L(t), where L(t) is the domain length. The present work is an extension of our previous study, and we illustrate how to solve a system of coupled reaction–diffusion equations on a growing domain. This system of equations can be used to study the spatial and temporal distributions of different generations of cells within a population that diffuses and proliferates within a growing tissue. The exact solution is obtained by applying an uncoupling transformation, and the uncoupled equations are solved separately before applying the inverse uncoupling transformation to give the coupled solution. We present several example calculations to illustrate different types of behaviour. The first example calculation corresponds to a situation where the initially–confined population diffuses sufficiently slowly that it is unable to reach the moving boundary at x = L(t). In contrast, the second example calculation corresponds to a situation where the initially–confined population is able to overcome the domain growth and reach the moving boundary at x = L(t). In its basic format, the uncoupling transformation at first appears to be restricted to deal only with the case where each generation of cells has a distinct proliferation rate. However, we also demonstrate how the uncoupling transformation can be used when each generation has the same proliferation rate by evaluating the exact solutions as an appropriate limit. PMID:26407013

Exact Solutions of Coupled Multispecies Linear Reaction-Diffusion Equations on a Uniformly Growing Domain.

PubMed

Simpson, Matthew J; Sharp, Jesse A; Morrow, Liam C; Baker, Ruth E

2015-01-01

Embryonic development involves diffusion and proliferation of cells, as well as diffusion and reaction of molecules, within growing tissues. Mathematical models of these processes often involve reaction-diffusion equations on growing domains that have been primarily studied using approximate numerical solutions. Recently, we have shown how to obtain an exact solution to a single, uncoupled, linear reaction-diffusion equation on a growing domain, 0 < x < L(t), where L(t) is the domain length. The present work is an extension of our previous study, and we illustrate how to solve a system of coupled reaction-diffusion equations on a growing domain. This system of equations can be used to study the spatial and temporal distributions of different generations of cells within a population that diffuses and proliferates within a growing tissue. The exact solution is obtained by applying an uncoupling transformation, and the uncoupled equations are solved separately before applying the inverse uncoupling transformation to give the coupled solution. We present several example calculations to illustrate different types of behaviour. The first example calculation corresponds to a situation where the initially-confined population diffuses sufficiently slowly that it is unable to reach the moving boundary at x = L(t). In contrast, the second example calculation corresponds to a situation where the initially-confined population is able to overcome the domain growth and reach the moving boundary at x = L(t). In its basic format, the uncoupling transformation at first appears to be restricted to deal only with the case where each generation of cells has a distinct proliferation rate. However, we also demonstrate how the uncoupling transformation can be used when each generation has the same proliferation rate by evaluating the exact solutions as an appropriate limit.

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.

A Novel Hyperbolization Procedure for The Two-Phase Six-Equation Flow Model

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

Samet Y. Kadioglu; Robert Nourgaliev; Nam Dinh

2011-10-01

We introduce a novel approach for the hyperbolization of the well-known two-phase six equation flow model. The six-equation model has been frequently used in many two-phase flow applications such as bubbly fluid flows in nuclear reactors. One major drawback of this model is that it can be arbitrarily non-hyperbolic resulting in difficulties such as numerical instability issues. Non-hyperbolic behavior can be associated with complex eigenvalues that correspond to characteristic matrix of the system. Complex eigenvalues are often due to certain flow parameter choices such as the definition of inter-facial pressure terms. In our method, we prevent the characteristic matrix receivingmore » complex eigenvalues by fine tuning the inter-facial pressure terms with an iterative procedure. In this way, the characteristic matrix possesses all real eigenvalues meaning that the characteristic wave speeds are all real therefore the overall two-phase flowmodel becomes hyperbolic. The main advantage of this is that one can apply less diffusive highly accurate high resolution numerical schemes that often rely on explicit calculations of real eigenvalues. We note that existing non-hyperbolic models are discretized mainly based on low order highly dissipative numerical techniques in order to avoid stability issues.« less

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.

Control of reaction-diffusion equations on time-evolving manifolds.

PubMed

Rossi, Francesco; Duteil, Nastassia Pouradier; Yakoby, Nir; Piccoli, Benedetto

2016-12-01

Among the main actors of organism development there are morphogens, which are signaling molecules diffusing in the developing organism and acting on cells to produce local responses. Growth is thus determined by the distribution of such signal. Meanwhile, the diffusion of the signal is itself affected by the changes in shape and size of the organism. In other words, there is a complete coupling between the diffusion of the signal and the change of the shapes. In this paper, we introduce a mathematical model to investigate such coupling. The shape is given by a manifold, that varies in time as the result of a deformation given by a transport equation. The signal is represented by a density, diffusing on the manifold via a diffusion equation. We show the non-commutativity of the transport and diffusion evolution by introducing a new concept of Lie bracket between the diffusion and the transport operator. We also provide numerical simulations showing this phenomenon.

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.

Transformations of fluxes and forces describing the simultaneous transport of water and heat in unsaturated porous media

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

Raats, P.A.C.

1975-12-01

Balances of mass for the water in N distinct phases and a balance of heat for the medium as a whole were formulated. Following Philip and de Vries, it was assumed that the flux of water in each phase is proportional to the gradient of the pressure in that phase and that the diffusive component of the flux of heat is proportional to the gradient of the temperature. Clapeyron equations were used to express the gradient of the pressure in any phase in terms of the gradient of the pressure in a reference state and of the temperature. The referencemore » state may be the water in one of the phases or the water in some measuring device such as a tensiometer or a psychrometer. Expressions for the total flux of water and for the diffusive flux of heat plus the convective flux of heat associated with the conversion from any phase to the reference state were shown to satisfy the onsager reciprocal relations. A theorem due to Meixner was used to delineate the class of fluxes and forces that preserves these relations. In particular, it was shown that if the gradients of water content and temperature are used as the driving forces, the onsager relations are no longer satisfied.« less

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.

Liquid Hydrogen Propellant Tank Sub-Surface Pressurization with Gaseous Helium

NASA Technical Reports Server (NTRS)

Stephens, J. R.; Cartagena, W.

2015-01-01

A series of tests were conducted to evaluate the performance of a propellant tank pressurization system with the pressurant diffuser intentionally submerged beneath the surface of the liquid. Propellant tanks and pressurization systems are typically designed with the diffuser positioned to apply pressurant gas directly into the tank ullage space when the liquid propellant is settled. Space vehicles, and potentially propellant depots, may need to conduct tank pressurization operations in micro-gravity environments where the exact location of the liquid relative to the diffuser is not well understood. If the diffuser is positioned to supply pressurant gas directly to the tank ullage space when the propellant is settled, then it may become partially or completely submerged when the liquid becomes unsettled in a microgravity environment. In such case, the pressurization system performance will be adversely affected requiring additional pressurant mass and longer pressurization times. This series of tests compares and evaluates pressurization system performance using the conventional method of supplying pressurant gas directly to the propellant tank ullage, and then supplying pressurant gas beneath the liquid surface. The pressurization tests were conducted on the Engineering Development Unit (EDU) located at Test Stand 300 at NASA Marshall Space Flight Center (MSFC). EDU is a ground based Cryogenic Fluid Management (CFM) test article supported by Glenn Research Center (GRC) and MSFC. A 150 ft3 propellant tank was filled with liquid hydrogen (LH2). The pressurization system used regulated ambient helium (GHe) as a pressurant, a variable position valve to maintain flow rate, and two identical independent pressurant diffusers. The ullage diffuser was located in the forward end of the tank and was completely exposed to the tank ullage. The submerged diffuser was located in the aft end of the tank and was completely submerged when the tank liquid level was 10% or greater. The ullage diffuser tests were conducted as a baseline to evaluate the performance of the pressurization system, and the submerged diffuser tests showed how the performance of the pressurization system was compromised when the diffuser was submerged in LH2. The test results are evaluated and compared, and included in this report for various propellant tank fill levels.

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.

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.

Three dimensional flow field inside compressor rotor, including blade boundary layers

NASA Technical Reports Server (NTRS)

Galmes, J. M.; Pouagere, M.; Lakshminarayana, B.

1982-01-01

The Reynolds stress equation, pressure strain correlation, and dissipative terms and diffusion are discussed in relation to turbulence modelling using the Reynolds stress model. Algebraic modeling of Reynolds stresses and calculation of the boundary layer over an axial cylinder are examined with regards to the kinetic energy model for turbulence modelling. The numerical analysis of blade and hub wall boundary layers, and an experimental study of rotor blade boundary layer in an axial flow compressor rotor are discussed. The Patankar-Spalding numerical method for two dimensional boundary layers is included.

Mixed convection peristaltic flow of third order nanofluid with an induced magnetic field.

PubMed

Noreen, Saima

2013-01-01

This research is concerned with the peristaltic flow of third order nanofluid in an asymmetric channel. The governing equations of third order nanofluid are modelled in wave frame of reference. Effect of induced magnetic field is considered. Long wavelength and low Reynolds number situation is tackled. Numerical solutions of the governing problem are computed and analyzed. The effects of Brownian motion and thermophoretic diffusion of nano particles are particularly emphasized. Physical quantities such as velocity, pressure rise, temperature, induced magnetic field and concentration distributions are discussed.

Aerodynamic design guidelines and computer program for estimation of subsonic wind tunnel performance

NASA Technical Reports Server (NTRS)

Eckert, W. T.; Mort, K. W.; Jope, J.

1976-01-01

General guidelines are given for the design of diffusers, contractions, corners, and the inlets and exits of non-return tunnels. A system of equations, reflecting the current technology, has been compiled and assembled into a computer program (a user's manual for this program is included) for determining the total pressure losses. The formulation presented is applicable to compressible flow through most closed- or open-throat, single-, double-, or non-return wind tunnels. A comparison of estimated performance with that actually achieved by several existing facilities produced generally good agreement.

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.

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.

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.

The effect of a realistic thermal diffusivity on numerical model of a subducting slab

NASA Astrophysics Data System (ADS)

Maierova, P.; Steinle-Neumann, G.; Cadek, O.

2010-12-01

A number of numerical studies of subducting slab assume simplified (constant or only depth-dependent) models of thermal conductivity. The available mineral physics data indicate, however, that thermal diffusivity is strongly temperature- and pressure-dependent and may also vary among different mantle materials. In the present study, we examine the influence of realistic thermal properties of mantle materials on the thermal state of the upper mantle and the dynamics of subducting slabs. On the basis of the data published in mineral physics literature we compile analytical relationships that approximate the pressure and temperature dependence of thermal diffusivity for major mineral phases of the mantle (olivine, wadsleyite, ringwoodite, garnet, clinopyroxenes, stishovite and perovskite). We propose a simplified composition of mineral assemblages predominating in the subducting slab and the surrounding mantle (pyrolite, mid-ocean ridge basalt, harzburgite) and we estimate their thermal diffusivity using the Hashin-Shtrikman bounds. The resulting complex formula for the diffusivity of each aggregate is then approximated by a simpler analytical relationship that is used in our numerical model as an input parameter. For the numerical modeling we use the Elmer software (open source finite element software for multiphysical problems, see http://www.csc.fi/english/pages/elmer). We set up a 2D Cartesian thermo-mechanical steady-state model of a subducting slab. The model is partly kinematic as the flow is driven by a boundary condition on velocity that is prescribed on the top of the subducting lithospheric plate. Reology of the material is non-linear and is coupled with the thermal equation. Using the realistic relationship for thermal diffusivity of mantle materials, we compute the thermal and flow fields for different input velocity and age of the subducting plate and we compare the results against the models assuming a constant thermal diffusivity. The importance of the realistic description of thermal properties in models of subducted slabs is discussed.

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

NASA Technical Reports Server (NTRS)

Loney, Norman W.

1994-01-01

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

Theoretical aspects of tidal and planetary wave propagation at thermospheric heights

NASA Technical Reports Server (NTRS)

Volland, H.; Mayr, H. G.

1977-01-01

A simple semiquantitative model is presented which allows analytic solutions of tidal and planetary wave propagation at thermospheric heights. This model is based on perturbation approximation and mode separation. The effects of viscosity and heat conduction are parameterized by Rayleigh friction and Newtonian cooling. Because of this simplicity, one gains a clear physical insight into basic features of atmospheric wave propagation. In particular, we discuss the meridional structures of pressure and horizontal wind (the solutions of Laplace's equation) and their modification due to dissipative effects at thermospheric heights. Furthermore, we solve the equations governing the height structure of the wave modes and arrive at a very simple asymptotic solution valid in the upper part of the thermosphere. That 'system transfer function' of the thermosphere allows one to estimate immediately the reaction of the thermospheric wave mode parameters such as pressure, temperature, and winds to an external heat source of arbitrary temporal and spatial distribution. Finally, the diffusion effects of the minor constituents due to the global wind circulation are discussed, and some results of numerical calculations are presented.

Numerical Prediction of Combustion-induced Noise using a hybrid LES/CAA approach

NASA Astrophysics Data System (ADS)

Ihme, Matthias; Pitsch, Heinz; Kaltenbacher, Manfred

2006-11-01

Noise generation in technical devices is an increasingly important problem. Jet engines in particular produce sound levels that not only are a nuisance but may also impair hearing. The noise emitted by such engines is generated by different sources such as jet exhaust, fans or turbines, and combustion. Whereas the former acoustic mechanisms are reasonably well understood, combustion-generated noise is not. A methodology for the prediction of combustion-generated noise is developed. In this hybrid approach unsteady acoustic source terms are obtained from an LES and the propagation of pressure perturbations are obtained using acoustic analogies. Lighthill's acoustic analogy and a non-linear wave equation, accounting for variable speed of sound, have been employed. Both models are applied to an open diffusion flame. The effects on the far field pressure and directivity due to the variation of speed of sound are analyzed. Results for the sound pressure level will be compared with experimental data.

Measurement and prediction of flow through a replica segment of a mildly atherosclerotic coronary artery of man

NASA Technical Reports Server (NTRS)

Back, L. H.; Radbill, J. R.; Cho, Y. I.; Crawford, D. W.

1986-01-01

Pressure distributions were measured along a hollow vascular axisymmetric replica of a segment of the left circumflex coronary artery of man with mildly atherosclerotic diffuse disease. A large range of physiological Reynolds numbers from about 60 to 500, including hyperemic response, was spanned in the flows investigation using a fluid simulating blood kinematic viscosity. Predicted pressure distributions from the numerical solution of the Navier-Stokes equations were similar in trend and magnitude to the measurements. Large variations in the predicted velocity profiles occurred along the lumen. The influence of the smaller scale multiple flow obstacles along the wall (lesion variations) led to sharp spikes in the predicted wall shear stresses. Reynolds number similarity was discussed, and estimates of what time averaged in vivo pressure drop and shear stress might be were given for a vessel segment.

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

Mutual diffusion of binary liquid mixtures containing methanol, ethanol, acetone, benzene, cyclohexane, toluene, and carbon tetrachloride

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

Guevara-Carrion, Gabriela; Janzen, Tatjana; Muñoz-Muñoz, Y. Mauricio

Mutual diffusion coefficients of all 20 binary liquid mixtures that can be formed out of methanol, ethanol, acetone, benzene, cyclohexane, toluene, and carbon tetrachloride without a miscibility gap are studied at ambient conditions of temperature and pressure in the entire composition range. The considered mixtures show a varying mixing behavior from almost ideal to strongly non-ideal. Predictive molecular dynamics simulations employing the Green-Kubo formalism are carried out. Radial distribution functions are analyzed to gain an understanding of the liquid structure influencing the diffusion processes. It is shown that cluster formation in mixtures containing one alcoholic component has a significant impactmore » on the diffusion process. The estimation of the thermodynamic factor from experimental vapor-liquid equilibrium data is investigated, considering three excess Gibbs energy models, i.e., Wilson, NRTL, and UNIQUAC. It is found that the Wilson model yields the thermodynamic factor that best suits the simulation results for the prediction of the Fick diffusion coefficient. Four semi-empirical methods for the prediction of the self-diffusion coefficients and nine predictive equations for the Fick diffusion coefficient are assessed and it is found that methods based on local composition models are more reliable. Finally, the shear viscosity and thermal conductivity are predicted and in most cases favorably compared with experimental literature values.« less

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.

Performance of a low-pressure-ratio centrifugal compressor with four diffuser designs

NASA Technical Reports Server (NTRS)

Klassen, H. A.

1973-01-01

A low-pressure-ratio centrifugal compressor was tested with four different diffuser configurations. One diffuser had airfoil vanes. Two were pipe diffusers. One pipe diffuser had 7.5 deg cone diffusing passages. The other had trumpet-shaped passages designed for linear static-pressure rise from throat to exit. The fourth configuration had flat vanes with elliptical leading edges similar to those of pipe diffusers. The side walls were contoured to produce a linear pressure rise. Peak compressor efficiencies were 0.82 with the airfoil vane and conical pipe diffusers, 0.80 with the trumpet, and 0.74 with the flat-vane design. Surge margin and useful range were greater for the airfoil-vane diffuser than for the other three.

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.

Diffusion of chemically reactive species in MHD oscillatory flow with thermal radiation in the presence of constant suction and injection

NASA Astrophysics Data System (ADS)

Sasikumar, J.; Bhuvaneshwari, S.; Govindarajan, A.

2018-04-01

In this project, it is proposed to investigate the effect of suction/injection on the unsteady oscillatory flow of an incompressible viscous electrically conducting fluid through a channel filled with porous medium and non-uniform wall temperature. The fluid is subjected to a uniform magnetic field normal to the channel and the velocity slip at the cold plate is taken into consideration. With the assumption of magnetic Reynolds number to be very small, the induced magnetic field is neglected. Assuming pressure gradient to be oscillatory across the ends of the channel, resulting flow as unsteady oscillatory flow. Under the usual Bousinessq approximation, a mathematical model representing this fluid flow consisting of governing equations with boundary conditions will be developed. Closed form solutions of the dimensionless governing equations of the fluid flow, namely momentum equation, energy equation and species concentration can be obtained . The effects of heat radiation and chemical reaction with suction and injection on temperature, velocity and species concentration profiles will be analysed with tables and graphs.

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

NASA Astrophysics Data System (ADS)

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

2017-09-01

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

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.

Fluid pressure waves trigger earthquakes

NASA Astrophysics Data System (ADS)

Mulargia, Francesco; Bizzarri, Andrea

2015-03-01

Fluids-essentially meteoric water-are present everywhere in the Earth's crust, occasionally also with pressures higher than hydrostatic due to the tectonic strain imposed on impermeable undrained layers, to the impoundment of artificial lakes or to the forced injections required by oil and gas exploration and production. Experimental evidence suggests that such fluids flow along preferred paths of high diffusivity, provided by rock joints and faults. Studying the coupled poroelastic problem, we find that such flow is ruled by a nonlinear partial differential equation amenable to a Barenblatt-type solution, implying that it takes place in form of solitary pressure waves propagating at a velocity which decreases with time as v ∝ t [1/(n - 1) - 1] with n ≳ 7. According to Tresca-Von Mises criterion, these waves appear to play a major role in earthquake triggering, being also capable to account for aftershock delay without any further assumption. The measure of stress and fluid pressure inside active faults may therefore provide direct information about fault potential instability.

Evaporation of LOX under supercritical and subcritical conditions

NASA Technical Reports Server (NTRS)

Yang, A. S.; Hsieh, W. H.; Kuo, K. K.; Brown, J. J.

1993-01-01

The evaporation of LOX under supercritical and subcritical conditions was studied experimentally and theoretically. In experiments, the evaporation rate and surface temperature were measured for LOX strand vaporizing in helium environments at pressures ranging from 5 to 68 atmospheres. Gas sampling and chromatography analysis were also employed to profile the gas composition above the LOX surface for the purpose of model validation. A comprehensive theoretical model was formulated and solved numerically to simulate the evaporation process of LOX at high pressures. The model was based on the conservation equations of mass, momentum, energy, and species concentrations for a multicomponent system, with consideration of gravitational body force, solubility of ambient gases in liquid, and variable thermophysical properties. Good agreement between predictions and measured oxygen mole fraction profiles was obtained. The effect of pressure on the distribution of the Lewis number, as well as the effect of variable diffusion coefficient, were further examined to elucidate the high-pressure transport behavior exhibited in the LOX vaporization process.

Stage design

DOEpatents

Shacter, J.

1975-12-01

A method is described of cycling gases through a plurality of diffusion stages comprising the steps of admitting the diffused gases from a first diffusion stage into an axial compressor, simultaneously admitting the undiffused gases from a second diffusion stage into an intermediate pressure zone of said compressor corresponding in pressure to the pressure of said undiffused gases, and then admitting the resulting compressed mixture of diffused and undiffused gases into a third diffusion stage.

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.

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

Calculating Mass Diffusion in High-Pressure Binary Fluids

NASA Technical Reports Server (NTRS)

Bellan, Josette; Harstad, Kenneth

2004-01-01

A comprehensive mathematical model of mass diffusion has been developed for binary fluids at high pressures, including critical and supercritical pressures. Heretofore, diverse expressions, valid for limited parameter ranges, have been used to correlate high-pressure binary mass-diffusion-coefficient data. This model will likely be especially useful in the computational simulation and analysis of combustion phenomena in diesel engines, gas turbines, and liquid rocket engines, wherein mass diffusion at high pressure plays a major role.

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

Large-scale optimization-based non-negative computational framework for diffusion equations: Parallel implementation and performance studies

DOE PAGES

Chang, Justin; Karra, Satish; Nakshatrala, Kalyana B.

2016-07-26

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

Experimental thermal conductivity, thermal diffusivity, and specific heat values for mixtures of nitrogen, oxygen, and argon

NASA Technical Reports Server (NTRS)

Perkins, R. A.; Cieszkiewicz, M. T.

1991-01-01

Experimental measurements of thermal conductivity and thermal diffusivity obtained with a transient hot-wire apparatus are reported for three mixtures of nitrogen, oxygen, and argon. Values of the specific heat, Cp, are calculated from these measured values and the density calculated with an equation of state. The measurements were made at temperatures between 65 and 303 K with pressures between 0.1 and 70 MPa. The data cover the vapor, liquid, and supercritical gas phases for the three mixtures. The total reported points are 1066 for the air mixture (78.11 percent nitrogen, 20.97 percent oxygen, and 0.92 percent argon), 1058 for the 50 percent nitrogen, 50 percent oxygen mixture, and 864 for the 25 percent nitrogen, 75 oxygen mixture. Empirical thermal conductivity correlations are provided for the three mixtures.

Numerical flux formulas for the Euler and Navier-Stokes equations. 2: Progress in flux-vector splitting

NASA Technical Reports Server (NTRS)

Coirier, William J.; Vanleer, Bram

1991-01-01

The accuracy of various numerical flux functions for the inviscid fluxes when used for Navier-Stokes computations is studied. The flux functions are benchmarked for solutions of the viscous, hypersonic flow past a 10 degree cone at zero angle of attack using first order, upwind spatial differencing. The Harten-Lax/Roe flux is found to give a good boundary layer representation, although its robustness is an issue. Some hybrid flux formulas, where the concepts of flux-vector and flux-difference splitting are combined, are shown to give unsatisfactory pressure distributions; there is still room for improvement. Investigations of low diffusion, pure flux-vector splittings indicate that a pure flux-vector splitting can be developed that eliminates spurious diffusion across the boundary layer. The resulting first-order scheme is marginally stable and not monotone.

Ionic Channels as Natural Nanodevices

DTIC Science & Technology

2006-05-01

introduce the numerical techniques required to simulate charge transport in ion channels. [1] Using Poisson- Nernst -Planck-type (PNP) equations ...Eisenberg. 2003. Ionic diffusion through protein channels: from molecular description to continuum equations . Nanotech 2003, 3: 439-442. 4...Nadler, B., Schuss, Z., Singer, A., and R. S. Eisenberg. 2004. Ionic diffusion through confined geometries: from Langevin equations to partial

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

NASA Astrophysics Data System (ADS)

Cairoli, Andrea; Baule, Adrian

2017-04-01

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

Assessment of diffuser pressure loss on WWTPs in Baden-Württemberg.

PubMed

Krampe, J

2011-01-01

Aeration of activated sludge is a critical treatment step for the operation of activated sludge plants. To achieve a cost effective treatment process, assessing and benchmarking of aeration system performance are important measures. A simple means of gauging the relative condition of a fine bubble diffused aeration system is to evaluate the pressure loss of the diffusers as oxygen transfer tests are rarely applied during the lifetime of an aeration system. This paper shows an assessment of fine bubble diffuser systems in Baden-Württemberg, Germany, based on the results of a questionnaire sent to 941 WWTPs. Apart from the results with regards to the diffuser pressure loss, this paper also presents information on the current state of diffuser technology such as types and materials as well as the diffuser cleaning methods used in Baden-Württemberg. The majority of the WWTPs were equipped with tube diffusers (71%) with 50% of all plants having EPDM membranes installed. Regular mechanical cleaning is the most common cleaning method followed by regular pressure release/air-bumping programs during operations. With regard to the diffuser pressure loss it was found that 50% of the evaluated plants had a diffuser pressure loss that was twice as high as measured for new diffusers.

Water Transport in the Micro Porous Layer and Gas Diffusion Layer of a Polymer Electrolyte Fuel Cell

NASA Astrophysics Data System (ADS)

Qin, C.; Hassanizadeh, S. M.

2015-12-01

In this work, a recently developed dynamic pore-network model is presented [1]. The model explicitly solves for both water pressure and capillary pressure. A semi-implicit scheme is used in updating water saturation in each pore body, which considerably increases the numerical stability at low capillary number values. Furthermore, a multiple-time-step algorithm is introduced to reduce the computational effort. A number of case studies of water transport in the micro porous layer (MPL) and gas diffusion layer (GDL) are conducted. We illustrate the role of MPL in reducing water flooding in the GDL. Also, the dynamic water transport through the MPL-GDL interface is explored in detail. This information is essential to the reduced continua model (RCM), which was developed for multiphase flow through thin porous layers [2, 3]. C.Z. Qin, Water transport in the gas diffusion layer of a polymer electrolyte fuel cell: dynamic pore-network modeling, J Electrochimical. Soci., 162, F1036-F1046, 2015. C.Z. Qin and S.M. Hassanizadeh, Multiphase flow through multilayers of thin porous media: general balance equations and constitutive relationships for a solid-gas-liquid three-phase system, Int. J. Heat Mass Transfer, 70, 693-708, 2014. C.Z. Qin and S.M. Hassanizadeh, A new approach to modeling water flooding in a polymer electrolyte fuel cell, Int. J. Hydrogen Energy, 40, 3348-3358, 2015.

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

NASA Astrophysics Data System (ADS)

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

2017-09-01

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

FDM study of ion exchange diffusion equation in glass

NASA Astrophysics Data System (ADS)

Zhou, Zigang; Yang, Yongjia; Wang, Qiang; Sun, Guangchun

2009-05-01

Ion-exchange technique in glass was developed to fabricate gradient refractive index optical devices. In this paper, the Finite Difference Method(FDM), which is used for the solution of ion-diffusion equation, is reported. This method transforms continual diffusion equation to separate difference equation. It unitizes the matrix of MATLAB program to solve the iteration process. The collation results under square boundary condition show that it gets a more accurate numerical solution. Compared to experiment data, the relative error is less than 0.2%. Furthermore, it has simply operation and kinds of output solutions. This method can provide better results for border-proliferation of the hexagonal and the channel devices too.

Gas-induced friction and diffusion of rigid rotors

NASA Astrophysics Data System (ADS)

Martinetz, Lukas; Hornberger, Klaus; Stickler, Benjamin A.

2018-05-01

We derive the Boltzmann equation for the rotranslational dynamics of an arbitrary convex rigid body in a rarefied gas. It yields as a limiting case the Fokker-Planck equation accounting for friction, diffusion, and nonconservative drift forces and torques. We provide the rotranslational friction and diffusion tensors for specular and diffuse reflection off particles with spherical, cylindrical, and cuboidal shape, and show that the theory describes thermalization, photophoresis, and the inverse Magnus effect in the free molecular regime.

Permeability Sensitivity Functions and Rapid Simulation of Hydraulic-Testing Measurements Using Perturbation Theory

NASA Astrophysics Data System (ADS)

Escobar Gómez, J. D.; Torres-Verdín, C.

2018-03-01

Single-well pressure-diffusion simulators enable improved quantitative understanding of hydraulic-testing measurements in the presence of arbitrary spatial variations of rock properties. Simulators of this type implement robust numerical algorithms which are often computationally expensive, thereby making the solution of the forward modeling problem onerous and inefficient. We introduce a time-domain perturbation theory for anisotropic permeable media to efficiently and accurately approximate the transient pressure response of spatially complex aquifers. Although theoretically valid for any spatially dependent rock/fluid property, our single-phase flow study emphasizes arbitrary spatial variations of permeability and anisotropy, which constitute key objectives of hydraulic-testing operations. Contrary to time-honored techniques, the perturbation method invokes pressure-flow deconvolution to compute the background medium's permeability sensitivity function (PSF) with a single numerical simulation run. Subsequently, the first-order term of the perturbed solution is obtained by solving an integral equation that weighs the spatial variations of permeability with the spatial-dependent and time-dependent PSF. Finally, discrete convolution transforms the constant-flow approximation to arbitrary multirate conditions. Multidimensional numerical simulation studies for a wide range of single-well field conditions indicate that perturbed solutions can be computed in less than a few CPU seconds with relative errors in pressure of <5%, corresponding to perturbations in background permeability of up to two orders of magnitude. Our work confirms that the proposed joint perturbation-convolution (JPC) method is an efficient alternative to analytical and numerical solutions for accurate modeling of pressure-diffusion phenomena induced by Neumann or Dirichlet boundary conditions.

Density-Dependent Conformable Space-time Fractional Diffusion-Reaction Equation and Its Exact Solutions

NASA Astrophysics Data System (ADS)

Hosseini, Kamyar; Mayeli, Peyman; Bekir, Ahmet; Guner, Ozkan

2018-01-01

In this article, a special type of fractional differential equations (FDEs) named the density-dependent conformable fractional diffusion-reaction (DDCFDR) equation is studied. Aforementioned equation has a significant role in the modelling of some phenomena arising in the applied science. The well-organized methods, including the \\exp (-φ (\\varepsilon )) -expansion and modified Kudryashov methods are exerted to generate the exact solutions of this equation such that some of the solutions are new and have been reported for the first time. Results illustrate that both methods have a great performance in handling the DDCFDR equation.

Cylindrical diffuser performance using a truncated plug nozzle

NASA Technical Reports Server (NTRS)

Galanga, F. L.; Mueller, T. J.

1976-01-01

Cylindrical diffuser performance for a truncated plug nozzle without external flow was tested in a blowdown wind tunnel. The nozzle was designed for an exit Mach number of 1.9 and the plug was conical in shape from the throat and converged to the axis of symmetry at an angle of 10 degrees. The diffuser section was fashioned into two 13.97 cm lengths to facilitate boring of the duct diameter and to allow for testing of two different duct lengths. A slotted hypotube was installed in the base of the diffuser to measure pressure distribution down the centerline of the diffuser. The data obtained included: the typical centerline and sidewall pressure ratio variation along the diffuser, cell pressure ratio vs overall pressure ratio for long and short diffusers and a comparison of minimum experimental cell pressure ratio vs area ratio.

Intensity Biased PSP Measurement

NASA Technical Reports Server (NTRS)

Subramanian, Chelakara S.; Amer, Tahani R.; Oglesby, Donald M.; Burkett, Cecil G., Jr.

2000-01-01

The current pressure sensitive paint (PSP) technique assumes a linear relationship (Stern-Volmer Equation) between intensity ratio (I(sub 0)/I) and pressure ratio (P/P(sub 0)) over a wide range of pressures (vacuum to ambient or higher). Although this may be valid for some PSPs, in most PSPs the relationship is nonlinear, particularly at low pressures (less than 0.2 psia when the oxygen level is low). This non-linearity can be attributed to variations in the oxygen quenching (de-activation) rates (which otherwise is assumed constant) at these pressures. Other studies suggest that some paints also have non-linear calibrations at high pressures; because of heterogeneous (non-uniform) oxygen diffusion and c quenching. Moreover, pressure sensitive paints require correction for the output intensity due to light intensity variation, paint coating variation, model dynamics, wind-off reference pressure variation, and temperature sensitivity. Therefore to minimize the measurement uncertainties due to these causes, an in- situ intensity correction method was developed. A non-oxygen quenched paint (which provides a constant intensity at all pressures, called non-pressure sensitive paint, NPSP) was used for the reference intensity (I(sub NPSP)) with respect to which all the PSP intensities (I) were measured. The results of this study show that in order to fully reap the benefits of this technique, a totally oxygen impermeable NPSP must be available.

Intensity Biased PSP Measurement

NASA Technical Reports Server (NTRS)

Subramanian, Chelakara S.; Amer, Tahani R.; Oglesby, Donald M.; Burkett, Cecil G., Jr.

2000-01-01

The current pressure sensitive paint (PSP) technique assumes a linear relationship (Stern-Volmer Equation) between intensity ratio (I(sub o)/I) and pressure ratio (P/P(sub o)) over a wide range of pressures (vacuum to ambient or higher). Although this may be valid for some PSPs, in most PSPs the relationship is nonlinear, particularly at low pressures (less than 0.2 psia when the oxygen level is low). This non-linearity can be attributed to variations in the oxygen quenching (de-activation) rates (which otherwise is assumed constant) at these pressures. Other studies suggest that some paints also have non-linear calibrations at high pressures; because of heterogeneous (non-uniform) oxygen diffusion and quenching. Moreover, pressure sensitive paints require correction for the output intensity due to light intensity variation, paint coating variation, model dynamics, wind-off reference pressure variation, and temperature sensitivity. Therefore to minimize the measurement uncertainties due to these causes, an insitu intensity correction method was developed. A non-oxygen quenched paint (which provides a constant intensity at all pressures, called non-pressure sensitive paint, NPSP) was used for the reference intensity (I(sub NPSP) with respect to which all the PSP intensities (I) were measured. The results of this study show that in order to fully reap the benefits of this technique, a totally oxygen impermeable NPSP must be available.

A Simple, Analytical Model of Collisionless Magnetic Reconnection in a Pair Plasma

NASA Technical Reports Server (NTRS)

Hesse, Michael; Zenitani, Seiji; Kuznetova, Masha; Klimas, Alex

2011-01-01

A set of conservation equations is utilized to derive balance equations in the reconnection diffusion region of a symmetric pair plasma. The reconnection electric field is assumed to have the function to maintain the current density in the diffusion region, and to impart thermal energy to the plasma by means of quasi-viscous dissipation. Using these assumptions it is possible to derive a simple set of equations for diffusion region parameters in dependence on inflow conditions and on plasma compressibility. These equations are solved by means of a simple, iterative, procedure. The solutions show expected features such as dominance of enthalpy flux in the reconnection outflow, as well as combination of adiabatic and quasi-viscous heating. Furthermore, the model predicts a maximum reconnection electric field of E(sup *)=0.4, normalized to the parameters at the inflow edge of the diffusion region.

A simple, analytical model of collisionless magnetic reconnection in a pair plasma

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

Hesse, Michael; Zenitani, Seiji; Kuznetsova, Masha

2009-10-15

A set of conservation equations is utilized to derive balance equations in the reconnection diffusion region of a symmetric pair plasma. The reconnection electric field is assumed to have the function to maintain the current density in the diffusion region and to impart thermal energy to the plasma by means of quasiviscous dissipation. Using these assumptions it is possible to derive a simple set of equations for diffusion region parameters in dependence on inflow conditions and on plasma compressibility. These equations are solved by means of a simple, iterative procedure. The solutions show expected features such as dominance of enthalpymore » flux in the reconnection outflow, as well as combination of adiabatic and quasiviscous heating. Furthermore, the model predicts a maximum reconnection electric field of E{sup *}=0.4, normalized to the parameters at the inflow edge of the diffusion region.« less

Alveolar ventilation to perfusion heterogeneity and diffusion impairment in a mathematical model of gas exchange

NASA Technical Reports Server (NTRS)

Vidal Melo, M. F.; Loeppky, J. A.; Caprihan, A.; Luft, U. C.

1993-01-01

This study describes a two-compartment model of pulmonary gas exchange in which alveolar ventilation to perfusion (VA/Q) heterogeneity and impairment of pulmonary diffusing capacity (D) are simultaneously taken into account. The mathematical model uses as input data measurements usually obtained in the lung function laboratory. It consists of two compartments and an anatomical shunt. Each compartment receives fractions of alveolar ventilation and blood flow. Mass balance equations and integration of Fick's law of diffusion are used to compute alveolar and blood O2 and CO2 values compatible with input O2 uptake and CO2 elimination. Two applications are presented. The first is a method to partition O2 and CO2 alveolar-arterial gradients into VA/Q and D components. The technique is evaluated in data of patients with chronic obstructive pulmonary disease (COPD). The second is a theoretical analysis of the effects of blood flow variation in alveolar and blood O2 partial pressures. The results show the importance of simultaneous consideration of D to estimate VA/Q heterogeneity in patients with diffusion impairment. This factor plays an increasing role in gas alveolar-arterial gradients as severity of COPD increases. Association of VA/Q heterogeneity and D may produce an increase of O2 arterial pressure with decreasing QT which would not be observed if only D were considered. We conclude that the presented computer model is a useful tool for description and interpretation of data from COPD patients and for performing theoretical analysis of variables involved in the gas exchange process.

Symmetry Reductions of Fourth-Order Nonlinear Diffusion Equations: Lubrication Model and Some Generalizations

NASA Astrophysics Data System (ADS)

Gandarias, M. L.; Medina, E.

Fourth-order nonlinear diffusion equations appear frequently in the description of physical processes, among these, the lubrication equation ut = (unuxxxx)x or the corresponding modified version ut = unuxxxx play an important role in the study of the interface movements. In this work we analyze the generalizations of the above equations given by ut = (f(u)uxxxx)x, ut = (f(u)uxxxx, and we find that if f(u) = un or f(u) = e-u the equations admit extra classical symmetries. The corresponding reductions are performed and some solutions are characterized.

Diffusion coefficients of oxygen and hemoglobin measured by facilitated oxygen diffusion through hemoglobin solutions.

PubMed

Bouwer, S T; Hoofd, L; Kreuzer, F

1997-03-07

Diffusion coefficients of oxygen (DO2) and hemoglobin (DHb) were obtained from measuring the oxygen flux through thin layers of hemoglobin solutions at 20 degrees C. The liquid layers were supported by a membrane and not soaked in any filter material. Oxygen fluxes were measured from the changes in oxygen partial pressure in the gas phases at both sides of the layer. A mathematical treatment is presented for correct evaluation of the measurements. Measurements were done for bovine and for human hemoglobin. Hemoglobin concentrations (CHb) were between 11 and 42 g/dl, which covers the concentrations in the erythrocyte. Both DO2 and DHb could be fitted to the empirical equation D = D0(1-CHb/C1)10-CHb/C2. The following parameters were obtained: DO = 1.80 x 10(-9) m2/s, C1 = 100 g/dl, C2 = 119 g/dl, for oxygen and D0 = 7.00 x 10(-11) m2/s, C1 = 46 g/dl, C2 = 128 g/dl, for hemoglobin. No difference between the diffusion coefficients of bovine or human hemoglobin was found. The diffusion coefficients of hemoglobin were higher than most values reported in the literature, probably because in this study the mobility of hemoglobin was not hindered by surrounding filter material.

Mixing of a passive scalar in isotropic and sheared homogeneous turbulence

NASA Technical Reports Server (NTRS)

Shirani, E.; Ferziger, J. H.; Reynolds, W. C.

1981-01-01

In order to calculate the velocity and scalar fields, the three dimensional, time-dependent equations of motion and the diffusion equation were solved numerically. The following cases were treated: isotropic, homogeneous turbulence with decay of a passive scalar; and homogeneous turbulent shear flow with a passive scalar whose mean varies linearly in the spanwise direction. The solutions were obtained at relatively low Reynolds numbers so that all of the turbulent scales could be resolved without modeling. Turbulent statistics such as integral length scales, Taylor microscales, Kolmogorov length scale, one- and two-point correlations of velocity-velocity and velocity-scalar, turbulent Prandtl/Schmidt number, r.m.s. values of velocities, the scalar quantity and pressure, skewness, decay rates, and decay exponents were calculated. The results are compared with the available expermental results, and good agreement is obtained.

Equation of state and some structural and dynamical properties of the confined Lennard-Jones fluid into carbon nanotube: A molecular dynamics study

NASA Astrophysics Data System (ADS)

Abbaspour, Mohsen; Akbarzadeh, Hamed; Salemi, Sirous; Abroodi, Mousarreza

2016-11-01

By considering the anisotropic pressure tensor, two separate equations of state (EoS) as functions of the density, temperature, and carbon nanotube (CNT) diameter have been proposed for the radial and axial directions for the confined Lennard-Jones (LJ) fluid into (11,11), (12,10), and (19,0) CNTs from 120 to 600 K using molecular dynamics (MD) simulations. We have also investigated the effects of the pore size, pore loading, chirality, and temperature on some of the structural and dynamical properties of the confined LJ fluid into (11,11), (12,10), (19,0), and (19,19) CNTs such as the radial density profile and self-diffusion coefficient. We have also determined the EoS for the confined LJ fluid into double and triple walled CNTs.

Theoretical study on the sound absorption of electrolytic solutions. I. Theoretical formulation.

PubMed

Yamaguchi, T; Matsuoka, T; Koda, S

2007-04-14

A theory is formulated that describes the sound absorption of electrolytic solutions due to the relative motion of ions, including the formation of ion pairs. The theory is based on the Kubo-Green formula for the bulk viscosity. The time correlation function of the pressure is projected onto the bilinear product of the density modes of ions. The time development of the product of density modes is described by the diffusive limit of the generalized Langevin equation, and approximate expressions for the three- and four-body correlation functions required are given with the hypernetted-chain integral equation theory. Calculations on the aqueous solutions of model electrolytes are performed. It is demonstrated that the theory describes both the activated barrier crossing between contact and solvent-separated ion pairs and the Coulombic correlation between ions.

Theoretical study on the sound absorption of electrolytic solutions. I. Theoretical formulation

NASA Astrophysics Data System (ADS)

Yamaguchi, T.; Matsuoka, T.; Koda, S.

2007-04-01

A theory is formulated that describes the sound absorption of electrolytic solutions due to the relative motion of ions, including the formation of ion pairs. The theory is based on the Kubo-Green formula for the bulk viscosity. The time correlation function of the pressure is projected onto the bilinear product of the density modes of ions. The time development of the product of density modes is described by the diffusive limit of the generalized Langevin equation, and approximate expressions for the three- and four-body correlation functions required are given with the hypernetted-chain integral equation theory. Calculations on the aqueous solutions of model electrolytes are performed. It is demonstrated that the theory describes both the activated barrier crossing between contact and solvent-separated ion pairs and the Coulombic correlation between ions.

Wave and pseudo-diffusion equations from squeezed states

NASA Technical Reports Server (NTRS)

Daboul, Jamil

1993-01-01

We show that the probability distributions P(sub n)(q,p;y) := the absolute value squared of (n(p,q;y), which are obtained from squeezed states, obey an interesting partial differential equation, to which we give two intuitive interpretations: as a wave equation in one space dimension; and as a pseudo-diffusion equation. We also study the corresponding Wehrl entropies S(sub n)(y), and we show that they have minima at zero squeezing, y = 0.

Gravitational instability of filamentary molecular clouds, including ambipolar diffusion; non-isothermal filament

NASA Astrophysics Data System (ADS)

Hosseinirad, Mohammad; Abbassi, Shahram; Roshan, Mahmood; Naficy, Kazem

2018-04-01

Recent observations of the filamentary molecular clouds show that their properties deviate from the isothermal equation of state. Theoretical investigations proposed that the logatropic and the polytropic equations of state with negative indexes can provide a better description for these filamentary structures. Here, we aim to compare the effects of these softer non-isothermal equations of state with their isothermal counterpart on the global gravitational instability of a filamentary molecular cloud. By incorporating the ambipolar diffusion, we use the non-ideal magnetohydrodynamics framework for a filament that is threaded by a uniform axial magnetic field. We perturb the fluid and obtain the dispersion relation both for the logatropic and polytropic equations of state by taking the effects of magnetic field and ambipolar diffusion into account. Our results suggest that, in absence of the magnetic field, a softer equation of state makes the system more prone to gravitational instability. We also observed that a moderate magnetic field is able to enhance the stability of the filament in a way that is sensitive to the equation of state in general. However, when the magnetic field is strong, this effect is suppressed and all the equations of state have almost the same stability properties. Moreover, we find that for all the considered equations of state, the ambipolar diffusion has destabilizing effects on the filament.

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

NASA Technical Reports Server (NTRS)

Wood, William A.

1997-01-01

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

Acoustics of multiscale sorptive porous materials

NASA Astrophysics Data System (ADS)

Venegas, R.; Boutin, C.; Umnova, O.

2017-08-01

This paper investigates sound propagation in multiscale rigid-frame porous materials that support mass transfer processes, such as sorption and different types of diffusion, in addition to the usual visco-thermo-inertial interactions. The two-scale asymptotic method of homogenization for periodic media is successively used to derive the macroscopic equations describing sound propagation through the material. This allowed us to conclude that the macroscopic mass balance is significantly modified by sorption, inter-scale (micro- to/from nanopore scales) mass diffusion, and inter-scale (pore to/from micro- and nanopore scales) pressure diffusion. This modification is accounted for by the dynamic compressibility of the effective saturating fluid that presents atypical properties that lead to slower speed of sound and higher sound attenuation, particularly at low frequencies. In contrast, it is shown that the physical processes occurring at the micro-nano-scale do not affect the macroscopic fluid flow through the material. The developed theory is exemplified by introducing an analytical model for multiscale sorptive granular materials, which is experimentally validated by comparing its predictions with acoustic measurements on granular activated carbons. Furthermore, we provide empirical evidence supporting an alternative method for measuring sorption and mass diffusion properties of multiscale sorptive materials using sound waves.

Gaseous diffusion system

DOEpatents

Garrett, George A.; Shacter, John

1978-01-01

1. A gaseous diffusion system comprising a plurality of diffusers connected in cascade to form a series of stages, each of said diffusers having a porous partition dividing it into a high pressure chamber and a low pressure chamber, and means for combining a portion of the enriched gas from a succeeding stage with a portion of the enriched gas from the low pressure chamber of each stage and feeding it into one extremity of the high pressure chamber thereof.

On ternary species mixing and combustion in isotropic turbulence at high pressure

NASA Astrophysics Data System (ADS)

Lou, Hong; Miller, Richard S.

2004-05-01

Effects of Soret and Dufour cross-diffusion, whereby both concentration and thermal diffusion occur in the presence of mass fraction, temperature, and pressure gradients, are investigated in the context of both binary and ternary species mixing and combustion in isotropic turbulence at large pressure. The compressible flow formulation is based on a cubic real-gas state equation, and includes generalized forms for heat and mass diffusion derived from nonequilibrium thermodynamics and fluctuation theory. A previously derived formulation of the generalized binary species heat and mass fluxes is first extended to the case of ternary species, and appropriate treatment of the thermal and mass diffusion factors is described. Direct numerical simulations (DNS) are then conducted for both binary and ternary species mixing and combustion in stationary isotropic turbulence. Mean flow temperatures and pressures of =700 K and =45 atm are considered to ensure that all species mixtures remain in the supercritical state such that phase changes do not occur. DNS of ternary species systems undergoing both pure mixing and a simple chemical reaction of the form O2+N2→2NO are then conducted. It is shown that stationary scalar states previously observed for binary mixing persist for the ternary species problem as well; however, the production and magnitude of the scalar variance is found to be altered for the intermediate molecular weight species as compared to the binary species case. The intermediate molecular weight species produces a substantially smaller scalar variance than the remaining species for all flows considered. For combustion of nonstoichiometric mixtures, a binary species mixture, characterized by stationary scalar states, results at long times after the lean reactant is depleted. The form of this final scalar distribution is observed to be similar to that found in the binary flow situation. A series of lower resolution simulations for a variety of species is then used to show the dependence of the stationary scalar variance on the turbulence Reynolds number, turbulence Mach number, species molecular weight ratio, and relative proportion of two species present in the flow after completion of combustion.

Strongly anomalous diffusion in sheared magnetic configurations

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

Vanden Eijnden, E.; Balescu, R.

1996-03-01

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

Continuum mesoscopic framework for multiple interacting species and processes on multiple site types and/or crystallographic planes.

PubMed

Chatterjee, Abhijit; Vlachos, Dionisios G

2007-07-21

While recently derived continuum mesoscopic equations successfully bridge the gap between microscopic and macroscopic physics, so far they have been derived only for simple lattice models. In this paper, general deterministic continuum mesoscopic equations are derived rigorously via nonequilibrium statistical mechanics to account for multiple interacting surface species and multiple processes on multiple site types and/or different crystallographic planes. Adsorption, desorption, reaction, and surface diffusion are modeled. It is demonstrated that contrary to conventional phenomenological continuum models, microscopic physics, such as the interaction potential, determines the final form of the mesoscopic equation. Models of single component diffusion and binary diffusion of interacting particles on single-type site lattice and of single component diffusion on complex microporous materials' lattices consisting of two types of sites are derived, as illustrations of the mesoscopic framework. Simplification of the diffusion mesoscopic model illustrates the relation to phenomenological models, such as the Fickian and Maxwell-Stefan transport models. It is demonstrated that the mesoscopic equations are in good agreement with lattice kinetic Monte Carlo simulations for several prototype examples studied.

Finite Difference Formulation for Prediction of Water Pollution

NASA Astrophysics Data System (ADS)

Johari, Hanani; Rusli, Nursalasawati; Yahya, Zainab

2018-03-01

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

Hydro-mechanical pressure response to fluid injection into finite aquifers highlights the non-local behavior of storage

NASA Astrophysics Data System (ADS)

De Simone, Silvia; Carrera, Jesus

2017-04-01

Specific storage reflects the volumetric deformation capacity of permeable media. Classical groundwater hydrology equals elastic storage to medium compressibility, which is a constant-in-time and locally-defined parameter. This allows simplifying the flow equation into a linear diffusion equation that is relatively easy to solve. However, the hydraulic gradients, generated by fluid injection or pumping, act as forces that push the medium in the direction of flow causing it to deform, even in regions where pressure has not changed. Actual deformation depends on the elastic properties of the medium, but also on aquifer geometry and on surrounding strata, which act like constraints to displacements. Therefore the storage results to be non-local (i.e., the volume of water released at a point depends on the poroelastic response over the whole aquifer) and the proper evaluation of transient pressure requires acknowledging the hydro-mechanical (HM) coupling, which is generally disregarded by conventional hydrogeology. Here we discuss whether HM coupling effects are relevant, which is of special interest for the activities of enhanced geothermics, waste disposal, CO2 storage or shale gas extraction. We propose analytic solutions to the HM problem of fluid injection (or extraction) into finite aquifers with one-dimensional or cylindrical geometries. We find that the deviation respect to traditional purely hydraulic solutions is significant when the aquifer has limited capacity to deform. The most relevant implications are that the response time is faster and the pressure variation greater than expected, which may be relevant for aquifer characterization and for the evaluation of pressure build-up due to fluid injection.

Prediction of Three-Dimensional Downward Flame Spread Characteristics over Poly(methyl methacrylate) Slabs in Different Pressure Environments.

PubMed

Zhao, Kun; Zhou, Xiao-Dong; Liu, Xue-Qiang; Lu, Lei; Wu, Zhi-Bo; Peng, Fei; Ju, Xiao-Yu; Yang, Li-Zhong

2016-11-22

The present study is aimed at predicting downward flame spread characteristics over poly(methyl methacrylate) (PMMA) with different sample dimensions in different pressure environments. Three-dimensional (3-D) downward flame spread experiments on free PMMA slabs were conducted at five locations with different altitudes, which provide different pressures. Pressure effects on the flame spread rate, profile of pyrolysis front and flame height were analyzed at all altitudes. The flame spread rate in the steady-state stage was calculated based on the balance on the fuel surface and fuel properties. Results show that flame spread rate increases exponentially with pressure, and the exponent of pressure further shows an increasing trend with the thickness of the sample. The angle of the pyrolysis front emerged on sample residue in the width direction, which indicates a steady-burning stage, varies clearly with sample thicknesses and ambient pressures. A global non-dimensional equation was proposed to predict the variation tendency of the angle of the pyrolysis front with pressure and was found to fit well with the measured results. In addition, the dependence of average flame height on mass burning rate, sample dimension and pressure was proposed based on laminar diffusion flame theory. The fitted exponent of experimental data is 1.11, which is close to the theoretical value.

Mathematical analysis of thermal diffusion shock waves

NASA Astrophysics Data System (ADS)

Gusev, Vitalyi; Craig, Walter; Livoti, Roberto; Danworaphong, Sorasak; Diebold, Gerald J.

2005-10-01

Thermal diffusion, also known as the Ludwig-Soret effect, refers to the separation of mixtures in a temperature gradient. For a binary mixture the time dependence of the change in concentration of each species is governed by a nonlinear partial differential equation in space and time. Here, an exact solution of the Ludwig-Soret equation without mass diffusion for a sinusoidal temperature field is given. The solution shows that counterpropagating shock waves are produced which slow and eventually come to a halt. Expressions are found for the shock time for two limiting values of the starting density fraction. The effects of diffusion on the development of the concentration profile in time and space are found by numerical integration of the nonlinear differential equation.

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

NASA Astrophysics Data System (ADS)

Remizov, I. D.

2012-07-01

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

Molecular dynamics studies of transport properties and equation of state of supercritical fluids

NASA Astrophysics Data System (ADS)

Nwobi, Obika C.

Many chemical propulsion systems operate with one or more of the reactants above the critical point in order to enhance their performance. Most of the computational fluid dynamics (CFD) methods used to predict these flows require accurate information on the transport properties and equation of state at these supercritical conditions. This work involves the determination of transport coefficients and equation of state of supercritical fluids by equilibrium molecular dynamics (MD) simulations on parallel computers using the Green-Kubo formulae and the virial equation of state, respectively. MD involves the solution of equations of motion of a system of molecules that interact with each other through an intermolecular potential. Provided that an accurate potential can be found for the system of interest, MD can be used regardless of the phase and thermodynamic conditions of the substances involved. The MD program uses the effective Lennard-Jones potential, with system sizes of 1000-1200 molecules and, simulations of 2,000,000 time-steps for computing transport coefficients and 200,000 time-steps for pressures. The computer code also uses linked cell lists for efficient sorting of molecules, periodic boundary conditions, and a modified velocity Verlet algorithm for particle displacement. Particle decomposition is used for distributing the molecules to different processors of a parallel computer. Simulations have been carried out on pure argon, nitrogen, oxygen and ethylene at various supercritical conditions, with self-diffusion coefficients, shear viscosity coefficients, thermal conductivity coefficients and pressures computed for most of the conditions. Results compare well with experimental and the National Institute of Standards and Technology (NIST) values. The results show that the number of molecules and the potential cut-off radius have no significant effect on the computed coefficients, while long-time integration is necessary for accurate determination of the coefficients.

Modeling boundary measurements of scattered light using the corrected diffusion approximation

PubMed Central

Lehtikangas, Ossi; Tarvainen, Tanja; Kim, Arnold D.

2012-01-01

We study the modeling and simulation of steady-state measurements of light scattered by a turbid medium taken at the boundary. In particular, we implement the recently introduced corrected diffusion approximation in two spatial dimensions to model these boundary measurements. This implementation uses expansions in plane wave solutions to compute boundary conditions and the additive boundary layer correction, and a finite element method to solve the diffusion equation. We show that this corrected diffusion approximation models boundary measurements substantially better than the standard diffusion approximation in comparison to numerical solutions of the radiative transport equation. PMID:22435102

Optical Oversampled Analog-to-Digital Conversion

DTIC Science & Technology

1992-06-29

hologram weights and interconnects in the digital image halftoning configuration. First, no temporal error diffusion occurs in the digital image... halftoning error diffusion ar- chitecture as demonstrated by Equation (6.1). Equation (6.2) ensures that the hologram weights sum to one so that the exact...optimum halftone image should be faster. Similarly, decreased convergence time suggests that an error diffusion filter with larger spatial dimensions

Modelling the radiotherapy effect in the reaction-diffusion equation.

PubMed

Borasi, Giovanni; Nahum, Alan

2016-09-01

In recent years, the reaction-diffusion (Fisher-Kolmogorov) equation has received much attention from the oncology research community due to its ability to describe the infiltrating nature of glioblastoma multiforme and its extraordinary resistance to any type of therapy. However, in a number of previous papers in the literature on applications of this equation, the term (R) expressing the 'External Radiotherapy effect' was incorrectly derived. In this note we derive an analytical expression for this term in the correct form to be included in the reaction-diffusion equation. The R term has been derived starting from the Linear-Quadratic theory of cell killing by ionizing radiation. The correct definition of R was adopted and the basic principles of differential calculus applied. The compatibility of the R term derived here with the reaction-diffusion equation was demonstrated. Referring to a typical glioblastoma tumour, we have compared the results obtained using our expression for the R term with the 'incorrect' expression proposed by other authors. Copyright © 2016 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.

NUMERICAL METHODS FOR SOLVING THE MULTI-TERM TIME-FRACTIONAL WAVE-DIFFUSION EQUATION.

PubMed

Liu, F; Meerschaert, M M; McGough, R J; Zhuang, P; Liu, Q

2013-03-01

In this paper, the multi-term time-fractional wave-diffusion equations are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], [1,2), [0,2), [0,3), [2,3) and [2,4), respectively. Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and techniques can also be extended to other kinds of the multi-term fractional time-space models with fractional Laplacian.

NUMERICAL METHODS FOR SOLVING THE MULTI-TERM TIME-FRACTIONAL WAVE-DIFFUSION EQUATION

PubMed Central

Liu, F.; Meerschaert, M.M.; McGough, R.J.; Zhuang, P.; Liu, Q.

2013-01-01

In this paper, the multi-term time-fractional wave-diffusion equations are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], [1,2), [0,2), [0,3), [2,3) and [2,4), respectively. Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and techniques can also be extended to other kinds of the multi-term fractional time-space models with fractional Laplacian. PMID:23772179

Traveling wavefront solutions to nonlinear reaction-diffusion-convection equations

NASA Astrophysics Data System (ADS)

Indekeu, Joseph O.; Smets, Ruben

2017-08-01

Physically motivated modified Fisher equations are studied in which nonlinear convection and nonlinear diffusion is allowed for besides the usual growth and spread of a population. It is pointed out that in a large variety of cases separable functions in the form of exponentially decaying sharp wavefronts solve the differential equation exactly provided a co-moving point source or sink is active at the wavefront. The velocity dispersion and front steepness may differ from those of some previously studied exact smooth traveling wave solutions. For an extension of the reaction-diffusion-convection equation, featuring a memory effect in the form of a maturity delay for growth and spread, also smooth exact wavefront solutions are obtained. The stability of the solutions is verified analytically and numerically.

Traveling wave solutions to a reaction-diffusion equation

NASA Astrophysics Data System (ADS)

Feng, Zhaosheng; Zheng, Shenzhou; Gao, David Y.

2009-07-01

In this paper, we restrict our attention to traveling wave solutions of a reaction-diffusion equation. Firstly we apply the Divisor Theorem for two variables in the complex domain, which is based on the ring theory of commutative algebra, to find a quasi-polynomial first integral of an explicit form to an equivalent autonomous system. Then through this first integral, we reduce the reaction-diffusion equation to a first-order integrable ordinary differential equation, and a class of traveling wave solutions is obtained accordingly. Comparisons with the existing results in the literature are also provided, which indicates that some analytical results in the literature contain errors. We clarify the errors and instead give a refined result in a simple and straightforward manner.

Nature of self-diffusion in two-dimensional fluids

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

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

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

Nature of self-diffusion in two-dimensional fluids

DOE PAGES

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

2017-12-18

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

Perturbed invariant subspaces and approximate generalized functional variable separation solution for nonlinear diffusion-convection equations with weak source

NASA Astrophysics Data System (ADS)

Xia, Ya-Rong; Zhang, Shun-Li; Xin, Xiang-Peng

2018-03-01

In this paper, we propose the concept of the perturbed invariant subspaces (PISs), and study the approximate generalized functional variable separation solution for the nonlinear diffusion-convection equation with weak source by the approximate generalized conditional symmetries (AGCSs) related to the PISs. Complete classification of the perturbed equations which admit the approximate generalized functional separable solutions (AGFSSs) is obtained. As a consequence, some AGFSSs to the resulting equations are explicitly constructed by way of examples.

Shapes of Buoyant and Nonbuoyant Methane Laminar Jet Diffusion Flames

NASA Technical Reports Server (NTRS)

Sunderland, Peter B.; Yuan, Zeng-Guang; Urban, David L.

1997-01-01

Laminar gas jet diffusion flames represent a fundamental combustion configuration. Their study has contributed to numerous advances in combustion, including the development of analytical and computational combustion tools. Laminar jet flames are pertinent also to turbulent flames by use of the laminar flamelet concept. Investigations into the shapes of noncoflowing microgravity laminar jet diffusion flames have primarily been pursued in the NASA Lewis 2.2-second drop tower, by Cochran and coworkers and by Bahadori and coworkers. These studies were generally conducted at atmospheric pressure; they involved soot-containing flames and reported luminosity lengths and widths instead of the flame-sheet dimensions which are of Greater value to theory evaluation and development. The seminal model of laminar diffusion flames is that of Burke and Schumann, who solved the conservation of momentum equation for a jet flame in a coflowing ambient by assuming the velocity of fuel, oxidizer and products to be constant throughout. Roper and coworkers improved upon this model by allowing for axial variations of velocity and found flame shape to be independent of coflow velocity. Roper's suggestion that flame height should be independent of gravity level is not supported by past or present observations. Other models have been presented by Klajn and Oppenheim, Markstein and De Ris, Villermaux and Durox, and Li et al. The common result of all these models (except in the buoyant regime) is that flame height is proportional to fuel mass flowrate, with flame width proving much more difficult to predict. Most existing flame models have been compared with shapes of flames containing soot, which is known to obscure the weak blue emission of flame sheets. The present work involves measurements of laminar gas jet diffusion flame shapes. Flame images have been obtained for buoyant and nonbuoyant methane flames burning in quiescent air at various fuel flow-rates, burner diameters and ambient pressures. Soot concentrations were minimized by selecting conditions at low flowrates and low ambient pressures; this allows identification of actual flame sheets associated with blue emissions of CH and CO2. The present modeling effort follows that of Roper and is useful in explaining many of the trends observed.

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.

Simulation of chemical-vapor-deposited silicon carbide for a cold wall vertical reactor

NASA Astrophysics Data System (ADS)

Lee, Y. L.; Sanchez, J. M.

1997-07-01

The growth rate of silicon carbide obtained by low-pressure chemical vapor deposition from tetramethylsilane is numerically simulated for a cold wall vertical reactor. The transport equations for momentum, heat, and mass transfer are simultaneously solved by employing the finite volume method. A model for reaction rate is also proposed in order to predict the measured growth rates [A. Figueras, S. Garelik, J. Santiso, R. Rodroguez-Clemente, B. Armas, C. Combescure, R. Berjoan, J.M. Saurel and R. Caplain, Mater. Sci. Eng. B 11 (1992) 83]. Finally, the effects of thermal diffusion on the growth rate are investigated.

Gas-film coefficients for the volatilization of ketones from water

USGS Publications Warehouse

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

1986-01-01

Volatilization is a significant process in determining the fate of many organic compounds in streams and rivers. Quantifying this process requires knowledge of the mass-transfer coefficient from water, which is a function of the gas-film and liquid-film coefficients. The gas-film coefficient can be determined by measuring the flux for the volatilization of pure organic liquids. Volatilization fluxes for acetone, 2-butanone, 2-pentanone, 3-pentanone, 4-methyl-2-pentanone, 2-heptanone, and 2-octanone were measured in the laboratory over a range of temperatures. Gas-film coefficients were then calculated from these fluxes and from vapor pressure data from the literature. An equation was developed for predicting the volatilization flux of pure liquid ketones as a function of vapor pressure and molecular weight. Large deviations were found for acetone, and these were attributed to the possibility that acetone may be hydrogen bonded. A second equation for predicting the flux as a function of molecular weight and temperature resulted in large deviations for 4methyl-2-pentanone. These deviations were attributed to the branched structure of this ketone. Four factors based on the theory of volatilization and relating the volatilization flux or rate to the vapor pressure, molecular weight, temperature, and molecular diffusion coefficient were not constant as suggested by the literature. The factors generally increased with molecular weight and with temperature. Values for acetone corresponded to ketones with a larger molecular weight, and the acetone factors showed the greatest dependence on temperature. Both of these results are characteristic of compounds that are hydrogen bonded. Relations from the literature commonly used for describing the dependence of the gas-film coefficient on molecular weight and molecular diffusion coefficient were not applicable to the ketone gas-film coefficients. The dependence on molecular weight and molecular diffusion coefficient was in general U-shaped with the largest coefficients observed for acetone, the next largest for 2octanone, and the smallest for 2-pentanone and 3-pentanone. The gas-film coefficient for acetone was much more dependent on temperature than were the coefficients for the other ketones. Such behavior is characteristic of hydrogen-bonded substances. Temperature dependencies of the other ketones were about twice the theoretical value, but were comparable to a literature value for water. Ratios of the ketone gas-film coefficients to the gasfilm coefficients for the evaporation of water were approximately constant for all the ketones except for acetone, whose values were considerably larger. The ratios increased with temperature; however, the increases were small except for acetone. These ratios can be combined with an equation from the literaure for predicting the gasfilm coefficient for evaporation of water from a canal to predict the gas-film coefficients for the volatilization of ketones from streams and rivers.

New Equations for the Sublimation Pressure and Melting Pressure of H2O Ice Ih

NASA Astrophysics Data System (ADS)

Wagner, Wolfgang; Riethmann, Thomas; Feistel, Rainer; Harvey, Allan H.

2011-12-01

New reference equations, adopted by the International Association for the Properties of Water and Steam (IAPWS), are presented for the sublimation pressure and melting pressure of ice Ih as a function of temperature. These equations are based on input values derived from the phase-equilibrium condition between the IAPWS-95 scientific standard for thermodynamic properties of fluid H2O and the equation of state of H2O ice Ih adopted by IAPWS in 2006, making them thermodynamically consistent with the bulk-phase properties. Compared to the previous IAPWS formulations, which were empirical fits to experimental data, the new equations have significantly less uncertainty. The sublimation-pressure equation covers the temperature range from 50 K to the vapor-liquid-solid triple point at 273.16 K. The ice Ih melting-pressure equation describes the entire melting curve from 273.16 K to the ice Ih-ice III-liquid triple point at 251.165 K. For completeness, we also give the IAPWS melting-pressure equation for ice III, which is slightly adjusted to agree with the ice Ih melting-pressure equation at the corresponding triple point, and the unchanged IAPWS melting-pressure equations for ice V, ice VI, and ice VII.

Effect of Cross-Linking on Free Volume Properties of PEG Based Thiol-Ene Networks

NASA Astrophysics Data System (ADS)

Ramakrishnan, Ramesh; Vasagar, Vivek; Nazarenko, Sergei

According to the Fox and Loshaek theory, in elastomeric networks, free volume decreases linearly with the cross-link density increase. The aim of this study is to show whether the poly(ethylene glycol) (PEG) based multicomponent thiol-ene elastomeric networks demonstrate this model behavior? Networks with a broad cross-link density range were prepared by changing the ratio of the trithiol crosslinker to PEG dithiol and then UV cured with PEG diene while maintaining 1:1 thiol:ene stoichiometry. Pressure-volume-temperature (PVT) data of the networks was generated from the high pressure dilatometry experiments which was fit using the Simha-Somcynsky Equation-of-State analysis to obtain the fractional free volume of the networks. Using Positron Annihilation Lifetime Spectroscopy (PALS) analysis, the average free volume hole size of the networks was also quantified. The fractional free volume and the average free volume hole size showed a linear change with the cross-link density confirming that the Fox and Loshaek theory can be applied to this multicomponent system. Gas diffusivities of the networks showed a good correlation with free volume. A free volume based model was developed to describe the gas diffusivity trends as a function of cross-link density.

Diffuse reflectance relations based on diffusion dipole theory for large absorption and reduced scattering

NASA Astrophysics Data System (ADS)

Bremmer, Rolf H.; van Gemert, Martin J. C.; Faber, Dirk J.; van Leeuwen, Ton G.; Aalders, Maurice C. G.

2013-08-01

Diffuse reflectance spectra are used to determine the optical properties of biological samples. In medicine and forensic science, the turbid objects under study often possess large absorption and/or scattering properties. However, data analysis is frequently based on the diffusion approximation to the radiative transfer equation, implying that it is limited to tissues where the reduced scattering coefficient dominates over the absorption coefficient. Nevertheless, up to absorption coefficients of 20 m at reduced scattering coefficients of 1 and 11.5 mm-1, we observed excellent agreement (r2=0.994) between reflectance measurements of phantoms and the diffuse reflectance equation proposed by Zonios et al. [Appl. Opt. 38, 6628-6637 (1999)], derived as an approximation to one of the diffusion dipole equations of Farrell et al. [Med. Phys. 19, 879-888 (1992)]. However, two parameters were fitted to all phantom experiments, including strongly absorbing samples, implying that the reflectance equation differs from diffusion theory. Yet, the exact diffusion dipole approximation at high reduced scattering and absorption also showed agreement with the phantom measurements. The mathematical structure of the diffuse reflectance relation used, derived by Zonios et al. [Appl. Opt. 38, 6628-6637 (1999)], explains this observation. In conclusion, diffuse reflectance relations derived as an approximation to the diffusion dipole theory of Farrell et al. can analyze reflectance ratios accurately, even for much larger absorption than reduced scattering coefficients. This allows calibration of fiber-probe set-ups so that the object's diffuse reflectance can be related to its absorption even when large. These findings will greatly expand the application of diffuse reflection spectroscopy. In medicine, it may allow the use of blue/green wavelengths and measurements on whole blood, and in forensic science, it may allow inclusion of objects such as blood stains and cloth at crime scenes.

Diffusion Monte Carlo calculations of Xenon melting under pressure

NASA Astrophysics Data System (ADS)

Shulenburger, L.; Mattsson, T. R.

2011-03-01

The slope of the melting temperature as a function of pressure yields, via the Clausius-Clapeyron equation, important information regarding the changes in density, energy, and entropy. It is therefore crucial to resolve the long-standing differences in melt lines under pressure between Diamond Anvil Cell data (low/flat melt line) and other methods, including density functional theory (DFT) simulations 1 (high/steep melt line). The disagreement for Ta was recently resolved 2 and although a similar situation exists in the literature on Xe,3 the resolution may be quite different. For example, DFT with its lack of van der Waals forces is a prima facie less credible simulation method for Xe, although excellent agreement has been obtained between calculations of the Hugoniot of Xe and experiments.4 We investigate whether this theoretical shortcoming is significant for the melting transition by applying diffusion Monte Carlo. The energy differences obtained in this way are compared to the DFT results in order to address any systematic errors that may be present near the melting transition. 1 Taioli et al. PRB 75, 214103 (2007); 2 Dewaele et al. PRL 104, 255701 (2010); 3 Belonoshko el al. PRB 74, 054114 (2006); 4 Root et al. PRL 105, 085501 (2010) Sandia National Laboratories is a multiprogram laboratory managed and operated by Sandia Corp. for the US Dep. of Energy's National Nuclear Security Administration under Contract DE-AC04-94AL85000.

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

NASA Astrophysics Data System (ADS)

Padrino, Juan C.; Zhang, Duan Z.

2016-11-01

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

Analysis and Modeling of a Two-Phase Jet Pump of a Flow Boiling Test Facility for Aerospace Applications

NASA Technical Reports Server (NTRS)

Sherif, S. A.; Steadham, Justin M.

1996-01-01

Jet pumps are devices capable of pumping fluids to a higher pressure employing a nozzle/diffuser/mixing chamber combination. A primary fluid is usually allowed to pass through a converging-diverging nozzle where it can accelerate to supersonic speeds at the nozzle exit. The relatively high kinetic energy that the primary fluid possesses at the nozzle exit is accompanied by a low pressure region in order to satisfy Bernoulli's equation. The low pressure region downstream of the nozzle exit permits a secondary fluid to be entrained into and mixed with the primary fluid in a mixing chamber located downstream of the nozzle. Several combinations may exist in terms of the nature of the primary and secondary fluids in so far as whether they are single or two-phase fluids. Depending on this, the jet pump may be classified as gas/gas, gas/liquid, liquid/liquid, two-phase/liquid, or similar combinations. The mixing chamber serves to create a homogeneous single-phase or two-phase mixture which enters a diffuser where the high kinetic energy of the fluid is converted into pressure energy. If the fluid mixture entering the diffuser is in the supersonic flow regime, a normal shock wave usually develops inside the diffuser. If the fluid mixture is one that can easily change phase, a condensation shock would normally develop. Because of the overall rise in pressure in the diffuser as well as the additional rise in pressure across the shock layer, condensation becomes more likely. Associated with the pressure rise across the shock is a velocity reduction from the supersonic to the subsonic range. If the two-phase flow entering the diffuser is predominantly gaseous with liquid droplets suspended in it, it will transform into a predominantly liquid flow containing gaseous bubbles (bubbly flow) somewhere in the diffuser. While past researchers have been able to model the two-phase flow jet pump using the one-dimensional assumption with no shock waves and no phase change, there is no research known to the authors apart from that of Anand (1992) which accounted for condensation shocks. One of the objectives of this research effort is to develop a comprehensive model in which the effects of phase slip and inter-phase heat transfer as well as the wall friction and shock waves are accounted for. While this modeling effort is predominantly analytical in nature and is primarily intended to provide a parametric understanding of the jet pump performance under different operating scenarios, another parallel effort employing a commercial CFD code is also implemented. The latter effort is primarily intended to model an axisymmetric counterpart of the problem in question. The viability of using the CFD code to model a two-phase flow jet pump will be assessed by attempting to recreate some of the existing performance data of similar jet pumps. The code will eventually be used to generate the jet pump performance characteristics of several scenarios involving jet pump geometries as well as flow regimes in order to be able to determine an optimum design which would be suitable for a two-phase flow boiling test facility at NASA-Marshall. Because of the extensive nature of the analytical model developed, the following section will only provide very brief highlights of it, while leaving the details to a more complete report submitted to the NASA colleague. This report will also contain some of the simulation results obtained using the CFD code.

A prediction model of compressor with variable-geometry diffuser based on elliptic equation and partial least squares

PubMed Central

Yang, Chuanlei; Wang, Yinyan; Wang, Hechun

2018-01-01

To achieve a much more extensive intake air flow range of the diesel engine, a variable-geometry compressor (VGC) is introduced into a turbocharged diesel engine. However, due to the variable diffuser vane angle (DVA), the prediction for the performance of the VGC becomes more difficult than for a normal compressor. In the present study, a prediction model comprising an elliptical equation and a PLS (partial least-squares) model was proposed to predict the performance of the VGC. The speed lines of the pressure ratio map and the efficiency map were fitted with the elliptical equation, and the coefficients of the elliptical equation were introduced into the PLS model to build the polynomial relationship between the coefficients and the relative speed, the DVA. Further, the maximal order of the polynomial was investigated in detail to reduce the number of sub-coefficients and achieve acceptable fit accuracy simultaneously. The prediction model was validated with sample data and in order to present the superiority of compressor performance prediction, the prediction results of this model were compared with those of the look-up table and back-propagation neural networks (BPNNs). The validation and comparison results show that the prediction accuracy of the new developed model is acceptable, and this model is much more suitable than the look-up table and the BPNN methods under the same condition in VGC performance prediction. Moreover, the new developed prediction model provides a novel and effective prediction solution for the VGC and can be used to improve the accuracy of the thermodynamic model for turbocharged diesel engines in the future. PMID:29410849

The dynamics of oceanic fronts. Part 1: The Gulf Stream

NASA Technical Reports Server (NTRS)

Kao, T. W.

1970-01-01

The establishment and maintenance of the mean hydrographic properties of large scale density fronts in the upper ocean is considered. The dynamics is studied by posing an initial value problem starting with a near surface discharge of buoyant water with a prescribed density deficit into an ambient stationary fluid of uniform density. The full time dependent diffusion and Navier-Stokes equations for a constant Coriolis parameter are used in this study. Scaling analysis reveals three independent length scales of the problem, namely a radius of deformation or inertial length scale, Lo, a buoyance length scale, ho, and a diffusive length scale, hv. Two basic dimensionless parameters are then formed from these length scales, the thermal (or more precisely, the densimetric) Rossby number, Ro = Lo/ho and the Ekman number, E = hv/ho. The governing equations are then suitably scaled and the resulting normalized equations are shown to depend on E alone for problems of oceanic interest. Under this scaling, the solutions are similar for all Ro. It is also shown that 1/Ro is a measure of the frontal slope. The governing equations are solved numerically and the scaling analysis is confirmed. The solution indicates that an equilibrium state is established. The front can then be rendered stationary by a barotropic current from a larger scale along-front pressure gradient. In that quasisteady state, and for small values of E, the main thermocline and the inclined isopycnics forming the front have evolved, together with the along-front jet. Conservation of potential vorticity is also obtained in the light water pool. The surface jet exhibits anticyclonic shear in the light water pool and cyclonic shear across the front.

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

Broda, Jill Terese

The neutron flux across the nuclear reactor core is of interest to reactor designers and others. The diffusion equation, an integro-differential equation in space and energy, is commonly used to determine the flux level. However, the solution of a simplified version of this equation when automated is very time consuming. Since the flux level changes with time, in general, this calculation must be made repeatedly. Therefore solution techniques that speed the calculation while maintaining accuracy are desirable. One factor that contributes to the solution time is the spatial flux shape approximation used. It is common practice to use the samemore » order flux shape approximation in each energy group even though this method may not be the most efficient. The one-dimensional, two-energy group diffusion equation was solved, for the node average flux and core k-effective, using two sets of spatial shape approximations for each of three reactor types. A fourth-order approximation in both energy groups forms the first set of approximations used. The second set used combines a second-order approximation with a fourth-order approximation in energy group two. Comparison of the results from the two approximation sets show that the use of a different order spatial flux shape approximation results in considerable loss in accuracy for the pressurized water reactor modeled. However, the loss in accuracy is small for the heavy water and graphite reactors modeled. The use of different order approximations in each energy group produces mixed results. Further investigation into the accuracy and computing time is required before any quantitative advantage of the use of the second-order approximation in energy group one and the fourth-order approximation in energy group two can be determined.« less

A prediction model of compressor with variable-geometry diffuser based on elliptic equation and partial least squares.

PubMed

Li, Xu; Yang, Chuanlei; Wang, Yinyan; Wang, Hechun

2018-01-01

To achieve a much more extensive intake air flow range of the diesel engine, a variable-geometry compressor (VGC) is introduced into a turbocharged diesel engine. However, due to the variable diffuser vane angle (DVA), the prediction for the performance of the VGC becomes more difficult than for a normal compressor. In the present study, a prediction model comprising an elliptical equation and a PLS (partial least-squares) model was proposed to predict the performance of the VGC. The speed lines of the pressure ratio map and the efficiency map were fitted with the elliptical equation, and the coefficients of the elliptical equation were introduced into the PLS model to build the polynomial relationship between the coefficients and the relative speed, the DVA. Further, the maximal order of the polynomial was investigated in detail to reduce the number of sub-coefficients and achieve acceptable fit accuracy simultaneously. The prediction model was validated with sample data and in order to present the superiority of compressor performance prediction, the prediction results of this model were compared with those of the look-up table and back-propagation neural networks (BPNNs). The validation and comparison results show that the prediction accuracy of the new developed model is acceptable, and this model is much more suitable than the look-up table and the BPNN methods under the same condition in VGC performance prediction. Moreover, the new developed prediction model provides a novel and effective prediction solution for the VGC and can be used to improve the accuracy of the thermodynamic model for turbocharged diesel engines in the future.

The contribution of air-fluidization to the mobility of rapid flowslides involving fine particles

NASA Astrophysics Data System (ADS)

Stilmant, Frédéric; Dewals, Benjamin; Archambeau, Pierre; Erpicum, Sébastien; Pirotton, Michel

2016-04-01

Air-fluidization can be the origin of the long runout of gravitational flows involving fine particles such as ash. An excessive air pore pressure dramatically reduces the friction angle of the material as long as this pressure has not been dissipated, which occurs during the flow. This phenomenon can be modelled thanks to the 2D depth-averaged equations of mass and momentum conservation and an additional transport equation for basal pore pressure evolution (Iverson and Denlinger, 2001). In this contribution, we discuss the application of this model in relation to recent experimental results on air-fluidized flows by Roche et al. (2008) and Roche (2012). The experimental results were used to set a priori the value of the diffusion coefficient in the model, taking into account the difference of scale between the experiments and real-world applications. We also compare the model predictions against detailed observations of a well-documented historical event, the collapse of a fly-ash heap in Belgium (Stilmant et al., 2015). In particular, we analyse the influence of the different components of the model on the results (pore pressure dissipation vs. pore pressure generation). The diffusion coefficient which characterizes the dissipation of air pore pressure is found sufficiently low for maintaining a fluidized flow over hundreds of meters. The study concludes that an air-fluidization theory is consistent with the field observations. These findings are particularly interesting as they seem not in line with the mainstream acceptation in landslide modelling that air generally plays a secondary role (e.g., Legros, 2002). References Iverson, R.M., Denlinger, R.P., 2001. Flow of variably fluidized granular masses across three-dimensional terrain - 1. Coulomb mixture theory. J. Geophys. Res. 106, 537 552. Legros, F., 2002. The mobility of long-runout landslides. Eng. Geol. 63, 301-331. Roche, O., 2012. Depositional processes and gas pore pressure in pyroclastic flows: an experimental perspective. Bull. Volcanol. 74, 1807-1820. Roche, O., Montserrat, S., Niño, Y., Tamburrino, A., 2008. Experimental observations of water-like behavior of initially fluidized, dam break granular flows and their relevance for the propagation of ash-rich pyroclastic flows. J. Geophys. Res. 113, B12203. Stilmant, F., Pirotton, M., Archambeau, P., Erpicum, S., & Dewals, B. (2015). Can the collapse of a fly ash heap develop into an air-fluidized flow? - Reanalysis of the Jupille accident (1961). Geomorphology, 228, 746-755.

On solutions of the fifth-order dispersive equations with porous medium type non-linearity

NASA Astrophysics Data System (ADS)

Kocak, Huseyin; Pinar, Zehra

2018-07-01

In this work, we focus on obtaining the exact solutions of the fifth-order semi-linear and non-linear dispersive partial differential equations, which have the second-order diffusion-like (porous-type) non-linearity. The proposed equations were not studied in the literature in the sense of the exact solutions. We reveal solutions of the proposed equations using the classical Riccati equations method. The obtained exact solutions, which can play a key role to simulate non-linear waves in the medium with dispersion and diffusion, are illustrated and discussed in details.

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.

Stochastic models for tumoral growth

NASA Astrophysics Data System (ADS)

Escudero, Carlos

2006-02-01

Strong experimental evidence has indicated that tumor growth belongs to the molecular beam epitaxy universality class. This type of growth is characterized by the constraint of cell proliferation to the tumor border and the surface diffusion of cells at the growing edge. Tumor growth is thus conceived as a competition for space between the tumor and the host, and cell diffusion at the tumor border is an optimal strategy adopted for minimizing the pressure and helping tumor development. Two stochastic partial differential equations are reported in this paper in order to correctly model the physical properties of tumoral growth in (1+1) and (2+1) dimensions. The advantage of these models is that they reproduce the correct geometry of the tumor and are defined in terms of polar variables. An analysis of these models allows us to quantitatively estimate the response of the tumor to an unfavorable perturbation during growth.

B2.5-Eirene modeling of radial transport in the MAGPIE linear plasma device

NASA Astrophysics Data System (ADS)

Owen, L. W.; Caneses, J. F.; Canik, J.; Lore, J. D.; Corr, C.; Blackwell, B.; Bonnin, X.; Rapp, J.

2017-05-01

Radial transport in helicon heated hydrogen plasmas in the MAGnetized Plasma Interaction Experiment (MAGPIE) is studied with the B2.5-Eirene (SOLPS5.0) code. Radial distributions of plasma density, temperature and ambipolar potential are computed for several magnetic field configurations and compared to double Langmuir probe measurements. Evidence for an unmagnetized ion population is seen in the requirement for a convective pinch term in the continuity equation in order to fit the centrally peaked density profile data. The measured slightly hollow electron temperature profiles are reproduced with combinations of on-axis and edge heating which can be interpreted as helicon and Trivelpiece-Gould wave absorption, respectively. Pressure gradient driven radial charged particle diffusion is chosen to describe the diffusive particle flux since the hollowness of the temperature profiles assists the establishment of on-axis density peaking.

All-optical technique for measuring thermal properties of materials at static high pressure

NASA Astrophysics Data System (ADS)

Pangilinan, G. I.; Ladouceur, H. D.; Russell, T. P.

2000-10-01

The development and implementation of an all-optical technique for measuring thermal transport properties of materials at high pressure in a gem anvil cell are reported. Thermal transport properties are determined by propagating a thermal wave in a material subjected to high pressures, and measuring the temperature as a function of time using an optical sensor embedded downstream in the material. Optical beams are used to deposit energy and to measure the sensor temperature and replace the resistive heat source and the thermocouples of previous methods. This overcomes the problems introduced with pressure-induced resistance changes and the spatial limitations inherent in previous high-pressure experimentation. Consistent with the heat conduction equation, the material's specific heat, thermal conductivity, and thermal diffusivity (κ) determine the sensor's temperature rise and its temporal profile. The all-optical technique described focuses on room-temperature thermal properties but can easily be applied to a wide temperature range (77-600 K). Measurements of thermal transport properties at pressure up to 2.0 GPa are reported, although extension to much higher pressures are feasible. The thermal properties of NaCl, a commonly used material for high-pressure experiments are measured and shown to be consistent with those obtained using the traditional methods.

Void Formation during Diffusion - Two-Dimensional Approach

NASA Astrophysics Data System (ADS)

Wierzba, Bartek

2016-06-01

The final set of equations defining the interdiffusion process in solid state is presented. The model is supplemented by vacancy evolution equation. The competition between the Kirkendall shift, backstress effect and vacancy migration is considered. The proper diffusion flux based on the Nernst-Planck formula is proposed. As a result, the comparison of the experimental and calculated evolution of the void formation in the Fe-Pd diffusion couple is shown.

New Solution of Diffusion-Advection Equation for Cosmic-Ray Transport Using Ultradistributions

NASA Astrophysics Data System (ADS)

Rocca, M. C.; Plastino, A. R.; Plastino, A.; Ferri, G. L.; de Paoli, A.

2015-11-01

In this paper we exactly solve the diffusion-advection equation (DAE) for cosmic-ray transport. For such a purpose we use the Theory of Ultradistributions of J. Sebastiao e Silva, to give a general solution for the DAE. From the ensuing solution, we obtain several approximations as limiting cases of various situations of physical and astrophysical interest. One of them involves Solar cosmic-rays' diffusion.

A Least-Squares Transport Equation Compatible with Voids

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

Hansen, Jon; Peterson, Jacob; Morel, Jim

Standard second-order self-adjoint forms of the transport equation, such as the even-parity, odd-parity, and self-adjoint angular flux equation, cannot be used in voids. Perhaps more important, they experience numerical convergence difficulties in near-voids. Here we present a new form of a second-order self-adjoint transport equation that has an advantage relative to standard forms in that it can be used in voids or near-voids. Our equation is closely related to the standard least-squares form of the transport equation with both equations being applicable in a void and having a nonconservative analytic form. However, unlike the standard least-squares form of the transportmore » equation, our least-squares equation is compatible with source iteration. It has been found that the standard least-squares form of the transport equation with a linear-continuous finite-element spatial discretization has difficulty in the thick diffusion limit. Here we extensively test the 1D slab-geometry version of our scheme with respect to void solutions, spatial convergence rate, and the intermediate and thick diffusion limits. We also define an effective diffusion synthetic acceleration scheme for our discretization. Our conclusion is that our least-squares S n formulation represents an excellent alternative to existing second-order S n transport formulations« less

Fourth order Douglas implicit scheme for solving three dimension reaction diffusion equation with non-linear source term

NASA Astrophysics Data System (ADS)

Hasnain, Shahid; Saqib, Muhammad; Mashat, Daoud Suleiman

2017-07-01

This research paper represents a numerical approximation to non-linear three dimension reaction diffusion equation with non-linear source term from population genetics. Since various initial and boundary value problems exist in three dimension reaction diffusion phenomena, which are studied numerically by different numerical methods, here we use finite difference schemes (Alternating Direction Implicit and Fourth Order Douglas Implicit) to approximate the solution. Accuracy is studied in term of L2, L∞ and relative error norms by random selected grids along time levels for comparison with analytical results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. Numerical results showed that Fourth Order Douglas Implicit scheme is very efficient and reliable for solving 3-D non-linear reaction diffusion equation.

A new nonlinear diffusion formalism in a magnetized plasma - Application to space physics and astrophysics

NASA Technical Reports Server (NTRS)

Karimbadi, H.; Krauss-Varban, D.

1992-01-01

A novel diffusion formalism that takes into account the finite width of resonances is presented. The resonance diagram technique is shown to reproduce the details of the particle orbits very accurately, and can be used to determine the acceleration/scattering in the presence of a given wave spectrum. Ways in which the nonlinear orbits can be incorporated into the diffusion equation are shown. The resulting diffusion equation is an extension of the Q-L theory to cases where the waves have large amplitudes and/or are coherent. This new equation does not have a gap at 90 deg in cases where the individual orbits can cross the gap. The conditions under which the resonance gap at 90-deg pitch angle exits are also examined.

Inner clot diffusion and permeation during fibrinolysis.

PubMed Central

Diamond, S L; Anand, S

1993-01-01

A model of fibrinolysis was developed using multicomponent convection-diffusion equations with homogeneous reaction and heterogeneous adsorption and reaction. Fibrin is the dissolving stationary phase and plasminogen, tissue plasminogen activator (tPA), urokinase (uPA), and plasmin are the soluble mobile species. The model is based on an accurate molecular description of the fibrin fiber and protofibril structure and contains no adjustable parameters and one phenomenological parameter estimated from experiment. The model can predict lysis fronts moving across fibrin clots (fine or coarse fibers) of various densities under different administration regimes using uPA and tPA. We predict that pressure-driven permeation is the major mode of transport that allows for kinetically significant thrombolysis during clinical situations. Without permeation, clot lysis would be severely diffusion limited and would require hundreds of minutes. Adsorption of tPA to fibrin under conditions of permeation was a nonequilibrium process that tended to front load clots with tPA. Protein engineering efforts to design optimal thrombolytics will likely be affected by the permeation processes that occur during thrombolysis. PMID:8312497

Unsteady Oxygen Transfer in Space-Filling Models of the Pulmonary Acinus

NASA Astrophysics Data System (ADS)

Hofemeier, Philipp; Shachar-Berman, Lihi; Filoche, Marcel; Sznitman, Josue

2014-11-01

Diffusional screening in the pulmonary acinus is a well-known physical phenomenon that results from the depletion of fresh oxygen in proximal acinar generations diffusing through the alveolar wall membranes and effectively creating a gradient in the oxygen partial pressure along the acinar airways. Until present, most studies have focused on steady-state oxygen diffusion in generic sub-acinar structures and discarded convective oxygen transport due to low Peclet numbers in this region. Such studies, however, fall typically short in capturing the complex morphology of acinar airways as well as the oscillatory nature of convecive acinar breathing. Here, we revisit this problem and solve the convective-diffusive transport equations in breathing 3D acinar structures, underlining the significance of convective flows in proximal acinar generations as well as recirculating alveolar flow patterns. In particular, to assess diffusional screening, we monitor time-dependent efficiencies of the acinus under cyclic breathing motion. Our study emphasizes the necessity of capturing both a dynamically breathing and anatomically-realistic model of the sub-acinus to characterize unsteady oxygen transport across the acinar walls.

Mixed convection of magnetohydrodynamic nanofluids inside microtubes at constant wall temperature

NASA Astrophysics Data System (ADS)

Moshizi, S. A.; Zamani, M.; Hosseini, S. J.; Malvandi, A.

2017-05-01

Laminar fully developed mixed convection of magnetohydrodynamic nanofluids inside microtubes at a constant wall temperature (CWT) under the effects of a variable directional magnetic field is investigated numerically. Nanoparticles are assumed to have slip velocities relative to the base fluid owing to thermophoretic diffusion (temperature gradient driven force) and Brownian diffusion (concentration gradient driven force). The no-slip boundary condition is avoided at the fluid-solid mixture to assess the non-equilibrium region at the fluid-solid interface. A scale analysis is performed to estimate the relative significance of the pertaining parameters that should be included in the governing equations. After the effects of pertinent parameters on the pressure loss and heat transfer enhancement were considered, the figure of merit (FoM) is employed to evaluate and optimize the thermal performance of heat exchange equipment. The results indicate the optimum thermal performance is obtained when the thermophoresis overwhelms the Brownian diffusion, which is for larger nanoparticles. This enhancement boosts when the buoyancy force increases. In addition, increasing the magnetic field strength and slippage at the fluid-solid interface enhances the thermal performance.

Finite-volume scheme for anisotropic diffusion

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

Es, Bram van, E-mail: bramiozo@gmail.com; FOM Institute DIFFER, Dutch Institute for Fundamental Energy Research, The Netherlands"1; Koren, Barry

In this paper, we apply a special finite-volume scheme, limited to smooth temperature distributions and Cartesian grids, to test the importance of connectivity of the finite volumes. The area of application is nuclear fusion plasma with field line aligned temperature gradients and extreme anisotropy. We apply the scheme to the anisotropic heat-conduction equation, and compare its results with those of existing finite-volume schemes for anisotropic diffusion. Also, we introduce a general model adaptation of the steady diffusion equation for extremely anisotropic diffusion problems with closed field lines.

Stochastic interpretation of the advection-diffusion equation and its relevance to bed load transport

NASA Astrophysics Data System (ADS)

Ancey, C.; Bohorquez, P.; Heyman, J.

2015-12-01

The advection-diffusion equation is one of the most widespread equations in physics. It arises quite often in the context of sediment transport, e.g., for describing time and space variations in the particle activity (the solid volume of particles in motion per unit streambed area). Phenomenological laws are usually sufficient to derive this equation and interpret its terms. Stochastic models can also be used to derive it, with the significant advantage that they provide information on the statistical properties of particle activity. These models are quite useful when sediment transport exhibits large fluctuations (typically at low transport rates), making the measurement of mean values difficult. Among these stochastic models, the most common approach consists of random walk models. For instance, they have been used to model the random displacement of tracers in rivers. Here we explore an alternative approach, which involves monitoring the evolution of the number of particles moving within an array of cells of finite length. Birth-death Markov processes are well suited to this objective. While the topic has been explored in detail for diffusion-reaction systems, the treatment of advection has received no attention. We therefore look into the possibility of deriving the advection-diffusion equation (with a source term) within the framework of birth-death Markov processes. We show that in the continuum limit (when the cell size becomes vanishingly small), we can derive an advection-diffusion equation for particle activity. Yet while this derivation is formally valid in the continuum limit, it runs into difficulty in practical applications involving cells or meshes of finite length. Indeed, within our stochastic framework, particle advection produces nonlocal effects, which are more or less significant depending on the cell size and particle velocity. Albeit nonlocal, these effects look like (local) diffusion and add to the intrinsic particle diffusion (dispersal due to velocity fluctuations), with the important consequence that local measurements depend on both the intrinsic properties of particle displacement and the dimensions of the measurement system.

Solutions for the diurnally forced advection-diffusion equation to estimate bulk fluid velocity and diffusivity in streambeds from temperature time series

NASA Astrophysics Data System (ADS)

Luce, C.; Tonina, D.; Gariglio, F. P.; Applebee, R.

2012-12-01

Differences in the diurnal variations of temperature at different depths in streambed sediments are commonly used for estimating vertical fluxes of water in the streambed. We applied spatial and temporal rescaling of the advection-diffusion equation to derive two new relationships that greatly extend the kinds of information that can be derived from streambed temperature measurements. The first equation provides a direct estimate of the Peclet number from the amplitude decay and phase delay information. The analytical equation is explicit (e.g. no numerical root-finding is necessary), and invertable. The thermal front velocity can be estimated from the Peclet number when the thermal diffusivity is known. The second equation allows for an independent estimate of the thermal diffusivity directly from the amplitude decay and phase delay information. Several improvements are available with the new information. The first equation uses a ratio of the amplitude decay and phase delay information; thus Peclet number calculations are independent of depth. The explicit form also makes it somewhat faster and easier to calculate estimates from a large number of sensors or multiple positions along one sensor. Where current practice requires a priori estimation of streambed thermal diffusivity, the new approach allows an independent calculation, improving precision of estimates. Furthermore, when many measurements are made over space and time, expectations of the spatial correlation and temporal invariance of thermal diffusivity are valuable for validation of measurements. Finally, the closed-form explicit solution allows for direct calculation of propagation of uncertainties in error measurements and parameter estimates, providing insight about error expectations for sensors placed at different depths in different environments as a function of surface temperature variation amplitudes. The improvements are expected to increase the utility of temperature measurement methods for studying groundwater-surface water interactions across space and time scales. We discuss the theoretical implications of the new solutions supported by examples with data for illustration and validation.

The dynamics of oceanic fronts. I - The Gulf Stream

NASA Technical Reports Server (NTRS)

Kao, T. W.

1980-01-01

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

Research and Development of Methods for Estimating Physicochemical Properties of Organic Compounds of Environmental Concern

DTIC Science & Technology

1979-02-01

coefficient (at equilibrium) when hysteresis is apparent. 6. Coefficient n in Freundlich equation for 1/n soil or sediment adsorption isotherms ýX - KC . 7...Biodegradation Chemical structures cal clasaes (e.g., Diffusion Correlations phenols). General Diffusion coefficients Equations terms for organic...OF THE FATE AND TRANSPORT OF ORGANIC CHEMICALS Adsorption coefficients: K, n* from Freundlich equation + Desorption coefficients: K’*, n’* from

Reactive-Diffusive-Advective Traveling Waves in a Family of Degenerate Nonlinear Equations.

PubMed

Sánchez-Garduño, Faustino; Pérez-Velázquez, Judith

This paper deals with the analysis of existence of traveling wave solutions (TWS) for a diffusion-degenerate (at D (0) = 0) and advection-degenerate (at h '(0) = 0) reaction-diffusion-advection (RDA) equation. Diffusion is a strictly increasing function and the reaction term generalizes the kinetic part of the Fisher-KPP equation. We consider different forms of the convection term h ( u ): (1)   h '( u ) is constant k , (2)   h '( u ) = ku with k > 0, and (3) it is a quite general form which guarantees the degeneracy in the advective term. In Case 1, we prove that the task can be reduced to that for the corresponding equation, where k = 0, and then previous results reported from the authors can be extended. For the other two cases, we use both analytical and numerical tools. The analysis we carried out is based on the restatement of searching TWS for the full RDA equation into a two-dimensional dynamical problem. This consists of searching for the conditions on the parameter values for which there exist heteroclinic trajectories of the ordinary differential equations (ODE) system in the traveling wave coordinates. Throughout the paper we obtain the dynamics by using tools coming from qualitative theory of ODE.

Reactive-Diffusive-Advective Traveling Waves in a Family of Degenerate Nonlinear Equations

PubMed Central

Sánchez-Garduño, Faustino

2016-01-01

This paper deals with the analysis of existence of traveling wave solutions (TWS) for a diffusion-degenerate (at D(0) = 0) and advection-degenerate (at h′(0) = 0) reaction-diffusion-advection (RDA) equation. Diffusion is a strictly increasing function and the reaction term generalizes the kinetic part of the Fisher-KPP equation. We consider different forms of the convection term h(u): (1)  h′(u) is constant k, (2)  h′(u) = ku with k > 0, and (3) it is a quite general form which guarantees the degeneracy in the advective term. In Case 1, we prove that the task can be reduced to that for the corresponding equation, where k = 0, and then previous results reported from the authors can be extended. For the other two cases, we use both analytical and numerical tools. The analysis we carried out is based on the restatement of searching TWS for the full RDA equation into a two-dimensional dynamical problem. This consists of searching for the conditions on the parameter values for which there exist heteroclinic trajectories of the ordinary differential equations (ODE) system in the traveling wave coordinates. Throughout the paper we obtain the dynamics by using tools coming from qualitative theory of ODE. PMID:27689131

High-pressure spectroscopic measurement on diffusion with a diamond-anvil cell

NASA Astrophysics Data System (ADS)

Aoki, K.; Katoh, Eriko; Yamawaki, H.; Fujihisa, H.; Sakashita, M.

2003-04-01

We report a diamond-anvil-cell (DAC) technique developed for spectroscopic measurement on the diffusion process in molecular solids at high pressure. The diffusion processes of atoms, molecules, or their ionic species are investigated for a bilayer specimen by measuring the variation of infrared vibrational spectra with time. The experimental procedures for the protonic and molecular diffusion measurements on ice at 400 K and 10.2 GPa are presented as an example study. The in situ spectroscopic technique with a DAC significantly extends the pressure range accessible for diffusion measurement. The diffusion process at a rate of 10-16-10-14 m2/s can currently be observed at temperatures of 300-600 K and pressures up to several tens of gigaPascals.

The operational stability of a centrifugal compressor and its dependence on the characteristics of the subcomponents

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

Hunziker, R.; Gyarmathy, G.

1994-04-01

A centrifugal compressor was tested with three different diffusers with circular-arc vanes. The vane inlet angle was varied from 15 to 30 deg. Detailed static wall pressure measurements show that the pressure field in the diffuser inlet is very sensitive to flow rate. The stability limit regularly occurred at the flow rate giving the maximum pressure rise for the overall stage. Mild surge arises as a dynamic instability of the compression system. The analysis of the pressure rise characteristic of each individual subcomponent (impeller, diffuser inlet, diffuser channel,...) reveals their contribution to the overall pressure rise. The diffuser channels playmore » an inherently destabilizing role while the impeller and the diffuser inlet are typically stabilizing. The stability limit was mainly determined by a change in the characteristic of the diffuser inlet. Further, the stability limit was found to be independent of the development of inducer-tip recirculation.« less

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.

Pyroclastic flow transport dynamics for a Montserrat volcano eruption

NASA Astrophysics Data System (ADS)

Cordoba, G.; Sparks, S.; del Risco, E.

2003-04-01

A two phase model of pyroclastic flows dynamics which account for the bed load and suspended load is shown. The model uses the compressible Navier-Stokes equations coupled with the convection-diffusion equation in order to take into account for the sedimentation. The skin friction is taken into account by using the wall functions. In despite of the complex mathematical formulation of the model, it has been implemented in a Personal Computer due to an assumption of two phase one velocity model which reduce the number of equations in the system. This non-linear equation system is solved numerically by using the Finite Element Method. This numerical method let us move the mesh in the direction of the deposition and then accounting for the shape of the bed and the thickness of the deposit The model is applied to the Montserrat's White River basin which extend from the dome to the sea, located about 4 Km away and then compared with the field data from the Boxing Day (26 December, 1997) eruption. Additionally some features as the temporary evolution of the dynamical pressure, particle concentration and temperature along the path at each time step is shown.

Nonlocal electrical diffusion equation

NASA Astrophysics Data System (ADS)

Gómez-Aguilar, J. F.; Escobar-Jiménez, R. F.; Olivares-Peregrino, V. H.; Benavides-Cruz, M.; Calderón-Ramón, C.

2016-07-01

In this paper, we present an analysis and modeling of the electrical diffusion equation using the fractional calculus approach. This alternative representation for the current density is expressed in terms of the Caputo derivatives, the order for the space domain is 0<β≤1 and for the time domain is 0<γ≤2. We present solutions for the full fractional equation involving space and time fractional derivatives using numerical methods based on Fourier variable separation. The case with spatial fractional derivatives leads to Levy flight type phenomena, while the time fractional equation is related to sub- or super diffusion. We show that the mathematical concept of fractional derivatives can be useful to understand the behavior of semiconductors, the design of solar panels, electrochemical phenomena and the description of anomalous complex processes.

Numerical simulation of supersonic water vapor jet impinging on a flat plate

NASA Astrophysics Data System (ADS)

Kuzuu, Kazuto; Aono, Junya; Shima, Eiji

2012-11-01

We investigated supersonic water vapor jet impinging on a flat plate through numerical simulation. This simulation is for estimating heating effect of a reusable sounding rocket during vertical landing. The jet from the rocket bottom is supersonic, M=2 to 3, high temperature, T=2000K, and over-expanded. Atmospheric condition is a stationary standard air. The simulation is base on the full Navier-Stokes equations, and the flow is numerically solved by an unstructured compressible flow solver, in-house code LS-FLOW-RG. In this solver, the transport properties of muti-species gas and mass conservation equations of those species are considered. We employed DDES method as a turbulence model. For verification and validation, we also carried out a simulation under the condition of air, and compared with the experimental data. Agreement between our results and the experimental data are satisfactory. Through this simulation, we calculated the flow under some exit pressure conditions, and discuss the effects of pressure ratio on flow structures, heat transfer and so on. Furthermore, we also investigated diffusion effects of water vapor, and we confirmed that these phenomena are generated by the interaction of atmospheric air and affects the heat transfer to the surrounding environment.

Predictive models for pressure-driven fluid infusions into brain parenchyma

NASA Astrophysics Data System (ADS)

Raghavan, Raghu; Brady, Martin

2011-10-01

Direct infusions into brain parenchyma of biological therapeutics for serious brain diseases have been, and are being, considered. However, individual brains, as well as distinct cytoarchitectural regions within brains, vary in their response to fluid flow and pressure. Further, the tissue responds dynamically to these stimuli, requiring a nonlinear treatment of equations that would describe fluid flow and drug transport in brain. We here report in detail on an individual-specific model and a comparison of its prediction with simulations for living porcine brains. Two critical features we introduced into our model—absent from previous ones, but requirements for any useful simulation—are the infusion-induced interstitial expansion and the backflow. These are significant determinants of the flow. Another feature of our treatment is the use of cross-property relations to obtain individual-specific parameters that are coefficients in the equations. The quantitative results are at least encouraging, showing a high fraction of overlap between the computed and measured volumes of distribution of a tracer molecule and are potentially clinically useful. Several improvements are called for; principally a treatment of the interstitial expansion more fundamentally based on poroelasticity and a better delineation of the diffusion tensor of a particle confined to the interstitial spaces.

First-principles modeling of quantum nuclear effects and atomic interactions in solid 4He at high pressure

NASA Astrophysics Data System (ADS)

Cazorla, Claudio; Boronat, Jordi

2015-01-01

We present a first-principles computational study of solid 4He at T =0 K and pressures up to ˜160 GPa. Our computational strategy consists in using van der Waals density functional theory (DFT-vdW) to describe the electronic degrees of freedom in this material, and the diffusion Monte Carlo (DMC) method to solve the Schrödinger equation describing the behavior of the quantum nuclei. For this, we construct an analytical interaction function based on the pairwise Aziz potential that closely matches the volume variation of the cohesive energy calculated with DFT-vdW in dense helium. Interestingly, we find that the kinetic energy of solid 4He does not increase appreciably with compression for P ≥85 GPa. Also, we show that the Lindemann ratio in dense solid 4He amounts to 0.10 almost independently of pressure. The reliability of customary quasiharmonic DFT (QH DFT) approaches in describing quantum nuclear effects in solids is also studied. We find that QH DFT simulations, although provide a reasonable equation of state in agreement with experiments, are not able to reproduce correctly these critical effects in compressed 4He. In particular, we disclose huge discrepancies of at least ˜50 % in the calculated 4He kinetic energies using both the QH DFT and present DFT-DMC methods.

Rock deformation models and fluid leak-off in hydraulic fracturing

NASA Astrophysics Data System (ADS)

Yarushina, Viktoriya M.; Bercovici, David; Oristaglio, Michael L.

2013-09-01

Fluid loss into reservoir rocks during hydraulic fracturing is modelled via a poro-elastoplastic pressure diffusion equation in which the total compressibility is a sum of fluid, rock and pore space compressibilities. Inclusion of pore compressibility and porosity-dependent permeability in the model leads to a strong pressure dependence of leak-off (i.e. drainage rate). Dilation of the matrix due to fluid invasion causes higher rates of fluid leak-off. The present model is appropriate for naturally fractured and tight gas reservoirs as well as for soft and poorly consolidated formations whose mechanical behaviour departs from simple elastic laws. Enhancement of the leak-off coefficient by dilation, predicted by the new model, may help explain the low percentage recovery of fracturing fluid (usually between 5 and 50 per cent) in shale gas stimulation by hydraulic fracturing.

Adaptive multigrid domain decomposition solutions for viscous interacting flows

NASA Technical Reports Server (NTRS)

Rubin, Stanley G.; Srinivasan, Kumar

1992-01-01

Several viscous incompressible flows with strong pressure interaction and/or axial flow reversal are considered with an adaptive multigrid domain decomposition procedure. Specific examples include the triple deck structure surrounding the trailing edge of a flat plate, the flow recirculation in a trough geometry, and the flow in a rearward facing step channel. For the latter case, there are multiple recirculation zones, of different character, for laminar and turbulent flow conditions. A pressure-based form of flux-vector splitting is applied to the Navier-Stokes equations, which are represented by an implicit lowest-order reduced Navier-Stokes (RNS) system and a purely diffusive, higher-order, deferred-corrector. A trapezoidal or box-like form of discretization insures that all mass conservation properties are satisfied at interfacial and outflow boundaries, even for this primitive-variable, non-staggered grid computation.

Numerical analysis for the fractional diffusion and fractional Buckmaster equation by the two-step Laplace Adam-Bashforth method

NASA Astrophysics Data System (ADS)

Jain, Sonal

2018-01-01

In this paper, we aim to use the alternative numerical scheme given by Gnitchogna and Atangana for solving partial differential equations with integer and non-integer differential operators. We applied this method to fractional diffusion model and fractional Buckmaster models with non-local fading memory. The method yields a powerful numerical algorithm for fractional order derivative to implement. Also we present in detail the stability analysis of the numerical method for solving the diffusion equation. This proof shows that this method is very stable and also converges very quickly to exact solution and finally some numerical simulation is presented.

Pseudodynamic systems approach based on a quadratic approximation of update equations for diffuse optical tomography.

PubMed

Biswas, Samir Kumar; Kanhirodan, Rajan; Vasu, Ram Mohan; Roy, Debasish

2011-08-01

We explore a pseudodynamic form of the quadratic parameter update equation for diffuse optical tomographic reconstruction from noisy data. A few explicit and implicit strategies for obtaining the parameter updates via a semianalytical integration of the pseudodynamic equations are proposed. Despite the ill-posedness of the inverse problem associated with diffuse optical tomography, adoption of the quadratic update scheme combined with the pseudotime integration appears not only to yield higher convergence, but also a muted sensitivity to the regularization parameters, which include the pseudotime step size for integration. These observations are validated through reconstructions with both numerically generated and experimentally acquired data.

The diffusion approximation. An application to radiative transfer in clouds

NASA Technical Reports Server (NTRS)

Arduini, R. F.; Barkstrom, B. R.

1976-01-01

It is shown how the radiative transfer equation reduces to the diffusion equation. To keep the mathematics as simple as possible, the approximation is applied to a cylindrical cloud of radius R and height h. The diffusion equation separates in cylindrical coordinates and, in a sample calculation, the solution is evaluated for a range of cloud radii with cloud heights of 0.5 km and 1.0 km. The simplicity of the method and the speed with which solutions are obtained give it potential as a tool with which to study the effects of finite-sized clouds on the albedo of the earth-atmosphere system.

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.

Partial regularity of weak solutions to a PDE system with cubic nonlinearity

NASA Astrophysics Data System (ADS)

Liu, Jian-Guo; Xu, Xiangsheng

2018-04-01

In this paper we investigate regularity properties of weak solutions to a PDE system that arises in the study of biological transport networks. The system consists of a possibly singular elliptic equation for the scalar pressure of the underlying biological network coupled to a diffusion equation for the conductance vector of the network. There are several different types of nonlinearities in the system. Of particular mathematical interest is a term that is a polynomial function of solutions and their partial derivatives and this polynomial function has degree three. That is, the system contains a cubic nonlinearity. Only weak solutions to the system have been shown to exist. The regularity theory for the system remains fundamentally incomplete. In particular, it is not known whether or not weak solutions develop singularities. In this paper we obtain a partial regularity theorem, which gives an estimate for the parabolic Hausdorff dimension of the set of possible singular points.

A computational study of the flowfield surrounding the Aeroassist Flight Experiment vehicle

NASA Technical Reports Server (NTRS)

Gnoffo, Peter A.; Greene, Francis A.

1987-01-01

A symmetric total variation diminishing (STVD) algorithm has been applied to the solution of the three-dimensional hypersonic flowfield surrounding the Aeroassist Flight Experiment (AFE) vehicle. Both perfect-gas and chemical nonequilibrium models have been used. The perfect-gas flows were computed at two different Reynolds numbers, including a flight trajectory point at maximum dynamic pressure, and on two different grids. Procedures for coupling the solution of the species continuity equations with the Navier-Stokes equations in the presence of chemical nonequilibrium are reviewed and tested on the forebody of the AFE and on the complete flowfield assuming noncatalytic wall and no species diffusion. Problems with the STVD algorithm unique to flows with variable thermodynamic properties (real gas) are identified and algorithm modifications are suggested. A potential heating problem caused by strong flow impingement on the nozzle lip in the near wake at 0-deg angle of attack has been identified.

Counterion accumulation effects on a suspension of DNA molecules: Equation of state and pressure-driven denaturation

NASA Astrophysics Data System (ADS)

Nicasio-Collazo, Luz Adriana; Delgado-González, Alexandra; Hernández-Lemus, Enrique; Castañeda-Priego, Ramón

2017-04-01

The study of the effects associated with the electrostatic properties of DNA is of fundamental importance to understand both its molecular properties at the single molecule level, like the rigidity of the chain, and its interaction with other charged bio-molecules, including other DNA molecules; such interactions are crucial to maintain the thermodynamic stability of the intra-cellular medium. In the present work, we combine the Poisson-Boltzmann mean-field theory with an irreversible thermodynamic approximation to analyze the effects of counterion accumulation inside DNA on both the denaturation profile of the chain and the equation of state of the suspension. To this end, we model the DNA molecule as a porous charged cylinder immersed in an aqueous solution. These thermo-electrostatic effects are explicitly studied in the particular case of some genes for which damage in their sequence is associated with diffuse large B-cell lymphoma.

On Entropy Production in the Madelung Fluid and the Role of Bohm's Potential in Classical Diffusion

NASA Astrophysics Data System (ADS)

Heifetz, Eyal; Tsekov, Roumen; Cohen, Eliahu; Nussinov, Zohar

2016-07-01

The Madelung equations map the non-relativistic time-dependent Schrödinger equation into hydrodynamic equations of a virtual fluid. While the von Neumann entropy remains constant, we demonstrate that an increase of the Shannon entropy, associated with this Madelung fluid, is proportional to the expectation value of its velocity divergence. Hence, the Shannon entropy may grow (or decrease) due to an expansion (or compression) of the Madelung fluid. These effects result from the interference between solutions of the Schrödinger equation. Growth of the Shannon entropy due to expansion is common in diffusive processes. However, in the latter the process is irreversible while the processes in the Madelung fluid are always reversible. The relations between interference, compressibility and variation of the Shannon entropy are then examined in several simple examples. Furthermore, we demonstrate that for classical diffusive processes, the "force" accelerating diffusion has the form of the positive gradient of the quantum Bohm potential. Expressing then the diffusion coefficient in terms of the Planck constant reveals the lower bound given by the Heisenberg uncertainty principle in terms of the product between the gas mean free path and the Brownian momentum.

Building 1D resonance broadened quasilinear (RBQ) code for fast ions Alfvénic relaxations

NASA Astrophysics Data System (ADS)

Gorelenkov, Nikolai; Duarte, Vinicius; Berk, Herbert

2016-10-01

The performance of the burning plasma is limited by the confinement of superalfvenic fusion products, e.g. alpha particles, which are capable of resonating with the Alfvénic eigenmodes (AEs). The effect of AEs on fast ions is evaluated using a resonance line broadened diffusion coefficient. The interaction of fast ions and AEs is captured for cases where there are either isolated or overlapping modes. A new code RBQ1D is being built which constructs diffusion coefficients based on realistic eigenfunctions that are determined by the ideal MHD code NOVA. The wave particle interaction can be reduced to one-dimensional dynamics where for the Alfvénic modes typically the particle kinetic energy is nearly constant. Hence to a good approximation the Quasi-Linear (QL) diffusion equation only contains derivatives in the angular momentum. The diffusion equation is then one dimensional that is efficiently solved simultaneously for all particles with the equation for the evolution of the wave angular momentum. The evolution of fast ion constants of motion is governed by the QL diffusion equations which are adapted to find the ion distribution function.

Non-standard finite difference and Chebyshev collocation methods for solving fractional diffusion equation

NASA Astrophysics Data System (ADS)

Agarwal, P.; El-Sayed, A. A.

2018-06-01

In this paper, a new numerical technique for solving the fractional order diffusion equation is introduced. This technique basically depends on the Non-Standard finite difference method (NSFD) and Chebyshev collocation method, where the fractional derivatives are described in terms of the Caputo sense. The Chebyshev collocation method with the (NSFD) method is used to convert the problem into a system of algebraic equations. These equations solved numerically using Newton's iteration method. The applicability, reliability, and efficiency of the presented technique are demonstrated through some given numerical examples.

Importance of Ambipolar Electric Field in the Ion Loss from Mars- Results from a Multi-fluid MHD Model with the Electron Pressure Equation Included

NASA Astrophysics Data System (ADS)

Ma, Y.; Dong, C.; van der Holst, B.; Nagy, A. F.; Bougher, S. W.; Toth, G.; Cravens, T.; Yelle, R. V.; Jakosky, B. M.

2017-12-01

The multi-fluid (MF) magnetohydrodynamic (MHD) model of Mars is further improved by solving an additional electron pressure equation. Through the electron pressure equation, the electron temperature is calculated based on the effects from various electrons related heating and cooling processes (e.g. photo-electron heating, electron-neutral collision and electron-ion collision), and thus the improved model is able to calculate the electron temperature and the electron pressure force self-consistently. Electron thermal conductivity is also considered in the calculation. Model results of a normal case with electron pressure equation included (MFPe) are compared in detail to an identical case using the regular MF model to identify the effect of the improved physics. We found that when the electron pressure equation is included, the general interaction patterns are similar to that of the case with no electron pressure equation. The model with electron pressure equation predicts that electron temperature is much larger than the ion temperature in the ionosphere, consistent with both Viking and MAVEN observations. The inclusion of electron pressure equation significantly increases the total escape fluxes predicted by the model, indicating the importance of the ambipolar electric field(electron pressure gradient) in driving the ion loss from Mars.

Contamination of liquid oxygen by pressurized gaseous nitrogen

NASA Technical Reports Server (NTRS)

Zuckerwar, Allan J.; King, Tracy K.; Ngo, Kim Chi

1989-01-01

The penetration of pressurized gaseous nitrogen (GN2) into liquid oxygen (LOX) was investigated experimentally in the 7-inch High Temperature Tunnel, the pilot tunnel for the 8-foot High Temperature Tunnel (8'HTT) at Langley Research Center. A preliminary test using a nuclear monitor revealed the extent of the liquid nitrogen (LN2) build-up at the LOX interface as a function of GN2 pressure. Then an adaptation of the differential flash vaporization technique was used to determine the binary diffusivity of the LOX-LN2 system at a temperature of 90.2 K. The measured value D equals 0.000086 sq cm/s + or - 25 percent together with two prior measurements at lower temperatures revealed an excellent fit to the Arrhenius equation, yielding a pre-exponential factor D sub 0 equals 0.0452 sq cm/s and an activation enthalpy H equals 1.08 kcal/mol. At a pressure of 1700 psi and holding time of 15 min, the penetration of LN2 into LOX (to a 1 percent contamination level) was found to be 0.9 cm, indicating but minimal impact upon 8'HTT operations.

The effect of the YBCO-PST composite composition on the superconducting carrier concentration determined by microwave studies under high pressure

NASA Astrophysics Data System (ADS)

Krupski, M.; Stankowski, J.; Przybył, S.; Andrzejewski, B.; Kaczmarek, A.; Hilczer, B.; Marfaing, J.; Caranoni, C.

1999-07-01

The effect of hydrostatic pressure ( p<0.6 GPa) on the superconducting critical temperature Tc in YBa 2Cu 3O 7- δ-Pb(Sc 0.5Ta 0.5)O 3 (YBCO-PST) composite is measured by the method of magnetically modulated microwave absorption (MMMA). The Tc dependence on the PST fraction in weight x (0, 0.25, 0.5 and 0.75) is approximated by an inverted parabola function whereas the influence of pressure on Tc is represented by the equation: d Tc/d p=0.61(2)-1.72(6) x. The result may be explained assuming that PST phase in YBCO-PST composite influences the superconducting carrier concentration similar to the chemical substitution in YBa 2Cu 3O 7 [J.J. Neumeier, H.A. Zimmermann, Phys. Rev. B 47 (1993) 8385]. It is suggested that ions from PST diffuse to YBCO cell during the sintering of the composite.

Applicability of the Fokker-Planck equation to the description of diffusion effects on nucleation

NASA Astrophysics Data System (ADS)

Sorokin, M. V.; Dubinko, V. I.; Borodin, V. A.

2017-01-01

The nucleation of islands in a supersaturated solution of surface adatoms is considered taking into account the possibility of diffusion profile formation in the island vicinity. It is shown that the treatment of diffusion-controlled cluster growth in terms of the Fokker-Planck equation is justified only provided certain restrictions are satisfied. First of all, the standard requirement that diffusion profiles of adatoms quickly adjust themselves to the actual island sizes (adiabatic principle) can be realized only for sufficiently high island concentration. The adiabatic principle is essential for the probabilities of adatom attachment to and detachment from island edges to be independent of the adatom diffusion profile establishment kinetics, justifying the island nucleation treatment as the Markovian stochastic process. Second, it is shown that the commonly used definition of the "diffusion" coefficient in the Fokker-Planck equation in terms of adatom attachment and detachment rates is justified only provided the attachment and detachment are statistically independent, which is generally not the case for the diffusion-limited growth of islands. We suggest a particular way to define the attachment and detachment rates that allows us to satisfy this requirement as well. When applied to the problem of surface island nucleation, our treatment predicts the steady-state nucleation barrier, which coincides with the conventional thermodynamic expression, even though no thermodynamic equilibrium is assumed and the adatom diffusion is treated explicitly. The effect of adatom diffusional profiles on the nucleation rate preexponential factor is also discussed. Monte Carlo simulation is employed to analyze the applicability domain of the Fokker-Planck equation and the diffusion effect beyond it. It is demonstrated that a diffusional cloud is slowing down the nucleation process for a given monomer interaction with the nucleus edge.

Diffusion Processes Satisfying a Conservation Law Constraint

DOE PAGES

Bakosi, J.; Ristorcelli, J. R.

2014-03-04

We investigate coupled stochastic differential equations governing N non-negative continuous random variables that satisfy a conservation principle. In various fields a conservation law requires that a set of fluctuating variables be non-negative and (if appropriately normalized) sum to one. As a result, any stochastic differential equation model to be realizable must not produce events outside of the allowed sample space. We develop a set of constraints on the drift and diffusion terms of such stochastic models to ensure that both the non-negativity and the unit-sum conservation law constraint are satisfied as the variables evolve in time. We investigate the consequencesmore » of the developed constraints on the Fokker-Planck equation, the associated system of stochastic differential equations, and the evolution equations of the first four moments of the probability density function. We show that random variables, satisfying a conservation law constraint, represented by stochastic diffusion processes, must have diffusion terms that are coupled and nonlinear. The set of constraints developed enables the development of statistical representations of fluctuating variables satisfying a conservation law. We exemplify the results with the bivariate beta process and the multivariate Wright-Fisher, Dirichlet, and Lochner’s generalized Dirichlet processes.« less

Diffusion Processes Satisfying a Conservation Law Constraint

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

Bakosi, J.; Ristorcelli, J. R.

We investigate coupled stochastic differential equations governing N non-negative continuous random variables that satisfy a conservation principle. In various fields a conservation law requires that a set of fluctuating variables be non-negative and (if appropriately normalized) sum to one. As a result, any stochastic differential equation model to be realizable must not produce events outside of the allowed sample space. We develop a set of constraints on the drift and diffusion terms of such stochastic models to ensure that both the non-negativity and the unit-sum conservation law constraint are satisfied as the variables evolve in time. We investigate the consequencesmore » of the developed constraints on the Fokker-Planck equation, the associated system of stochastic differential equations, and the evolution equations of the first four moments of the probability density function. We show that random variables, satisfying a conservation law constraint, represented by stochastic diffusion processes, must have diffusion terms that are coupled and nonlinear. The set of constraints developed enables the development of statistical representations of fluctuating variables satisfying a conservation law. We exemplify the results with the bivariate beta process and the multivariate Wright-Fisher, Dirichlet, and Lochner’s generalized Dirichlet processes.« less

Modelling oxygen self-diffusion in UO 2 under pressure

DOE PAGES

Cooper, Michael William D.; Grimes, R. W.; Fitzpatrick, M. E.; ...

2015-10-22

Access to values for oxygen self-diffusion over a range of temperatures and pressures in UO 2 is important to nuclear fuel applications. Here, elastic and expansivity data are used in the framework of a thermodynamic model, the cBΩ model, to derive the oxygen self-diffusion coefficient in UO 2 over a range of pressures (0–10 GPa) and temperatures (300–1900 K). Furthermore, the significant reduction in oxygen self-diffusion as a function of increasing hydrostatic pressure, and the associated increase in activation energy, is identified.

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

NASA Astrophysics Data System (ADS)

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

2014-12-01

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

A model for shrinkage strain in photo polymerization of dental composites.

PubMed

Petrovic, Ljubomir M; Atanackovic, Teodor M

2008-04-01

We formulate a new model for the shrinkage strain developed during photo polymerization in dental composites. The model is based on the diffusion type fractional order equation, since it has been proved that polymerization reaction is diffusion controlled (Atai M, Watts DC. A new kinetic model for the photo polymerization shrinkage-strain of dental composites and resin-monomers. Dent Mater 2006;22:785-91). Our model strongly confirms the observation by Atai and Watts (see reference details above) and their experimental results. The shrinkage strain is modeled by a nonlinear differential equation in (see reference details above) and that equation must be solved numerically. In our approach, we use the linear fractional order differential equation to describe the strain rate due to photo polymerization. This equation is solved exactly. As shrinkage is a consequence of the polymerization reaction and polymerization reaction is diffusion controlled, we postulate that shrinkage strain rate is described by a diffusion type equation. We find explicit form of solution to this equation and determine the strain in the resin monomers. Also by using equations of linear viscoelasticity, we determine stresses in the polymer due to the shrinkage. The time evolution of stresses implies that the maximal stresses are developed at the very beginning of the polymerization process. The stress in a dental composite that is light treated has the largest value short time after the treatment starts. The strain settles at the constant value in the time of about 100s (for the cases treated in Atai and Watts). From the model developed here, the shrinkage strain of dental composites and resin monomers is analytically determined. The maximal value of stresses is important, since this value must be smaller than the adhesive bond strength at cavo-restoration interface. The maximum stress determined here depends on the diffusivity coefficient. Since diffusivity coefficient increases as polymerization proceeds, it follows that the periods of light treatments should be shorter at the beginning of the treatment and longer at the end of the treatment, with dark interval between the initial low intensity and following high intensity curing. This is because at the end of polymerization the stress relaxation cannot take place.

OH density measured by PLIF in a nanosecond atmospheric pressure diffuse discharge in humid air under steep high voltage pulses

NASA Astrophysics Data System (ADS)

Ouaras, K.; Magne, L.; Pasquiers, S.; Tardiveau, P.; Jeanney, P.; Bournonville, B.

2018-04-01

The spatiotemporal distributions of the OH radical density are measured using planar laser induced fluorescence in the afterglow of a nanosecond diffuse discharge at atmospheric pressure in humid air. The diffuse discharge is generated between a pin and a grounded plate electrodes within a gap of 18 mm. The high voltage pulse applied to the pin ranges from 65 to 85 kV with a rise time of 2 ns. The specific electrical energy transferred to the gas ranges from 5 to 40 J l‑1. The influence of H2O concentration is studied from 0.5% to 1.5%. An absolute calibration of OH density is performed using a six-level transient rate equation model to simulate the dynamics of OH excitation by the laser, taking into account collisional processes during the optical pumping and the fluorescence. Rayleigh scattering measurements are used to achieve the geometrical part of the calibration. A local maximum of OH density is found in the pin area whatever the operating conditions. For 85 kV and 1% of H2O, this peak reaches a value of 2.0 × 1016 cm‑3 corresponding to 8% of H2O dissociation. The temporal decay of the spatially averaged OH density is found to be similar as in the afterglow of a homogeneous photo-triggered discharge for which a self-consistent modeling is done. These tools are then used to bring discussion elements on OH kinetics.

A Radiation Transfer Solver for Athena Using Short Characteristics

NASA Astrophysics Data System (ADS)

Davis, Shane W.; Stone, James M.; Jiang, Yan-Fei

2012-03-01

We describe the implementation of a module for the Athena magnetohydrodynamics (MHD) code that solves the time-independent, multi-frequency radiative transfer (RT) equation on multidimensional Cartesian simulation domains, including scattering and non-local thermodynamic equilibrium (LTE) effects. The module is based on well known and well tested algorithms developed for modeling stellar atmospheres, including the method of short characteristics to solve the RT equation, accelerated Lambda iteration to handle scattering and non-LTE effects, and parallelization via domain decomposition. The module serves several purposes: it can be used to generate spectra and images, to compute a variable Eddington tensor (VET) for full radiation MHD simulations, and to calculate the heating and cooling source terms in the MHD equations in flows where radiation pressure is small compared with gas pressure. For the latter case, the module is combined with the standard MHD integrators using operator splitting: we describe this approach in detail, including a new constraint on the time step for stability due to radiation diffusion modes. Implementation of the VET method for radiation pressure dominated flows is described in a companion paper. We present results from a suite of test problems for both the RT solver itself and for dynamical problems that include radiative heating and cooling. These tests demonstrate that the radiative transfer solution is accurate and confirm that the operator split method is stable, convergent, and efficient for problems of interest. We demonstrate there is no need to adopt ad hoc assumptions of questionable accuracy to solve RT problems in concert with MHD: the computational cost for our general-purpose module for simple (e.g., LTE gray) problems can be comparable to or less than a single time step of Athena's MHD integrators, and only few times more expensive than that for more general (non-LTE) problems.

Analyses on the Performance and Interaction Between the Impeller and Casing in a Small-Size Turbo-Compressor

NASA Astrophysics Data System (ADS)

Kim, Youn-Jea; Kim, Dong-Won

The effects of casing shapes on the performance and the interaction between an impeller and a casing in a small-size turbo-compressor are investigated. Numerical analysis is conducted for the turbo-compressor with circular and single volute casings from the inlet to a discharge nozzle. The optimum design for each element is important to develop the small-size turbo-compressor using alternative refrigerant as a working fluid. Typically, the rotating speed of the compressor is in the range of 40000-45000rpm because of the small size of an impeller diameter. A blade of an impeller has backswept two-dimensional shape due to tip clearance and a vane diffuser has wedge type. In order to predict the flow pattern inside the entire impeller, the vaneless diffuser and the casing, calculations with multiple frames of reference method between the rotating and stationery parts of the domain are carried out. For compressible turbulent flow fields, the continuity and time-averaged three-dimensional Navier-Stokes equations are employed. To evaluate the performance of two types of casings, the static pressure recovery and loss coefficients are obtained with various flow rates. Also, static pressure distributions around casings are studied for different casing shapes, which are very important to predict the distribution of radial load. To prove the accuracy of numerical results, measurements of static pressure around the casing and pressure difference between the inlet and the outlet of the compressor are performed for the circular casing. The comparison of experimental and numerical results is conducted, and reasonable agreement is obtained.

Effect of water phase transition on dynamic ruptures with thermal pressurization: Numerical simulations with changes in physical properties of water

NASA Astrophysics Data System (ADS)

Urata, Yumi; Kuge, Keiko; Kase, Yuko

2015-02-01

Phase transitions of pore water have never been considered in dynamic rupture simulations with thermal pressurization (TP), although they may control TP. From numerical simulations of dynamic rupture propagation including TP, in the absence of any water phase transition process, we predict that frictional heating and TP are likely to change liquid pore water into supercritical water for a strike-slip fault under depth-dependent stress. This phase transition causes changes of a few orders of magnitude in viscosity, compressibility, and thermal expansion among physical properties of water, thus affecting the diffusion of pore pressure. Accordingly, we perform numerical simulations of dynamic ruptures with TP, considering physical properties that vary with the pressure and temperature of pore water on a fault. To observe the effects of the phase transition, we assume uniform initial stress and no fault-normal variations in fluid density and viscosity. The results suggest that the varying physical properties decrease the total slip in cases with high stress at depth and small shear zone thickness. When fault-normal variations in fluid density and viscosity are included in the diffusion equation, they activate TP much earlier than the phase transition. As a consequence, the total slip becomes greater than that in the case with constant physical properties, eradicating the phase transition effect. Varying physical properties do not affect the rupture velocity, irrespective of the fault-normal variations. Thus, the phase transition of pore water has little effect on dynamic ruptures. Fault-normal variations in fluid density and viscosity may play a more significant role.

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

NASA Technical Reports Server (NTRS)

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

1994-01-01

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

Catalytic conversion reactions mediated by single-file diffusion in linear nanopores: hydrodynamic versus stochastic behavior.

PubMed

Ackerman, David M; Wang, Jing; Wendel, Joseph H; Liu, Da-Jiang; Pruski, Marek; Evans, James W

2011-03-21

We analyze the spatiotemporal behavior of species concentrations in a diffusion-mediated conversion reaction which occurs at catalytic sites within linear pores of nanometer diameter. Diffusion within the pores is subject to a strict single-file (no passing) constraint. Both transient and steady-state behavior is precisely characterized by kinetic Monte Carlo simulations of a spatially discrete lattice-gas model for this reaction-diffusion process considering various distributions of catalytic sites. Exact hierarchical master equations can also be developed for this model. Their analysis, after application of mean-field type truncation approximations, produces discrete reaction-diffusion type equations (mf-RDE). For slowly varying concentrations, we further develop coarse-grained continuum hydrodynamic reaction-diffusion equations (h-RDE) incorporating a precise treatment of single-file diffusion in this multispecies system. The h-RDE successfully describe nontrivial aspects of transient behavior, in contrast to the mf-RDE, and also correctly capture unreactive steady-state behavior in the pore interior. However, steady-state reactivity, which is localized near the pore ends when those regions are catalytic, is controlled by fluctuations not incorporated into the hydrodynamic treatment. The mf-RDE partly capture these fluctuation effects, but cannot describe scaling behavior of the reactivity.

Cross-Diffusion Induced Turing Instability and Amplitude Equation for a Toxic-Phytoplankton-Zooplankton Model with Nonmonotonic Functional Response

NASA Astrophysics Data System (ADS)

Han, Renji; Dai, Binxiang

2017-06-01

The spatiotemporal pattern induced by cross-diffusion of a toxic-phytoplankton-zooplankton model with nonmonotonic functional response is investigated in this paper. The linear stability analysis shows that cross-diffusion is the key mechanism for the formation of spatial patterns. By taking cross-diffusion rate as bifurcation parameter, we derive amplitude equations near the Turing bifurcation point for the excited modes in the framework of a weakly nonlinear theory, and the stability analysis of the amplitude equations interprets the structural transitions and stability of various forms of Turing patterns. Furthermore, we illustrate the theoretical results via numerical simulations. It is shown that the spatiotemporal distribution of the plankton is homogeneous in the absence of cross-diffusion. However, when the cross-diffusivity is greater than the critical value, the spatiotemporal distribution of all the plankton species becomes inhomogeneous in spaces and results in different kinds of patterns: spot, stripe, and the mixture of spot and stripe patterns depending on the cross-diffusivity. Simultaneously, the impact of toxin-producing rate of toxic-phytoplankton (TPP) species and natural death rate of zooplankton species on pattern selection is also explored.

Bessel Fourier orientation reconstruction: an analytical EAP reconstruction using multiple shell acquisitions in diffusion MRI.

PubMed

Hosseinbor, Ameer Pasha; Chung, Moo K; Wu, Yu-Chien; Alexander, Andrew L

2011-01-01

The estimation of the ensemble average propagator (EAP) directly from q-space DWI signals is an open problem in diffusion MRI. Diffusion spectrum imaging (DSI) is one common technique to compute the EAP directly from the diffusion signal, but it is burdened by the large sampling required. Recently, several analytical EAP reconstruction schemes for multiple q-shell acquisitions have been proposed. One, in particular, is Diffusion Propagator Imaging (DPI) which is based on the Laplace's equation estimation of diffusion signal for each shell acquisition. Viewed intuitively in terms of the heat equation, the DPI solution is obtained when the heat distribution between temperatuere measurements at each shell is at steady state. We propose a generalized extension of DPI, Bessel Fourier Orientation Reconstruction (BFOR), whose solution is based on heat equation estimation of the diffusion signal for each shell acquisition. That is, the heat distribution between shell measurements is no longer at steady state. In addition to being analytical, the BFOR solution also includes an intrinsic exponential smootheing term. We illustrate the effectiveness of the proposed method by showing results on both synthetic and real MR datasets.

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

NASA Astrophysics Data System (ADS)

Carnaffan, Sean; Kawai, Reiichiro

2017-06-01

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

Anomalous Transport of Cosmic Rays in a Nonlinear Diffusion Model

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

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

2017-05-20

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

Some Fundamental Issues of Mathematical Simulation in Biology

NASA Astrophysics Data System (ADS)

Razzhevaikin, V. N.

2018-02-01

Some directions of simulation in biology leading to original formulations of mathematical problems are overviewed. Two of them are discussed in detail: the correct solvability of first-order linear equations with unbounded coefficients and the construction of a reaction-diffusion equation with nonlinear diffusion for a model of genetic wave propagation.

Flow of variably fluidized granular masses across three-dimensional terrain I. Coulomb mixture theory

USGS Publications Warehouse

Iverson, R.M.; Denlinger, R.P.

2001-01-01

Rock avalanches, debris flows, and related phenomena consist of grain-fluid mixtures that move across three-dimensional terrain. In all these phenomena the same basic forces, govern motion, but differing mixture compositions, initial conditions, and boundary conditions yield varied dynamics and deposits. To predict motion of diverse grain-fluid masses from initiation to deposition, we develop a depth-averaged, threedimensional mathematical model that accounts explicitly for solid- and fluid-phase forces and interactions. Model input consists of initial conditions, path topography, basal and internal friction angles of solid grains, viscosity of pore fluid, mixture density, and a mixture diffusivity that controls pore pressure dissipation. Because these properties are constrained by independent measurements, the model requires little or no calibration and yields readily testable predictions. In the limit of vanishing Coulomb friction due to persistent high fluid pressure the model equations describe motion of viscous floods, and in the limit of vanishing fluid stress they describe one-phase granular avalanches. Analysis of intermediate phenomena such as debris flows and pyroclastic flows requires use of the full mixture equations, which can simulate interaction of high-friction surge fronts with more-fluid debris that follows. Special numerical methods (described in the companion paper) are necessary to solve the full equations, but exact analytical solutions of simplified equations provide critical insight. An analytical solution for translational motion of a Coulomb mixture accelerating from rest and descending a uniform slope demonstrates that steady flow can occur only asymptotically. A solution for the asymptotic limit of steady flow in a rectangular channel explains why shear may be concentrated in narrow marginal bands that border a plug of translating debris. Solutions for static equilibrium of source areas describe conditions of incipient slope instability, and other static solutions show that nonuniform distributions of pore fluid pressure produce bluntly tapered vertical profiles at the margins of deposits. Simplified equations and solutions may apply in additional situations identified by a scaling analysis. Assessment of dimensionless scaling parameters also reveals that miniature laboratory experiments poorly simulate the dynamics of full-scale flows in which fluid effects are significant. Therefore large geophysical flows can exhibit dynamics not evident at laboratory scales.

Flow of variably fluidized granular masses across three-dimensional terrain: 1. Coulomb mixture theory

NASA Astrophysics Data System (ADS)

Iverson, Richard M.; Denlinger, Roger P.

2001-01-01

Rock avalanches, debris flows, and related phenomena consist of grain-fluid mixtures that move across three-dimensional terrain. In all these phenomena the same basic forces govern motion, but differing mixture compositions, initial conditions, and boundary conditions yield varied dynamics and deposits. To predict motion of diverse grain-fluid masses from initiation to deposition, we develop a depth-averaged, three-dimensional mathematical model that accounts explicitly for solid- and fluid-phase forces and interactions. Model input consists of initial conditions, path topography, basal and internal friction angles of solid grains, viscosity of pore fluid, mixture density, and a mixture diffusivity that controls pore pressure dissipation. Because these properties are constrained by independent measurements, the model requires little or no calibration and yields readily testable predictions. In the limit of vanishing Coulomb friction due to persistent high fluid pressure the model equations describe motion of viscous floods, and in the limit of vanishing fluid stress they describe one-phase granular avalanches. Analysis of intermediate phenomena such as debris flows and pyroclastic flows requires use of the full mixture equations, which can simulate interaction of high-friction surge fronts with more-fluid debris that follows. Special numerical methods (described in the companion paper) are necessary to solve the full equations, but exact analytical solutions of simplified equations provide critical insight. An analytical solution for translational motion of a Coulomb mixture accelerating from rest and descending a uniform slope demonstrates that steady flow can occur only asymptotically. A solution for the asymptotic limit of steady flow in a rectangular channel explains why shear may be concentrated in narrow marginal bands that border a plug of translating debris. Solutions for static equilibrium of source areas describe conditions of incipient slope instability, and other static solutions show that nonuniform distributions of pore fluid pressure produce bluntly tapered vertical profiles at the margins of deposits. Simplified equations and solutions may apply in additional situations identified by a scaling analysis. Assessment of dimensionless scaling parameters also reveals that miniature laboratory experiments poorly simulate the dynamics of full-scale flows in which fluid effects are significant. Therefore large geophysical flows can exhibit dynamics not evident at laboratory scales.

Density-driven transport of gas phase chemicals in unsaturated soils

NASA Astrophysics Data System (ADS)

Fen, Chiu-Shia; Sun, Yong-tai; Cheng, Yuen; Chen, Yuanchin; Yang, Whaiwan; Pan, Changtai

2018-01-01

Variations of gas phase density are responsible for advective and diffusive transports of organic vapors in unsaturated soils. Laboratory experiments were conducted to explore dense gas transport (sulfur hexafluoride, SF6) from different source densities through a nitrogen gas-dry soil column. Gas pressures and SF6 densities at transient state were measured along the soil column for three transport configurations (horizontal, vertically upward and vertically downward transport). These measurements and others reported in the literature were compared with simulation results obtained from two models based on different diffusion approaches: the dusty gas model (DGM) equations and a Fickian-type molar fraction-based diffusion expression. The results show that the DGM and Fickian-based models predicted similar dense gas density profiles which matched the measured data well for horizontal transport of dense gas at low to high source densities, despite the pressure variations predicted in the soil column were opposite to the measurements. The pressure evolutions predicted by both models were in trend similar to the measured ones for vertical transport of dense gas. However, differences between the dense gas densities predicted by the DGM and Fickian-based models were discernible for vertically upward transport of dense gas even at low source densities, as the DGM-based predictions matched the measured data better than the Fickian results did. For vertically downward transport, the dense gas densities predicted by both models were not greatly different from our experimental measurements, but substantially greater than the observations obtained from the literature, especially at high source densities. Further research will be necessary for exploring factors affecting downward transport of dense gas in soil columns. Use of the measured data to compute flux components of SF6 showed that the magnitudes of diffusive flux component based on the Fickian-type diffusion expressions in terms of molar concentration, molar fraction and mass density fraction gradient were almost the same. However, they were greater than the result computed with the mass fraction gradient for > 24% and the DGM-based result for more than one time. As a consequence, the DGM-based total flux of SF6 was in magnitude greatly less than the Fickian result not only for horizontal transport (diffusion-dominating) but also for vertical transport (advection and diffusion) of dense gas. Particularly, the Fickian-based total flux was more than two times in magnitude as much as the DGM result for vertically upward transport of dense gas.

Numerical study of centrifugal compressor stage vaneless diffusers

NASA Astrophysics Data System (ADS)

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

2015-08-01

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

Integral approximations to classical diffusion and smoothed particle hydrodynamics

DOE PAGES

Du, Qiang; Lehoucq, R. B.; Tartakovsky, A. M.

2014-12-31

The contribution of the paper is the approximation of a classical diffusion operator by an integral equation with a volume constraint. A particular focus is on classical diffusion problems associated with Neumann boundary conditions. By exploiting this approximation, we can also approximate other quantities such as the flux out of a domain. Our analysis of the model equation on the continuum level is closely related to the recent work on nonlocal diffusion and peridynamic mechanics. In particular, we elucidate the role of a volumetric constraint as an approximation to a classical Neumann boundary condition in the presence of physical boundary.more » The volume-constrained integral equation then provides the basis for accurate and robust discretization methods. As a result, an immediate application is to the understanding and improvement of the Smoothed Particle Hydrodynamics (SPH) method.« less

Effects of high-energy particles on accretion flows onto a super massive black hole

NASA Astrophysics Data System (ADS)

Kimura, Shigeo

We study effects of high-energy particles on the accretion flow onto a supermassive black hole and luminosities of escaping particles such as protons, neutrons, gamma-rays, and neutrinos. We formulate a one-dimensional model of the two-component accretion flow consisting of thermal particles and high-energy particles, supposing that some fraction of viscous dissipation energy is converted to the acceleration of high-energy particles. The thermal component is governed by fluid dynamics while the high-energy particles obey the moment equations of the diffusion-convection equation. By solving the time evolution of these equations, we obtain advection dominated flows as steady state solutions. Effects of the high-energy particles on the flow structure turn out to be very small because the compressional heating is so effective that the thermal component always provides the major part of the pressure. We calculate luminosities of escaping particles for these steady solutions. For a broad range of mass accretion rates, escaping particles can extract the energy about one-thousandth of the accretion energy. We also discuss some implications on relativistic jet production by escaping particles.

The structure of the solution obtained with Reynolds-stress-transport models at the free-stream edges of turbulent flows

NASA Astrophysics Data System (ADS)

Cazalbou, J.-B.; Chassaing, P.

2002-02-01

The behavior of Reynolds-stress-transport models at the free-stream edges of turbulent flows is investigated. Current turbulent-diffusion models are found to produce propagative (possibly weak) solutions of the same type as those reported earlier by Cazalbou, Spalart, and Bradshaw [Phys. Fluids 6, 1797 (1994)] for two-equation models. As in the latter study, an analysis is presented that provides qualitative information on the flow structure predicted near the edge if a condition on the values of the diffusion constants is satisfied. In this case, the solution appears to be fairly insensitive to the residual free-stream turbulence levels needed with conventional numerical methods. The main specific result is that, depending on the diffusion model, the propagative solution can force turbulence toward definite and rather extreme anisotropy states at the edge (one- or two-component limit). This is not the case with the model of Daly and Harlow [Phys. Fluids 13, 2634 (1970)]; it may be one of the reasons why this "old" scheme is still the most widely used, even in recent Reynolds-stress-transport models. In addition, the analysis helps us to interpret some difficulties encountered in computing even very simple flows with Lumley's pressure-diffusion model [Adv. Appl. Mech. 18, 123 (1978)]. A new realizability condition, according to which the diffusion model should not globally become "anti-diffusive," is introduced, and a recalibration of Lumley's model satisfying this condition is performed using information drawn from the analysis.

Characteristics of Perforated Diffusers at Free-stream Mach Number 1.90

NASA Technical Reports Server (NTRS)

Hunczak, Henry R; Kremzier, Emil J

1950-01-01

An investigation was conducted at Mach number 1.90 to determine pressure recovery and mass-flow characteristics of series of perforated convergent-divergent supersonic diffusers. Pressure recoveries as high as 96 percent were obtained, but at reduced mass flows through the diffuser. Theoretical considerations of effect of perforation distribution on shock stability in converging section of diffuser are presented and correlated with experimental data. A method of estimating relative importance of pressure recovery and mass flow on internal thrust coefficient basis is given and a comparison of various diffusers investigated is made.

Spin diffusion and torques in disordered antiferromagnets

NASA Astrophysics Data System (ADS)

Manchon, Aurelien

2017-03-01

We have developed a drift-diffusion equation of spin transport in collinear bipartite metallic antiferromagnets. Starting from a model tight-binding Hamiltonian, we obtain the quantum kinetic equation within Keldysh formalism and expand it to the lowest order in spatial gradient using Wigner expansion method. In the diffusive limit, these equations track the spatio-temporal evolution of the spin accumulations and spin currents on each sublattice of the antiferromagnet. We use these equations to address the nature of the spin transfer torque in (i) a spin-valve composed of a ferromagnet and an antiferromagnet, (ii) a metallic bilayer consisting of an antiferromagnet adjacent to a heavy metal possessing spin Hall effect, and in (iii) a single antiferromagnet possessing spin Hall effect. We show that the latter can experience a self-torque thanks to the non-vanishing spin Hall effect in the antiferromagnet.

Breakdown of the reaction-diffusion master equation with nonelementary rates

NASA Astrophysics Data System (ADS)

Smith, Stephen; Grima, Ramon

2016-05-01

The chemical master equation (CME) is the exact mathematical formulation of chemical reactions occurring in a dilute and well-mixed volume. The reaction-diffusion master equation (RDME) is a stochastic description of reaction-diffusion processes on a spatial lattice, assuming well mixing only on the length scale of the lattice. It is clear that, for the sake of consistency, the solution of the RDME of a chemical system should converge to the solution of the CME of the same system in the limit of fast diffusion: Indeed, this has been tacitly assumed in most literature concerning the RDME. We show that, in the limit of fast diffusion, the RDME indeed converges to a master equation but not necessarily the CME. We introduce a class of propensity functions, such that if the RDME has propensities exclusively of this class, then the RDME converges to the CME of the same system, whereas if the RDME has propensities not in this class, then convergence is not guaranteed. These are revealed to be elementary and nonelementary propensities, respectively. We also show that independent of the type of propensity, the RDME converges to the CME in the simultaneous limit of fast diffusion and large volumes. We illustrate our results with some simple example systems and argue that the RDME cannot generally be an accurate description of systems with nonelementary rates.

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

NASA Astrophysics Data System (ADS)

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

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

Fick's second law transformed: one path to cloaking in mass diffusion.

PubMed

Guenneau, S; Puvirajesinghe, T M

2013-06-06

Here, we adapt the concept of transformational thermodynamics, whereby the flux of temperature is controlled via anisotropic heterogeneous diffusivity, for the diffusion and transport of mass concentration. The n-dimensional, time-dependent, anisotropic heterogeneous Fick's equation is considered, which is a parabolic partial differential equation also applicable to heat diffusion, when convection occurs, for example, in fluids. This theory is illustrated with finite-element computations for a liposome particle surrounded by a cylindrical multi-layered cloak in a water-based environment, and for a spherical multi-layered cloak consisting of layers of fluid with an isotropic homogeneous diffusivity, deduced from an effective medium approach. Initial potential applications could be sought in bioengineering.

Stefan-Maxwell Relations and Heat Flux with Anisotropic Transport Coefficients for Ionized Gases in a Magnetic Field with Application to the Problem of Ambipolar Diffusion

NASA Astrophysics Data System (ADS)

Kolesnichenko, A. V.; Marov, M. Ya.

2018-01-01

The defining relations for the thermodynamic diffusion and heat fluxes in a multicomponent, partially ionized gas mixture in an external electromagnetic field have been obtained by the methods of the kinetic theory. Generalized Stefan-Maxwell relations and algebraic equations for anisotropic transport coefficients (the multicomponent diffusion, thermal diffusion, electric and thermoelectric conductivity coefficients as well as the thermal diffusion ratios) associated with diffusion-thermal processes have been derived. The defining second-order equations are derived by the Chapman-Enskog procedure using Sonine polynomial expansions. The modified Stefan-Maxwell relations are used for the description of ambipolar diffusion in the Earth's ionospheric plasma (in the F region) composed of electrons, ions of many species, and neutral particles in a strong electromagnetic field.

Pressure Characteristics of a Diffuser in a Ram RDE Propulsive Device

DTIC Science & Technology

2017-07-21

Continuous detonation Rotating-detonation- engine Ethylene-air Diffuser Pressure feedback Modeling and simulation Office of Naval Research 875 N. Randolph...RDE PROPULSIVE DEVICE INTRODUCTION This report focuses on the diffuser of a ram Rotating Detonation Engine (RDE) device. A ram RDE is a ramjet with...the constant pressure combustion chamber replaced with a Rotating Detonation Engine combustor to accomplish pressure gain combustion. A ram engine

From quantum stochastic differential equations to Gisin-Percival state diffusion

NASA Astrophysics Data System (ADS)

Parthasarathy, K. R.; Usha Devi, A. R.

2017-08-01

Starting from the quantum stochastic differential equations of Hudson and Parthasarathy [Commun. Math. Phys. 93, 301 (1984)] and exploiting the Wiener-Itô-Segal isomorphism between the boson Fock reservoir space Γ (L2(R+ ) ⊗(Cn⊕Cn ) ) and the Hilbert space L2(μ ) , where μ is the Wiener probability measure of a complex n-dimensional vector-valued standard Brownian motion {B (t ) ,t ≥0 } , we derive a non-linear stochastic Schrödinger equation describing a classical diffusion of states of a quantum system, driven by the Brownian motion B. Changing this Brownian motion by an appropriate Girsanov transformation, we arrive at the Gisin-Percival state diffusion equation [N. Gisin and J. Percival, J. Phys. A 167, 315 (1992)]. This approach also yields an explicit solution of the Gisin-Percival equation, in terms of the Hudson-Parthasarathy unitary process and a randomized Weyl displacement process. Irreversible dynamics of system density operators described by the well-known Gorini-Kossakowski-Sudarshan-Lindblad master equation is unraveled by coarse-graining over the Gisin-Percival quantum state trajectories.

Recursion equations in predicting band width under gradient elution.

PubMed

Liang, Heng; Liu, Ying

2004-06-18

The evolution of solute zone under gradient elution is a typical problem of non-linear continuity equation since the local diffusion coefficient and local migration velocity of the mass cells of solute zones are the functions of position and time due to space- and time-variable mobile phase composition. In this paper, based on the mesoscopic approaches (Lagrangian description, the continuity theory and the local equilibrium assumption), the evolution of solute zones in space- and time-dependent fields is described by the iterative addition of local probability density of the mass cells of solute zones. Furthermore, on macroscopic levels, the recursion equations have been proposed to simulate zone migration and spreading in reversed-phase high-performance liquid chromatography (RP-HPLC) through directly relating local retention factor and local diffusion coefficient to local mobile phase concentration. This new approach differs entirely from the traditional theories on plate concept with Eulerian description, since band width recursion equation is actually the accumulation of local diffusion coefficients of solute zones to discrete-time slices. Recursion equations and literature equations were used in dealing with same experimental data in RP-HPLC, and the comparison results show that the recursion equations can accurately predict band width under gradient elution.

The accuracy of the compressible Reynolds equation for predicting the local pressure in gas-lubricated textured parallel slider bearings

PubMed Central

Qiu, Mingfeng; Bailey, Brian N.; Stoll, Rob

2014-01-01

The validity of the compressible Reynolds equation to predict the local pressure in a gas-lubricated, textured parallel slider bearing is investigated. The local bearing pressure is numerically simulated using the Reynolds equation and the Navier-Stokes equations for different texture geometries and operating conditions. The respective results are compared and the simplifying assumptions inherent in the application of the Reynolds equation are quantitatively evaluated. The deviation between the local bearing pressure obtained with the Reynolds equation and the Navier-Stokes equations increases with increasing texture aspect ratio, because a significant cross-film pressure gradient and a large velocity gradient in the sliding direction develop in the lubricant film. Inertia is found to be negligible throughout this study. PMID:25049440

Generalized quantum Fokker-Planck, diffusion, and Smoluchowski equations with true probability distribution functions.

PubMed

Banik, Suman Kumar; Bag, Bidhan Chandra; Ray, Deb Shankar

2002-05-01

Traditionally, quantum Brownian motion is described by Fokker-Planck or diffusion equations in terms of quasiprobability distribution functions, e.g., Wigner functions. These often become singular or negative in the full quantum regime. In this paper a simple approach to non-Markovian theory of quantum Brownian motion using true probability distribution functions is presented. Based on an initial coherent state representation of the bath oscillators and an equilibrium canonical distribution of the quantum mechanical mean values of their coordinates and momenta, we derive a generalized quantum Langevin equation in c numbers and show that the latter is amenable to a theoretical analysis in terms of the classical theory of non-Markovian dynamics. The corresponding Fokker-Planck, diffusion, and Smoluchowski equations are the exact quantum analogs of their classical counterparts. The present work is independent of path integral techniques. The theory as developed here is a natural extension of its classical version and is valid for arbitrary temperature and friction (the Smoluchowski equation being considered in the overdamped limit).

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

PubMed

Sevilla, Francisco J; Gómez Nava, Luis A

2014-08-01

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

On the Role of Built-in Electric Fields on the Ignition of Oxide Coated NanoAluminum: Ion Mobility versus Fickian Diffusion

DTIC Science & Technology

2010-01-01

on Al ion diffu- sion can be computed using the Nernst –Planck equation . The Nernst –Plank equation is given in Eq. 4,22 J = − D dC dx − zFDC RT d dx...The use of the bulk diffusion equation is reason- able since during the time scales considered the movement of only the atoms initially on the surface

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

NASA Astrophysics Data System (ADS)

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

2017-07-01

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

Flow regimes for fluid injection into a confined porous medium

DOE PAGES

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

2015-02-24

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

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

Modeling studies of gas movement and moisture migration at Yucca Mountain, Nevada

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

Tsang, Y.W.; Pruess, K.

1991-06-01

Modeling studies on moisture redistribution processes that are mediated by gas phase flow and diffusion have been carried out. The problem addressed is the effect of a lowered humidity of the soil gas at the land surface on moisture removal from Yucca Mountain, the potential site for a high-level nuclear waste repository. At the land surface, humid formation gas contacts much drier atmospheric air. Near this contact, the humidity of the soil gas may be considerably lower than at greater depth, where the authors expect equilibrium with the liquid phase and close to 100% humidity. The lower relative humidity ofmore » the soil gas may be modeled by imposing, at the land surface, an additional negative capillary suction corresponding to vapor pressure lowering according to Kelvin`s Equation, thus providing a driving force for the upward movement of moisture in both the vapor and liquid phases. Sensitivity studies show that moisture removal from Yucca Mountain arising from the lowered-relative-humidity boundary condition is controlled by vapor diffusion. There is much experimental evidence in the soil literature that diffusion of vapor is enhanced due to pore-level phase change effects by a few orders of magnitude. Modeling results presented here will account for this enhancement in vapor diffusion.« less

Intrinsic Compressive Stress in Polycrystalline Films is Localized at Edges of the Grain Boundaries.

PubMed

Vasco, Enrique; Polop, Celia

2017-12-22

The intrinsic compression that arises in polycrystalline thin films under high atomic mobility conditions has been attributed to the insertion or trapping of adatoms inside grain boundaries. This compression is a consequence of the stress field resulting from imperfections in the solid and causes the thermomechanical fatigue that is estimated to be responsible for 90% of mechanical failures in current devices. We directly measure the local distribution of residual intrinsic stress in polycrystalline thin films on nanometer scales, using a pioneering method based on atomic force microscopy. Our results demonstrate that, at odds with expectations, compression is not generated inside grain boundaries but at the edges of gaps where the boundaries intercept the surface. We describe a model wherein this compressive stress is caused by Mullins-type surface diffusion towards the boundaries, generating a kinetic surface profile different from the mechanical equilibrium profile by the Laplace-Young equation. Where the curvatures of both profiles differ, an intrinsic stress is generated in the form of Laplace pressure. The Srolovitz-type surface diffusion that results from the stress counters the Mullins-type diffusion and stabilizes the kinetic surface profile, giving rise to a steady compression regime. The proposed mechanism of competition between surface diffusions would explain the flux and time dependency of compressive stress in polycrystalline thin films.

A Diffuse Interface Model with Immiscibility Preservation

PubMed Central

Tiwari, Arpit; Freund, Jonathan B.; Pantano, Carlos

2013-01-01

A new, simple, and computationally efficient interface capturing scheme based on a diffuse interface approach is presented for simulation of compressible multiphase flows. Multi-fluid interfaces are represented using field variables (interface functions) with associated transport equations that are augmented, with respect to an established formulation, to enforce a selected interface thickness. The resulting interface region can be set just thick enough to be resolved by the underlying mesh and numerical method, yet thin enough to provide an efficient model for dynamics of well-resolved scales. A key advance in the present method is that the interface regularization is asymptotically compatible with the thermodynamic mixture laws of the mixture model upon which it is constructed. It incorporates first-order pressure and velocity non-equilibrium effects while preserving interface conditions for equilibrium flows, even within the thin diffused mixture region. We first quantify the improved convergence of this formulation in some widely used one-dimensional configurations, then show that it enables fundamentally better simulations of bubble dynamics. Demonstrations include both a spherical bubble collapse, which is shown to maintain excellent symmetry despite the Cartesian mesh, and a jetting bubble collapse adjacent a wall. Comparisons show that without the new formulation the jet is suppressed by numerical diffusion leading to qualitatively incorrect results. PMID:24058207

Intrinsic Compressive Stress in Polycrystalline Films is Localized at Edges of the Grain Boundaries

NASA Astrophysics Data System (ADS)

Vasco, Enrique; Polop, Celia

2017-12-01

The intrinsic compression that arises in polycrystalline thin films under high atomic mobility conditions has been attributed to the insertion or trapping of adatoms inside grain boundaries. This compression is a consequence of the stress field resulting from imperfections in the solid and causes the thermomechanical fatigue that is estimated to be responsible for 90% of mechanical failures in current devices. We directly measure the local distribution of residual intrinsic stress in polycrystalline thin films on nanometer scales, using a pioneering method based on atomic force microscopy. Our results demonstrate that, at odds with expectations, compression is not generated inside grain boundaries but at the edges of gaps where the boundaries intercept the surface. We describe a model wherein this compressive stress is caused by Mullins-type surface diffusion towards the boundaries, generating a kinetic surface profile different from the mechanical equilibrium profile by the Laplace-Young equation. Where the curvatures of both profiles differ, an intrinsic stress is generated in the form of Laplace pressure. The Srolovitz-type surface diffusion that results from the stress counters the Mullins-type diffusion and stabilizes the kinetic surface profile, giving rise to a steady compression regime. The proposed mechanism of competition between surface diffusions would explain the flux and time dependency of compressive stress in polycrystalline thin films.

Edge-based nonlinear diffusion for finite element approximations of convection-diffusion equations and its relation to algebraic flux-correction schemes.

PubMed

Barrenechea, Gabriel R; Burman, Erik; Karakatsani, Fotini

2017-01-01

For the case of approximation of convection-diffusion equations using piecewise affine continuous finite elements a new edge-based nonlinear diffusion operator is proposed that makes the scheme satisfy a discrete maximum principle. The diffusion operator is shown to be Lipschitz continuous and linearity preserving. Using these properties we provide a full stability and error analysis, which, in the diffusion dominated regime, shows existence, uniqueness and optimal convergence. Then the algebraic flux correction method is recalled and we show that the present method can be interpreted as an algebraic flux correction method for a particular definition of the flux limiters. The performance of the method is illustrated on some numerical test cases in two space dimensions.

Fractal Model of Fission Product Release in Nuclear Fuel

NASA Astrophysics Data System (ADS)

Stankunas, Gediminas

2012-09-01

A model of fission gas migration in nuclear fuel pellet is proposed. Diffusion process of fission gas in granular structure of nuclear fuel with presence of inter-granular bubbles in the fuel matrix is simulated by fractional diffusion model. The Grunwald-Letnikov derivative parameter characterizes the influence of porous fuel matrix on the diffusion process of fission gas. A finite-difference method for solving fractional diffusion equations is considered. Numerical solution of diffusion equation shows correlation of fission gas release and Grunwald-Letnikov derivative parameter. Calculated profile of fission gas concentration distribution is similar to that obtained in the experimental studies. Diffusion of fission gas is modeled for real RBMK-1500 fuel operation conditions. A functional dependence of Grunwald-Letnikov derivative parameter with fuel burn-up is established.

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.

Performance Characteristics of Plane-Wall Two-Dimensional Diffusers

NASA Technical Reports Server (NTRS)

Reid, Elliott G

1953-01-01

Experiments have been made at Stanford University to determine the performance characteristics of plane-wall, two-dimensional diffusers which were so proportioned as to insure reasonable approximation of two-dimensional flow. All of the diffusers had identical entrance cross sections and discharged directly into a large plenum chamber; the test program included wide variations of divergence angle and length. During all tests a dynamic pressure of 60 pounds per square foOt was maintained at the diffuser entrance and the boundary layer there was thin and fully turbulent. The most interesting flow characteristics observed were the occasional appearance of steady, unseparated, asymmetric flow - which was correlated with the boundary-layer coalescence - and the rapid deterioration of flow steadiness - which occurred as soon as the divergence angle for maximum static pressure recovery was exceeded. Pressure efficiency was found to be controlled almost exclusively by divergence angle, whereas static pressure recovery was markedly influenced by area ratio (or length) as well as divergence angle. Volumetric efficiency. diminished as area ratio increased, and at a greater rate with small lengths than with large ones. Large values of the static-pressure-recovery coefficient were attained only with long diffusers of large area ratio; under these conditions pressure efficiency was high and. volumetric efficiency low. Auxiliary tests with asymmetric diffusers demonstrated that longitudinal pressure gradient, rather than wall divergence angle, controlled flow separation. Others showed that the addition of even a short exit duct of uniform section augmented pressure recovery. Finally, it was found that the installation of a thin, central, longitudinal partition suppressed flow separation in short diffusers and thereby improved pressure recovery

Entropy-scaling laws for diffusion coefficients in liquid metals under high pressures

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

Cao, Qi-Long, E-mail: qlcao@mail.ustc.edu.cn; Shao, Ju-Xiang; Wang, Fan-Hou, E-mail: eatonch@gmail.com

2015-04-07

Molecular dynamic simulations on the liquid copper and tungsten are used to investigate the empirical entropy-scaling laws D{sup *}=A exp(BS{sub ex}), proposed independently by Rosenfeld and Dzugutov for diffusion coefficient, under high pressure conditions. We show that the scaling laws hold rather well for them under high pressure conditions. Furthermore, both the original diffusion coefficients and the reduced diffusion coefficients exhibit an Arrhenius relationship D{sub M}=D{sub M}{sup 0} exp(−E{sub M}/K{sub B}T), (M=un,R,D) and the activation energy E{sub M} increases with increasing pressure, the diffusion pre-exponential factors (D{sub R}{sup 0} and D{sub D}{sup 0}) are nearly independent of the pressure and element. Themore » pair correlation entropy, S{sub 2}, depends linearly on the reciprocal temperature S{sub 2}=−E{sub S}/T, and the activation energy, E{sub S}, increases with increasing pressure. In particular, the ratios of the activation energies (E{sub un}, E{sub R}, and E{sub D}) obtained from diffusion coefficients to the activation energy, E{sub S}, obtained from the entropy keep constants in the whole pressure range. Therefore, the entropy-scaling laws for the diffusion coefficients and the Arrhenius law are linked via the temperature dependence of entropy.« less

Dusty Pair Plasma—Wave Propagation and Diffusive Transition of Oscillations

NASA Astrophysics Data System (ADS)

Atamaniuk, Barbara; Turski, Andrzej J.

2011-11-01

The crucial point of the paper is the relation between equilibrium distributions of plasma species and the type of propagation or diffusive transition of plasma response to a disturbance. The paper contains a unified treatment of disturbance propagation (transport) in the linearized Vlasov electron-positron and fullerene pair plasmas containing charged dust impurities, based on the space-time convolution integral equations. Electron-positron-dust/ion (e-p-d/i) plasmas are rather widespread in nature. Space-time responses of multi-component linearized Vlasov plasmas on the basis of multiple integral equations are invoked. An initial-value problem for Vlasov-Poisson/Ampère equations is reduced to the one multiple integral equation and the solution is expressed in terms of forcing function and its space-time convolution with the resolvent kernel. The forcing function is responsible for the initial disturbance and the resolvent is responsible for the equilibrium velocity distributions of plasma species. By use of resolvent equations, time-reversibility, space-reflexivity and the other symmetries are revealed. The symmetries carry on physical properties of Vlasov pair plasmas, e.g., conservation laws. Properly choosing equilibrium distributions for dusty pair plasmas, we can reduce the resolvent equation to: (i) the undamped dispersive wave equations, (ii) and diffusive transport equations of oscillations.

A GENERALIZED MATHEMATICAL SCHEME TO ANALYTICALLY SOLVE THE ATMOSPHERIC DIFFUSION EQUATION WITH DRY DEPOSITION. (R825689C072)

EPA Science Inventory

Abstract

A generalized mathematical scheme is developed to simulate the turbulent dispersion of pollutants which are adsorbed or deposit to the ground. The scheme is an analytical (exact) solution of the atmospheric diffusion equation with height-dependent wind speed a...

Efficient numerical simulation of non-integer-order space-fractional reaction-diffusion equation via the Riemann-Liouville operator

NASA Astrophysics Data System (ADS)

Owolabi, Kolade M.

2018-03-01

In this work, we are concerned with the solution of non-integer space-fractional reaction-diffusion equations with the Riemann-Liouville space-fractional derivative in high dimensions. We approximate the Riemann-Liouville derivative with the Fourier transform method and advance the resulting system in time with any time-stepping solver. In the numerical experiments, we expect the travelling wave to arise from the given initial condition on the computational domain (-∞, ∞), which we terminate in the numerical experiments with a large but truncated value of L. It is necessary to choose L large enough to allow the waves to have enough space to distribute. Experimental results in high dimensions on the space-fractional reaction-diffusion models with applications to biological models (Fisher and Allen-Cahn equations) are considered. Simulation results reveal that fractional reaction-diffusion equations can give rise to a range of physical phenomena when compared to non-integer-order cases. As a result, most meaningful and practical situations are found to be modelled with the concept of fractional calculus.

An iterative phase-space explicit discontinuous Galerkin method for stellar radiative transfer in extended atmospheres

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

de Almeida, Valmor F.

In this work, a phase-space discontinuous Galerkin (PSDG) method is presented for the solution of stellar radiative transfer problems. It allows for greater adaptivity than competing methods without sacrificing generality. The method is extensively tested on a spherically symmetric, static, inverse-power-law scattering atmosphere. Results for different sizes of atmospheres and intensities of scattering agreed with asymptotic values. The exponentially decaying behavior of the radiative field in the diffusive-transparent transition region, and the forward peaking behavior at the surface of extended atmospheres were accurately captured. The integrodifferential equation of radiation transfer is solved iteratively by alternating between the radiative pressure equationmore » and the original equation with the integral term treated as an energy density source term. In each iteration, the equations are solved via an explicit, flux-conserving, discontinuous Galerkin method. Finite elements are ordered in wave fronts perpendicular to the characteristic curves so that elemental linear algebraic systems are solved quickly by sweeping the phase space element by element. Two implementations of a diffusive boundary condition at the origin are demonstrated wherein the finite discontinuity in the radiation intensity is accurately captured by the proposed method. This allows for a consistent mechanism to preserve photon luminosity. The method was proved to be robust and fast, and a case is made for the adequacy of parallel processing. In addition to classical two-dimensional plots, results of normalized radiation intensity were mapped onto a log-polar surface exhibiting all distinguishing features of the problem studied.« less