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Sample records for additional transport equations

  1. Transport equations in tokamak plasmas

    SciTech Connect

    Callen, J. D.; Hegna, C. C.; Cole, A. J.

    2010-05-15

    Tokamak plasma transport equations are usually obtained by flux surface averaging the collisional Braginskii equations. However, tokamak plasmas are not in collisional regimes. Also, ad hoc terms are added for neoclassical effects on the parallel Ohm's law, fluctuation-induced transport, heating, current-drive and flow sources and sinks, small magnetic field nonaxisymmetries, magnetic field transients, etc. A set of self-consistent second order in gyroradius fluid-moment-based transport equations for nearly axisymmetric tokamak plasmas has been developed using a kinetic-based approach. The derivation uses neoclassical-based parallel viscous force closures, and includes all the effects noted above. Plasma processes on successive time scales and constraints they impose are considered sequentially: compressional Alfven waves (Grad-Shafranov equilibrium, ion radial force balance), sound waves (pressure constant along field lines, incompressible flows within a flux surface), and collisions (electrons, parallel Ohm's law; ions, damping of poloidal flow). Radial particle fluxes are driven by the many second order in gyroradius toroidal angular torques on a plasma species: seven ambipolar collision-based ones (classical, neoclassical, etc.) and eight nonambipolar ones (fluctuation-induced, polarization flows from toroidal rotation transients, etc.). The plasma toroidal rotation equation results from setting to zero the net radial current induced by the nonambipolar fluxes. The radial particle flux consists of the collision-based intrinsically ambipolar fluxes plus the nonambipolar fluxes evaluated at the ambipolarity-enforcing toroidal plasma rotation (radial electric field). The energy transport equations do not involve an ambipolar constraint and hence are more directly obtained. The 'mean field' effects of microturbulence on the parallel Ohm's law, poloidal ion flow, particle fluxes, and toroidal momentum and energy transport are all included self-consistently. The

  2. Transport Equations In Tokamak Plasmas

    NASA Astrophysics Data System (ADS)

    Callen, J. D.

    2009-11-01

    Tokamak plasma transport equations are usually obtained by flux surface averaging the collisional Braginskii equations. However, tokamak plasmas are not in collisional regimes. Also, ad hoc terms are added for: neoclassical effects on the parallel Ohm's law (trapped particle effects on resistivity, bootstrap current); fluctuation-induced transport; heating, current-drive and flow sources and sinks; small B field non-axisymmetries; magnetic field transients etc. A set of self-consistent second order in gyroradius fluid-moment-based transport equations for nearly axisymmetric tokamak plasmas has been developed recently using a kinetic-based framework. The derivation uses neoclassical-based parallel viscous force closures, and includes all the effects noted above. Plasma processes on successive time scales (and constraints they impose) are considered sequentially: compressional Alfv'en waves (Grad-Shafranov equilibrium, ion radial force balance); sound waves (pressure constant along field lines, incompressible flows within a flux surface); and ion collisions (damping of poloidal flow). Radial particle fluxes are driven by the many second order in gyroradius toroidal angular torques on the plasma fluid: 7 ambipolar collision-based ones (classical, neoclassical, etc.) and 8 non-ambipolar ones (fluctuation-induced, polarization flows from toroidal rotation transients etc.). The plasma toroidal rotation equation [1] results from setting to zero the net radial current induced by the non-ambipolar fluxes. The radial particle flux consists of the collision-based intrinsically ambipolar fluxes plus the non-ambipolar fluxes evaluated at the ambipolarity-enforcing toroidal plasma rotation (radial electric field). The energy transport equations do not involve an ambipolar constraint and hence are more directly obtained. The resultant transport equations will be presented and contrasted with the usual ones. [4pt] [1] J.D. Callen, A.J. Cole, C.C. Hegna, ``Toroidal Rotation In

  3. The gBL transport equations

    SciTech Connect

    Mynick, H.E.

    1989-05-01

    The transport equations arising from the ''generalized Balescu- Lenard'' (gBL) collision operator are obtained, and some of their properties examined. The equations contain neoclassical and turbulent transport as two special cases, having the same structure. The resultant theory offers potential explanation for a number of results not well understood, including the anomalous pinch, observed ratios of Q/GAMMAT on TFTR, and numerical reproduction of ASDEX profiles by a model for turbulent transport invoked without derivation, but by analogy to neoclassical theory. The general equations are specialized to consideration of a number of particular transport mechanisms of interest. 10 refs.

  4. Transport equations for multicomponent anisotropic space plasmas - A review

    NASA Technical Reports Server (NTRS)

    Barakat, A. R.; Schunk, R. W.

    1982-01-01

    An attempt is made to present a unified approach to the study of transport phenomena in multicomponent anisotropic space plasmas. In particular, a system of generalized transport equations is presented that can be applied to widely different plasma flow conditions. The generalized transport equations can describe subsonic and supersonic flows, collision-dominated and collisionless flows, plasma flows in rapidly changing magnetic field configurations, multicomponent plasma flows with large temperature differences between the interacting species, and plasma flows that contain anisotropic temperature distributions. In addition, if Maxwell's equations of electricity and magnetism are added to the system of transport equations, they can be used to model electrostatic shocks, double layers, and magnetic merging processes. These transport equations also contain terms which act to regulate both the heat flow and temperature anisotropy, processes which appear to be operating in the solar wind.

  5. Solving Parker's transport equation with stochastic differential equations on GPUs

    NASA Astrophysics Data System (ADS)

    Dunzlaff, P.; Strauss, R. D.; Potgieter, M. S.

    2015-07-01

    The numerical solution of transport equations for energetic charged particles in space is generally very costly in terms of time. Besides the use of multi-core CPUs and computer clusters in order to decrease the computation times, high performance calculations on graphics processing units (GPUs) have become available during the last years. In this work we introduce and describe a GPU-accelerated implementation of Parker's equation using Stochastic Differential Equations (SDEs) for the simulation of the transport of energetic charged particles with the CUDA toolkit, which is the focus of this work. We briefly discuss the set of SDEs arising from Parker's transport equation and their application to boundary value problems such as that of the Jovian magnetosphere. We compare the runtimes of the GPU code with a CPU version of the same algorithm. Compared to the CPU implementation (using OpenMP and eight threads) we find a performance increase of about a factor of 10-60, depending on the assumed set of parameters. Furthermore, we benchmark our simulation using the results of an existing SDE implementation of Parker's transport equation.

  6. Mechanistic equations for membrane transport of multicomponent solutions.

    PubMed

    Suchanek, G

    2006-03-01

    In the present article, mechanistic equations for membrane transport of N + 1-component solutions have been derived. The major specific investigation result is the introduction - for ternary solutions - of two diffusion coefficients omega(d1) and omega(d2) for solutes, as well as two cross coefficients omega(d12) and omega(d21) for these solutes. The latter parameters may be treated as coefficients of interdiffusion. The expansion of the description of substance transport to include the N + 1-component solutions does not formulate any additional physical phenomena other than those which are formulated by the transport equations for three-component solutions.

  7. Numerical solution of the electron transport equation

    NASA Astrophysics Data System (ADS)

    Woods, Mark

    The electron transport equation has been solved many times for a variety of reasons. The main difficulty in its numerical solution is that it is a very stiff boundary value problem. The most common numerical methods for solving boundary value problems are symmetric collocation methods and shooting methods. Both of these types of methods can only be applied to the electron transport equation if the boundary conditions are altered with unrealistic assumptions because they require too many points to be practical. Further, they result in oscillating and negative solutions, which are physically meaningless for the problem at hand. For these reasons, all numerical methods for this problem to date are a bit unusual because they were designed to try and avoid the problem of extreme stiffness. This dissertation shows that there is no need to introduce spurious boundary conditions or invent other numerical methods for the electron transport equation. Rather, there already exists methods for very stiff boundary value problems within the numerical analysis literature. We demonstrate one such method in which the fast and slow modes of the boundary value problem are essentially decoupled. This allows for an upwind finite difference method to be applied to each mode as is appropriate. This greatly reduces the number of points needed in the mesh, and we demonstrate how this eliminates the need to define new boundary conditions. This method is verified by showing that under certain restrictive assumptions, the electron transport equation has an exact solution that can be written as an integral. We show that the solution from the upwind method agrees with the quadrature evaluation of the exact solution. This serves to verify that the upwind method is properly solving the electron transport equation. Further, it is demonstrated that the output of the upwind method can be used to compute auroral light emissions.

  8. Pdf - Transport equations for chemically reacting flows

    NASA Technical Reports Server (NTRS)

    Kollmann, W.

    1989-01-01

    The closure problem for the transport equations for pdf and the characteristic functions of turbulent, chemically reacting flows is addressed. The properties of the linear and closed equations for the characteristic functional for Eulerian and Lagrangian variables are established, and the closure problem for the finite-dimensional case is discussed for pdf and characteristic functions. It is shown that the closure for the scalar dissipation term in the pdf equation developed by Dopazo (1979) and Kollmann et al. (1982) results in a single integral, in contrast to the pdf, where double integration is required. Some recent results using pdf methods obtained for turbulent flows with combustion, including effects of chemical nonequilibrium, are discussed.

  9. Maximal stochastic transport in the Lorenz equations

    NASA Astrophysics Data System (ADS)

    Agarwal, Sahil; Wettlaufer, John

    2015-11-01

    We calculate the stochastic upper bounds for the Lorenz equations using an extension of the background method. In analogy with Rayleigh-Benard convection the upper bounds are for heat transport versus Rayleigh number. As might be expected the stochastic upper bounds are larger than the deterministic counterpart of Souza and Doering (2015), but their variation with noise amplitude exhibits surprising behavior. Below the transition to chaotic dynamics the upper bounds increase monotonically with noise amplitude. However, in the chaotic regime this monotonicity is lost; at a particular Rayleigh number the bound may increase or decrease with noise amplitude. The origin of this behavior is the coupling between the noise and unstable periodic orbits. This is confirmed by examining the close returns plots of the full solutions to the stochastic equations. Finally, we note that these solutions demonstrate that the effect of noise is equivalent to the effect of chaos.

  10. A transport equation for eddy viscosity

    NASA Technical Reports Server (NTRS)

    Durbin, P. A.; Yang, Z.

    1992-01-01

    A transport equation for eddy viscosity is proposed for wall bounded turbulent flows. The proposed model reduces to a quasi-homogeneous form far from surfaces. Near to a surface, the nonhomogeneous effect of the wall is modeled by an elliptic relaxation model. All the model terms are expressed in local variables and are coordinate independent; the model is intended to be used in complex flows. Turbulent channel flow and turbulent boundary layer flows with/without pressure gradient are calculated using the present model. Comparisons between model calculations and direct numerical simulation or experimental data show good agreement.

  11. Maximal stochastic transport in the Lorenz equations

    NASA Astrophysics Data System (ADS)

    Agarwal, Sahil; Wettlaufer, J. S.

    2016-01-01

    We calculate the stochastic upper bounds for the Lorenz equations using an extension of the background method. In analogy with Rayleigh-Bénard convection the upper bounds are for heat transport versus Rayleigh number. As might be expected, the stochastic upper bounds are larger than the deterministic counterpart of Souza and Doering [1], but their variation with noise amplitude exhibits interesting behavior. Below the transition to chaotic dynamics the upper bounds increase monotonically with noise amplitude. However, in the chaotic regime this monotonicity depends on the number of realizations in the ensemble; at a particular Rayleigh number the bound may increase or decrease with noise amplitude. The origin of this behavior is the coupling between the noise and unstable periodic orbits, the degree of which depends on the degree to which the ensemble represents the ergodic set. This is confirmed by examining the close returns plots of the full solutions to the stochastic equations and the numerical convergence of the noise correlations. The numerical convergence of both the ensemble and time averages of the noise correlations is sufficiently slow that it is the limiting aspect of the realization of these bounds. Finally, we note that the full solutions of the stochastic equations demonstrate that the effect of noise is equivalent to the effect of chaos.

  12. Stable Difference Schemes for the Neutron Transport Equation

    NASA Astrophysics Data System (ADS)

    Ashyralyev, Allaberen; Taskin, Abdulgafur

    2011-09-01

    The initial boundary value problem for the neutron transport equation is considered. The first and second orders of accuracy difference schemes for the approximate solution of this problem are presented. In applications, the stability estimates for solutions of difference schemes for the approximate solution of the neutron transport equation are obtained. Numerical techniques are developed and algorithms are tested on an example in MATLAB.

  13. Neutron-transport equation in a general curvelinear coordinate system

    SciTech Connect

    Takahashi, H

    1981-01-01

    Different from a fission reactor, a fusion reactor has complex geometry, such as toroidal geometry. Neutron transport equation for the toroidal coordinate system has been derived by using coordinate transformation from the cartesian coordinate. These methods require rather tedious calculations. Presented here is a simple method to formulate the neutron transport equation in the general curvelinear coordinate system. The equations for parabolic cylinder and toroidal coordinate systems are derived as an example.

  14. A Least-Squares Transport Equation Compatible with Voids

    SciTech Connect

    Hansen, Jon; Peterson, Jacob; Morel, Jim; Ragusa, Jean; Wang, Yaqi

    2014-12-01

    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 transport 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 Sn formulation represents an excellent alternative to existing second-order Sn transport formulations

  15. An integral equation arising in two group neutron transport theory

    NASA Astrophysics Data System (ADS)

    Cassell, J. S.; Williams, M. M. R.

    2003-07-01

    An integral equation describing the fuel distribution necessary to maintain a flat flux in a nuclear reactor in two group transport theory is reduced to the solution of a singular integral equation. The formalism developed enables the physical aspects of the problem to be better understood and its relationship with the corresponding diffusion theory model is highlighted. The integral equation is solved by reducing it to a non-singular Fredholm equation which is then evaluated numerically.

  16. Transport equations for partially ionized reactive plasma in magnetic field

    NASA Astrophysics Data System (ADS)

    Zhdanov, V. M.; Stepanenko, A. A.

    2016-06-01

    Transport equations for partially ionized reactive plasma in magnetic field taking into account the internal degrees of freedom and electronic excitation of plasma particles are derived. As a starting point of analysis the kinetic equation with a binary collision operator written in the Wang-Chang and Uhlenbeck form and with a reactive collision integral allowing for arbitrary chemical reactions is used. The linearized variant of Grad's moment method is applied to deduce the systems of moment equations for plasma and also full and reduced transport equations for plasma species nonequilibrium parameters.

  17. Packaging and Transportation of Additional Neptunium Oxide

    SciTech Connect

    Watkins, R.; Jordan, J.; Hensel, S.

    2010-05-05

    The Savannah River Site's HB-Line Facility completed a second neptunium oxide production campaign in which nine (9) additional cans of neptunium oxide were produced and shipped to the Idaho National Laboratory and Oak Ridge National Laboratory in the 9975 shipping container. These additional cans were from a different feed solution than the first fifty (50) cans of neptunium oxide that were previously produced and shipped via a Letter of Amendment to the 9975 Safety Analysis Report for Packaging (SARP) content table. This paper will address the challenges associated with demonstrating the neptunium oxide produced from the additional feed solution was equivalent to the original neptunium oxide and within the content description of the Letter of Amendment.

  18. ANALYSIS OF A NUMERICAL SOLVER FOR RADIATIVE TRANSPORT EQUATION.

    PubMed

    Gao, Hao; Zhao, Hongkai

    2013-01-01

    We analyze a numerical algorithm for solving radiative transport equation with vacuum or reflection boundary condition that was proposed in [4] with angular discretization by finite element method and spatial discretization by discontinuous Galerkin or finite difference method.

  19. Strongly asymmetric discrete Painlevé equations: The additive case

    NASA Astrophysics Data System (ADS)

    Grammaticos, B.; Ramani, A.; Tamizhmani, K. M.; Tamizhmani, T.; Satsuma, J.

    2014-05-01

    We examine a class of discrete Painlevé equations which present a strong asymmetry. These equations can be written as a system of two equations, the right-hand-sides of which do not have the same functional form. We limit here our investigation to two canonical families of the Quispel-Roberts-Thompson (QRT) classification both of which lead to difference equations. Several new integrable discrete systems are identified.

  20. Asphalt and asphalt additives. Transportation research record

    SciTech Connect

    Not Available

    1992-01-01

    Contents: use of asphalt emulsions for in-place recycling: oregon experience; gap-graded cold asphalt concrete: benefits of polymer-modified asphalt cement and fibers; cold in-place recycling for rehabilitation and widening of low-volume flexible pavements in indiana; in situ cold recycling of bituminous pavements with polymer-modified high float emulsions; evaluation of new generation of antistripping additives; correlation between performance-related characteristics of asphalt cement and its physicochemical parameters using corbett's fractions and hpgc; reaction rates and hardening susceptibilities as determined from pressure oxygen vessel aging of asphalts; evaluation of aging characteristics of asphalts by using tfot and rtfot at different temperature levels; summary of asphalt additive performance at selected sites; relating asphalt absorption to properties of asphalt cement and aggregate; study of the effectiveness of styrene-butadiene rubber latex in hot mix asphalt mixes; stability of straight and polymer-modified asphalts.

  1. A new least-squares transport equation compatible with voids

    SciTech Connect

    Hansen, J. B.; Morel, J. E.

    2013-07-01

    We define a new least-squares transport equation that is applicable in voids, can be solved using source iteration with diffusion-synthetic acceleration, and requires only the solution of an independent set of second-order self-adjoint equations for each direction during each source iteration. We derive the equation, discretize it using the S{sub n} method in conjunction with a linear-continuous finite-element method in space, and computationally demonstrate various of its properties. (authors)

  2. Kinetic theory of transport processes in partially ionized reactive plasma, I: General transport equations

    NASA Astrophysics Data System (ADS)

    Zhdanov, V. M.; Stepanenko, A. A.

    2016-03-01

    In this paper we derive the set of general transport equations for multicomponent partially ionized reactive plasma in the presence of electric and magnetic fields taking into account the internal degrees of freedom and electronic excitation of plasma particles. Our starting point is a generalized Boltzmann equation with the collision integral in the Wang-Chang and Uhlenbeck form and a reactive collision integral. We obtain a set of conservation equations for such plasma and employ a linearized variant of Grad's moment method to derive the system of moment (or transport) equations for the plasma species nonequilibrium parameters. Full and reduced transport equations, resulting from the linearized system of moment equations, are presented, which can be used to obtain transport relations and expressions for transport coefficients of electrons and heavy plasma particles (molecules, atoms and ions) in partially ionized reactive plasma.

  3. Macroscopic heat transport equations and heat waves in nonequilibrium states

    NASA Astrophysics Data System (ADS)

    Guo, Yangyu; Jou, David; Wang, Moran

    2017-03-01

    Heat transport may behave as wave propagation when the time scale of processes decreases to be comparable to or smaller than the relaxation time of heat carriers. In this work, a generalized heat transport equation including nonlinear, nonlocal and relaxation terms is proposed, which sums up the Cattaneo-Vernotte, dual-phase-lag and phonon hydrodynamic models as special cases. In the frame of this equation, the heat wave propagations are investigated systematically in nonequilibrium steady states, which were usually studied around equilibrium states. The phase (or front) speed of heat waves is obtained through a perturbation solution to the heat differential equation, and found to be intimately related to the nonlinear and nonlocal terms. Thus, potential heat wave experiments in nonequilibrium states are devised to measure the coefficients in the generalized equation, which may throw light on understanding the physical mechanisms and macroscopic modeling of nanoscale heat transport.

  4. Central role of the observable electric potential in transport equations.

    PubMed

    Garrido, J; Compañ, V; López, M L

    2001-07-01

    Nonequilibrium systems are usually studied in the framework of transport equations that involve the true electric potential (TEP), a nonobservable variable. Nevertheless another electric potential, the observable electric potential (OEP), may be defined to construct a useful set of transport equations. In this paper several basic characteristics of the OEP are deduced and emphasized: (i) the OEP distribution depends on thermodynamic state of the solution, (ii) the observable equations have a reference value for all other transport equations, (iii) the bridge that connects the OEP with a certain TEP is usually defined by the ion activity coefficient, (iv) the electric charge density is a nonobservable variable, and (v) the OEP formulation constitutes a natural model for studying the fluxes in membrane systems.

  5. Transport equations for the inflationary trispectrum

    SciTech Connect

    Anderson, Gemma J.; Seery, David; Mulryne, David J. E-mail: D.Mulryne@qmul.ac.uk

    2012-10-01

    We use transport techniques to calculate the trispectrum produced in multiple-field inflationary models with canonical kinetic terms. Our method allows the time evolution of the local trispectrum parameters, τ{sub NL} and g{sub NL}, to be tracked throughout the inflationary phase. We illustrate our approach using examples. We give a simplified method to calculate the superhorizon part of the relation between field fluctuations on spatially flat hypersurfaces and the curvature perturbation on uniform density slices, ζ, and obtain its third-order part for the first time. We clarify how the 'backwards' formalism of Yokoyama et al. relates to our analysis and other recent work. We supply explicit formulae which enable each inflationary observable to be computed in any canonical model of interest, using a suitable first-order ODE solver.

  6. Optical Testing Using the Transport-of-Intensity Equation

    SciTech Connect

    Dorrer, C; Zuegel, J.D.

    2008-03-12

    The transport-of-intensity equation links the intensity and phase of an optical source to the longitudinal variation of its intensity in the presence of Fresnel diffraction. This equation can be used to provide a simple, accurate spatial-phase measurement for optical testing of flat surfaces. The properties of this approach are derived. The experimental demonstration is performed by quantifying the surface variations induced by the magnetorheological finishing process on laser rods.

  7. A rain splash transport equation assimilating field and laboratory measurements

    USGS Publications Warehouse

    Dunne, T.; Malmon, D.V.; Mudd, S.M.

    2010-01-01

    Process-based models of hillslope evolution require transport equations relating sediment flux to its major controls. An equation for rain splash transport in the absence of overland flow was constructed by modifying an approach developed by Reeve (1982) and parameterizing it with measurements from single-drop laboratory experiments and simulated rainfall on a grassland in East Africa. The equation relates rain splash to hillslope gradient, the median raindrop diameter of a storm, and ground cover density; the effect of soil texture on detachability can be incorporated from other published results. The spatial and temporal applicability of such an equation for rain splash transport in the absence of overland flow on uncultivated hillslopes can be estimated from hydrological calculations. The predicted transport is lower than landscape-averaged geologic erosion rates from Kenya but is large enough to modify short, slowly eroding natural hillslopes as well as microtopographic interrill surfaces between which overland flow transports the mobilized sediment. Copyright 2010 by the American Geophysical Union. Copyright 2010 by the American Geophysical Union.

  8. Least-squares finite element discretizations of neutron transport equations in 3 dimensions

    SciTech Connect

    Manteuffel, T.A; Ressel, K.J.; Starkes, G.

    1996-12-31

    The least-squares finite element framework to the neutron transport equation introduced in is based on the minimization of a least-squares functional applied to the properly scaled neutron transport equation. Here we report on some practical aspects of this approach for neutron transport calculations in three space dimensions. The systems of partial differential equations resulting from a P{sub 1} and P{sub 2} approximation of the angular dependence are derived. In the diffusive limit, the system is essentially a Poisson equation for zeroth moment and has a divergence structure for the set of moments of order 1. One of the key features of the least-squares approach is that it produces a posteriori error bounds. We report on the numerical results obtained for the minimum of the least-squares functional augmented by an additional boundary term using trilinear finite elements on a uniform tesselation into cubes.

  9. A massively parallel semi-Lagrangian algorithm for solving the transport equation

    SciTech Connect

    Manson, Russell; Wang, Dali

    2010-01-01

    The scalar transport equation underpins many models employed in science, engineering, technology and business. Application areas include, but are not restricted to, pollution transport, weather forecasting, video analysis and encoding (the optical flow equation), options and stock pricing (the Black-Scholes equation) and spatially explicit ecological models. Unfortunately finding numerical solutions to this equation which are fast and accurate is not trivial. Moreover, finding such numerical algorithms that can be implemented on high performance computer architectures efficiently is challenging. In this paper the authors describe a massively parallel algorithm for solving the advection portion of the transport equation. We present an approach here which is different to that used in most transport models and which we have tried and tested for various scenarios. The approach employs an intelligent domain decomposition based on the vector field of the system equations and thus automatically partitions the computational domain into algorithmically autonomous regions. The solution of a classic pure advection transport problem is shown to be conservative, monotonic and highly accurate at large time steps. Additionally we demonstrate that the algorithm is highly efficient for high performance computer architectures and thus offers a route towards massively parallel application.

  10. Analysis of Transition-Sensitized Turbulent Transport Equations

    NASA Technical Reports Server (NTRS)

    Rumsey, Christopher L.; Thacker, William D.; Gatski, Thomas B.; Grosch, Chester E,

    2005-01-01

    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 cross the boundary layer by the solid boundary. The dominating dynamics in the disturbance kinetic energy and dissipation rate equations are described. These results are then used to formulate transition-sensitized turbulent transport equations, which are solved in a two-step process and applied to zero-pressure-gradient flow over a flat plate. Computed results are in good agreement with experimental data.

  11. Dissipative quantum transport in silicon nanowires based on Wigner transport equation

    NASA Astrophysics Data System (ADS)

    Barraud, Sylvain

    2011-11-01

    In this work, we present a one-dimensional model of quantum electron transport for silicon nanowire transistor that makes use of the Wigner function formalism and that takes into account the carrier scattering. Effect of scattering on the current-voltage (I-V) characteristics is assessed using both the relaxation time approximation and the Boltzmann collision operator. Similarly to the classical transport theory, the scattering mechanisms are included in the Wigner formulation through the addition of a collision term in the Liouville equation. As compared to the relaxation time, the Boltzmann collision operator approach is considered to be more realistic because it provides a better description of the scattering events. Within the Fermi golden rule approximation, the standard collision term is described for both acoustic phonon and surface-roughness interactions. It is introduced in the discretized version of the Liouville equation to obtain the Wigner distribution function and the current density. The model is then applied to study the impact of each scattering mechanism on short-channel electrical performance of silicon nanowire transistors for different gate lengths and nanowire widths.

  12. Analysis of discrete reaction-diffusion equations for autocatalysis and continuum diffusion equations for transport

    SciTech Connect

    Wang, Chi-Jen

    2013-01-01

    In this thesis, we analyze both the spatiotemporal behavior of: (A) non-linear “reaction” models utilizing (discrete) reaction-diffusion equations; and (B) spatial transport problems on surfaces and in nanopores utilizing the relevant (continuum) diffusion or Fokker-Planck equations. Thus, there are some common themes in these studies, as they all involve partial differential equations or their discrete analogues which incorporate a description of diffusion-type processes. However, there are also some qualitative differences, as shall be discussed below.

  13. A bedload transport equation for the Cerastoderma edule cockle

    NASA Astrophysics Data System (ADS)

    Anta, Jose; Peña, Enrique; Puertas, Jerónimo; Cea, Luis

    2013-02-01

    Hydrodynamics play an important role in the structure of many marine ecosystems of bivalves. After severe storm periods, large amounts of the Cerastoderma edule stocks were transported from the Lombos do Ulla shellfish bed (Spain). This paper presents the results of laboratory experiments carried out to analyze the bedload transport of this bivalve emulating the stormy shellfish bed conditions. Flow velocities were measured using particle image velocimetry and the double averaged methodology was applied to determine the main flow characteristics over different cockle patches. The flow structure exhibits properties of skimming and isolated flows depending on the density of bivalves. Bed shear stress was determined from the log-law and the cockles were geometrically characterized in order to derive specific bedload transport equations in a conventional deterministic sediment transport framework. The obtained formulas can be implemented in common numerical codes to further analyze mollusk stability, bedload transport and dispersal in their aquatic systems.

  14. Numerical Study of Fractional Ensemble Average Transport Equations

    NASA Astrophysics Data System (ADS)

    Kim, S.; Park, Y.; Gyeong, C. B.; Lee, O.

    2014-12-01

    In this presentation, a newly developed theory is applied to the case of stationary and non-stationary stochastic advective flow field, and a numerical solution method is presented for the resulting fractional Fokker-Planck equation (fFPE), which describes the evolution of the probability density function (PDF) of contaminant concentration. The derived fFPE is evaluated for three different form: 1) purely advective form, 2) second-order moment form and 3) second-order cumulant form. The Monte Carlo analysis of the fractional governing equation is then performed in a stochastic flow field, generated by a fractional Brownian motion for the stationary and non-stationary stochastic advection, in order to provide a benchmark for the results obtained from the fFPEs. When compared to the Monte Carlo simulation based PDFs and their ensemble average, the second-order cumulant form gives a good fit in terms of the shape and mode of the PDF of the contaminant concentration. Therefore, it is quite promising that the non-Fickian transport behavior can be modeled by the derived fractional ensemble average transport equations either by means of the long memory in the underlying stochastic flow, or by means of the time-space non-stationarity of the underlying stochastic flow, or by means of the time and space fractional derivatives of the transport equations. This subject is supported by Korea Ministry of Environment as "The Eco Innovation Project : Non-point source pollution control research group"

  15. Moment transport equations for the primordial curvature perturbation

    SciTech Connect

    Mulryne, David J.; Seery, David; Wesley, Daniel E-mail: d.seery@sussex.ac.uk

    2011-04-01

    In a recent publication, we proposed that inflationary perturbation theory can be reformulated in terms of a probability transport equation, whose moments determine the correlation properties of the primordial curvature perturbation. In this paper we generalize this formulation to an arbitrary number of fields. We deduce ordinary differential equations for the evolution of the moments of ζ on superhorizon scales, which can be used to obtain an evolution equation for the dimensionless bispectrum, f{sub NL}. Our equations are covariant in field space and allow identification of the source terms responsible for evolution of f{sub NL}. In a model with M scalar fields, the number of numerical integrations required to obtain solutions of these equations scales like O(M{sup 3}). The performance of the moment transport algorithm means that numerical calculations with M >> 1 fields are straightforward. We illustrate this performance with a numerical calculation of f{sub NL} in Nflation models containing M ∼ 10{sup 2} fields, finding agreement with existing analytic calculations. We comment briefly on extensions of the method beyond the slow-roll approximation, or to calculate higher order parameters such as g{sub NL}.

  16. Validation of transport models using additive flux minimization technique

    NASA Astrophysics Data System (ADS)

    Pankin, A. Y.; Kruger, S. E.; Groebner, R. J.; Hakim, A.; Kritz, A. H.; Rafiq, T.

    2013-10-01

    A new additive flux minimization technique is proposed for carrying out the verification and validation (V&V) of anomalous transport models. In this approach, the plasma profiles are computed in time dependent predictive simulations in which an additional effective diffusivity is varied. The goal is to obtain an optimal match between the computed and experimental profile. This new technique has several advantages over traditional V&V methods for transport models in tokamaks and takes advantage of uncertainty quantification methods developed by the applied math community. As a demonstration of its efficiency, the technique is applied to the hypothesis that the paleoclassical density transport dominates in the plasma edge region in DIII-D tokamak discharges. A simplified version of the paleoclassical model that utilizes the Spitzer resistivity for the parallel neoclassical resistivity and neglects the trapped particle effects is tested in this paper. It is shown that a contribution to density transport, in addition to the paleoclassical density transport, is needed in order to describe the experimental profiles. It is found that more additional diffusivity is needed at the top of the H-mode pedestal, and almost no additional diffusivity is needed at the pedestal bottom. The implementation of this V&V technique uses the FACETS::Core transport solver and the DAKOTA toolkit for design optimization and uncertainty quantification. The FACETS::Core solver is used for advancing the plasma density profiles. The DAKOTA toolkit is used for the optimization of plasma profiles and the computation of the additional diffusivity that is required for the predicted density profile to match the experimental profile.

  17. The Lorentz gas in Kaluza's MHD: Transport equations

    NASA Astrophysics Data System (ADS)

    Sandoval-Villalbazo, Alfredo; Sagaceta-Mejia, Alma Rocio; Mondragon-Suarez, Jose Humberto

    2016-11-01

    Relativistic kinetic theory is applied to the study of the transport processes present in a Lorentz gas, using a geometric five-dimensional space-time. While the conventional transport equations are recovered in the Newtonian limit, it is shown that relativistic corrections to the conduction and diffusion fluxes arise within this formalism. A brief review of the conceptual advantages of the Kaluza-type approach to magnetohydrodynamics is also given. The authors acknowledge support from CONACyT through Grant CB2011/167563.

  18. Transport equations for subdiffusion with nonlinear particle interaction.

    PubMed

    Straka, P; Fedotov, S

    2015-02-07

    We show how the nonlinear interaction effects 'volume filling' and 'adhesion' can be incorporated into the fractional subdiffusive transport of cells and individual organisms. To this end, we use microscopic random walk models with anomalous trapping and systematically derive generic non-Markovian and nonlinear governing equations for the mean concentrations of the subdiffusive cells or organisms. We uncover an interesting interaction between the nonlinearities and the non-Markovian nature of the transport. In the subdiffusive case, this interaction manifests itself in a nontrivial combination of nonlinear terms with fractional derivatives. In the long time limit, however, these equations simplify to a form without fractional operators. This provides an easy method for the study of aggregation phenomena. In particular, this enables us to show that volume filling can prevent "anomalous aggregation," which occurs in subdiffusive systems with a spatially varying anomalous exponent.

  19. Random attractors for the stochastic coupled fractional Ginzburg-Landau equation with additive noise

    SciTech Connect

    Shu, Ji E-mail: 530282863@qq.com; Li, Ping E-mail: 530282863@qq.com; Zhang, Jia; Liao, Ou

    2015-10-15

    This paper is concerned with the stochastic coupled fractional Ginzburg-Landau equation with additive noise. We first transform the stochastic coupled fractional Ginzburg-Landau equation into random equations whose solutions generate a random dynamical system. Then we prove the existence of random attractor for random dynamical system.

  20. Transport of gyration-dominated space plasmas of thermal origin. I - Generalized transport equations

    NASA Technical Reports Server (NTRS)

    Gombosi, Tamas I.; Rasmussen, Craig E.

    1991-01-01

    Grad's 20-moment set of transport equations has been examined in the limit of strong external magnetic fields. This simplified set of equations describes the transport of mass and parallel momentum as well as the transport of parallel and perpendicular energy and heat flow in the magnetic field direction. The effect of collisions was calculated assuming a modified relaxation model. Wave speeds and normal modes of the simplified set of equations were examined for an ion and electron gas. It was found that four of the ten normal modes are electron thermal-heat waves which approximately decouple from the six ion waves in the system. When low-frequency waves are considered (slow-wave approximation), this allows the electron energy and heat flow equations to be solved separately from the ion equations and in a time-independent fashion. When this was done, it was found that, under certain conditions, these equations predict an infinite electron perpendicular temperature, Te-perpendicular, in the collisionless regime. This occurs whenever Te-perpendicular is greater than the parallel temperature, at any point along collisionless and diverging magnetic field lines. When applied appropriately, the significantly simplified set of equations derived here are well suited for application to a large variety of problems in planetary ionospheres and magnetospheres.

  1. Error transport equation boundary conditions for the Euler and Navier-Stokes equations

    NASA Astrophysics Data System (ADS)

    Phillips, Tyrone S.; Derlaga, Joseph M.; Roy, Christopher J.; Borggaard, Jeff

    2017-02-01

    Discretization error is usually the largest and most difficult numerical error source to estimate for computational fluid dynamics, and boundary conditions often contribute a significant source of error. Boundary conditions are described with a governing equation to prescribe particular behavior at the boundary of a computational domain. Boundary condition implementations are considered sufficient when discretized with the same order of accuracy as the primary governing equations; however, careless implementations of boundary conditions can result in significantly larger numerical error. Investigations into different numerical implementations of Dirichlet and Neumann boundary conditions for Burgers' equation show a significant impact on the accuracy of Richardson extrapolation and error transport equation discretization error estimates. The development of boundary conditions for Burgers' equation shows significant improvements in discretization error estimates in general and a significant improvement in truncation error estimation. The latter of which is key to accurate residual-based discretization error estimation. This research investigates scheme consistent and scheme inconsistent implementations of inflow and outflow boundary conditions up to fourth order accurate and a formulation for a slip wall boundary condition for truncation error estimation are developed for the Navier-Stokes and Euler equations. The scheme consistent implementation resulted in much smoother truncation error near the boundaries and more accurate discretization error estimates.

  2. Renormalization group methods for the Reynolds stress transport equations

    NASA Technical Reports Server (NTRS)

    Rubinstein, R.

    1992-01-01

    The Yakhot-Orszag renormalization group is used to analyze the pressure gradient-velocity correlation and return to isotropy terms in the Reynolds stress transport equations. The perturbation series for the relevant correlations, evaluated to lowest order in the epsilon-expansion of the Yakhot-Orszag theory, are infinite series in tensor product powers of the mean velocity gradient and its transpose. Formal lowest order Pade approximations to the sums of these series produce a rapid pressure strain model of the form proposed by Launder, Reece, and Rodi, and a return to isotropy model of the form proposed by Rotta. In both cases, the model constants are computed theoretically. The predicted Reynolds stress ratios in simple shear flows are evaluated and compared with experimental data. The possibility is discussed of deriving higher order nonlinear models by approximating the sums more accurately. The Yakhot-Orszag renormalization group provides a systematic procedure for deriving turbulence models. Typical applications have included theoretical derivation of the universal constants of isotropic turbulence theory, such as the Kolmogorov constant, and derivation of two equation models, again with theoretically computed constants and low Reynolds number forms of the equations. Recent work has applied this formalism to Reynolds stress modeling, previously in the form of a nonlinear eddy viscosity representation of the Reynolds stresses, which can be used to model the simplest normal stress effects. The present work attempts to apply the Yakhot-Orszag formalism to Reynolds stress transport modeling.

  3. Benchmark solutions for the galactic ion transport equations: Energy and spatially dependent problems

    NASA Technical Reports Server (NTRS)

    Ganapol, Barry D.; Townsend, Lawrence W.; Wilson, John W.

    1989-01-01

    Nontrivial benchmark solutions are developed for the galactic ion transport (GIT) equations in the straight-ahead approximation. These equations are used to predict potential radiation hazards in the upper atmosphere and in space. Two levels of difficulty are considered: (1) energy independent, and (2) spatially independent. The analysis emphasizes analytical methods never before applied to the GIT equations. Most of the representations derived have been numerically implemented and compared to more approximate calculations. Accurate ion fluxes are obtained (3 to 5 digits) for nontrivial sources. For monoenergetic beams, both accurate doses and fluxes are found. The benchmarks presented are useful in assessing the accuracy of transport algorithms designed to accommodate more complex radiation protection problems. In addition, these solutions can provide fast and accurate assessments of relatively simple shield configurations.

  4. Number-resolved master equation approach to quantum measurement and quantum transport

    NASA Astrophysics Data System (ADS)

    Li, Xin-Qi

    2016-08-01

    In addition to the well-known Landauer-Büttiker scattering theory and the nonequilibrium Green's function technique for mesoscopic transports, an alternative (and very useful) scheme is quantum master equation approach. In this article, we review the particle-number ( n)-resolved master equation ( n-ME) approach and its systematic applications in quantum measurement and quantum transport problems. The n-ME contains rich dynamical information, allowing efficient study of topics such as shot noise and full counting statistics analysis. Moreover, we also review a newly developed master equation approach (and its n-resolved version) under self-consistent Born approximation. The application potential of this new approach is critically examined via its ability to recover the exact results for noninteracting systems under arbitrary voltage and in presence of strong quantum interference, and the challenging non-equilibrium Kondo effect.

  5. Vorticity Preserving Flux Corrected Transport Scheme for the Acoustic Equations

    SciTech Connect

    Lung, Tyler B.; Roe, Phil; Morgan, Nathaniel R.

    2012-08-15

    Long term research goals are to develop an improved cell-centered Lagrangian Hydro algorithm with the following qualities: 1. Utilizes Flux Corrected Transport (FCT) to achieve second order accuracy with multidimensional physics; 2. Does not rely on the one-dimensional Riemann problem; and 3. Implements a form of vorticity control. Short term research goals are to devise and implement a 2D vorticity preserving FCT solver for the acoustic equations on an Eulerian mesh: 1. Develop a flux limiting mechanism for systems of governing equations with symmetric wave speeds; 2. Verify the vorticity preserving properties of the scheme; and 3. Compare the performance of the scheme to traditional MUSCL-Hancock and other algorithms.

  6. Quantum-mechanical transport equation for atomic systems.

    NASA Technical Reports Server (NTRS)

    Berman, P. R.

    1972-01-01

    A quantum-mechanical transport equation (QMTE) is derived which should be applicable to a wide range of problems involving the interaction of radiation with atoms or molecules which are also subject to collisions with perturber atoms. The equation follows the time evolution of the macroscopic atomic density matrix elements of atoms located at classical position R and moving with classical velocity v. It is quantum mechanical in the sense that all collision kernels or rates which appear have been obtained from a quantum-mechanical theory and, as such, properly take into account the energy-level variations and velocity changes of the active (emitting or absorbing) atom produced in collisions with perturber atoms. The present formulation is better suited to problems involving high-intensity external fields, such as those encountered in laser physics.

  7. Effect of viscoelastic relaxation on moisture transport in foods. Part I: solution of general transport equation.

    PubMed

    Singh, Pawan P; Maier, Dirk E; Cushman, John H; Haghighi, Kamyar; Corvalan, Carlos

    2004-07-01

    Within the framework of continuum mechanics, Singh et al. developed an integro-differential equation, which applies to both Darcian (Fickian) and non-Darcian (non-Fickian) modes of fluid transport in swelling biological systems. A dimensionless form of the equation was obtained and transformed from moving Eulerian to the stationary Lagrangian coordinates. Here a solution scheme for the transport equation is developed to predict moisture transport and viscoelastic stresses in spheroidal biopolymeric materials. The equation was solved numerically and results used for predicting drying and sorption curves, moisture profiles, and viscoelastic stresses in soybeans. The Lagrangian solution was obtained by assembling together several schemes: the finite element method was used to discretize the equation in space; non-linearity was addressed using the Newton-Raphson method; the Volterra term was handled via a time integration scheme of Patlashenko et al. and the Galerkin rule was used to solve the time-differential term. The solution obtained in Lagrangian coordinates was transformed back to the Eulerian coordinates. In part II of this sequence we present the numerical results.

  8. A New 2D-Transport, 1D-Diffusion Approximation of the Boltzmann Transport equation

    SciTech Connect

    Larsen, Edward

    2013-06-17

    The work performed in this project consisted of the derivation, implementation, and testing of a new, computationally advantageous approximation to the 3D Boltz- mann transport equation. The solution of the Boltzmann equation is the neutron flux in nuclear reactor cores and shields, but solving this equation is difficult and costly. The new “2D/1D” approximation takes advantage of a special geometric feature of typical 3D reactors to approximate the neutron transport physics in a specific (ax- ial) direction, but not in the other two (radial) directions. The resulting equation is much less expensive to solve computationally, and its solutions are expected to be sufficiently accurate for many practical problems. In this project we formulated the new equation, discretized it using standard methods, developed a stable itera- tion scheme for solving the equation, implemented the new numerical scheme in the MPACT code, and tested the method on several realistic problems. All the hoped- for features of this new approximation were seen. For large, difficult problems, the resulting 2D/1D solution is highly accurate, and is calculated about 100 times faster than a 3D discrete ordinates simulation.

  9. An efficient numerical solution of the transient storage equations for solute transport in small streams

    USGS Publications Warehouse

    Runkel, Robert L.; Chapra, Steven C.

    1993-01-01

    Several investigators have proposed solute transport models that incorporate the effects of transient storage. Transient storage occurs in small streams when portions of the transported solute become isolated in zones of water that are immobile relative to water in the main channel (e.g., pools, gravel beds). Transient storage is modeled by adding a storage term to the advection-dispersion equation describing conservation of mass for the main channel. In addition, a separate mass balance equation is written for the storage zone. Although numerous applications of the transient storage equations may be found in the literature, little attention has been paid to the numerical aspects of the approach. Of particular interest is the coupled nature of the equations describing mass conservation for the main channel and the storage zone. In the work described herein, an implicit finite difference technique is developed that allows for a decoupling of the governing differential equations. This decoupling method may be applied to other sets of coupled equations such as those describing sediment-water interactions for toxic contaminants. For the case at hand, decoupling leads to a 50% reduction in simulation run time. Computational costs may be further reduced through efficient application of the Thomas algorithm. These techniques may be easily incorporated into existing codes and new applications in which simulation run time is of concern.

  10. Modeling of Flow Transition Using an Intermittency Transport Equation

    NASA Technical Reports Server (NTRS)

    Suzen, Y. B.; Huang, P. G.

    1999-01-01

    A new transport equation for intermittency factor is proposed to model transitional flows. The intermittent behavior of the transitional flows is incorporated into the computations by modifying the eddy viscosity, mu(sub t), obtainable from a turbulence model, with the intermittency factor, gamma: mu(sub t, sup *) = gamma.mu(sub t). In this paper, Menter's SST model (Menter, 1994) is employed to compute mu(sub t) and other turbulent quantities. The proposed intermittency transport equation can be considered as a blending of two models - Steelant and Dick (1996) and Cho and Chung (1992). The former was proposed for near-wall flows and was designed to reproduce the streamwise variation of the intermittency factor in the transition zone following Dhawan and Narasimha correlation (Dhawan and Narasimha, 1958) and the latter was proposed for free shear flows and was used to provide a realistic cross-stream variation of the intermittency profile. The new model was used to predict the T3 series experiments assembled by Savill (1993a, 1993b) including flows with different freestream turbulence intensities and two pressure-gradient cases. For all test cases good agreements between the computed results and the experimental data are observed.

  11. Transport equations of electrodiffusion processes in the laboratory reference frame.

    PubMed

    Garrido, Javier

    2006-02-23

    The transport equations of electrodiffusion processes use three reference frames for defining the fluxes: Fick's reference in diffusion, solvent-fixed reference in transference numbers, and laboratory fluxes in electric conductivity. The convenience of using only one reference frame is analyzed here from the point of view of the thermodynamics of irreversible processes. A relation between the fluxes of ions and solvent and the electric current density is deduced first from a mass and volume balance. This is then used to show that (i) the laboratory and Fick's diffusion coefficients are identical and (ii) the transference numbers of both the solvent and the ion in the laboratory reference frame are related. Finally, four experimental methods for the measurement of ion transference numbers are analyzed critically. New expressions for evaluating transference numbers for the moving boundary method and the chronopotentiometry technique are deduced. It is concluded that the ion transport equation in the laboratory reference frame plays a key role in the description of electrodiffusion processes.

  12. Neglected transport equations: extended Rankine-Hugoniot conditions and J -integrals for fracture

    NASA Astrophysics Data System (ADS)

    Davey, K.; Darvizeh, R.

    2016-09-01

    Transport equations in integral form are well established for analysis in continuum fluid dynamics but less so for solid mechanics. Four classical continuum mechanics transport equations exist, which describe the transport of mass, momentum, energy and entropy and thus describe the behaviour of density, velocity, temperature and disorder, respectively. However, one transport equation absent from the list is particularly pertinent to solid mechanics and that is a transport equation for movement, from which displacement is described. This paper introduces the fifth transport equation along with a transport equation for mechanical energy and explores some of the corollaries resulting from the existence of these equations. The general applicability of transport equations to discontinuous physics is discussed with particular focus on fracture mechanics. It is well established that bulk properties can be determined from transport equations by application of a control volume methodology. A control volume can be selected to be moving, stationary, mass tracking, part of, or enclosing the whole system domain. The flexibility of transport equations arises from their ability to tolerate discontinuities. It is insightful thus to explore the benefits derived from the displacement and mechanical energy transport equations, which are shown to be beneficial for capturing the physics of fracture arising from a displacement discontinuity. Extended forms of the Rankine-Hugoniot conditions for fracture are established along with extended forms of J -integrals.

  13. Nodal collocation approximation for the multidimensional PL equations applied to transport source problems

    SciTech Connect

    Verdu, G.; Capilla, M.; Talavera, C. F.; Ginestar, D.

    2012-07-01

    PL equations are classical high order approximations to the transport equations which are based on the expansion of the angular dependence of the angular neutron flux and the nuclear cross sections in terms of spherical harmonics. A nodal collocation method is used to discretize the PL equations associated with a neutron source transport problem. The performance of the method is tested solving two 1D problems with analytical solution for the transport equation and a classical 2D problem. (authors)

  14. Generation of a Complete Set of Additive Shape-Invariant Potentials from an Euler Equation

    SciTech Connect

    Bougie, Jonathan; Gangopadhyaya, Asim; Mallow, Jeffry V.

    2010-11-19

    In supersymmetric quantum mechanics, shape invariance is a sufficient condition for solvability. We show that all conventional additive shape-invariant superpotentials that are independent of ({h_bar}/2{pi}) can be generated from two partial differential equations. One of these is equivalent to the one-dimensional Euler equation expressing momentum conservation for inviscid fluid flow, and it is closed by the other. We solve these equations, generate the set of all conventional shape-invariant superpotentials, and show that there are no others in this category. We then develop an algorithm for generating all additive shape-invariant superpotentials including those that depend on ({h_bar}/2{pi}) explicitly.

  15. Generation of a complete set of additive shape-invariant potentials from an Euler equation.

    PubMed

    Bougie, Jonathan; Gangopadhyaya, Asim; Mallow, Jeffry V

    2010-11-19

    In supersymmetric quantum mechanics, shape invariance is a sufficient condition for solvability. We show that all conventional additive shape-invariant superpotentials that are independent of ℏ can be generated from two partial differential equations. One of these is equivalent to the one-dimensional Euler equation expressing momentum conservation for inviscid fluid flow, and it is closed by the other. We solve these equations, generate the set of all conventional shape-invariant superpotentials, and show that there are no others in this category. We then develop an algorithm for generating all additive shape-invariant superpotentials including those that depend on ℏ explicitly.

  16. Application study of transport intensity equation in quantitative phase reconstruction

    NASA Astrophysics Data System (ADS)

    Song, Xiaojun; Cheng, Wei; Wei, Chunjuan; Xue, Liang; Liu, Weijing; Bai, Baodan; Chu, Fenghong

    2016-10-01

    In order to improve detection speed and accuracy of biological cells, a quantitative non-interference optical phase recovery method is proposed in commercial microscope, taking the red blood cells as the classical phase objects. Three bright field micrographs were collected in the experiment. Utilizing the transport intensity equation (TIE), the quantitative phase distributions of red blood cell are gained and agree well with the previous optical phase models. Analysis shows that the resolution of introduced system reaches sub-micron. This method not only quickly gives quantitative phase distribution of cells, but also measures a large number of cells simultaneously. So it is potential in the use of real-time observing and quantitative analyzing of cells in vivo.

  17. Heat conduction in multifunctional nanotrusses studied using Boltzmann transport equation

    NASA Astrophysics Data System (ADS)

    Dou, Nicholas G.; Minnich, Austin J.

    2016-01-01

    Materials that possess low density, low thermal conductivity, and high stiffness are desirable for engineering applications, but most materials cannot realize these properties simultaneously due to the coupling between them. Nanotrusses, which consist of hollow nanoscale beams architected into a periodic truss structure, can potentially break these couplings due to their lattice architecture and nanoscale features. In this work, we study heat conduction in the exact nanotruss geometry by solving the frequency-dependent Boltzmann transport equation using a variance-reduced Monte Carlo algorithm. We show that their thermal conductivity can be described with only two parameters, solid fraction and wall thickness. Our simulations predict that nanotrusses can realize unique combinations of mechanical and thermal properties that are challenging to achieve in typical materials.

  18. Renormalization group analysis of the Reynolds stress transport equation

    NASA Technical Reports Server (NTRS)

    Rubinstein, R.; Barton, J. M.

    1992-01-01

    The pressure velocity correlation and return to isotropy term in the Reynolds stress transport equation are analyzed using the Yakhot-Orszag renormalization group. The perturbation series for the relevant correlations, evaluated to lowest order in the epsilon-expansion of the Yakhot-Orszag theory, are infinite series in tensor product powers of the mean velocity gradient and its transpose. Formal lowest order Pade approximations to the sums of these series produce a fast pressure strain model of the form proposed by Launder, Reece, and Rodi, and a return to isotropy model of the form proposed by Rotta. In both cases, the model constant are computed theoretically. The predicted Reynolds stress ratios in simple shear flows are evaluated and compared with experimental data. The possibility is discussed of driving higher order nonlinear models by approximating the sums more accurately.

  19. Heat conduction in multifunctional nanotrusses studied using Boltzmann transport equation

    SciTech Connect

    Dou, Nicholas G.; Minnich, Austin J.

    2016-01-04

    Materials that possess low density, low thermal conductivity, and high stiffness are desirable for engineering applications, but most materials cannot realize these properties simultaneously due to the coupling between them. Nanotrusses, which consist of hollow nanoscale beams architected into a periodic truss structure, can potentially break these couplings due to their lattice architecture and nanoscale features. In this work, we study heat conduction in the exact nanotruss geometry by solving the frequency-dependent Boltzmann transport equation using a variance-reduced Monte Carlo algorithm. We show that their thermal conductivity can be described with only two parameters, solid fraction and wall thickness. Our simulations predict that nanotrusses can realize unique combinations of mechanical and thermal properties that are challenging to achieve in typical materials.

  20. A simple Boltzmann transport equation for ballistic to diffusive transient heat transport

    SciTech Connect

    Maassen, Jesse Lundstrom, Mark

    2015-04-07

    Developing simplified, but accurate, theoretical approaches to treat heat transport on all length and time scales is needed to further enable scientific insight and technology innovation. Using a simplified form of the Boltzmann transport equation (BTE), originally developed for electron transport, we demonstrate how ballistic phonon effects and finite-velocity propagation are easily and naturally captured. We show how this approach compares well to the phonon BTE, and readily handles a full phonon dispersion and energy-dependent mean-free-path. This study of transient heat transport shows (i) how fundamental temperature jumps at the contacts depend simply on the ballistic thermal resistance, (ii) that phonon transport at early times approach the ballistic limit in samples of any length, and (iii) perceived reductions in heat conduction, when ballistic effects are present, originate from reductions in temperature gradient. Importantly, this framework can be recast exactly as the Cattaneo and hyperbolic heat equations, and we discuss how the key to capturing ballistic heat effects is to use the correct physical boundary conditions.

  1. Linear dynamic system approach to groundwater solute transport equation

    SciTech Connect

    Cho, W.C.

    1984-01-01

    Groundwater pollution in the United States has been recognized in the 1980's to be extensive both in degree and geographic distribution. It has been recognized that in many cases groundwater pollution is essentially irreversible from the engineering or economic viewpoint. Under the best circumstance the problem is complicated by insufficient amounts of field data which is costly to obtain. In general, the governing partial differential equation of solute transport is spatially discretized either using finite difference or finite element scheme. The time derivative is also approximated by finite difference. In this study, only the spatial discretization is performed using finite element method and the time derivative is retained in continuous form. The advantage is that special features of finite element are maintained but most important of all is that the equation can be rearranged to be in a standard form of linear dynamic system. Two problems were studied in detail: one is the determination of the locatio of groundwater pollution source(s). The problem is equivalent to identifying an input to the dynamic system and is solved by using the sensitivity theorem. The other one is the prediction of pollutant concentration at a given time at a given location. The eigenvalue technique was employed to solve this problem and the detailed procedures of the computation were delineated.

  2. A flexible nonlinear diffusion acceleration method for the SN transport equations discretized with discontinuous finite elements

    NASA Astrophysics Data System (ADS)

    Schunert, Sebastian; Wang, Yaqi; Gleicher, Frederick; Ortensi, Javier; Baker, Benjamin; Laboure, Vincent; Wang, Congjian; DeHart, Mark; Martineau, Richard

    2017-06-01

    This work presents a flexible nonlinear diffusion acceleration (NDA) method that discretizes both the SN 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 is 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. 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

  3. Intuitionistic fuzzy stability of a general mixed additive-cubic equation

    NASA Astrophysics Data System (ADS)

    Xu, Tian Zhou; Rassias, John Michael; Xu, Wan Xin

    2010-06-01

    We establish some stability results concerning the general mixed additive-cubic functional equation, f(kx +y)+f(kx -y)=kf(x +y)+kf(x -y)+2f(kx)-2kf(x ),in intuitionistic fuzzy normed spaces. In addition, we show under some suitable conditions that an approximately mixed additive-cubic function can be approximated by a mixed additive and cubic mapping.

  4. Modeling uranium transport in acidic contaminated groundwater with base addition.

    PubMed

    Zhang, Fan; Luo, Wensui; Parker, Jack C; Brooks, Scott C; Watson, David B; Jardine, Philip M; Gu, Baohua

    2011-06-15

    This study investigates reactive transport modeling in a column of uranium(VI)-contaminated sediments with base additions in the circulating influent. The groundwater and sediment exhibit oxic conditions with low pH, high concentrations of NO(3)(-), SO(4)(2-), U and various metal cations. Preliminary batch experiments indicate that additions of strong base induce rapid immobilization of U for this material. In the column experiment that is the focus of the present study, effluent groundwater was titrated with NaOH solution in an inflow reservoir before reinjection to gradually increase the solution pH in the column. An equilibrium hydrolysis, precipitation and ion exchange reaction model developed through simulation of the preliminary batch titration experiments predicted faster reduction of aqueous Al than observed in the column experiment. The model was therefore modified to consider reaction kinetics for the precipitation and dissolution processes which are the major mechanism for Al immobilization. The combined kinetic and equilibrium reaction model adequately described variations in pH, aqueous concentrations of metal cations (Al, Ca, Mg, Sr, Mn, Ni, Co), sulfate and U(VI). The experimental and modeling results indicate that U(VI) can be effectively sequestered with controlled base addition due to sorption by slowly precipitated Al with pH-dependent surface charge. The model may prove useful to predict field-scale U(VI) sequestration and remediation effectiveness.

  5. Probabilistic Analysis of the Upwind Scheme for Transport Equations

    NASA Astrophysics Data System (ADS)

    Delarue, François; Lagoutière, Frédéric

    2011-01-01

    We provide a probabilistic analysis of the upwind scheme for d-dimensional transport equations. We associate a Markov chain with the numerical scheme and then obtain a backward representation formula of Kolmogorov type for the numerical solution. We then understand that the error induced by the scheme is governed by the fluctuations of the Markov chain around the characteristics of the flow. We show, in various situations, that the fluctuations are of diffusive type. As a by-product, we recover recent results due to Merlet and Vovelle (Numer Math 106: 129-155, 2007) and Merlet (SIAM J Numer Anal 46(1):124-150, 2007): we prove that the scheme is of order 1/2 in {L^{infty}([0,T],L^1(mathbb R^d))} for an integrable initial datum of bounded variation and of order 1/2- ɛ, for all ɛ > 0, in {L^{infty}([0,T] × mathbb R^d)} for an initial datum of Lipschitz regularity. Our analysis provides a new interpretation of the numerical diffusion phenomenon.

  6. Multimodal computational microscopy based on transport of intensity equation

    NASA Astrophysics Data System (ADS)

    Li, Jiaji; Chen, Qian; Sun, Jiasong; Zhang, Jialin; Zuo, Chao

    2016-12-01

    Transport of intensity equation (TIE) is a powerful tool for phase retrieval and quantitative phase imaging, which requires intensity measurements only at axially closely spaced planes without a separate reference beam. It does not require coherent illumination and works well on conventional bright-field microscopes. The quantitative phase reconstructed by TIE gives valuable information that has been encoded in the complex wave field by passage through a sample of interest. Such information may provide tremendous flexibility to emulate various microscopy modalities computationally without requiring specialized hardware components. We develop a requisite theory to describe such a hybrid computational multimodal imaging system, which yields quantitative phase, Zernike phase contrast, differential interference contrast, and light field moment imaging, simultaneously. It makes the various observations for biomedical samples easy. Then we give the experimental demonstration of these ideas by time-lapse imaging of live HeLa cell mitosis. Experimental results verify that a tunable lens-based TIE system, combined with the appropriate postprocessing algorithm, can achieve a variety of promising imaging modalities in parallel with the quantitative phase images for the dynamic study of cellular processes.

  7. 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.

  8. A new approach to NMR chemical shift additivity parameters using simultaneous linear equation method.

    PubMed

    Shahab, Yosif A; Khalil, Rabah A

    2006-10-01

    A new approach to NMR chemical shift additivity parameters using simultaneous linear equation method has been introduced. Three general nitrogen-15 NMR chemical shift additivity parameters with physical significance for aliphatic amines in methanol and cyclohexane and their hydrochlorides in methanol have been derived. A characteristic feature of these additivity parameters is the individual equation can be applied to both open-chain and rigid systems. The factors that influence the (15)N chemical shift of these substances have been determined. A new method for evaluating conformational equilibria at nitrogen in these compounds using the derived additivity parameters has been developed. Conformational analyses of these substances have been worked out. In general, the results indicate that there are four factors affecting the (15)N chemical shift of aliphatic amines; paramagnetic term (p-character), lone pair-proton interactions, proton-proton interactions, symmetry of alkyl substituents and molecular association.

  9. A Photon Free Method to Solve Radiation Transport Equations

    SciTech Connect

    Chang, B

    2006-09-05

    The multi-group discrete-ordinate equations of radiation transfer is solved for the first time by Newton's method. It is a photon free method because the photon variables are eliminated from the radiation equations to yield a N{sub group}XN{sub direction} smaller but equivalent system of equations. The smaller set of equations can be solved more efficiently than the original set of equations. Newton's method is more stable than the Semi-implicit Linear method currently used by conventional radiation codes.

  10. Conditional probability calculations for the nonlinear Schrödinger equation with additive noise.

    PubMed

    Terekhov, I S; Vergeles, S S; Turitsyn, S K

    2014-12-05

    The method for the computation of the conditional probability density function for the nonlinear Schrödinger equation with additive noise is developed. We present in a constructive form the conditional probability density function in the limit of small noise and analytically derive it in a weakly nonlinear case. The general theory results are illustrated using fiber-optic communications as a particular, albeit practically very important, example.

  11. The nature of the sunspot phenomenon. I - Solutions of the heat transport equation

    NASA Technical Reports Server (NTRS)

    Parker, E. N.

    1974-01-01

    It is pointed out that sunspots represent a disruption in the uniform flow of heat through the convective zone. The basic sunspot structure is, therefore, determined by the energy transport equation. The solutions of this equation for the case of stochastic heat transport are examined. It is concluded that a sunspot is basically a region of enhanced, rather than inhibited, energy transport and emissivity. The heat flow equations are discussed and attention is given to the shallow depth of the sunspot phenomenon. The sunspot is seen as a heat engine of high efficiency which converts most of the heat flux into hydromagnetic waves.

  12. 49 CFR 172.820 - Additional planning requirements for transportation by rail.

    Code of Federal Regulations, 2011 CFR

    2011-10-01

    ... Additional planning requirements for transportation by rail. (a) General. Each rail carrier transporting in... transported (instead of only highway route controlled quantities of Class 7 materials) and for all Division 6.1 materials transported (instead of only Division 6.1 poison inhalation hazard materials). (c)...

  13. 49 CFR 172.820 - Additional planning requirements for transportation by rail.

    Code of Federal Regulations, 2010 CFR

    2010-10-01

    ... Additional planning requirements for transportation by rail. (a) General. Each rail carrier transporting in... materials transported (instead of only highway route controlled quantities of Class 7 materials) and for all Division 6.1 materials transported (instead of only Division 6.1 poison inhalation hazard materials)....

  14. Equation of state and transport coefficients for dense plasmas.

    PubMed

    Blancard, C; Faussurier, G

    2004-01-01

    We hereby present a model to describe the thermodynamic and transport properties of dense plasmas. The electronic and ionic structures are determined self-consistently using finite-temperature density functional theory and Gibbs-Bogolyubov inequality. The main thermodynamic quantities, i.e., internal energy, pressure, entropy, and sound speed, are obtained by numerical differentiation of the plasma total Helmholtz free energy. Electronic electrical and thermal conductivities are calculated from the Ziman approach. Ionic transport coefficients are estimated using those of hard-sphere system and the Rosenfeld semiempirical "universal" correspondence between excess entropy and dimensionless transport coefficients of dense fluids. Numerical results and comparisons with experiments are presented and discussed.

  15. Simple jumping process with memory: Transport equation and diffusion

    NASA Astrophysics Data System (ADS)

    Kamińska, A.; Srokowski, T.

    2004-06-01

    We present a stochastic jumping process, defined in terms of jump-size probability density and jumping rate, which is a generalization of the well-known kangaroo process. The definition takes into account two process values: after and before the jump. Therefore, the process is able to preserve memory about its previous values. It possesses a simple stationary limit. Its master equation is interpreted as the kinetic equation with variable collision rate. The process can be easily applied to model systems which relax to distributions other than Maxwellian. The case of a constant jumping rate corresponds to the diffusion process, either normal or ballistic.

  16. Transport equation for plasmas in a stationary-homogeneous turbulence

    SciTech Connect

    Wang, Shaojie

    2016-02-15

    For a plasma in a stationary homogeneous turbulence, the Fokker-Planck equation is derived from the nonlinear Vlasov equation by introducing the entropy principle. The ensemble average in evaluating the kinetic diffusion tensor, whose symmetry has been proved, can be computed in a straightforward way when the fluctuating particle trajectories are provided. As an application, it has been shown that a mean parallel electric filed can drive a particle flux through the Stokes-Einstein relation, independent of the details of the fluctuations.

  17. AN EXACT PEAK CAPTURING AND OSCILLATION-FREE SCHEME TO SOLVE ADVECTION-DISPERSION TRANSPORT EQUATIONS

    EPA Science Inventory

    An exact peak capturing and essentially oscillation-free (EPCOF) algorithm, consisting of advection-dispersion decoupling, backward method of characteristics, forward node tracking, and adaptive local grid refinement, is developed to solve transport equations. This algorithm repr...

  18. TLC scheme for numerical solution of the transport equation on equilateral triangular meshes

    SciTech Connect

    Walters, W.F.

    1983-01-01

    A new triangular linear characteristic TLC scheme for numerically solving the transport equation on equilateral triangular meshes has been developed. This scheme uses the analytic solution of the transport equation in the triangle as its basis. The data on edges of the triangle are assumed linear as is the source representation. A characteristic approach or nodal approach is used to obtain the analytic solution. Test problems indicate that the new TLC is superior to the widely used DITRI scheme for accuracy.

  19. Eigen decomposition solution to the one-dimensional time-dependent photon transport equation.

    PubMed

    Handapangoda, Chintha C; Pathirana, Pubudu N; Premaratne, Malin

    2011-02-14

    The time-dependent one-dimensional photon transport (radiative transfer) equation is widely used to model light propagation through turbid media with a slab geometry, in a vast number of disciplines. Several numerical and semi-analytical techniques are available to accurately solve this equation. In this work we propose a novel efficient solution technique based on eigen decomposition of the vectorized version of the photon transport equation. Using clever transformations, the four variable integro-differential equation is reduced to a set of first order ordinary differential equations using a combination of a spectral method and the discrete ordinates method. An eigen decomposition approach is then utilized to obtain the closed-form solution of this reduced set of ordinary differential equations.

  20. The Dissipation Rate Transport Equation and Subgrid-Scale Models in Rotating Turbulence

    NASA Technical Reports Server (NTRS)

    Rubinstein, Robert; Ye, Zhou

    1997-01-01

    The dissipation rate transport equation remains the most uncertain part of turbulence modeling. The difficulties arc increased when external agencies like rotation prevent straightforward dimensional analysis from determining the correct form of the modelled equation. In this work, the dissipation rate transport equation and subgrid scale models for rotating turbulence are derived from an analytical statistical theory of rotating turbulence. In the strong rotation limit, the theory predicts a turbulent steady state in which the inertial range energy spectrum scales as k(sup -2) and the turbulent time scale is the inverse rotation rate. This scaling has been derived previously by heuristic arguments.

  1. Analytical Theory of the Destruction Terms in Dissipation Rate Transport Equations

    NASA Technical Reports Server (NTRS)

    Rubinstein, Robert; Zhou, Ye

    1996-01-01

    Modeled dissipation rate transport equations are often derived by invoking various hypotheses to close correlations in the corresponding exact equations. D. C. Leslie suggested that these models might be derived instead from Kraichnan's wavenumber space integrals for inertial range transport power. This suggestion is applied to the destruction terms in the dissipation rate equations for incompressible turbulence, buoyant turbulence, rotating incompressible turbulence, and rotating buoyant turbulence. Model constants like C(epsilon 2) are expressed as integrals; convergence of these integrals implies the absence of Reynolds number dependence in the corresponding destruction term. The dependence of C(epsilon 2) on rotation rate emerges naturally; sensitization of the modeled dissipation rate equation to rotation is not required. A buoyancy related effect which is absent in the exact transport equation for temperature variance dissipation, but which sometimes improves computational predictions, also arises naturally. Both the presence of this effect and the appropriate time scale in the modeled transport equation depend on whether Bolgiano or Kolmogorov inertial range scaling applies. A simple application of these methods leads to a preliminary, dissipation rate equation for rotating buoyant turbulence.

  2. The adjoint neutron transport equation and the statistical approach for its solution

    NASA Astrophysics Data System (ADS)

    Saracco, P.; Dulla, S.; Ravetto, P.

    2016-11-01

    The adjoint equation was introduced in the early days of neutron transport and its solution, the neutron importance, has been used for several applications in neutronics. The work presents at first a critical review of the adjoint neutron transport equation. Afterwards, the adjont model is constructed for a reference physical situation, for which an analytical approach is viable, i.e. an infinite homogeneous scattering medium. This problem leads to an equation that is the adjoint of the slowing-down equation, which is well known in nuclear reactor physics. A general closed-form analytical solution to such adjoint equation is obtained by a procedure that can be used also to derive the classical Placzek functions. This solution constitutes a benchmark for any statistical or numerical approach to the adjoint equation. A sampling technique to evaluate the adjoint flux for the transport equation is then proposed and physically interpreted as a transport model for pseudo-particles. This can be done by introducing appropriate kernels describing the transfer of the pseudo-particles in the phase space. This technique allows estimating the importance function by a standard Monte Carlo approach. The sampling scheme is validated by comparison with the analytical results previously obtained.

  3. Conservative differencing of the electron Fokker-Planck transport equation

    SciTech Connect

    Langdon, A.B.

    1981-01-12

    We need to extend the applicability and improve the accuracy of kinetic electron transport codes. In this paper, special attention is given to modelling of e-e collisions, including the dominant contributions arising from anisotropy. The electric field and spatial gradient terms are also considered. I construct finite-difference analogues to the Fokker-Planck integral-differential collision operator, which conserve the particle number, momentum and energy integrals (sums) regardless of the coarseness of the velocity zoning. Such properties are usually desirable, but are especially useful, for example, when there are spatial regions and/or time intervals in which the plasma is cool, so that the collision operator acts rapidly and the velocity distribution is poorly resolved, yet it is crucial that gross conservation properties be respected in hydro-transport applications, such as in the LASNEX code. Some points are raised concerning spatial differencing and time integration.

  4. Explicit solutions of the radiative transport equation in the P{sub 3} approximation

    SciTech Connect

    Liemert, André Kienle, Alwin

    2014-11-01

    Purpose: Explicit solutions of the monoenergetic radiative transport equation in the P{sub 3} approximation have been derived which can be evaluated with nearly the same computational effort as needed for solving the standard diffusion equation (DE). In detail, the authors considered the important case of a semi-infinite medium which is illuminated by a collimated beam of light. Methods: A combination of the classic spherical harmonics method and the recently developed method of rotated reference frames is used for solving the P{sub 3} equations in closed form. Results: The derived solutions are illustrated and compared to exact solutions of the radiative transport equation obtained via the Monte Carlo (MC) method as well as with other approximated analytical solutions. It is shown that for the considered cases which are relevant for biomedical optics applications, the P{sub 3} approximation is close to the exact solution of the radiative transport equation. Conclusions: The authors derived exact analytical solutions of the P{sub 3} equations under consideration of boundary conditions for defining a semi-infinite medium. The good agreement to Monte Carlo simulations in the investigated domains, for example, in the steady-state and time domains, as well as the short evaluation time needed suggests that the derived equations can replace the often applied solutions of the diffusion equation for the homogeneous semi-infinite medium.

  5. Analytical solution for one-dimensional advection-dispersion transport equation with distance-dependent coefficients

    NASA Astrophysics Data System (ADS)

    Pérez Guerrero, J. S.; Skaggs, T. H.

    2010-08-01

    SummaryMathematical models describing contaminant transport in heterogeneous porous media are often formulated as an advection-dispersion transport equation with distance-dependent transport coefficients. In this work, a general analytical solution is presented for the linear, one-dimensional advection-dispersion equation with distance-dependent coefficients. An integrating factor is employed to obtain a transport equation that has a self-adjoint differential operator, and a solution is found using the generalized integral transform technique (GITT). It is demonstrated that an analytical expression for the integrating factor exists for several transport equation formulations of practical importance in groundwater transport modeling. Unlike nearly all solutions available in the literature, the current solution is developed for a finite spatial domain. As an illustration, solutions for the particular case of a linearly increasing dispersivity are developed in detail and results are compared with solutions from the literature. Among other applications, the current analytical solution will be particularly useful for testing or benchmarking numerical transport codes because of the incorporation of a finite spatial domain.

  6. UBVRI PHOTOMETRIC STANDARD STARS AROUND THE CELESTIAL EQUATOR: UPDATES AND ADDITIONS

    SciTech Connect

    Landolt, Arlo U.

    2009-05-15

    New broadband UBVRI photoelectric observations on the Johnson-Kron-Cousins photometric system have been made of 202 stars around the sky, and centered at the celestial equator. These stars constitute both an update of and additions to a previously published list of equatorial photometric standard stars. The list is capable of providing, for both celestial hemispheres, an internally consistent homogeneous broadband standard photometric system around the sky. When these new measurements are included with those previously published by Landolt (1992), the entire list of standard stars in this paper encompasses the magnitude range 8.90 < V < 16.30, and the color index range -0.35 < (B - V) < +2.30.

  7. Sparse Additive Ordinary Differential Equations for Dynamic Gene Regulatory Network Modeling.

    PubMed

    Wu, Hulin; Lu, Tao; Xue, Hongqi; Liang, Hua

    2014-04-02

    The gene regulation network (GRN) is a high-dimensional complex system, which can be represented by various mathematical or statistical models. The ordinary differential equation (ODE) model is one of the popular dynamic GRN models. High-dimensional linear ODE models have been proposed to identify GRNs, but with a limitation of the linear regulation effect assumption. In this article, we propose a sparse additive ODE (SA-ODE) model, coupled with ODE estimation methods and adaptive group LASSO techniques, to model dynamic GRNs that could flexibly deal with nonlinear regulation effects. The asymptotic properties of the proposed method are established and simulation studies are performed to validate the proposed approach. An application example for identifying the nonlinear dynamic GRN of T-cell activation is used to illustrate the usefulness of the proposed method.

  8. UBVRI Photometric Standard Stars Around the Celestial Equator: Updates and Additions

    NASA Astrophysics Data System (ADS)

    Landolt, Arlo U.

    2009-05-01

    New broadband UBVRI photoelectric observations on the Johnson-Kron-Cousins photometric system have been made of 202 stars around the sky, and centered at the celestial equator. These stars constitute both an update of and additions to a previously published list of equatorial photometric standard stars. The list is capable of providing, for both celestial hemispheres, an internally consistent homogeneous broadband standard photometric system around the sky. When these new measurements are included with those previously published by Landolt (1992), the entire list of standard stars in this paper encompasses the magnitude range 8.90 < V < 16.30, and the color index range -0.35 < (B - V) < +2.30.

  9. Sparse Additive Ordinary Differential Equations for Dynamic Gene Regulatory Network Modeling

    PubMed Central

    Wu, Hulin; Lu, Tao; Xue, Hongqi; Liang, Hua

    2014-01-01

    Summary The gene regulation network (GRN) is a high-dimensional complex system, which can be represented by various mathematical or statistical models. The ordinary differential equation (ODE) model is one of the popular dynamic GRN models. High-dimensional linear ODE models have been proposed to identify GRNs, but with a limitation of the linear regulation effect assumption. In this article, we propose a sparse additive ODE (SA-ODE) model, coupled with ODE estimation methods and adaptive group LASSO techniques, to model dynamic GRNs that could flexibly deal with nonlinear regulation effects. The asymptotic properties of the proposed method are established and simulation studies are performed to validate the proposed approach. An application example for identifying the nonlinear dynamic GRN of T-cell activation is used to illustrate the usefulness of the proposed method. PMID:25061254

  10. Interfacial area transport equation for bubbly to cap-bubbly transition flows

    NASA Astrophysics Data System (ADS)

    Worosz, Theodore S.

    To fully realize the benefit of the two-group interfacial area transport equation (IATE) as a constitutive model for the interfacial area concentration in the two-fluid model, it is imperative that models be developed to dynamically transition from one-group to two-group flows. With this in mind, the two-group IATE is derived in detail to establish new expansion source terms that correctly account for the effects of intergroup bubble transport. In addition to this theoretical effort, the state-of-the-art four-sensor conductivity probe is used to establish a reliable experimental database of local two-phase flow parameters to characterize one-group to two-group transition flows and to support model development. The experiments are performed in verticalupward air-water two-phase flow in a 5.08cm pipe. Additionally, the local conductivity probe is improved through systematic studies into: 1) signal "ghosting" electrical interference among probe sensors, 2) sampling frequency sensitivity, 3) measurement duration sensitivity, and 4) probe sensor orientation. Wake-dominated bubble transport characterizes the transition from onegroup to two-group flows. Therefore, the necessary intergroup and intragroup wake entrainment source terms that are required for two-group interfacial area transport in transition flows are developed. Furthermore, an approach is developed to initiate the shearing-off source and reduce the one-group interaction mechanisms as an established two-group flow develops. The new interfacial area transport model for one-group to two-group transition flows is evaluated against the experimental database. The model accurately captures the exchange of void fraction and interfacial area concentration between group-I and group-II in transition flows. Overall, the group-I void fraction and interfacial area concentration are predicted within +/-6% and +/-4%, respectively, of the experimental data. The group-II void fraction and interfacial area concentration are

  11. Examination of transport equations pertaining to permeable elastic tubules such as Henle's loop.

    PubMed Central

    Basmadjian, D; Baines, A D

    1978-01-01

    The transport equations applicable to loops of Henle and similar elastic permeable tubules were re-examined to assess the effect of radial transport resistance in the lumen and tubule geometry on solute transport. Active transport at the wall as well as external gradients equivalent to a 2--1,000-fold concentration increase per centimeter of distance were considered. Wall permeabilities and active transport constants were varied up to 2 . 10(-2) cm/s. It is shown that for conditions applicable to the loop of Henle, resistance to radial solute transfer in the lumen is negligible, both for passive and active transmural transport with concomitant water flux, and that axial dispersion further reduces that resistance. These conclusions apply equally to conical and elliptical geometries likely to arise in loop operation. The validity of Poiseuille's equation for these geometries is discussed. Ii is concluded that the one-dimensional transport equations are a valid representation of loop operation. Images FIGURE 1 PMID:737282

  12. Transport equations for low-energy solar particles in evolving interplanetary magnetic fields

    NASA Technical Reports Server (NTRS)

    Ng, C. K.

    1988-01-01

    Two new forms of a simplified Fokker-Planck equation are derived for the transport of low-energy solar energetic particles in an evolving interplanetary magnetic field, carried by a variable radial solar wind. An idealized solution suggests that the 'invariant' anisotropy direction reported by Allum et al. (1974) may be explained within the conventional theoretical framework. The equations may be used to relate studies of solar particle propagation to solar wind transients, and vice versa.

  13. Exact and efficient solution of the radiative transport equation for the semi-infinite medium

    NASA Astrophysics Data System (ADS)

    Liemert, André; Kienle, Alwin

    2013-06-01

    An accurate and efficient solution of the radiative transport equation is proposed for modeling the propagation of photons in the three-dimensional anisotropically scattering half-space medium. The exact refractive index mismatched boundary condition is considered and arbitrary rotationally invariant scattering functions can be applied. The obtained equations are verified with Monte Carlo simulations in the steady-state, temporal frequency, and time domains resulting in an excellent agreement.

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

    SciTech Connect

    Szoke, A.; Brooks, E. D.

    2016-07-12

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

  15. Boundary conditions for probability density function transport equations in fluid mechanics.

    PubMed

    Valiño, Luis; Hierro, Juan

    2003-04-01

    The behavior of the probability density function (PDF) transport equation at the limits of the probability space is studied from the point of view of fluid mechanics. Different boundary conditions are considered depending on the nature of the variable considered (velocity, scalar, and position). A study of the implications of entrance and exit conditions is performed, showing that a new term should be added to the PDF transport equation to preserve normalization in some nonstationary processes. In practice, this term is taken into account naturally in particle methods. Finally, the existence of discontinuities at the limits is also investigated.

  16. Solving the transport equation with quadratic finite elements: Theory and applications

    SciTech Connect

    Ferguson, J.M.

    1997-12-31

    At the 4th Joint Conference on Computational Mathematics, the author presented a paper introducing a new quadratic finite element scheme (QFEM) for solving the transport equation. In the ensuing year the author has obtained considerable experience in the application of this method, including solution of eigenvalue problems, transmission problems, and solution of the adjoint form of the equation as well as the usual forward solution. He will present detailed results, and will also discuss other refinements of his transport codes, particularly for 3-dimensional problems on rectilinear and non-rectilinear grids.

  17. Equations of state and transport properties of mixtures in the warm dense regime

    SciTech Connect

    Hou, Yong; Dai, Jiayu; Kang, Dongdong; Ma, Wen; Yuan, Jianmin

    2015-02-15

    We have performed average-atom molecular dynamics to simulate the CH and LiH mixtures in the warm dense regime, and obtained equations of state and the ionic transport properties. The electronic structures are calculated by using the modified average-atom model, which have included the broadening of energy levels, and the ion-ion pair potentials of mixtures are constructed based on the temperature-dependent density functional theory. The ionic transport properties, such as ionic diffusion and shear viscosity, are obtained through the ionic velocity correlation functions. The equations of state and transport properties for carbon, hydrogen and lithium, hydrogen mixtures in a wide region of density and temperature are calculated. Through our computing the average ionization degree, average ion-sphere diameter and transition properties in the mixture, it is shown that transport properties depend not only on the ionic mass but also on the average ionization degree.

  18. h-Refinement for simple corner balance scheme of SN transport equation on distorted meshes

    NASA Astrophysics Data System (ADS)

    Yang, Rong; Yuan, Guangwei

    2016-11-01

    The transport sweep algorithm is a common method for solving discrete ordinate transport equation, but it breaks down once a concave cell appears in spatial meshes. To deal with this issue a local h-refinement for simple corner balance (SCB) scheme of SN transport equation on arbitrary quadrilateral meshes is presented in this paper by using a new subcell partition. It follows that a hybrid mesh with both triangle and quadrilateral cells is generated, and the geometric quality of these cells improves, especially it is ensured that all cells become convex. Combining with the original SCB scheme, an adaptive transfer algorithm based on the hybrid mesh is constructed. Numerical experiments are presented to verify the utility and accuracy of the new algorithm, especially for some application problems such as radiation transport coupled with Lagrangian hydrodynamic flow. The results show that it performs well on extremely distorted meshes with concave cells, on which the original SCB scheme does not work.

  19. Un-collided-flux preconditioning for the first order transport equation

    SciTech Connect

    Rigley, M.; Koebbe, J.; Drumm, C.

    2013-07-01

    Two codes were tested for the first order neutron transport equation using finite element methods. The un-collided-flux solution is used as a preconditioner for each of these methods. These codes include a least squares finite element method and a discontinuous finite element method. The performance of each code is shown on problems in one and two dimensions. The un-collided-flux preconditioner shows good speedup on each of the given methods. The un-collided-flux preconditioner has been used on the second-order equation, and here we extend those results to the first order equation. (authors)

  20. Analytical Tests for Ray Effect Errors in Discrete Ordinate Methods for Solving the Neutron Transport Equation

    SciTech Connect

    Chang, B

    2004-03-22

    This paper contains three analytical solutions of transport problems which can be used to test ray-effect errors in the numerical solutions of the Boltzmann Transport Equation (BTE). We derived the first two solutions and the third was shown to us by M. Prasad. Since this paper is intended to be an internal LLNL report, no attempt was made to find the original derivations of the solutions in the literature in order to cite the authors for their work.

  1. Additive Runge-Kutta Schemes for Convection-Diffusion-Reaction Equations

    NASA Technical Reports Server (NTRS)

    Kennedy, Christopher A.; Carpenter, Mark H.

    2001-01-01

    Additive Runge-Kutta (ARK) methods are investigated for application to the spatially discretized one-dimensional convection-diffusion-reaction (CDR) equations. First, accuracy, stability, conservation, and dense output are considered for the general case when N different Runge-Kutta methods are grouped into a single composite method. Then, implicit-explicit, N = 2, additive Runge-Kutta ARK2 methods from third- to fifth-order are presented that allow for integration of stiff terms by an L-stable, stiffly-accurate explicit, singly diagonally implicit Runge-Kutta (ESDIRK) method while the nonstiff terms are integrated with a traditional explicit Runge-Kutta method (ERK). Coupling error terms are of equal order to those of the elemental methods. Derived ARK2 methods have vanishing stability functions for very large values of the stiff scaled eigenvalue, z(exp [I]) goes to infinity, and retain high stability efficiency in the absence of stiffness, z(exp [I]) goes to zero. Extrapolation-type stage-value predictors are provided based on dense-output formulae. Optimized methods minimize both leading order ARK2 error terms and Butcher coefficient magnitudes as well as maximize conservation properties. Numerical tests of the new schemes on a CDR problem show negligible stiffness leakage and near classical order convergence rates. However, tests on three simple singular-perturbation problems reveal generally predictable order reduction. Error control is best managed with a PID-controller. While results for the fifth-order method are disappointing, both the new third- and fourth-order methods are at least as efficient as existing ARK2 methods while offering error control and stage-value predictors.

  2. Exact dynamics of dissipative electronic systems and quantum transport: Hierarchical equations of motion approach.

    PubMed

    Jin, Jinshuang; Zheng, Xiao; Yan, YiJing

    2008-06-21

    A generalized quantum master equation theory that governs the exact, nonperturbative quantum dissipation and quantum transport is formulated in terms of hierarchically coupled equations of motion for an arbitrary electronic system in contact with electrodes under either a stationary or a nonstationary electrochemical potential bias. The theoretical construction starts with the influence functional in path integral, in which the electron creation and annihilation operators are Grassmann variables. Time derivatives on the influence functionals are then performed in a hierarchical manner. Both the multiple-frequency dispersion and the non-Markovian reservoir parametrization schemes are considered for the desired hierarchy construction. The resulting hierarchical equations of motion formalism is in principle exact and applicable to arbitrary electronic systems, including Coulomb interactions, under the influence of arbitrary time-dependent applied bias voltage and external fields. Both the conventional quantum master equation and the real-time diagrammatic formalism of Schon and co-workers can be readily obtained at well defined limits of the present theory. We also show that for a noninteracting electron system, the present hierarchical equations of motion formalism terminates at the second tier exactly, and the Landuer-Buttiker transport current expression is recovered. The present theory renders an exact and numerically tractable tool to evaluate various transient and stationary quantum transport properties of many-electron systems, together with the involving nonperturbative dissipative dynamics.

  3. Exact dynamics of dissipative electronic systems and quantum transport: Hierarchical equations of motion approach

    NASA Astrophysics Data System (ADS)

    Jin, Jinshuang; Zheng, Xiao; Yan, Yijing

    2008-06-01

    A generalized quantum master equation theory that governs the exact, nonperturbative quantum dissipation and quantum transport is formulated in terms of hierarchically coupled equations of motion for an arbitrary electronic system in contact with electrodes under either a stationary or a nonstationary electrochemical potential bias. The theoretical construction starts with the influence functional in path integral, in which the electron creation and annihilation operators are Grassmann variables. Time derivatives on the influence functionals are then performed in a hierarchical manner. Both the multiple-frequency dispersion and the non-Markovian reservoir parametrization schemes are considered for the desired hierarchy construction. The resulting hierarchical equations of motion formalism is in principle exact and applicable to arbitrary electronic systems, including Coulomb interactions, under the influence of arbitrary time-dependent applied bias voltage and external fields. Both the conventional quantum master equation and the real-time diagrammatic formalism of Schön and co-workers can be readily obtained at well defined limits of the present theory. We also show that for a noninteracting electron system, the present hierarchical equations of motion formalism terminates at the second tier exactly, and the Landuer-Büttiker transport current expression is recovered. The present theory renders an exact and numerically tractable tool to evaluate various transient and stationary quantum transport properties of many-electron systems, together with the involving nonperturbative dissipative dynamics.

  4. Exact analytical solutions for contaminant transport in rivers 1. The equilibrium advection-dispersion equation

    Technology Transfer Automated Retrieval System (TEKTRAN)

    Analytical solutions of the advection-dispersion equation and related models are indispensable for predicting or analyzing contaminant transport processes in streams and rivers, as well as in other surface water bodies. Many useful analytical solutions originated in disciplines other than surface-w...

  5. Analytical solution for the advection-dispersion transport equation in layered media

    Technology Transfer Automated Retrieval System (TEKTRAN)

    The advection-dispersion transport equation with first-order decay was solved analytically for multi-layered media using the classic integral transform technique (CITT). The solution procedure used an associated non-self-adjoint advection-diffusion eigenvalue problem that had the same form and coef...

  6. Solvability of certain inverse problems for the nonstationary kinetic transport equation

    NASA Astrophysics Data System (ADS)

    Volkov, N. P.

    2016-09-01

    Linear and nonlinear inverse problems for the nonstationary multispeed anisotropic kinetic transport equation are studied. Sufficient conditions for the existence and uniqueness of weak solutions to these problems in various function spaces are found. The proofs of the corresponding theorems imply that solutions of the inverse problems under study can be obtained by applying the method of successive approximations.

  7. An asymptotic-preserving Lagrangian algorithm for the time-dependent anisotropic heat transport equation

    SciTech Connect

    Chacon, Luis; del-Castillo-Negrete, Diego; Hauck, Cory D.

    2014-09-01

    We propose a Lagrangian numerical algorithm for a time-dependent, anisotropic temperature transport equation in magnetized plasmas in the large guide field regime. The approach is based on an analytical integral formal solution of the parallel (i.e., along the magnetic field) transport equation with sources, and it is able to accommodate both local and non-local parallel heat flux closures. The numerical implementation is based on an operator-split formulation, with two straightforward steps: a perpendicular transport step (including sources), and a Lagrangian (field-line integral) parallel transport step. Algorithmically, the first step is amenable to the use of modern iterative methods, while the second step has a fixed cost per degree of freedom (and is therefore scalable). Accuracy-wise, the approach is free from the numerical pollution introduced by the discrete parallel transport term when the perpendicular to parallel transport coefficient ratio X /X becomes arbitrarily small, and is shown to capture the correct limiting solution when ε = X⊥L2/X1L2 → 0 (with L∥∙ L⊥ , the parallel and perpendicular diffusion length scales, respectively). Therefore, the approach is asymptotic-preserving. We demonstrate the capabilities of the scheme with several numerical experiments with varying magnetic field complexity in two dimensions, including the case of transport across a magnetic island.

  8. Asymptotic-preserving methods for hyperbolic and transport equations with random inputs and diffusive scalings

    SciTech Connect

    Jin, Shi; Xiu, Dongbin; Zhu, Xueyu

    2015-05-15

    In this paper we develop a set of stochastic numerical schemes for hyperbolic and transport equations with diffusive scalings and subject to random inputs. The schemes are asymptotic preserving (AP), in the sense that they preserve the diffusive limits of the equations in discrete setting, without requiring excessive refinement of the discretization. Our stochastic AP schemes are extensions of the well-developed deterministic AP schemes. To handle the random inputs, we employ generalized polynomial chaos (gPC) expansion and combine it with stochastic Galerkin procedure. We apply the gPC Galerkin scheme to a set of representative hyperbolic and transport equations and establish the AP property in the stochastic setting. We then provide several numerical examples to illustrate the accuracy and effectiveness of the stochastic AP schemes.

  9. Iterative method for bioluminescence tomography based on the radiative transport equation

    NASA Astrophysics Data System (ADS)

    Cong, Wenxiang; Wang, Ge

    2006-08-01

    Bioluminescence tomography (BLT) is a new molecular imaging modality, which helps study cancer and other diseases, develop drugs, and so on. This technology localizes and quantifies a bioluminescent source inside a living transgenic mouse, and is very useful in many biomedical applications. In this paper, we propose a novel algorithm based on the radiative transport equation to reconstruct the bioluminescence source distribution from data measured on the external surface of a mouse. Our approach transforms the transport equation into an integral equation of the second kind, and establishes a linear system to link the measured photon fluence rate with the unknown light source variables. A regularization measure is taken to overcome the ill-posedness of the inverse problem. Then, an iterative optimization technique with a simple constrain is employed to compute the desirable solution. The physical phantom experiments have been performed to demonstrate the feasibility of the reconstruction method, and evaluate its performance in terms of source location and power estimation.

  10. Coupling lattice Boltzmann and continuum equations for flow and reactive transport in porous media.

    SciTech Connect

    Coon, Ethan; Porter, Mark L.; Kang, Qinjun; Moulton, John D.; Lichtner, Peter C.

    2012-06-18

    In spatially and temporally localized instances, capturing sub-reservoir scale information is necessary. Capturing sub-reservoir scale information everywhere is neither necessary, nor computationally possible. The lattice Boltzmann Method for solving pore-scale systems. At the pore-scale, LBM provides an extremely scalable, efficient way of solving Navier-Stokes equations on complex geometries. Coupling pore-scale and continuum scale systems via domain decomposition. By leveraging the interpolations implied by pore-scale and continuum scale discretizations, overlapping Schwartz domain decomposition is used to ensure continuity of pressure and flux. This approach is demonstrated on a fractured medium, in which Navier-Stokes equations are solved within the fracture while Darcy's equation is solved away from the fracture Coupling reactive transport to pore-scale flow simulators allows hybrid approaches to be extended to solve multi-scale reactive transport.

  11. Vectorization of the time-dependent Boltzmann transport equation: Application to deep penetration problems

    NASA Astrophysics Data System (ADS)

    Cobos, Agustín C.; Poma, Ana L.; Alvarez, Guillermo D.; Sanz, Darío E.

    2016-10-01

    We introduce an alternative method to calculate the steady state solution of the angular photon flux after a numerical evolution of the time-dependent Boltzmann transport equation (BTE). After a proper discretization the transport equation was converted into an ordinary system of differential equations that can be iterated as a weighted Richardson algorithm. As a different approach, in this work the time variable regulates the iteration process and convergence criteria is based on physical parameters. Positivity and convergence was assessed from first principles and a modified Courant-Friedrichs-Lewy condition was devised to guarantee convergence. The Penelope Monte Carlo method was used to test the convergence and accuracy of our approach for different phase space discretizations. Benchmarking was performed by calculation of total fluence and photon spectra in different one-dimensional geometries irradiated with 60Co and 6 MV photon beams and radiological applications were devised.

  12. Proton dose approximation in arbitrary convex geometry. [via Boltzmann transport equation

    NASA Technical Reports Server (NTRS)

    Wilson, J. W.; Khandelwal, G. S.

    1974-01-01

    An expansion is derived for the solution to the transport equation in two dimensions subject to boundary conditions given for an arbitrary convex region. Questions of high-energy transport are considered along with the properties of the dose response function. The expansion of the solution of the transport equation is presented in terms of a parameter which measures the lateral dispersion of an unidirectional beam. This parameter is usually small and the expansion is expected to converge rapidly. The dominant term in the expansion is related to fluence-to-dose conversion factors in a semiinfinite slab for normal incidence. A convenient parameterization of the conversion factors is provided along with numerical examples.

  13. Preservation of physical properties of stochastic Maxwell equations with additive noise via stochastic multi-symplectic methods

    SciTech Connect

    Chen, Chuchu Hong, Jialin Zhang, Liying

    2016-02-01

    Stochastic Maxwell equations with additive noise are a system of stochastic Hamiltonian partial differential equations intrinsically, possessing the stochastic multi-symplectic conservation law. It is shown that the averaged energy increases linearly with respect to the evolution of time and the flow of stochastic Maxwell equations with additive noise preserves the divergence in the sense of expectation. Moreover, we propose three novel stochastic multi-symplectic methods to discretize stochastic Maxwell equations in order to investigate the preservation of these properties numerically. We make theoretical discussions and comparisons on all of the three methods to observe that all of them preserve the corresponding discrete version of the averaged divergence. Meanwhile, we obtain the corresponding dissipative property of the discrete averaged energy satisfied by each method. Especially, the evolution rates of the averaged energies for all of the three methods are derived which are in accordance with the continuous case. Numerical experiments are performed to verify our theoretical results.

  14. Non-dispersive carrier transport in molecularly doped polymers and the convection-diffusion equation

    NASA Astrophysics Data System (ADS)

    Tyutnev, A. P.; Parris, P. E.; Saenko, V. S.

    2015-08-01

    We reinvestigate the applicability of the concept of trap-free carrier transport in molecularly doped polymers and the possibility of realistically describing time-of-flight (TOF) current transients in these materials using the classical convection-diffusion equation (CDE). The problem is treated as rigorously as possible using boundary conditions appropriate to conventional time of flight experiments. Two types of pulsed carrier generation are considered. In addition to the traditional case of surface excitation, we also consider the case where carrier generation is spatially uniform. In our analysis, the front electrode is treated as a reflecting boundary, while the counter electrode is assumed to act either as a neutral contact (not disturbing the current flow) or as an absorbing boundary at which the carrier concentration vanishes. As expected, at low fields transient currents exhibit unusual behavior, as diffusion currents overwhelm drift currents to such an extent that it becomes impossible to determine transit times (and hence, carrier mobilities). At high fields, computed transients are more like those typically observed, with well-defined plateaus and sharp transit times. Careful analysis, however, reveals that the non-dispersive picture, and predictions of the CDE contradict both experiment and existing disorder-based theories in important ways, and that the CDE should be applied rather cautiously, and even then only for engineering purposes.

  15. Additives

    NASA Technical Reports Server (NTRS)

    Smalheer, C. V.

    1973-01-01

    The chemistry of lubricant additives is discussed to show what the additives are chemically and what functions they perform in the lubrication of various kinds of equipment. Current theories regarding the mode of action of lubricant additives are presented. The additive groups discussed include the following: (1) detergents and dispersants, (2) corrosion inhibitors, (3) antioxidants, (4) viscosity index improvers, (5) pour point depressants, and (6) antifouling agents.

  16. Addition of simultaneous heat and solute transport and variable fluid viscosity to SEAWAT

    USGS Publications Warehouse

    Thorne, D.; Langevin, C.D.; Sukop, M.C.

    2006-01-01

    SEAWAT is a finite-difference computer code designed to simulate coupled variable-density ground water flow and solute transport. This paper describes a new version of SEAWAT that adds the ability to simultaneously model energy and solute transport. This is necessary for simulating the transport of heat and salinity in coastal aquifers for example. This work extends the equation of state for fluid density to vary as a function of temperature and/or solute concentration. The program has also been modified to represent the effects of variable fluid viscosity as a function of temperature and/or concentration. The viscosity mechanism is verified against an analytical solution, and a test of temperature-dependent viscosity is provided. Finally, the classic Henry-Hilleke problem is solved with the new code. ?? 2006 Elsevier Ltd. All rights reserved.

  17. Variational approach to extracting the phonon mean free path distribution from the spectral Boltzmann transport equation

    NASA Astrophysics Data System (ADS)

    Chiloyan, Vazrik; Zeng, Lingping; Huberman, Samuel; Maznev, Alexei A.; Nelson, Keith A.; Chen, Gang

    2016-04-01

    The phonon Boltzmann transport equation (BTE) is a powerful tool for studying nondiffusive thermal transport. Here, we develop a new universal variational approach to solving the BTE that enables extraction of phonon mean free path (MFP) distributions from experiments exploring nondiffusive transport. By utilizing the known Fourier heat conduction solution as a trial function, we present a direct approach to calculating the effective thermal conductivity from the BTE. We demonstrate this technique on the transient thermal grating experiment, which is a useful tool for studying nondiffusive thermal transport and probing the MFP distribution of materials. We obtain a closed form expression for a suppression function that is materials dependent, successfully addressing the nonuniversality of the suppression function used in the past, while providing a general approach to studying thermal properties in the nondiffusive regime.

  18. Thermal transport at the nanoscale: A Fourier's law vs. phonon Boltzmann equation study

    NASA Astrophysics Data System (ADS)

    Kaiser, J.; Feng, T.; Maassen, J.; Wang, X.; Ruan, X.; Lundstrom, M.

    2017-01-01

    Steady-state thermal transport in nanostructures with dimensions comparable to the phonon mean-free-path is examined. Both the case of contacts at different temperatures with no internal heat generation and contacts at the same temperature with internal heat generation are considered. Fourier's law results are compared to finite volume method solutions of the phonon Boltzmann equation in the gray approximation. When the boundary conditions are properly specified, results obtained using Fourier's law without modifying the bulk thermal conductivity are in essentially exact quantitative agreement with the phonon Boltzmann equation in the ballistic and diffusive limits. The errors between these two limits are examined in this paper. For the four cases examined, the error in the apparent thermal conductivity as deduced from a correct application of Fourier's law is less than 6%. We also find that the Fourier's law results presented here are nearly identical to those obtained from a widely used ballistic-diffusive approach but analytically much simpler. Although limited to steady-state conditions with spatial variations in one dimension and to a gray model of phonon transport, the results show that Fourier's law can be used for linear transport from the diffusive to the ballistic limit. The results also contribute to an understanding of how heat transport at the nanoscale can be understood in terms of the conceptual framework that has been established for electron transport at the nanoscale.

  19. TRANSPORT EQUATION FOR MHD TURBULENCE: APPLICATION TO PARTICLE ACCELERATION AT INTERPLANETARY SHOCKS

    SciTech Connect

    Sokolov, Igor V.; Gombosi, Tamas I.; Roussev, Ilia I.; Skender, Marina; Usmanov, Arcadi V. E-mail: tamas@umich.edu E-mail: Arcadi.Usmanov.1@gsfc.nasa.gov

    2009-05-01

    The aim of the present paper is to unify the various transport equations for turbulent waves that are used in different areas of space physics. Here, we mostly focus on the magnetohydrodynamic turbulence, in particular the Alfvenic turbulence. The applied methods, however, are general and can be extended to other forms of turbulence, for example the acoustic turbulence, or Langmuir plasma waves. With minor modifications, the derivations followed here can be extended for relativistic motions, thus making it possible to apply them to the wave transport in astrophysical objects with high plasma speeds (radiojets), or strong gravity (black hole surroundings)

  20. Electron and ion transport equations in computational weakly-ionized plasmadynamics

    SciTech Connect

    Parent, Bernard; Macheret, Sergey O.; Shneider, Mikhail N.

    2014-02-15

    A new set of ion and electron transport equations is proposed to simulate steady or unsteady quasi-neutral or non-neutral multicomponent weakly-ionized plasmas through the drift–diffusion approximation. The proposed set of equations is advantaged over the conventional one by being considerably less stiff in quasi-neutral regions because it can be integrated in conjunction with a potential equation based on Ohm's law rather than Gauss's law. The present approach is advantaged over previous attempts at recasting the system by being applicable to plasmas with several types of positive ions and negative ions and by not requiring changes to the boundary conditions. Several test cases of plasmas enclosed by dielectrics and of glow discharges between electrodes show that the proposed equations yield the same solution as the standard equations but require 10 to 100 times fewer iterations to reach convergence whenever a quasi-neutral region forms. Further, several grid convergence studies indicate that the present approach exhibits a higher resolution (and hence requires fewer nodes to reach a given level of accuracy) when ambipolar diffusion is present. Because the proposed equations are not intrinsically linked to specific discretization or integration schemes and exhibit substantial advantages with no apparent disadvantage, they are generally recommended as a substitute to the fluid models in which the electric field is obtained from Gauss's law as long as the plasma remains weakly-ionized and unmagnetized.

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

    SciTech Connect

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

    2015-08-04

    We present simulations of a four component mixture of HCNO with orbital free molecular dynamics (OFMD). These simulations were conducted for 5–200 eV with densities ranging between 0.184 and 36.8 g/cm3. We extract the equation of state from the simulations and compare to average atom models. We found that we only need to add a cold curve model to find excellent agreement. In addition, we studied mass transport properties. We present fits to the self-diffusion and shear viscosity that are able to reproduce the transport properties over the parameter range studied. We compare these OFMD results to models based on the Coulomb coupling parameter and one-component plasmas.

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

    DOE PAGES

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

    2015-08-04

    We present simulations of a four component mixture of HCNO with orbital free molecular dynamics (OFMD). These simulations were conducted for 5–200 eV with densities ranging between 0.184 and 36.8 g/cm3. We extract the equation of state from the simulations and compare to average atom models. We found that we only need to add a cold curve model to find excellent agreement. In addition, we studied mass transport properties. We present fits to the self-diffusion and shear viscosity that are able to reproduce the transport properties over the parameter range studied. We compare these OFMD results to models based onmore » the Coulomb coupling parameter and one-component plasmas.« less

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

    PubMed

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

    2015-08-01

    We present simulations of a four-component mixture of HCNO with orbital free molecular dynamics (OFMD). These simulations were conducted for 5-200 eV with densities ranging between 0.184 and 36.8 g/cm3. We extract the equation of state from the simulations and compare to average atom models. We found that we only need to add a cold curve model to find excellent agreement. Additionally, we studied mass transport properties. We present fits to the self-diffusion and shear viscosity that are able to reproduce the transport properties over the parameter range studied. We compare these OFMD results to models based on the Coulomb coupling parameter and one-component plasmas.

  4. Improved master equation approach to quantum transport: from Born to self-consistent Born approximation.

    PubMed

    Jin, Jinshuang; Li, Jun; Liu, Yu; Li, Xin-Qi; Yan, YiJing

    2014-06-28

    Beyond the second-order Born approximation, we propose an improved master equation approach to quantum transport under self-consistent Born approximation. The basic idea is to replace the free Green's function in the tunneling self-energy diagram by an effective reduced propagator under the Born approximation. This simple modification has remarkable consequences. It not only recovers the exact results for quantum transport through noninteracting systems under arbitrary voltages, but also predicts the challenging nonequilibrium Kondo effect. Compared to the nonequilibrium Green's function technique that formulates the calculation of specific correlation functions, the master equation approach contains richer dynamical information to allow more efficient studies for such as the shot noise and full counting statistics.

  5. Numerical solution of the time dependent neutron transport equation by the method of the characteristics

    NASA Astrophysics Data System (ADS)

    Talamo, Alberto

    2013-05-01

    This study presents three numerical algorithms to solve the time dependent neutron transport equation by the method of the characteristics. The algorithms have been developed taking into account delayed neutrons and they have been implemented into the novel MCART code, which solves the neutron transport equation for two-dimensional geometry and an arbitrary number of energy groups. The MCART code uses regular mesh for the representation of the spatial domain, it models up-scattering, and takes advantage of OPENMP and OPENGL algorithms for parallel computing and plotting, respectively. The code has been benchmarked with the multiplication factor results of a Boiling Water Reactor, with the analytical results for a prompt jump transient in an infinite medium, and with PARTISN and TDTORT results for cross section and source transients. The numerical simulations have shown that only two numerical algorithms are stable for small time steps.

  6. Benchmark solutions for the galactic heavy-ion transport equations with energy and spatial coupling

    NASA Technical Reports Server (NTRS)

    Ganapol, Barry D.; Townsend, Lawrence W.; Lamkin, Stanley L.; Wilson, John W.

    1991-01-01

    Nontrivial benchmark solutions are developed for the galactic heavy ion transport equations in the straightahead approximation with energy and spatial coupling. Analytical representations of the ion fluxes are obtained for a variety of sources with the assumption that the nuclear interaction parameters are energy independent. The method utilizes an analytical LaPlace transform inversion to yield a closed form representation that is computationally efficient. The flux profiles are then used to predict ion dose profiles, which are important for shield design studies.

  7. Discontinuous Galerkin finite element method applied to the 1-D spherical neutron transport equation

    SciTech Connect

    Machorro, Eric . E-mail: machorro@amath.washington.edu

    2007-04-10

    Discontinuous Galerkin finite element methods are used to estimate solutions to the non-scattering 1-D spherical neutron transport equation. Various trial and test spaces are compared in the context of a few sample problems whose exact solution is known. Certain trial spaces avoid unphysical behaviors that seem to plague other methods. Comparisons with diamond differencing and simple corner-balancing are presented to highlight these improvements.

  8. 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.

  9. Quantum transport equations for low-dimensional multiband electronic systems: I.

    PubMed

    Kupčić, I; Rukelj, Z; Barišić, S

    2013-04-10

    A systematic method of calculating the dynamical conductivity tensor in a general multiband electronic model with strong boson-mediated electron-electron interactions is described. The theory is based on the exact semiclassical expression for the coupling between valence electrons and electromagnetic fields and on the self-consistent Bethe-Salpeter equations for the electron-hole propagators. The general diagrammatic perturbation expressions for the intraband and interband single-particle conductivity are determined. The relations between the intraband Bethe-Salpeter equation, the quantum transport equation and the ordinary transport equation are briefly discussed within the memory-function approximation. The effects of the Lorentz dipole-dipole interactions on the dynamical conductivity of low-dimensional spα models are described in the same approximation. Such formalism proves useful in studies of different (pseudo)gapped states of quasi-one-dimensional systems with the metal-to-insulator phase transitions and can be easily extended to underdoped two-dimensional high-Tc superconductors.

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

    NASA Astrophysics Data System (ADS)

    Bodin, Jacques

    2015-03-01

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

  11. Analytical solutions of a fractional diffusion-advection equation for solar cosmic-ray transport

    SciTech Connect

    Litvinenko, Yuri E.; Effenberger, Frederic

    2014-12-01

    Motivated by recent applications of superdiffusive transport models to shock-accelerated particle distributions in the heliosphere, we analytically solve a one-dimensional fractional diffusion-advection equation for the particle density. We derive an exact Fourier transform solution, simplify it in a weak diffusion approximation, and compare the new solution with previously available analytical results and with a semi-numerical solution based on a Fourier series expansion. We apply the results to the problem of describing the transport of energetic particles, accelerated at a traveling heliospheric shock. Our analysis shows that significant errors may result from assuming an infinite initial distance between the shock and the observer. We argue that the shock travel time should be a parameter of a realistic superdiffusive transport model.

  12. Analytical Solutions of a Fractional Diffusion-advection Equation for Solar Cosmic-Ray Transport

    NASA Astrophysics Data System (ADS)

    Litvinenko, Yuri E.; Effenberger, Frederic

    2014-12-01

    Motivated by recent applications of superdiffusive transport models to shock-accelerated particle distributions in the heliosphere, we analytically solve a one-dimensional fractional diffusion-advection equation for the particle density. We derive an exact Fourier transform solution, simplify it in a weak diffusion approximation, and compare the new solution with previously available analytical results and with a semi-numerical solution based on a Fourier series expansion. We apply the results to the problem of describing the transport of energetic particles, accelerated at a traveling heliospheric shock. Our analysis shows that significant errors may result from assuming an infinite initial distance between the shock and the observer. We argue that the shock travel time should be a parameter of a realistic superdiffusive transport model.

  13. 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

  14. Effects of microscopic transport coefficients on fission observables calculated by the Langevin equation

    NASA Astrophysics Data System (ADS)

    Usang, M. D.; Ivanyuk, F. A.; Ishizuka, C.; Chiba, S.

    2016-10-01

    Nuclear fission is treated by using the Langevin dynamical description with macroscopic and microscopic transport coefficients (mass and friction tensors), and it is elucidated how the microscopic (shell and pairing) effects in the transport coefficients, especially their dependence on temperature, affects various fission observables. We found that the microscopic transport coefficients, calculated by linear response theory, change drastically as a function of temperature: in general, the friction increases with growing temperature while the mass tensor decreases. This temperature dependence brings a noticeable change in the mass distribution and kinetic energies of fission fragments from nuclei around 236U at an excitation energy of 20 MeV. The prescission kinetic energy decreases from 25 MeV at low temperature to about 2.5 MeV at high temperature. In contrast, the Coulomb kinetic energy increases as the temperature increases. Interpolating the microscopic transport coefficients among the various temperatures enabled our Langevin equation to use the microscopic transport coefficients at a deformation-dependent local temperature of the dynamical evolution. This allowed us to compare directly the fission observables of both macroscopic and microscopic calculations, and we found almost identical results under the conditions considered in this work.

  15. The use of Galerkin finite-element methods to solve mass-transport equations

    USGS Publications Warehouse

    Grove, David B.

    1977-01-01

    The partial differential equation that describes the transport and reaction of chemical solutes in porous media was solved using the Galerkin finite-element technique. These finite elements were superimposed over finite-difference cells used to solve the flow equation. Both convection and flow due to hydraulic dispersion were considered. Linear and Hermite cubic approximations (basis functions) provided satisfactory results: however, the linear functions were computationally more efficient for two-dimensional problems. Successive over relaxation (SOR) and iteration techniques using Tchebyschef polynomials were used to solve the sparce matrices generated using the linear and Hermite cubic functions, respectively. Comparisons of the finite-element methods to the finite-difference methods, and to analytical results, indicated that a high degree of accuracy may be obtained using the method outlined. The technique was applied to a field problem involving an aquifer contaminated with chloride, tritium, and strontium-90. (Woodard-USGS)

  16. Semi-empirical equation of limiting current for cobalt electrodeposition in the presence of magnetic field and additive electrolyte

    NASA Astrophysics Data System (ADS)

    Sudibyo, Aziz, N.

    2016-02-01

    One of the available methods to solve a roughening in cobalt electrodeposition is magneto electrodeposition (MED) in the presence of additive electrolyte. Semi-empirical equation of limiting current under a magnetic field for cobalt MED in the presence of boric acid as an additive electrolyte was successfully developed. This semi empirical equation shows the effects of the electrode area (A), the concentration of the electro active species (C), the diffusion coefficient of the electro active species (D), the kinematic viscosity of the electrolyte (v), magnetic strength (B) and the number of electrons involved in the redox process (n). The presence of boric acid led to decrease in the limiting current, but the acid was found useful as a buffer to avoid the local pH rise caused by parallel hydrogen evolution reaction (HER).

  17. The Slab Albedo Problem Using Singular Eigenfunctions and the Third Form of the Transport Equation

    NASA Astrophysics Data System (ADS)

    Kaskas, Ayþe; Tezcan, Cevdet

    1997-01-01

    The albedo and the transmission factor for slabs are obtained using the infinite medium Green's function in terms of the singular eigenfunctions in the third form of the transport equation. Our analytical results are simple as in FN-method and the convergence of the numerical results is as faster as in the CN-method. Calculations are also carried out by various incoming angular fluxes and uncollided neutrons are taken into account. Our numerical results are in very good agreement with the results of the CN method.

  18. Solution of transport equations in layered media with refractive index mismatch using the PN-method.

    PubMed

    Phillips, Kevin G; Jacques, Steven L

    2009-10-01

    The PN-method is a spectral discretization technique used to obtain numerical solutions to the radiative transport equation. To the best of our knowledge, the PN-method has yet to be generalized to the case of refractive index mismatch in layered slabs used to numerically simulate skin. Our main contribution is the application of a collocation method that takes into account refractive index mismatch at layer interfaces. The stability, convergence, and accuracy of the method are established. Example calculations demonstrating the flexibility of the method are performed.

  19. Unified description of equation of state and transport properties of nuclear matter

    SciTech Connect

    Benhar, Omar; Farina, Nicola; Valli, Marco; Fiorilla, Salvatore

    2008-10-13

    Correlated basis function perturbation theory and the formalism of cluster expansions have been recently employed to obtain an effective interaction from a state-of-the-art nucleon nucleon potential model. The approach based on the effective interaction allows for a consistent description of the nuclear matter ground state and nucleon-nucleon scattering in the nuclear medium. This paper reports the the results of numerical calculations of different properties of nuclear and neutron matter, including the equation of state and the shear viscosity and thermal conductivity transport coefficients, carried out using the effective interaction.

  20. Gluon transport equation with effective mass and dynamical onset of Bose–Einstein condensation

    DOE PAGES

    Blaizot, Jean-Paul; Jiang, Yin; Liao, Jinfeng

    2016-05-01

    In this paper we study the transport equation describing a dense system of gluons, in the small scattering angle approximation, taking into account medium-generated effective masses of the gluons. We focus on the case of overpopulated systems that are driven to Bose–Einstein condensation on their way to thermalization. Lastly, the presence of a mass modifies the dispersion relation of the gluon, as compared to the massless case, but it is shown that this does not change qualitatively the scaling behavior in the vicinity of the onset.

  1. Simulating photon-transport in uniform media using the radiative transport equation: a study using the Neumann-series approach

    PubMed Central

    Jha, Abhinav K.; Kupinski, Matthew A.; Masumura, Takahiro; Clarkson, Eric; Maslov, Alexey V.; Barrett, Harrison H.

    2014-01-01

    We present the implementation, validation, and performance of a Neumann-series approach for simulating light propagation at optical wavelengths in uniform media using the radiative transport equation (RTE). The RTE is solved for an anisotropic-scattering medium in a spherical harmonic basis for a diffuse-optical-imaging setup. The main objectives of this paper are threefold: to present the theory behind the Neumann-series form for the RTE, to design and develop the mathematical methods and the software to implement the Neumann series for a diffuse-optical-imaging setup, and, finally, to perform an exhaustive study of the accuracy, practical limitations, and computational efficiency of the Neumann-series method. Through our results, we demonstrate that the Neumann-series approach can be used to model light propagation in uniform media with small geometries at optical wavelengths. PMID:23201893

  2. A Bayesian additive model for understanding public transport usage in special events.

    PubMed

    Rodrigues, Filipe; Borysov, Stanislav; Ribeiro, Bernardete; Pereira, Francisco

    2016-12-02

    Public special events, like sports games, concerts and festivals are well known to create disruptions in transportation systems, often catching the operators by surprise. Although these are usually planned well in advance, their impact is difficult to predict, even when organisers and transportation operators coordinate. The problem highly increases when several events happen concurrently. To solve these problems, costly processes, heavily reliant on manual search and personal experience, are usual practice in large cities like Singapore, London or Tokyo. This paper presents a Bayesian additive model with Gaussian process components that combines smart card records from public transport with context information about events that is continuously mined from the Web. We develop an efficient approximate inference algorithm using expectation propagation, which allows us to predict the total number of public transportation trips to the special event areas, thereby contributing to a more adaptive transportation system. Furthermore, for multiple concurrent event scenarios, the proposed algorithm is able to disaggregate gross trip counts into their most likely components related to specific events and routine behavior. Using real data from Singapore, we show that the presented model outperforms the best baseline model by up to 26% in R2 and also has explanatory power for its individual components.

  3. Theoretical analysis of integral neutron transport equation using collision probability method with quadratic flux approach

    SciTech Connect

    Shafii, Mohammad Ali Meidianti, Rahma Wildian, Fitriyani, Dian; Tongkukut, Seni H. J.; Arkundato, Artoto

    2014-09-30

    Theoretical analysis of integral neutron transport equation using collision probability (CP) method with quadratic flux approach has been carried out. In general, the solution of the neutron transport using the CP method is performed with the flat flux approach. In this research, the CP method is implemented in the cylindrical nuclear fuel cell with the spatial of mesh being conducted into non flat flux approach. It means that the neutron flux at any point in the nuclear fuel cell are considered different each other followed the distribution pattern of quadratic flux. The result is presented here in the form of quadratic flux that is better understanding of the real condition in the cell calculation and as a starting point to be applied in computational calculation.

  4. A Piecewise Bi-Linear Discontinuous Finite Element Spatial Discretization of the Sn Transport Equation

    SciTech Connect

    Bailey, T S; Chang, J H; Warsa, J S; Adams, M L

    2010-12-22

    We present a new spatial discretization of the discrete-ordinates transport equation in two-dimensional Cartesian (X-Y) geometry for arbitrary polygonal meshes. The discretization is a discontinuous finite element method (DFEM) that utilizes piecewise bi-linear (PWBL) basis functions, which are formally introduced in this paper. We also present a series of numerical results on quadrilateral and polygonal grids and compare these results to a variety of other spatial discretizations that have been shown to be successful on these grid types. Finally, we note that the properties of the PWBL basis functions are such that the leading-order piecewise bi-linear discontinuous finite element (PWBLD) solution will satisfy a reasonably accurate diffusion discretization in the thick diffusion limit, making the PWBLD method a viable candidate for many different classes of transport problems.

  5. Representative equations for the thermodynamic and transport properties of fluids near the gas-liquid critical point

    NASA Technical Reports Server (NTRS)

    Sengers, J. V.; Basu, R. S.; Sengers, J. M. H. L.

    1981-01-01

    A survey is presented of representative equations for various thermophysical properties of fluids in the critical region. Representative equations for the transport properties are included. Semi-empirical modifications of the theoretically predicted asymtotic critical behavior that yield simple and practical representations of the fluid properties in the critical region are emphasized.

  6. A posteriori testing of the flame surface density transport equation for LES

    NASA Astrophysics Data System (ADS)

    Ma, T.; Stein, O. T.; Chakraborty, N.; Kempf, A. M.

    2014-01-01

    Flame Surface Density (FSD) models for Large Eddy Simulation (LES) are implemented and tested for a canonical configuration and a practical bluff body stabilised burner, comparing common algebraic closures with a transport equation closure in the context of turbulent premixed combustion. The transported method is expected to yield advantages over algebraic closures, as the equilibrium of subgrid production and destruction of FSD is no longer enforced and resolved processes of strain, propagation and curvature are explicitly accounted for. These advantages might have the potential to improve the ability to capture large-scale unsteady flame propagation in situations with combustion instabilities or situations where the flame encounters progressive wrinkling with time. The initial study of a propagating turbulent flame in wind-tunnel turbulence shows that the Algebraic Flame Surface Density (FSDA) method can predict an excessively wrinkled flame under fine grid conditions, potentially increasing the consumption rate of reactants to artificially higher levels. In contrast, the Flame Surface Density Transport (FSDT) closure predicts a smooth flame front and avoids the formation of artificial flame cusps when the grid is refined. Five FSDA models and the FSDT approach are then applied to the LES of the Volvo Rig. The predicted mean velocities are found to be relatively insensitive to the use of the FSDT and FSDA approaches, whereas temperature predictions exhibit appreciable differences for different formulations. The FSDT approach yields very similar temperature predictions to two of the tested FSDA models, quantitatively capturing the mean temperature. Grid refinement is found to improve the FSDT predictions of the mean flame spread. Overall, the paper demonstrates that the apparently complicated FSD transport equation approach can be implemented and applied to realistic, strongly wrinkled flames with good success, and opens up the field for further work to improve

  7. Initiation and Modification of Reaction by Energy Addition: Kinetic and Transport Phenomena

    DTIC Science & Technology

    1993-10-01

    MODIFICATION OF REACTION BY ENERGY ADDITION: KINETIC AND TRANSPORT PHENOMENA by Francis E. Fendell and Mau-Song Chou Center for Propulsion Technology...TA - A2 L AUHOWAC - F49620-90-C-0070 Francis E. Fendell and Mau-Song Chou 7. PEMOS101IG ORGANIZATION NAME(S AND...a gaseous mixture is more pertinent for the supersonic-combustor applications of interest to the Air Force (compare Figs. 1 and 2) (Carrier, Fendell

  8. Rate constant calculations of the C2 + HCN → CCCN+H addition via the Master Equation.

    PubMed

    da Silva, Washington Barbosa; Albernaz, Alessandra F; Barreto, Patricia R P; Correa, Eberth

    2017-04-01

    The addition of C2 to HCN is of relevant interest in astrochemistry. We studied the pathways of this addition to produce CCCN and estimated its reaction rate using the Master Equation in the circumstellar environment. From the results of this study, it was possible to show that a different pathway in the Surface Potential Energy-PES can also be investigated. In a circumstellar envelop environment, with temperatures varying between 1000 K and 2000 K, the abundances of these species are favorable to this kind of addition, and our branching ratio for the rate constant showed that the new pathway is more favorable in comparison with other possibilities for this range of temperatures in this environment, and must be taken into account in any computation of the rate constant. Graphical Abstract Branching ratios of pathways involved in the C2 + HCN → CCCN+H addition, at a temperature range of 1000-2000 K.

  9. Implementation of the interfacial area transport equation in trace for boiling two-phase flows

    NASA Astrophysics Data System (ADS)

    Bernard, Matthew S.

    Correctly predicting the interfacial area concentration (a i) is vital to the overall accuracy of the two-fluid model because ai describes the amount of surface area that exists between the two-phases, and is therefore directly related to interfacial mass, momentum and energy transfer. The conventional method for specifying ai in the two-fluid model is through flow regime-based empirical correlations coupled with regime transition criteria. However, a more physically consistent approach to predicting ai is through the interfacial area transport equation (IATE), which can address the deficiencies of the flow regime-based approach. Some previous studies have been performed to demonstrate the feasibility of IATE in developmental versions of the nuclear reactor systems analysis code, TRACE. However, a full TRACE version capable of predicting boiling two-phase flows with the IATE has not been established. Therefore, the current work develops a version of TRACE that is capable of predicting boiling two-phase flows using the IATE. The development is carried out in stages. First, a version of TRACE which employs the two-group IATE for adiabatic, vertical upward, air-water conditions is developed. An in-depth assessment on the existing experimental database is performed to select reliable experimental data for code assessment. Then, the implementation is assessed against the qualified air-water two-phase flow experimental data. Good agreement is observed between the experimental data for ai and the TRACE code with an average error of +/-9% for all conditions. Following the initial development, one-group IATE models for vertical downward and horizontal two-phase flows are implemented and assessed against qualified data. Finally, IATE models capable of predicting subcooled boiling two-phase flows are implemented. An assessment of the models shows that TRACE is capable of generating ai in subcooled boiling two-phase flows with the IATE and that heat transfer effects dominate

  10. A numerical spectral approach to solve the dislocation density transport equation

    NASA Astrophysics Data System (ADS)

    Djaka, K. S.; Taupin, V.; Berbenni, S.; Fressengeas, C.

    2015-09-01

    A numerical spectral approach is developed to solve in a fast, stable and accurate fashion, the quasi-linear hyperbolic transport equation governing the spatio-temporal evolution of the dislocation density tensor in the mechanics of dislocation fields. The approach relies on using the Fast Fourier Transform algorithm. Low-pass spectral filters are employed to control both the high frequency Gibbs oscillations inherent to the Fourier method and the fast-growing numerical instabilities resulting from the hyperbolic nature of the transport equation. The numerical scheme is validated by comparison with an exact solution in the 1D case corresponding to dislocation dipole annihilation. The expansion and annihilation of dislocation loops in 2D and 3D settings are also produced and compared with finite element approximations. The spectral solutions are shown to be stable, more accurate for low Courant numbers and much less computation time-consuming than the finite element technique based on an explicit Galerkin-least squares scheme.

  11. Analytical solutions of the one-dimensional advection-dispersion solute transport equation subject to time-dependent boundary conditions

    Technology Transfer Automated Retrieval System (TEKTRAN)

    Analytical solutions of the advection-dispersion solute transport equation remain useful for a large number of applications in science and engineering. In this paper we extend the Duhamel theorem, originally established for diffusion type problems, to the case of advective-dispersive transport subj...

  12. Equations of the surface harmonics method for solving time-dependent neutron transport problems and their verification

    NASA Astrophysics Data System (ADS)

    Boyarinov, V. F.; Kondrushin, A. E.; Fomichenko, P. A.

    2013-12-01

    Time-dependent equations of the surface harmonics method (SHM) are obtained for planar one-dimensional geometry. The equations are verified by calculations of test problems from Benchmark Problem Book ANL-7416, and the capabilities and efficiency of applying the SHM for solving the time-dependent neutron transport equation in the diffusion approximation are demonstrated. The results of the work show that the implementation of the SHG for full-scale computations will make possible substantial progress in the efficient solution of time-dependent problems of neutron transport in nuclear reactors.

  13. FAST TRACK PAPER: A study of the applicability and divergence of the ray series using a modified transport equation

    NASA Astrophysics Data System (ADS)

    Buske, Stefan; Kravtsov, Yury A.

    2005-01-01

    In this paper, we study an extension of the standard ray-theoretical transport equation. We include a higher-order term of the ray series and obtain a modified frequency-dependent transport equation. This equation is solved analytically and numerically for an elastic 1-D model. The analysis of the results documents that the ray series diverges just at the boundary of applicability of the underlying high-frequency approximation. This implies that taking into account higher-order terms in the ray series neither improves accuracy nor allows a shift of the boundary of its applicability towards lower frequencies.

  14. Predicting fractional bed load transport rates: Application of the Wilcock-Crowe equations to a regulated gravel bed river

    USGS Publications Warehouse

    Gaeuman, D.; Andrews, E.D.; Kraus, A.; Smith, W.

    2009-01-01

    Bed load samples from four locations in the Trinity River of northern California are analyzed to evaluate the performance of the Wilcock-Crowe bed load transport equations for predicting fractional bed load transport rates. Bed surface particles become smaller and the fraction of sand on the bed increases with distance downstream from Lewiston Dam. The dimensionless reference shear stress for the mean bed particle size (t*rm) is largest near the dam, but varies relatively little between the more downstream locations. The relation between t*rm and the reference shear stresses for other size fractions is constant across all locations. Total bed load transport rates predicted with the Wilcock-Crowe equations are within a factor of 2 of sampled transport rates for 68% of all samples. The Wilcock-Crowe equations nonetheless consistently under-predict the transport of particles larger than 128 mm, frequently by more than an order of magnitude. Accurate prediction of the transport rates of the largest particles is important for models in which the evolution of the surface grain size distribution determines subsequent bed load transport rates. Values of term estimated from bed load samples are up to 50% larger than those predicted with the Wilcock-Crowe equations, and sampled bed load transport approximates equal mobility across a wider range of grain sizes than is implied by the equations. Modifications to theWilcock-Crowe equation for determining t*rm and the hiding function used to scale term to other grain size fractions are proposed to achieve the best fit to observed bed load transport in the Trinity River. Copyright 2009 by the American eophysical Union.

  15. Hopf bifurcation in a nonlocal nonlinear transport equation stemming from stochastic neural dynamics.

    PubMed

    Drogoul, Audric; Veltz, Romain

    2017-02-01

    In this work, we provide three different numerical evidences for the occurrence of a Hopf bifurcation in a recently derived [De Masi et al., J. Stat. Phys. 158, 866-902 (2015) and Fournier and löcherbach, Ann. Inst. H. Poincaré Probab. Stat. 52, 1844-1876 (2016)] mean field limit of a stochastic network of excitatory spiking neurons. The mean field limit is a challenging nonlocal nonlinear transport equation with boundary conditions. The first evidence relies on the computation of the spectrum of the linearized equation. The second stems from the simulation of the full mean field. Finally, the last evidence comes from the simulation of the network for a large number of neurons. We provide a "recipe" to find such bifurcation which nicely complements the works in De Masi et al. [J. Stat. Phys. 158, 866-902 (2015)] and Fournier and löcherbach [Ann. Inst. H. Poincaré Probab. Stat. 52, 1844-1876 (2016)]. This suggests in return to revisit theoretically these mean field equations from a dynamical point of view. Finally, this work shows how the noise level impacts the transition from asynchronous activity to partial synchronization in excitatory globally pulse-coupled networks.

  16. Hopf bifurcation in a nonlocal nonlinear transport equation stemming from stochastic neural dynamics

    NASA Astrophysics Data System (ADS)

    Drogoul, Audric; Veltz, Romain

    2017-02-01

    In this work, we provide three different numerical evidences for the occurrence of a Hopf bifurcation in a recently derived [De Masi et al., J. Stat. Phys. 158, 866-902 (2015) and Fournier and löcherbach, Ann. Inst. H. Poincaré Probab. Stat. 52, 1844-1876 (2016)] mean field limit of a stochastic network of excitatory spiking neurons. The mean field limit is a challenging nonlocal nonlinear transport equation with boundary conditions. The first evidence relies on the computation of the spectrum of the linearized equation. The second stems from the simulation of the full mean field. Finally, the last evidence comes from the simulation of the network for a large number of neurons. We provide a "recipe" to find such bifurcation which nicely complements the works in De Masi et al. [J. Stat. Phys. 158, 866-902 (2015)] and Fournier and löcherbach [Ann. Inst. H. Poincaré Probab. Stat. 52, 1844-1876 (2016)]. This suggests in return to revisit theoretically these mean field equations from a dynamical point of view. Finally, this work shows how the noise level impacts the transition from asynchronous activity to partial synchronization in excitatory globally pulse-coupled networks.

  17. Global Error Bounds for the Petrov-Galerkin Discretization of the Neutron Transport Equation

    SciTech Connect

    Chang, B; Brown, P; Greenbaum, A; Machorro, E

    2005-01-21

    In this paper, we prove that the numerical solution of the mono-directional neutron transport equation by the Petrov-Galerkin method converges to the true solution in the L{sup 2} norm at the rate of h{sup 2}. Since consistency has been shown elsewhere, the focus here is on stability. We prove that the system of Petrov-Galerkin equations is stable by showing that the 2-norm of the inverse of the matrix for the system of equations is bounded by a number that is independent of the order of the matrix. This bound is equal to the length of the longest path that it takes a neutron to cross the domain in a straight line. A consequence of this bound is that the global error of the Petrov-Galerkin approximation is of the same order of h as the local truncation error. We use this result to explain the widely held observation that the solution of the Petrov-Galerkin method is second accurate for one class of problems, but is only first order accurate for another class of problems.

  18. Numerical solution of the compressible Navier-Stokes equations using density gradients as additional dependent variables. M.S. Thesis

    NASA Technical Reports Server (NTRS)

    Kwon, J. H.

    1977-01-01

    Numerical solution of two dimensional, time dependent, compressible viscous Navier-Stokes equations about arbitrary bodies was treated using density gradients as additional dependent variables. Thus, six dependent variables were computed with the SOR iteration method. Besides formulation for pressure gradient terms, a formulation for computing the body density was presented. To approximate the governing equations, an implicit finite difference method was employed. In computing the solution for the flow about a circular cylinder, a problem arose near the wall at both stagnation points. Thus, computations with various conditions were tried to examine the problem. Also, computations with and without formulations are compared. The flow variables were computed on 37 by 40 field first, then on an 81 by 40 field.

  19. An upscaled two-equation model of transport in porous media through unsteady-state closure of volume averaged formulations

    NASA Astrophysics Data System (ADS)

    Chaynikov, S.; Porta, G.; Riva, M.; Guadagnini, A.

    2012-04-01

    We focus on a theoretical analysis of nonreactive solute transport in porous media through the volume averaging technique. Darcy-scale transport models based on continuum formulations typically include large scale dispersive processes which are embedded in a pore-scale advection diffusion equation through a Fickian analogy. This formulation has been extensively questioned in the literature due to its inability to depict observed solute breakthrough curves in diverse settings, ranging from the laboratory to the field scales. The heterogeneity of the pore-scale velocity field is one of the key sources of uncertainties giving rise to anomalous (non-Fickian) dispersion in macro-scale porous systems. Some of the models which are employed to interpret observed non-Fickian solute behavior make use of a continuum formulation of the porous system which assumes a two-region description and includes a bimodal velocity distribution. A first class of these models comprises the so-called ''mobile-immobile'' conceptualization, where convective and dispersive transport mechanisms are considered to dominate within a high velocity region (mobile zone), while convective effects are neglected in a low velocity region (immobile zone). The mass exchange between these two regions is assumed to be controlled by a diffusive process and is macroscopically described by a first-order kinetic. An extension of these ideas is the two equation ''mobile-mobile'' model, where both transport mechanisms are taken into account in each region and a first-order mass exchange between regions is employed. Here, we provide an analytical derivation of two region "mobile-mobile" meso-scale models through a rigorous upscaling of the pore-scale advection diffusion equation. Among the available upscaling methodologies, we employ the Volume Averaging technique. In this approach, the heterogeneous porous medium is supposed to be pseudo-periodic, and can be represented through a (spatially) periodic unit cell

  20. Solution of the within-group multidimensional discrete ordinates transport equations on massively parallel architectures

    NASA Astrophysics Data System (ADS)

    Zerr, Robert Joseph

    2011-12-01

    The integral transport matrix method (ITMM) has been used as the kernel of new parallel solution methods for the discrete ordinates approximation of the within-group neutron transport equation. The ITMM abandons the repetitive mesh sweeps of the traditional source iterations (SI) scheme in favor of constructing stored operators that account for the direct coupling factors among all the cells and between the cells and boundary surfaces. The main goals of this work were to develop the algorithms that construct these operators and employ them in the solution process, determine the most suitable way to parallelize the entire procedure, and evaluate the behavior and performance of the developed methods for increasing number of processes. This project compares the effectiveness of the ITMM with the SI scheme parallelized with the Koch-Baker-Alcouffe (KBA) method. The primary parallel solution method involves a decomposition of the domain into smaller spatial sub-domains, each with their own transport matrices, and coupled together via interface boundary angular fluxes. Each sub-domain has its own set of ITMM operators and represents an independent transport problem. Multiple iterative parallel solution methods have investigated, including parallel block Jacobi (PBJ), parallel red/black Gauss-Seidel (PGS), and parallel GMRES (PGMRES). The fastest observed parallel solution method, PGS, was used in a weak scaling comparison with the PARTISN code. Compared to the state-of-the-art SI-KBA with diffusion synthetic acceleration (DSA), this new method without acceleration/preconditioning is not competitive for any problem parameters considered. The best comparisons occur for problems that are difficult for SI DSA, namely highly scattering and optically thick. SI DSA execution time curves are generally steeper than the PGS ones. However, until further testing is performed it cannot be concluded that SI DSA does not outperform the ITMM with PGS even on several thousand or tens of

  1. Nonlinear diffusion acceleration for the multigroup transport equation discretized with S{sub N} and continuous FEM with rattlesnake

    SciTech Connect

    Wang, Y.

    2013-07-01

    Nonlinear diffusion acceleration (NDA) can improve the performance of a neutron transport solver significantly especially for the multigroup eigenvalue problems. The high-order transport equation and the transport-corrected low-order diffusion equation form a nonlinear system in NDA, which can be solved via a Picard iteration. The consistency of the correction of the low-order equation is important to ensure the stabilization and effectiveness of the iteration. It also makes the low-order equation preserve the scalar flux of the high-order equation. In this paper, the consistent correction for a particular discretization scheme, self-adjoint angular flux (SAAF) formulation with discrete ordinates method (S{sub N}) and continuous finite element method (CFEM) is proposed for the multigroup neutron transport equation. Equations with the anisotropic scatterings and a void treatment are included. The Picard iteration with this scheme has been implemented and tested with RattleS{sub N}ake, a MOOSE-based application at INL. Convergence results are presented. (authors)

  2. Performance assessment of several equations of state and second virial coefficients in modified Enskog theory: Results for transport properties

    NASA Astrophysics Data System (ADS)

    Kiani, M.; Alavianmehr, M. M.; Otoofat, M.; Mohsenipour, A. A.; Ghatee, A.

    2015-11-01

    In this work, we identify a simple method for predicting transport properties of fluids over wide ranges of temperatures and pressure. In this respect, the capability of several equations of state (EOS) and second virial coefficient correlations to predict transport properties of fluids including carbon dioxide, methane and argon using modified Enskog theory (MET) is investigated. The transport properties in question are viscosity and thermal conductivity. The results indicate that the SRK EOS employed in the modified Enskog theory outperforms other equations of state. The average absolute deviation was found to be 12.2 and 18.5% for, respectively, the calculated thermal conductivity and viscosity using the MET.

  3. Transport Equations Resolution By N-BEE Anti-Dissipative Scheme In 2D Model Of Low Pressure Glow Discharge

    SciTech Connect

    Kraloua, B.; Hennad, A.

    2008-09-23

    The aim of this paper is to determine electric and physical properties by 2D modelling of glow discharge low pressure in continuous regime maintained by term constant source. This electric discharge is confined in reactor plan-parallel geometry. This reactor is filled by Argon monatomic gas. Our continuum model the order two is composed the first three moments the Boltzmann's equations coupled with Poisson's equation by self consistent method. These transport equations are discretized by the finite volumes method. The equations system is resolved by a new technique, it is about the N-BEE explicit scheme using the time splitting method.

  4. Boltzmann equation and Monte Carlo studies of electron transport in resistive plate chambers

    NASA Astrophysics Data System (ADS)

    Bošnjaković, D.; Petrović, Z. Lj; White, R. D.; Dujko, S.

    2014-10-01

    A multi term theory for solving the Boltzmann equation and Monte Carlo simulation technique are used to investigate electron transport in Resistive Plate Chambers (RPCs) that are used for timing and triggering purposes in many high energy physics experiments at CERN and elsewhere. Using cross sections for electron scattering in C2H2F4, iso-C4H10 and SF6 as an input in our Boltzmann and Monte Carlo codes, we have calculated data for electron transport as a function of reduced electric field E/N in various C2H2F4/iso-C4H10/SF6 gas mixtures used in RPCs in the ALICE, CMS and ATLAS experiments. Emphasis is placed upon the explicit and implicit effects of non-conservative collisions (e.g. electron attachment and/or ionization) on the drift and diffusion. Among many interesting and atypical phenomena induced by the explicit effects of non-conservative collisions, we note the existence of negative differential conductivity (NDC) in the bulk drift velocity component with no indication of any NDC for the flux component in the ALICE timing RPC system. We systematically study the origin and mechanisms for such phenomena as well as the possible physical implications which arise from their explicit inclusion into models of RPCs. Spatially-resolved electron transport properties are calculated using a Monte Carlo simulation technique in order to understand these phenomena.

  5. Phase-space finite elements in a least-squares solution of the transport equation

    SciTech Connect

    Drumm, C.; Fan, W.; Pautz, S.

    2013-07-01

    The linear Boltzmann transport equation is solved using a least-squares finite element approximation in the space, angular and energy phase-space variables. The method is applied to both neutral particle transport and also to charged particle transport in the presence of an electric field, where the angular and energy derivative terms are handled with the energy/angular finite elements approximation, in a manner analogous to the way the spatial streaming term is handled. For multi-dimensional problems, a novel approach is used for the angular finite elements: mapping the surface of a unit sphere to a two-dimensional planar region and using a meshing tool to generate a mesh. In this manner, much of the spatial finite-elements machinery can be easily adapted to handle the angular variable. The energy variable and the angular variable for one-dimensional problems make use of edge/beam elements, also building upon the spatial finite elements capabilities. The methods described here can make use of either continuous or discontinuous finite elements in space, angle and/or energy, with the use of continuous finite elements resulting in a smaller problem size and the use of discontinuous finite elements resulting in more accurate solutions for certain types of problems. The work described in this paper makes use of continuous finite elements, so that the resulting linear system is symmetric positive definite and can be solved with a highly efficient parallel preconditioned conjugate gradients algorithm. The phase-space finite elements capability has been built into the Sceptre code and applied to several test problems, including a simple one-dimensional problem with an analytic solution available, a two-dimensional problem with an isolated source term, showing how the method essentially eliminates ray effects encountered with discrete ordinates, and a simple one-dimensional charged-particle transport problem in the presence of an electric field. (authors)

  6. libmpdata++ 0.1: a library of parallel MPDATA solvers for systems of generalised transport equations

    NASA Astrophysics Data System (ADS)

    Jaruga, A.; Arabas, S.; Jarecka, D.; Pawlowska, H.; Smolarkiewicz, P. K.; Waruszewski, M.

    2014-11-01

    This paper accompanies first release of libmpdata++, a C++ library implementing the Multidimensional Positive-Definite Advection Transport Algorithm (MPDATA). The library offers basic numerical solvers for systems of generalised transport equations. The solvers are forward-in-time, conservative and non-linearly stable. The libmpdata++ library covers the basic second-order-accurate formulation of MPDATA, its third-order variant, the infinite-gauge option for variable-sign fields and a flux-corrected transport extension to guarantee non-oscillatory solutions. The library is equipped with a non-symmetric variational elliptic solver for implicit evaluation of pressure gradient terms. All solvers offer parallelisation through domain decomposition using shared-memory parallelisation. The paper describes the library programming interface, and serves as a user guide. Supported options are illustrated with benchmarks discussed in the MPDATA literature. Benchmark descriptions include code snippets as well as quantitative representations of simulation results. Examples of applications include: homogeneous transport in one, two and three dimensions in Cartesian and spherical domains; shallow-water system compared with analytical solution (originally derived for a 2-D case); and a buoyant convection problem in an incompressible Boussinesq fluid with interfacial instability. All the examples are implemented out of the library tree. Regardless of the differences in the problem dimensionality, right-hand-side terms, boundary conditions and parallelisation approach, all the examples use the same unmodified library, which is a key goal of libmpdata++ design. The design, based on the principle of separation of concerns, prioritises the user and developer productivity. The libmpdata++ library is implemented in C++, making use of the Blitz++ multi-dimensional array containers, and is released as free/libre and open-source software.

  7. libmpdata++ 1.0: a library of parallel MPDATA solvers for systems of generalised transport equations

    NASA Astrophysics Data System (ADS)

    Jaruga, A.; Arabas, S.; Jarecka, D.; Pawlowska, H.; Smolarkiewicz, P. K.; Waruszewski, M.

    2015-04-01

    This paper accompanies the first release of libmpdata++, a C++ library implementing the multi-dimensional positive-definite advection transport algorithm (MPDATA) on regular structured grid. The library offers basic numerical solvers for systems of generalised transport equations. The solvers are forward-in-time, conservative and non-linearly stable. The libmpdata++ library covers the basic second-order-accurate formulation of MPDATA, its third-order variant, the infinite-gauge option for variable-sign fields and a flux-corrected transport extension to guarantee non-oscillatory solutions. The library is equipped with a non-symmetric variational elliptic solver for implicit evaluation of pressure gradient terms. All solvers offer parallelisation through domain decomposition using shared-memory parallelisation. The paper describes the library programming interface, and serves as a user guide. Supported options are illustrated with benchmarks discussed in the MPDATA literature. Benchmark descriptions include code snippets as well as quantitative representations of simulation results. Examples of applications include homogeneous transport in one, two and three dimensions in Cartesian and spherical domains; a shallow-water system compared with analytical solution (originally derived for a 2-D case); and a buoyant convection problem in an incompressible Boussinesq fluid with interfacial instability. All the examples are implemented out of the library tree. Regardless of the differences in the problem dimensionality, right-hand-side terms, boundary conditions and parallelisation approach, all the examples use the same unmodified library, which is a key goal of libmpdata++ design. The design, based on the principle of separation of concerns, prioritises the user and developer productivity. The libmpdata++ library is implemented in C++, making use of the Blitz++ multi-dimensional array containers, and is released as free/libre and open-source software.

  8. Finite element approximation of the radiative transport equation in a medium with piece-wise constant refractive index

    SciTech Connect

    Lehtikangas, O.; Tarvainen, T.; Kim, A.D.; Arridge, S.R.

    2015-02-01

    The radiative transport equation can be used as a light transport model in a medium with scattering particles, such as biological tissues. In the radiative transport equation, the refractive index is assumed to be constant within the medium. However, in biomedical media, changes in the refractive index can occur between different tissue types. In this work, light propagation in a medium with piece-wise constant refractive index is considered. Light propagation in each sub-domain with a constant refractive index is modeled using the radiative transport equation and the equations are coupled using boundary conditions describing Fresnel reflection and refraction phenomena on the interfaces between the sub-domains. The resulting coupled system of radiative transport equations is numerically solved using a finite element method. The approach is tested with simulations. The results show that this coupled system describes light propagation accurately through comparison with the Monte Carlo method. It is also shown that neglecting the internal changes of the refractive index can lead to erroneous boundary measurements of scattered light.

  9. A non-equilibrium equation-of-motion approach to quantum transport utilizing projection operators.

    PubMed

    Ochoa, Maicol A; Galperin, Michael; Ratner, Mark A

    2014-11-12

    We consider a projection operator approach to the non-equilibrium Green function equation-of-motion (PO-NEGF EOM) method. The technique resolves problems of arbitrariness in truncation of an infinite chain of EOMs and prevents violation of symmetry relations resulting from the truncation (equivalence of left- and right-sided EOMs is shown and symmetry with respect to interchange of Fermi or Bose operators before truncation is preserved). The approach, originally developed by Tserkovnikov (1999 Theor. Math. Phys. 118 85) for equilibrium systems, is reformulated to be applicable to time-dependent non-equilibrium situations. We derive a canonical form of EOMs, thus explicitly demonstrating a proper result for the non-equilibrium atomic limit in junction problems. A simple practical scheme applicable to quantum transport simulations is formulated. We perform numerical simulations within simple models and compare results of the approach to other techniques and (where available) also to exact results.

  10. High throughput solution of Boltzmann transport equation: phonons, thermal conductivity and beyond

    NASA Astrophysics Data System (ADS)

    Plata, Jose; Nath, Pinku; Usanmaz, Demet; Toher, Cormac; Fornari, Marco; Buongiorno Nardelli, Marco; Curtarolo, Stefano

    Quantatively accurate predictions of the lattice thermal conductivity have important implications for key technologies ranging from thermoelectrics to thermal barrier coatings. Of the many approaches with varying computational costs and accuracy, which have been developed in the last years, the solution of the Boltzmann transport equation (BTE) is the only approach that guarantees accurate predictions of this property. We have implemented this methodology in the AFLOW high throughput materials science framework, which enables us to compute these anharmonic force constants and solve BTE to obtain the lattice thermal conductivity and related properties automatically in a single step. This technique can be combined with less expensive methodologies previously implemented in AFLOW to create an efficient and fast framework to accelerate the discovery of materials with interesting thermal properties.

  11. Verification of transport equations in a general purpose commercial CFD code.

    NASA Astrophysics Data System (ADS)

    Melot, Matthieu; Nennemann, Bernd; Deschênes, Claire

    2016-11-01

    In this paper, the Verification and Validation methodology is presented. This method aims to increase the reliability and the trust that can be placed into complex CFD simulations. The first step of this methodology, the code verification is presented in greater details. The CFD transport equations in steady state, transient and Arbitrary Eulerian Lagrangian (ALE, used for transient moving mesh) formulations in Ansys CFX are verified. It is shown that the expected spatial and temporal order of convergence are achieved for the steady state and the transient formulations. Unfortunately this is not completely the case for the ALE formulation. As for a lot of other commercial and in-house CFD codes, the temporal convergence of the velocity is limited to a first order where a second order would have been expected.

  12. An asymptotic-preserving scheme for the semiconductor Boltzmann equation toward the energy-transport limit

    SciTech Connect

    Hu, Jingwei; Wang, Li

    2015-01-15

    We design an asymptotic-preserving scheme for the semiconductor Boltzmann equation which leads to an energy-transport system for electron mass and energy as mean free path goes to zero. As opposed to the classical drift-diffusion limit where the stiff collisions are all in one scale, new difficulties arise in the two-scale stiff collision terms because the simple BGK penalization [15] fails to drive the solution to the correct limit. We propose to set up a spatially dependent threshold on the penalization of the stiffer collision operator such that the evolution of the solution resembles a Hilbert expansion at the continuous level. Formal asymptotic analysis and numerical results confirm the efficiency and accuracy of our scheme.

  13. Phase retrieval based on cosine grating modulation and transport of intensity equation

    NASA Astrophysics Data System (ADS)

    Chen, Ya-ping; Zhang, Quan-bing; Cheng, Hong; Qian, Yi; Lv, Qian-qian

    2016-10-01

    In order to calculate the lost phase from the intensity information effectively, a new method of phase retrieval which based on cosine grating modulation and transport of intensity equation is proposed. Firstly, the cosine grating is loaded on the spatial light modulator in the horizontal and vertical direction respectively, and the corresponding amplitude of the light field is modulated. Then the phase is calculated by its gradient which is extracted from different direction modulation light illumination. The capability of phase recovery of the proposed method in the presence of noise is tested by simulation experiments. And the results show that the proposed algorithm has a better resilience than the traditional Fourier transform algorithm at low frequency noise. Furthermore, the phase object of different scales can be retrieved using the proposed algorithm effectively by changing the frequency of cosine grating, which can control the imaging motion expediently.

  14. Optical cryptosystem based on phase-truncated Fresnel diffraction and transport of intensity equation.

    PubMed

    Zhang, Chenggong; He, Wenqi; Wu, Jiachen; Peng, Xiang

    2015-04-06

    A novel optical cryptosystem based on phase-truncated Fresnel diffraction (PTFD) and transport of intensity equation (TIE) is proposed. By using the phase truncation technique, a phase-encoded plaintext could be encrypted into a real-valued noise-like intensity distribution by employing a random amplitude mask (RAM) and a random phase mask (RPM), which are regarded as two secret keys. For decryption, a generalized amplitude-phase retrieval (GAPR) algorithm combined with the TIE method are proposed to recover the plaintext with the help of two keys. Different from the current phase-truncated-based optical cryptosystems which need record the truncated phase as decryption keys, our scheme do not need the truncated phase because of the introducing of the TIE method. Moreover, the proposed scheme is expected to against existing attacks. A set of numerical simulation results show the feasibility and security of the proposed method.

  15. On a 1D nonlocal transport equation with nonlocal velocity and subcritical or supercritical diffusion

    NASA Astrophysics Data System (ADS)

    Lazar, Omar

    2016-11-01

    We study a 1D transport equation with nonlocal velocity with subcritical or supercritical dissipation. For all data in the weighted Sobolev space Hk (wλ,κ) ∩L∞, where k = max ⁡ (0 , 3 / 2 - α) and wλ,κ is a given family of Muckenhoupt weights, we prove a global existence result in the subcritical case α ∈ (1 , 2). We also prove a local existence theorem for large data in H2 (wλ,κ) ∩L∞ in the supercritical case α ∈ (0 , 1). The proofs are based on the use of the weighted Littlewood-Paley theory, interpolation along with some new commutator estimates.

  16. Distribution Iteration: A Robust Alternative to Source Iteration for Solving the Discrete Ordinates Radiation Transport Equations in Slab and XY - Geometries

    DTIC Science & Technology

    2008-09-15

    differential equation that is coupled in space and angle. The discrete ordinates method discretizes the BTE in space and angle and the resulting...RADIATION TRANSPORT EQUATIONS IN SLAB AND XY - GEOMETRIES DISSERTATION Nicholas J. Prins, Lieutenant Colonel, USA AFIT/DS/ENP/08-S04...SOLVING THE DISCRETE ORDINATES RADIATION TRANSPORT EQUATIONS IN SLAB AND XY - GEOMETRIES DISSERTATION Presented to the Faculty Graduate

  17. Development and calibration of algebraic nonlinear models for terms in the Reynolds stress transport equations

    NASA Astrophysics Data System (ADS)

    Sjögren, Torbjörn; Johansson, Arne V.

    2000-06-01

    A simple and straightforward method is presented for the derivation and calibration of algebraic nonlinear models for terms in Reynolds stress turbulence closures. The method extensively utilizes data from direct numerical simulations to allow an investigation of the model performance over the entire Reynolds stress anisotropy-invariant map. The model constants are determined from the condition of minimizing the mean square error over the invariant map, in order to give good model behavior for as wide a class as possible of flow situations. A low Reynolds number closure is proposed based on the most general form for closing the Reynolds stress transport equations in terms of Reynolds stresses and total dissipation rate. It is shown that forcing the closure to satisfy realizability in a strict sense leads to a good model behavior even for the complicated flow situation near a wall, without any use of ad-hoc wall damping functions in the closure. The model behavior in homogeneous turbulent flow is analyzed by formulating equations for invariant measures, yielding several quite general results for the behavior of the present and other existing models. A new approach to the modeling effects of rotation in the context of Reynolds stress closures is presented and tested for some different homogeneous flows subjected to rotation.

  18. Smartphone based hand-held quantitative phase microscope using the transport of intensity equation method.

    PubMed

    Meng, Xin; Huang, Huachuan; Yan, Keding; Tian, Xiaolin; Yu, Wei; Cui, Haoyang; Kong, Yan; Xue, Liang; Liu, Cheng; Wang, Shouyu

    2016-12-20

    In order to realize high contrast imaging with portable devices for potential mobile healthcare, we demonstrate a hand-held smartphone based quantitative phase microscope using the transport of intensity equation method. With a cost-effective illumination source and compact microscope system, multi-focal images of samples can be captured by the smartphone's camera via manual focusing. Phase retrieval is performed using a self-developed Android application, which calculates sample phases from multi-plane intensities via solving the Poisson equation. We test the portable microscope using a random phase plate with known phases, and to further demonstrate its performance, a red blood cell smear, a Pap smear and monocot root and broad bean epidermis sections are also successfully imaged. Considering its advantages as an accurate, high-contrast, cost-effective and field-portable device, the smartphone based hand-held quantitative phase microscope is a promising tool which can be adopted in the future in remote healthcare and medical diagnosis.

  19. High Order Finite Volume Nonlinear Schemes for the Boltzmann Transport Equation

    SciTech Connect

    Bihari, B L; Brown, P N

    2005-03-29

    The authors apply the nonlinear WENO (Weighted Essentially Nonoscillatory) scheme to the spatial discretization of the Boltzmann Transport Equation modeling linear particle transport. The method is a finite volume scheme which ensures not only conservation, but also provides for a more natural handling of boundary conditions, material properties and source terms, as well as an easier parallel implementation and post processing. It is nonlinear in the sense that the stencil depends on the solution at each time step or iteration level. By biasing the gradient calculation towards the stencil with smaller derivatives, the scheme eliminates the Gibb's phenomenon with oscillations of size O(1) and reduces them to O(h{sup r}), where h is the mesh size and r is the order of accuracy. The current implementation is three-dimensional, generalized for unequally spaced meshes, fully parallelized, and up to fifth order accurate (WENO5) in space. For unsteady problems, the resulting nonlinear spatial discretization yields a set of ODE's in time, which in turn is solved via high order implicit time-stepping with error control. For the steady-state case, they need to solve the non-linear system, typically by Newton-Krylov iterations. There are several numerical examples presented to demonstrate the accuracy, non-oscillatory nature and efficiency of these high order methods, in comparison with other fixed-stencil schemes.

  20. New insights into self-heating in double-gate transistors by solving Boltzmann transport equations

    SciTech Connect

    Thu Trang Nghiêm, T.; Saint-Martin, J.; Dollfus, P.

    2014-08-21

    Electro-thermal effects become one of the most critical issues for continuing the downscaling of electron devices. To study this problem, a new efficient self-consistent electron-phonon transport model has been developed. Our model of phonon Boltzmann transport equation (pBTE) includes the decay of optical phonons into acoustic modes and a generation term given by electron-Monte Carlo simulation. The solution of pBTE uses an analytic phonon dispersion and the relaxation time approximation for acoustic and optical phonons. This coupled simulation is applied to investigate the self-heating effects in a 20 nm-long double gate MOSFET. The temperature profile per mode and the comparison between Fourier temperature and the effective temperature are discussed. Some significant differences occur mainly in the hot spot region. It is shown that under the influence of self-heating effects, the potential profile is modified and both the drain current and the electron ballisticity are reduced because of enhanced electron-phonon scattering rates.

  1. TH-E-BRE-02: A Forward Scattering Approximation to Dose Calculation Using the Linear Boltzmann Transport Equation

    SciTech Connect

    Catt, B; Snyder, M

    2014-06-15

    Purpose: To investigate the use of the linear Boltzmann transport equation as a dose calculation tool which can account for interface effects, while still having faster computation times than Monte Carlo methods. In particular, we introduce a forward scattering approximation, in hopes of improving calculation time without a significant hindrance to accuracy. Methods: Two coupled Boltzmann transport equations were constructed, one representing the fluence of photons within the medium, and the other, the fluence of electrons. We neglect the scattering term within the electron transport equation, resulting in an extreme forward scattering approximation to reduce computational complexity. These equations were then solved using a numerical technique for solving partial differential equations, known as a finite difference scheme, where the fluence at each discrete point in space is calculated based on the fluence at the previous point in the particle's path. Using this scheme, it is possible to develop a solution to the Boltzmann transport equations by beginning with boundary conditions and iterating across the entire medium. The fluence of electrons can then be used to find the dose at any point within the medium. Results: Comparisons with Monte Carlo simulations indicate that even simplistic techniques for solving the linear Boltzmann transport equation yield expected interface effects, which many popular dose calculation algorithms are not capable of predicting. Implementation of a forward scattering approximation does not appear to drastically reduce the accuracy of this algorithm. Conclusion: Optimized implementations of this algorithm have been shown to be very accurate when compared with Monte Carlo simulations, even in build up regions where many models fail. Use of a forward scattering approximation could potentially give a reasonably accurate dose distribution in a shorter amount of time for situations where a completely accurate dose distribution is not

  2. A Novel Algorithm for Solving the Multidimensional Neutron Transport Equation on Massively Parallel Architectures

    SciTech Connect

    Azmy, Yousry

    2014-06-10

    We employ the Integral Transport Matrix Method (ITMM) as the kernel of new parallel solution methods for the discrete ordinates approximation of the within-group neutron transport equation. The ITMM abandons the repetitive mesh sweeps of the traditional source iterations (SI) scheme in favor of constructing stored operators that account for the direct coupling factors among all the cells' fluxes and between the cells' and boundary surfaces' fluxes. The main goals of this work are to develop the algorithms that construct these operators and employ them in the solution process, determine the most suitable way to parallelize the entire procedure, and evaluate the behavior and parallel performance of the developed methods with increasing number of processes, P. The fastest observed parallel solution method, Parallel Gauss-Seidel (PGS), was used in a weak scaling comparison with the PARTISN transport code, which uses the source iteration (SI) scheme parallelized with the Koch-baker-Alcouffe (KBA) method. Compared to the state-of-the-art SI-KBA with diffusion synthetic acceleration (DSA), this new method- even without acceleration/preconditioning-is completitive for optically thick problems as P is increased to the tens of thousands range. For the most optically thick cells tested, PGS reduced execution time by an approximate factor of three for problems with more than 130 million computational cells on P = 32,768. Moreover, the SI-DSA execution times's trend rises generally more steeply with increasing P than the PGS trend. Furthermore, the PGS method outperforms SI for the periodic heterogeneous layers (PHL) configuration problems. The PGS method outperforms SI and SI-DSA on as few as P = 16 for PHL problems and reduces execution time by a factor of ten or more for all problems considered with more than 2 million computational cells on P = 4.096.

  3. Stochastic dynamics from the fractional Fokker-Planck-Kolmogorov equation: large-scale behavior of the turbulent transport coefficient.

    PubMed

    Milovanov, A V

    2001-04-01

    The formulation of the fractional Fokker-Planck-Kolmogorov (FPK) equation [Physica D 76, 110 (1994)] has led to important advances in the description of the stochastic dynamics of Hamiltonian systems. Here, the long-time behavior of the basic transport processes obeying the fractional FPK equation is analyzed. A derivation of the large-scale turbulent transport coefficient for a Hamiltonian system with 11 / 2 degrees of freedom is proposed in connection with the fractal structure of the particle chaotic trajectories. The principal transport regimes (i.e., a diffusion-type process, ballistic motion, subdiffusion in the limit of the frozen Hamiltonian, and behavior associated with self-organized criticality) are obtained as partial cases of the generalized transport law. A comparison with recent numerical and experimental studies is given.

  4. SU-E-T-270: Diffusion Synthetic Acceleration for Linear Boltzmann Transport Equation

    SciTech Connect

    Chen, G; Hong, X; Gao, H

    2015-06-15

    Purpose: Linear Boltzmann transport equation (LBTE) is as accurate as the Monte Carlo method (MC) for dose calculation in photon/particle therapy (LBTE is a deterministic and Eulerian formulation and MC is a statistical and Lagrangian description). An advantage of LBTE is that numerous acceleration techniques can be utilized for acceleration. This work is to explore the acceleration of LBTE via diffusion synthetic acceleration (DSA). Methods: For simplicity, two-dimensional, steady-state, and within-group LBTE is considered with two angular dimensions and two spatial dimensions. The discrete ordinate method is developed for solving this integro-differential equation. The angular variables are discretized using a level-symmetric quadrature set on the unit sphere. The spatial variables are discretized on the structured grid based on the diamond scheme. The source-iteration method (SI) is used to solve the discretized system.Since SI is slow in optically thick and highly scattering regime. DSA is developed to accelerate SI. The motivation for DSA is that diffusion equation (DE) is a good approximation of LBTE in the above regime. However, DE is much cheaper than LBTE computationally since DE only involves spatial variables. Thus, in each DSA iteration, DSA adds to the SI step a computationally-negligible DE step, i.e., to first solve DE with the SI residual as source term, and then compensate the SI solution with DE solution. Results: DSA was benchmarked and compared with SI. The difference between two methods was within 0.12% which verifies the accuracy of DSA, while DSA demonstrated the great advantage in speed, e.g., the reduction of iteration number to 6% and 4% respectively for cases with 100 and 1,000 scattering-absorption ratio that commonly occur in clinical dose calculation. Conclusion: DSA has been developed as one of many possible means for accelerating the numerical solver of LBTE for dose calculation. The authors were partially supported by the NSFC

  5. A fully coupled Monte Carlo/discrete ordinates solution to the neutron transport equation. Final report

    SciTech Connect

    Filippone, W.L.; Baker, R.S.

    1990-12-31

    The neutron transport equation is solved by a hybrid method that iteratively couples regions where deterministic (S{sub N}) and stochastic (Monte Carlo) methods are applied. Unlike previous hybrid methods, the Monte Carlo and S{sub N} regions are fully coupled in the sense that no assumption is made about geometrical separation or decoupling. The hybrid method provides a new means of solving problems involving both optically thick and optically thin regions that neither Monte Carlo nor S{sub N} is well suited for by themselves. The fully coupled Monte Carlo/S{sub N} technique consists of defining spatial and/or energy regions of a problem in which either a Monte Carlo calculation or an S{sub N} calculation is to be performed. The Monte Carlo region may comprise the entire spatial region for selected energy groups, or may consist of a rectangular area that is either completely or partially embedded in an arbitrary S{sub N} region. The Monte Carlo and S{sub N} regions are then connected through the common angular boundary fluxes, which are determined iteratively using the response matrix technique, and volumetric sources. The hybrid method has been implemented in the S{sub N} code TWODANT by adding special-purpose Monte Carlo subroutines to calculate the response matrices and volumetric sources, and linkage subrountines to carry out the interface flux iterations. The common angular boundary fluxes are included in the S{sub N} code as interior boundary sources, leaving the logic for the solution of the transport flux unchanged, while, with minor modifications, the diffusion synthetic accelerator remains effective in accelerating S{sub N} calculations. The special-purpose Monte Carlo routines used are essentially analog, with few variance reduction techniques employed. However, the routines have been successfully vectorized, with approximately a factor of five increase in speed over the non-vectorized version.

  6. Additive effects of serotonin transporter and tryptophan hydroxylase-2 gene variation on emotional processing.

    PubMed

    Herrmann, Martin J; Huter, Theresa; Müller, Frauke; Mühlberger, Andreas; Pauli, Paul; Reif, Andreas; Renner, Tobias; Canli, Turhan; Fallgatter, Andreas J; Lesch, Klaus-Peter

    2007-05-01

    Prior studies reported that functional variants of both the serotonin transporter (5-HTT) and tryptophan hydroxylase-2 genes (TPH2), 2 key regulators of the serotonergic signaling pathway, modulate amygdala activation during emotional processing. We addressed the question whether these 2 gene variants modulate each other, using an emotional picture-processing task. Specifically, we measured event-related potentials (ERPs) during a passive emotional picture perception task, focusing on ERPs for the early posterior negativity (EPN) around 240 ms and for the slow wave starting at 315 ms. We found evidence for increased neural activity at 240 ms in individuals who carried 1 or 2 copies of the low-expression short variant of the 5-HTT. Carriers of T variant of the TPH2 also showed a tendency toward increased neural activity at 240 ms. Moreover, we observed an additive effect of both genotypes for EPN, with highest neural activity to emotional stimuli in individuals carrying combination of both short variant of 5-HTT and T variant of TPH2. Our results indicate that both the 5-HTT and the TPH2 genotypes modulate the sensory encoding of affective stimuli during early steps of visual processing and reveal additive effects of 2 genes in the serotonergic control of emotion regulation.

  7. An inexact Newton method for fully-coupled solution of the Navier-Stokes equations with heat and mass transport

    SciTech Connect

    Shadid, J.N.; Tuminaro, R.S.; Walker, H.F.

    1997-02-01

    The solution of the governing steady transport equations for momentum, heat and mass transfer in flowing fluids can be very difficult. These difficulties arise from the nonlinear, coupled, nonsymmetric nature of the system of algebraic equations that results from spatial discretization of the PDEs. In this manuscript the authors focus on evaluating a proposed nonlinear solution method based on an inexact Newton method with backtracking. In this context they use a particular spatial discretization based on a pressure stabilized Petrov-Galerkin finite element formulation of the low Mach number Navier-Stokes equations with heat and mass transport. The discussion considers computational efficiency, robustness and some implementation issues related to the proposed nonlinear solution scheme. Computational results are presented for several challenging CFD benchmark problems as well as two large scale 3D flow simulations.

  8. Application of Exactly Linearized Error Transport Equations to AIAA CFD Prediction Workshops

    NASA Technical Reports Server (NTRS)

    Derlaga, Joseph M.; Park, Michael A.; Rallabhandi, Sriram

    2017-01-01

    The computational fluid dynamics (CFD) prediction workshops sponsored by the AIAA have created invaluable opportunities in which to discuss the predictive capabilities of CFD in areas in which it has struggled, e.g., cruise drag, high-lift, and sonic boom pre diction. While there are many factors that contribute to disagreement between simulated and experimental results, such as modeling or discretization error, quantifying the errors contained in a simulation is important for those who make decisions based on the computational results. The linearized error transport equations (ETE) combined with a truncation error estimate is a method to quantify one source of errors. The ETE are implemented with a complex-step method to provide an exact linearization with minimal source code modifications to CFD and multidisciplinary analysis methods. The equivalency of adjoint and linearized ETE functional error correction is demonstrated. Uniformly refined grids from a series of AIAA prediction workshops demonstrate the utility of ETE for multidisciplinary analysis with a connection between estimated discretization error and (resolved or under-resolved) flow features.

  9. New Techniques for Simulation of Ion Implantation by Numerical Integration of Boltzmann Transport Equation

    NASA Astrophysics Data System (ADS)

    Wang, Shyh-Wei; Guo, Shuang-Fa

    1998-01-01

    New techniques for more accurate and efficient simulation of ion implantations by a stepwise numerical integration of the Boltzmann transport equation (BTE) have been developed in this work. Instead of using uniform energy grid, a non-uniform grid is employed to construct the momentum distribution matrix. A more accurate simulation result is obtained for heavy ions implanted into silicon. In the same time, rather than utilizing the conventional Lindhard, Nielsen and Schoitt (LNS) approximation, an exact evaluation of the integrals involving the nuclear differential scattering cross-section (dσn=2πp dp) is proposed. The impact parameter p as a function of ion energy E and scattering angle φ is obtained by solving the magic formula iteratively and an interpolation techniques is devised during the simulation process. The simulation time using exact evaluation is about 3.5 times faster than that using the Littmark and Ziegler (LZ) spline fitted cross-section function for phosphorus implantation into silicon.

  10. Use of the generalized integral transform method for solving equations of solute transport in porous media

    NASA Astrophysics Data System (ADS)

    Liu, Chongxuan; Szecsody, Jim E.; Zachara, John M.; Ball, William P.

    The generalized integral transform technique (GITT) is applied to solve the one-dimensional advection-dispersion equation (ADE) in heterogeneous porous media coupled with either linear or nonlinear sorption and decay. When both sorption and decay are linear, analytical solutions are obtained using the GITT for one-dimensional ADEs with spatially and temporally variable flow and dispersion coefficient and arbitrary initial and boundary conditions. When either sorption or decay is nonlinear the solutions to ADEs with the GITT are hybrid analytical-numerical. In both linear and nonlinear cases, the forward and inverse integral transforms for the problems described in the paper are apparent and straightforward. Some illustrative examples with linear sorption and decay are presented to demonstrate the application and check the accuracy of the derived analytical solutions. The derived hybrid analytical-numerical solutions are checked against a numerical approach and demonstratively applied to a nonlinear transport example, which simulates a simplified system of iron oxide bioreduction with nonlinear sorption and nonlinear reaction kinetics.

  11. Optimum plane selection for transport-of-intensity-equation-based solvers.

    PubMed

    Martinez-Carranza, J; Falaggis, K; Kozacki, T

    2014-10-20

    Deterministic single beam phase retrieval techniques based on the transport of intensity equation (TIE) use the axial intensity derivative obtained from a series of intensities recorded along the propagation axis as an input to the TIE-based solver. The common belief is that, when reducing the error present in the axial intensity derivative, there will be minimal error in the retrieved phase. Thus, reported optimization schemes of measurement condition focuses on the minimization of error in the axial intensity derivative. As it is shown in this contribution, this assumption is not correct and leads to underestimating the value of plane separation, which increases the phase retrieval errors and sensitivity to noise of the TIE-based measurement system. Therefore, in this paper, a detailed analysis that shows the existence of an optimal separation that minimizes the error in the retrieved phase for a given TIE-based solver is carried out. The developed model is used to derive analytical expressions that provide an optimal plane separation for a given number of planes and level of noise for the case of equidistant plane separation. The obtained results are derived for the widely used Fourier-transform-based TIE solver, but it is shown that they can also be applied to multigrid-based techniques.

  12. A space–angle DGFEM approach for the Boltzmann radiation transport equation with local angular refinement

    SciTech Connect

    Kópházi, József Lathouwers, Danny

    2015-09-15

    In this paper a new method for the discretization of the radiation transport equation is presented, based on a discontinuous Galerkin method in space and angle that allows for local refinement in angle where any spatial element can support its own angular discretization. To cope with the discontinuous spatial nature of the solution, a generalized Riemann procedure is required to distinguish between incoming and outgoing contributions of the numerical fluxes. A new consistent framework is introduced that is based on the solution of a generalized eigenvalue problem. The resulting numerical fluxes for the various possible cases where neighboring elements have an equal, higher or lower level of refinement in angle are derived based on tensor algebra and the resulting expressions have a very clear physical interpretation. The choice of discontinuous trial functions not only has the advantage of easing local refinement, it also facilitates the use of efficient sweep-based solvers due to decoupling of unknowns on a large scale thereby approaching the efficiency of discrete ordinates methods with local angular resolution. The approach is illustrated by a series of numerical experiments. Results show high orders of convergence for the scalar flux on angular refinement. The generalized Riemann upwinding procedure leads to stable and consistent solutions. Further the sweep-based solver performs well when used as a preconditioner for a Krylov method.

  13. Dielectric interpretation of Lei-Ting nonlinear force-momentum-balance transport equation for isothermal resistivity

    NASA Astrophysics Data System (ADS)

    Horing, N. J. M.; Lei, X. L.; Cui, H. L.

    1986-05-01

    A dielectric interpretation of the nonlinear Lei-Ting force-momentum-balance transport equation for steady-state dc current flow is developed here in correspondence with standard techniques for calculating fast-particle energy loss to a plasmalike medium. In conjunction with this we interpret the result to be an isothermal resistivity calculated to lowest order in the impurity scattering potentials, isothermal in the sense that all energy dissipated is removed from the system, essentially instantaneously as it is generated, by a heat bath in contact with the system which maintains it at constant temperature throughout the nonlinear dc conduction process. On the basis of its isothermal character, we argue that the Lei-Ting dc resistivity calculated to lowest order in the impurity scattering potentials-whose linear limit is significantly different from the corresponding linear resistivity of an adiabatic character (for a system admitting no drainoff of dissipated energy, developing under a purely mechanical Hamiltonian)-is immune to serious critical objections of the type brought by Argyres and Sigel against similar lowest-order adiabatic linear resistivity calculations some time ago. Moreover, we also show that a dielectric Lei-Ting type formulation of linearized ac resistivity leads to the standard high-frequency linear resistivity formula, and that its zero-frequency limit naturally yields the isothermal dc linear Lei-Ting resistivity.

  14. Equations of state and transport properties of warm dense beryllium: a quantum molecular dynamics study.

    PubMed

    Wang, Cong; Long, Yao; Tian, Ming-Feng; He, Xian-Tu; Zhang, Ping

    2013-04-01

    We have calculated the equations of state, the viscosity and self-diffusion coefficients, and electronic transport coefficients of beryllium in the warm dense regime for densities from 4.0 to 6.0 g/cm(3) and temperatures from 1.0 to 10.0 eV by using quantum molecular dynamics simulations. The principal Hugoniot curve is in agreement with underground nuclear explosive and high-power laser experimental results up to ~20 Mbar. The calculated viscosity and self-diffusion coefficients are compared with the one-component plasma model, using effective charges given by the average-atom model. The Stokes-Einstein relationship, which connects viscosity and self-diffusion coefficients, is found to hold fairly well in the strong coupling regime. The Lorenz number, which is the ratio between thermal and electrical conductivities, is computed via Kubo-Greenwood formula and compared to the well-known Wiedemann-Franz law in the warm dense region.

  15. Critical assessment of the transport of intensity equation as a phase recovery technique in optical lithography

    NASA Astrophysics Data System (ADS)

    Shanker, Aamod; Sczyrba, Martin; Connolly, Brid; Kalk, Franklin; Neureuther, Andy; Waller, Laura

    2014-03-01

    Photomasks are expected to have phase effects near edges due to their 3D topography, which can be modeled as imaginary boundary layers in thin mask simulations. We apply a modified transport of intensity (TIE) phase imaging technique to through-focus aerial images of photomasks in order to recover polarization-dependent edge effects. We use AIMS measurements with 193nm light to study the dependence of recovered phase on mask type and geometry. The TIE is an intensity conservation equation that quantitatively relates phase in the wafer plane to intensity through-focus. Here, we develop a modified version of the TIE for strongly absorbing objects, and apply it to recover wafer plane phase of attenuating masks. The projection printer blurs the fields at the wafer plane by its point spread function, hence an effective deconvolution is used to predict the boundary layers at the mask that best approximate the measured thick mask edge effects. Computation required for the inverse problem is fast and independent of mask geometry, unlike FDTD computations.

  16. Modeling the flux of metabolites in the juvenile hormone biosynthesis pathway using generalized additive models and ordinary differential equations.

    PubMed

    Martínez-Rincón, Raúl O; Rivera-Pérez, Crisalejandra; Diambra, Luis; Noriega, Fernando G

    2017-01-01

    Juvenile hormone (JH) regulates development and reproductive maturation in insects. The corpora allata (CA) from female adult mosquitoes synthesize fluctuating levels of JH, which have been linked to the ovarian development and are influenced by nutritional signals. The rate of JH biosynthesis is controlled by the rate of flux of isoprenoids in the pathway, which is the outcome of a complex interplay of changes in precursor pools and enzyme levels. A comprehensive study of the changes in enzymatic activities and precursor pool sizes have been previously reported for the mosquito Aedes aegypti JH biosynthesis pathway. In the present studies, we used two different quantitative approaches to describe and predict how changes in the individual metabolic reactions in the pathway affect JH synthesis. First, we constructed generalized additive models (GAMs) that described the association between changes in specific metabolite concentrations with changes in enzymatic activities and substrate concentrations. Changes in substrate concentrations explained 50% or more of the model deviances in 7 of the 13 metabolic steps analyzed. Addition of information on enzymatic activities almost always improved the fitness of GAMs built solely based on substrate concentrations. GAMs were validated using experimental data that were not included when the model was built. In addition, a system of ordinary differential equations (ODE) was developed to describe the instantaneous changes in metabolites as a function of the levels of enzymatic catalytic activities. The results demonstrated the ability of the models to predict changes in the flux of metabolites in the JH pathway, and can be used in the future to design and validate experimental manipulations of JH synthesis.

  17. Modeling the flux of metabolites in the juvenile hormone biosynthesis pathway using generalized additive models and ordinary differential equations

    PubMed Central

    Martínez-Rincón, Raúl O.; Rivera-Pérez, Crisalejandra; Diambra, Luis; Noriega, Fernando G.

    2017-01-01

    Juvenile hormone (JH) regulates development and reproductive maturation in insects. The corpora allata (CA) from female adult mosquitoes synthesize fluctuating levels of JH, which have been linked to the ovarian development and are influenced by nutritional signals. The rate of JH biosynthesis is controlled by the rate of flux of isoprenoids in the pathway, which is the outcome of a complex interplay of changes in precursor pools and enzyme levels. A comprehensive study of the changes in enzymatic activities and precursor pool sizes have been previously reported for the mosquito Aedes aegypti JH biosynthesis pathway. In the present studies, we used two different quantitative approaches to describe and predict how changes in the individual metabolic reactions in the pathway affect JH synthesis. First, we constructed generalized additive models (GAMs) that described the association between changes in specific metabolite concentrations with changes in enzymatic activities and substrate concentrations. Changes in substrate concentrations explained 50% or more of the model deviances in 7 of the 13 metabolic steps analyzed. Addition of information on enzymatic activities almost always improved the fitness of GAMs built solely based on substrate concentrations. GAMs were validated using experimental data that were not included when the model was built. In addition, a system of ordinary differential equations (ODE) was developed to describe the instantaneous changes in metabolites as a function of the levels of enzymatic catalytic activities. The results demonstrated the ability of the models to predict changes in the flux of metabolites in the JH pathway, and can be used in the future to design and validate experimental manipulations of JH synthesis. PMID:28158248

  18. Interaction of Dopamine Transporter Gene and Observed Parenting Behaviors on Attention-Deficit/Hyperactivity Disorder: A Structural Equation Modeling Approach

    PubMed Central

    Li, James J.; Lee, Steve S.

    2012-01-01

    Objective Emerging evidence suggests that some individuals may be simultaneously more responsive to the effects from environmental adversity and enrichment (i.e., differential susceptibility). Given that parenting behavior and a variable number tandem repeat polymorphism in the 3′untranslated region of the dopamine transporter (DAT1) gene are each independently associated with ADHD, our goal was to evaluate the potential interactive effects of child DAT1 genotype with positive and negative parenting behaviors on childhood ADHD. Method We recruited an ethnically-diverse sample of 150 six to nine year-old boys and girls with and without ADHD. Children were genotyped for a common polymorphism of the DAT1 gene, and objective counts of observed parenting behavior (i.e., negativity and praise) were obtained from a valid parent-child interaction task. Structural equation modeling was used to examine the interactive effects of DAT1 and observed parenting with a latent ADHD factor. Results We detected a significant interaction between observed praise and child DAT1 (coded additively) which suggested that praise was associated with increased ADHD, but only among youth with the 9/10 genotype. In addition, a marginally significant interaction between DAT1 (coded additively and recessively) and observed negativity emerged for ADHD, such that negativity was positively associated with ADHD but only for youth with the 9/9 genotype. Conclusions Although differential susceptibility theory was not fully supported, These preliminary results suggest that interactive exchanges between parenting behavior and child genotype potentially contribute to the development of ADHD. Clinical implications for interactions between parenting behavior and child genotype are discussed. PMID:23153115

  19. Transport Equations for CAD Modeling of Al(x)Ga(1-x)N/GaN HEMTs

    NASA Technical Reports Server (NTRS)

    Freeman, Jon C.

    2003-01-01

    BEMTs formed from Al(x)Ga(1-x)N/GaN heterostructures are being investigated for high RF power and efficiency around the world by many groups, both academic and industrial. In these devices, the 2DEG formation is dominated by both spontaneous and piezoelectric polarization fields, with each component having nearly the same order of magnitude. The piezoelectric portion is induced by the mechanical strain in the structure, and to analyze these devices, one must incorporate the stress/strain relationships, along with the standard semiconductor transport equations. These equations for Wurtzite GaN are not easily found in the open literature, hence this paper summarizes them, along with the constitutive equations for piezoelectric materials. The equations are cast into the format for the Wurtzite crystal class, which is the most common way GaN is grown epitaxially.

  20. A deterministic solution of the first order linear Boltzmann transport equation in the presence of external magnetic fields

    SciTech Connect

    St Aubin, J. Keyvanloo, A.; Fallone, B. G.; Vassiliev, O.

    2015-02-15

    Purpose: Accurate radiotherapy dose calculation algorithms are essential to any successful radiotherapy program, considering the high level of dose conformity and modulation in many of today’s treatment plans. As technology continues to progress, such as is the case with novel MRI-guided radiotherapy systems, the necessity for dose calculation algorithms to accurately predict delivered dose in increasingly challenging scenarios is vital. To this end, a novel deterministic solution has been developed to the first order linear Boltzmann transport equation which accurately calculates x-ray based radiotherapy doses in the presence of magnetic fields. Methods: The deterministic formalism discussed here with the inclusion of magnetic fields is outlined mathematically using a discrete ordinates angular discretization in an attempt to leverage existing deterministic codes. It is compared against the EGSnrc Monte Carlo code, utilizing the emf-macros addition which calculates the effects of electromagnetic fields. This comparison is performed in an inhomogeneous phantom that was designed to present a challenging calculation for deterministic calculations in 0, 0.6, and 3 T magnetic fields oriented parallel and perpendicular to the radiation beam. The accuracy of the formalism discussed here against Monte Carlo was evaluated with a gamma comparison using a standard 2%/2 mm and a more stringent 1%/1 mm criterion for a standard reference 10 × 10 cm{sup 2} field as well as a smaller 2 × 2 cm{sup 2} field. Results: Greater than 99.8% (94.8%) of all points analyzed passed a 2%/2 mm (1%/1 mm) gamma criterion for all magnetic field strengths and orientations investigated. All dosimetric changes resulting from the inclusion of magnetic fields were accurately calculated using the deterministic formalism. However, despite the algorithm’s high degree of accuracy, it is noticed that this formalism was not unconditionally stable using a discrete ordinate angular discretization

  1. Evaluation of an analytic linear Boltzmann transport equation solver for high-density inhomogeneities

    SciTech Connect

    Lloyd, S. A. M.; Ansbacher, W.

    2013-01-15

    Purpose: Acuros external beam (Acuros XB) is a novel dose calculation algorithm implemented through the ECLIPSE treatment planning system. The algorithm finds a deterministic solution to the linear Boltzmann transport equation, the same equation commonly solved stochastically by Monte Carlo methods. This work is an evaluation of Acuros XB, by comparison with Monte Carlo, for dose calculation applications involving high-density materials. Existing non-Monte Carlo clinical dose calculation algorithms, such as the analytic anisotropic algorithm (AAA), do not accurately model dose perturbations due to increased electron scatter within high-density volumes. Methods: Acuros XB, AAA, and EGSnrc based Monte Carlo are used to calculate dose distributions from 18 MV and 6 MV photon beams delivered to a cubic water phantom containing a rectangular high density (4.0-8.0 g/cm{sup 3}) volume at its center. The algorithms are also used to recalculate a clinical prostate treatment plan involving a unilateral hip prosthesis, originally evaluated using AAA. These results are compared graphically and numerically using gamma-index analysis. Radio-chromic film measurements are presented to augment Monte Carlo and Acuros XB dose perturbation data. Results: Using a 2% and 1 mm gamma-analysis, between 91.3% and 96.8% of Acuros XB dose voxels containing greater than 50% the normalized dose were in agreement with Monte Carlo data for virtual phantoms involving 18 MV and 6 MV photons, stainless steel and titanium alloy implants and for on-axis and oblique field delivery. A similar gamma-analysis of AAA against Monte Carlo data showed between 80.8% and 87.3% agreement. Comparing Acuros XB and AAA evaluations of a clinical prostate patient plan involving a unilateral hip prosthesis, Acuros XB showed good overall agreement with Monte Carlo while AAA underestimated dose on the upstream medial surface of the prosthesis due to electron scatter from the high-density material. Film measurements

  2. STOMP Subsurface Transport Over Multiple Phases Version 1.0 Addendum: ECKEChem Equilibrium-Conservation-Kinetic Equation Chemistry and Reactive Transport

    SciTech Connect

    White, Mark D.; McGrail, B. Peter

    2005-12-01

    flow and transport simulator, STOMP (Subsurface Transport Over Multiple Phases). Prior to these code development activities, the STOMP simulator included sequential and scalable implementations for numerically simulating the injection of supercritical CO2 into deep saline aquifers. Additionally, the sequential implementations included operational modes that considered nonisothermal conditions and kinetic dissolution of CO2 into the saline aqueous phase. This addendum documents the advancement of these numerical simulation capabilities to include reactive transport in the STOMP simulator through the inclusion of the recently PNNL developed batch geochemistry solution module ECKEChem (Equilibrium-Conservation-Kinetic Equation Chemistry). Potential geologic reservoirs for sequestering CO2 include deep saline aquifers, hydrate-bearing formations, depleted or partially depleted natural gas and petroleum reservoirs, and coal beds. The mechanisms for sequestering carbon dioxide in geologic reservoirs include physical trapping, dissolution in the reservoir fluids, hydraulic trapping (hysteretic entrapment of nonwetting fluids), and chemical reaction. This document and the associated code development and verification work are concerned with the chemistry of injecting CO2 into geologic reservoirs. As geologic sequestration of CO2 via chemical reaction, namely precipitation reactions, are most dominate in deep saline aquifers, the principal focus of this document is the numerical simulation of CO2 injection, migration, and geochemical reaction in deep saline aquifers. The ECKEChem batch chemistry module was developed in a fashion that would allow its implementation into all operational modes of the STOMP simulator, making it a more versatile chemistry component. Additionally, this approach allows for verification of the ECKEChem module against more classical reactive transport problems involving aqueous systems.

  3. Transport equation approach to calculations of Hadamard Green functions and non-coincident DeWitt coefficients

    NASA Astrophysics Data System (ADS)

    Ottewill, Adrian C.; Wardell, Barry

    2011-11-01

    Building on an insight due to Avramidi, we provide a system of transport equations for determining key fundamental bitensors, including derivatives of the world function, σ(x,x'), the square root of the Van Vleck determinant, Δ1/2(x,x'), and the tail term, V(x,x'), appearing in the Hadamard form of the Green function. These bitensors are central to a broad range of problems from radiation reaction to quantum field theory in curved spacetime and quantum gravity. Their transport equations may be used either in a semi-recursive approach to determining their covariant Taylor series expansions, or as the basis of numerical calculations. To illustrate the power of the semi-recursive approach, we present an implementation in Mathematica, which computes very high order covariant series expansions of these objects. Using this code, a moderate laptop can, for example, calculate the coincidence limit [a7(x,x)] and V(x,x') to order (σa)20 in a matter of minutes. Results may be output in either a compact notation or in xTensor form. In a second application of the approach, we present a scheme for numerically integrating the transport equations as a system of coupled ordinary differential equations. As an example application of the scheme, we integrate along null geodesics to solve for V(x,x') in Nariai and Schwarzschild spacetimes.

  4. Enhanced lateral resolution for phase retrieval based on the transport of intensity equation with tilted illumination

    NASA Astrophysics Data System (ADS)

    Martinez-Carranza, J.; Falaggis, K.; Kozacki, T.

    2016-03-01

    Quantitative Phase Imaging based on the Transport of Intensity Equation (TIE) has shown to be a practical tool for retrieving the phase information of biological and technical samples. When recovering the phase information with the TIE, the maximum lateral resolution that can be obtained is limited by the numerical aperture (NA) of the optical system. In order to overcome this limitation, a system that combines structured illumination and TIE-like techniques have been proposed. These methodologies enlarge synthetically the NA of the optical system, and thus, the lateral resolution of the retrieved phase can be improved. However, the employment of structured illumination may bring error amplifications in the retrieved phase due to its sensitiveness to phase discontinuities and shot noise. In this work, we propose a new methodology that improves the lateral resolution of the retrieved phase beyond the diffraction limit avoiding the problems related with the structured illumination. The methodology presented here uses tilted illumination and a TIE solver. We show that when using this configuration, we can extend the set of recovered frequencies by adjusting the angle of the tilted wave-front. Further, our methodology is designed to extend the NA by employing less tilted angles than other similar techniques. Hence, the final retrieved phase will have an enhanced lateral resolution without amplifying the numerical errors and employing a few tilted angles. Moreover, we show that the algorithm presented here can be combined with other TIE algorithms that are used for suppressing the Low Frequency Artifacts (LFAs) usually present when using TIE based techniques.

  5. Equation of state and transport property measurements of warm dense matter.

    SciTech Connect

    Knudson, Marcus D.; Desjarlais, Michael Paul

    2009-10-01

    Location of the liquid-vapor critical point (c.p.) is one of the key features of equation of state models used in simulating high energy density physics and pulsed power experiments. For example, material behavior in the location of the vapor dome is critical in determining how and when coronal plasmas form in expanding wires. Transport properties, such as conductivity and opacity, can vary an order of magnitude depending on whether the state of the material is inside or outside of the vapor dome. Due to the difficulty in experimentally producing states near the vapor dome, for all but a few materials, such as Cesium and Mercury, the uncertainty in the location of the c.p. is of order 100%. These states of interest can be produced on Z through high-velocity shock and release experiments. For example, it is estimated that release adiabats from {approx}1000 GPa in aluminum would skirt the vapor dome allowing estimates of the c.p. to be made. This is within the reach of Z experiments (flyer plate velocity of {approx}30 km/s). Recent high-fidelity EOS models and hydrocode simulations suggest that the dynamic two-phase flow behavior observed in initial scoping experiments can be reproduced, providing a link between theory and experiment. Experimental identification of the c.p. in aluminum would represent the first measurement of its kind in a dynamic experiment. Furthermore, once the c.p. has been experimentally determined it should be possible to probe the electrical conductivity, opacity, reflectivity, etc. of the material near the vapor dome, using a variety of diagnostics. We propose a combined experimental and theoretical investigation with the initial emphasis on aluminum.

  6. Transport of interacting particles in a chain of cavities: Description through a modified Fick-Jacobs equation

    NASA Astrophysics Data System (ADS)

    Suárez, G. P.; Hoyuelos, M.; Mártin, H. O.

    2015-01-01

    We study the transport process of interacting Brownian particles in a tube of varying cross section. To describe this process we introduce a modified Fick-Jacobs equation, considering particles that interact through a hard-core potential. We were able to solve the equation with numerical methods for the case of symmetric and asymmetric cavities. We focused in the concentration of particles along the direction of the tube. We also preformed Monte Carlo simulations to evaluate the accuracy of the results, obtaining good agreement between theory and simulations.

  7. Performance comparison of Si, III–V double-gate n-type MOSFETs by deterministic Boltzmann transport equation solver

    NASA Astrophysics Data System (ADS)

    Di, Shaoyan; Shen, Lei; Chang, Pengying; Zhao, Kai; Lu, Tiao; Du, Gang; Liu, Xiaoyan

    2017-04-01

    A deterministic time-dependent Boltzmann transport equation (BTE) solver is employed to carry out a comparison work among 10 nm double-gate n-type MOSFETs with channel materials of Si, In0.53Ga0.47As, and GaSb in different surface orientations. Results show that the GaSb device has the highest drive current, while scattering affects carrier transport in the Si device the most. The InGaAs device exhibits the highest injection velocity but suffers from the density of state (DOS) bottleneck seriously.

  8. Application of the three-dimensional telegraph equation to cosmic-ray transport

    NASA Astrophysics Data System (ADS)

    Tautz, Robert C.; Lerche, Ian

    2016-10-01

    An analytical solution to the three-dimensional telegraph equation is presented. This equation has recently received some attention but so far the treatment has been one-dimensional. By using the structural similarity to the Klein-Gordon equation, the telegraph equation can be solved in closed form. Illustrative examples are used to discuss the qualitative differences from the diffusion solution. A comparison with a numerical test-particle simulation reveals that some features of an intensity profile can be better explained using the telegraph approach.

  9. Fast linear solver for radiative transport equation with multiple right hand sides in diffuse optical tomography

    PubMed Central

    Jia, Jingfei

    2015-01-01

    It is well known that radiative transfer equation (RTE) provides more accurate tomographic results than its diffusion approximation (DA). However, RTE-based tomographic reconstruction codes have limited applicability in practice due to their high computational cost. In this article, we propose a new efficient method for solving the RTE forward problem with multiple light sources in an all-at-once manner instead of solving it for each source separately. To this end, we introduce here a novel linear solver called block biconjugate gradient stabilized method (block BiCGStab) that makes full use of the shared information between different right hand sides to accelerate solution convergence. Two parallelized block BiCGStab methods are proposed for additional acceleration under limited threads situation. We evaluate the performance of this algorithm with numerical simulation studies involving the Delta-Eddington approximation to the scattering phase function. The results show that the single threading block RTE solver proposed here reduces computation time by a factor of 1.5~3 as compared to the traditional sequential solution method and the parallel block solver by a factor of 1.5 as compared to the traditional parallel sequential method. This block linear solver is, moreover, independent of discretization schemes and preconditioners used; thus further acceleration and higher accuracy can be expected when combined with other existing discretization schemes or preconditioners. PMID:26345531

  10. Fast linear solver for radiative transport equation with multiple right hand sides in diffuse optical tomography.

    PubMed

    Jia, Jingfei; Kim, Hyun K; Hielscher, Andreas H

    2015-12-01

    It is well known that radiative transfer equation (RTE) provides more accurate tomographic results than its diffusion approximation (DA). However, RTE-based tomographic reconstruction codes have limited applicability in practice due to their high computational cost. In this article, we propose a new efficient method for solving the RTE forward problem with multiple light sources in an all-at-once manner instead of solving it for each source separately. To this end, we introduce here a novel linear solver called block biconjugate gradient stabilized method (block BiCGStab) that makes full use of the shared information between different right hand sides to accelerate solution convergence. Two parallelized block BiCGStab methods are proposed for additional acceleration under limited threads situation. We evaluate the performance of this algorithm with numerical simulation studies involving the Delta-Eddington approximation to the scattering phase function. The results show that the single threading block RTE solver proposed here reduces computation time by a factor of 1.5~3 as compared to the traditional sequential solution method and the parallel block solver by a factor of 1.5 as compared to the traditional parallel sequential method. This block linear solver is, moreover, independent of discretization schemes and preconditioners used; thus further acceleration and higher accuracy can be expected when combined with other existing discretization schemes or preconditioners.

  11. Charged-particle transport in gases in electric and magnetic fields crossed at arbitrary angles: Multiterm solution of Boltzmann's equation.

    PubMed

    White, R D; Ness, K F; Robson, R E; Li, B

    1999-08-01

    A multiterm solution of the Boltzmann equation has been developed and used to calculate transport coefficients of charged-particle swarms in gases under the influence of electric and magnetic fields crossed at arbitrary angles psi. The hierarchy resulting from a spherical harmonic decomposition of the Boltzmann equation in the hydrodynamic regime [Ness, Phys. Rev. A 47, 327 (1993)] is solved numerically by representing the speed dependence of the phase-space distribution function in terms of an expansion in Sonine polynomials about a weighted sum of Maxwellian distributions at different temperatures. Results are given for charged-particle swarms in certain model gases over a range of psi and field strengths. The variation of the transport coefficients with psi is addressed using physical arguments. The errors associated with the two-term approximation and inadequacies of Legendre polynomial expansions are highlighted.

  12. Vasculature based model for characterizing the oxygen transport in skin tissues - analogy to the Weinbaum-Jiji bioheat equation

    NASA Astrophysics Data System (ADS)

    Ji, Yan; Liu, Jing

    Based on the conceptual three-layer microvascular structure of skin tissues proposed by Weinbaum et al. [20-25] and in analogy to the well known Weinbaum-Jiji (W-J) bioheat equation, a new oxygen transport model was established in this paper, which collectively included the contributions of the vascular geometry and the blood flow condition. The new one-dimensional three-layer oxygen transport model was then applied to predict the average oxygen concentration distribution in skin tissues and numerical solutions for the boundary value problem coupling the three layers were obtained. A simple expression for the tensor diffusivity (Deff) of oxygen transport over the deep tissue layer was presented, which was orders of magnitude higher than the intrinsic diffusivity (Dt) in tissue without blood flow. Effects of blood flow velocity and vascular geometry to the oxygen transport were investigated. Calculations indicated that the vascular geometry had significant effects on oxygen transport. The oxygen exchange between the arteries and veins was relatively small for the deep tissue layer. Further, the average oxygen concentration gradient appears low in intermediate layer due to large capillary perfusion. The theoretical results were implemented to interpret some previous experimental results and a better understanding on the oxygen transport across the vascularized living tissues was obtained. The strategy proposed in this paper may provide a feasible way to comprehensively characterize the oxygen transport behaviors in living tissues with real and complex vasculature.

  13. Kershaw closures for linear transport equations in slab geometry II: High-order realizability-preserving discontinuous-Galerkin schemes

    NASA Astrophysics Data System (ADS)

    Schneider, Florian

    2016-10-01

    This paper provides a generalization of the realizability-preserving discontinuous-Galerkin scheme given in [3] to general full-moment models that can be closed analytically. It is applied to the class of Kershaw closures, which are able to provide a cheap closure of the moment problem. This results in an efficient algorithm for the underlying linear transport equation. The efficiency of high-order methods is demonstrated using numerical convergence tests and non-smooth benchmark problems.

  14. Determination of transport wind speed in the gaussian plume diffusion equation for low-lying point sources

    NASA Astrophysics Data System (ADS)

    Wang, I. T.

    A general method for determining the effective transport wind speed, overlineu, in the Gaussian plume equation is discussed. Physical arguments are given for using the generalized overlineu instead of the often adopted release-level wind speed with the plume diffusion equation. Simple analytical expressions for overlineu applicable to low-level point releases and a wide range of atmospheric conditions are developed. A non-linear plume kinematic equation is derived using these expressions. Crosswind-integrated SF 6 concentration data from the 1983 PNL tracer experiment are used to evaluate the proposed analytical procedures along with the usual approach of using the release-level wind speed. Results of the evaluation are briefly discussed.

  15. Prediction of transport properties of dense gases and liquids by the Peng-Robinson (PR) equation of state

    NASA Astrophysics Data System (ADS)

    Sheng, W.; Chen, G.-J.; Lu, H.-C.

    1989-01-01

    An attempt is made in this work to combine the Enskog theory of transport properties with the simple cubic Peng-Robinson (PR) equation of state. The PR equation of state provides the density dependence of the equilibrium radial distribution function. A slight empirical modification of the Enskog equation is proposed to improve the accuracy of correlation of thermal conductivity and viscosity coefficient for dense gases and liquids. Extensive comparisons with experimental data of pure fluids are made for a wide range of fluid states with temperatures from 90 to 500 K and pressures from 1 to 740 atm. The total average absolute deviations are 2.67% and 2.02% for viscosity and thermal conductivity predictions, respectively. The proposed procedure for predicting viscosity and thermal conductivity is simple and straightforward. It requires only critical parameters and acentric factors for the fluids.

  16. Goal-based angular adaptivity applied to a wavelet-based discretisation of the neutral particle transport equation

    SciTech Connect

    Goffin, Mark A.; Buchan, Andrew G.; Dargaville, Steven; Pain, Christopher C.; Smith, Paul N.; Smedley-Stevenson, Richard P.

    2015-01-15

    A method for applying goal-based adaptive methods to the angular resolution of the neutral particle transport equation is presented. The methods are applied to an octahedral wavelet discretisation of the spherical angular domain which allows for anisotropic resolution. The angular resolution is adapted across both the spatial and energy dimensions. The spatial domain is discretised using an inner-element sub-grid scale finite element method. The goal-based adaptive methods optimise the angular discretisation to minimise the error in a specific functional of the solution. The goal-based error estimators require the solution of an adjoint system to determine the importance to the specified functional. The error estimators and the novel methods to calculate them are described. Several examples are presented to demonstrate the effectiveness of the methods. It is shown that the methods can significantly reduce the number of unknowns and computational time required to obtain a given error. The novelty of the work is the use of goal-based adaptive methods to obtain anisotropic resolution in the angular domain for solving the transport equation. -- Highlights: •Wavelet angular discretisation used to solve transport equation. •Adaptive method developed for the wavelet discretisation. •Anisotropic angular resolution demonstrated through the adaptive method. •Adaptive method provides improvements in computational efficiency.

  17. Macroscopic transport equations in many-body systems from microscopic exclusion processes in disordered media: a review

    NASA Astrophysics Data System (ADS)

    Galanti, Marta; Fanelli, Duccio; Piazza, Francesco

    2016-08-01

    Describing particle transport at the macroscopic or mesoscopic level in non-ideal environments poses fundamental theoretical challenges in domains ranging from inter and intra-cellular transport in biology to diffusion in porous media. Yet, often the nature of the constraints coming from many-body interactions or reflecting a complex and confining environment are better understood and modeled at the microscopic level. In this paper we review the subtle link between microscopic exclusion processes and the mean-field equations that ensue from them in the continuum limit. We show that in an inhomogeneous medium, i.e. when jumps are controlled by site-dependent hopping rates, one can obtain three different nonlinear advection-diffusion equations in the continuum limit, suitable for describing transport in the presence of quenched disorder and external fields, depending on the particular rule embodying site inequivalence at the microscopic level. In a situation that might be termed point-like scenario, when particles are treated as point-like objects, the effect of crowding as imposed at the microscopic level manifests in the mean-field equations only if some degree of inhomogeneity is enforced into the model. Conversely, when interacting agents are assigned a finite size, under the more realistic extended crowding framework, exclusion constraints persist in the unbiased macroscopic representation.

  18. Application of a time-convolutionless stochastic Schrödinger equation to energy transport and thermal relaxation.

    PubMed

    Biele, R; Timm, C; D'Agosta, R

    2014-10-01

    Quantum stochastic methods based on effective wave functions form a framework for investigating the generally non-Markovian dynamics of a quantum-mechanical system coupled to a bath. They promise to be computationally superior to the master-equation approach, which is numerically expensive for large dimensions of the Hilbert space. Here, we numerically investigate the suitability of a known stochastic Schrödinger equation that is local in time to give a description of thermal relaxation and energy transport. This stochastic Schrödinger equation can be solved with a moderate numerical cost, indeed comparable to that of a Markovian system, and reproduces the dynamics of a system evolving according to a general non-Markovian master equation. After verifying that it describes thermal relaxation correctly, we apply it for the first time to the energy transport in a spin chain. We also discuss a portable algorithm for the generation of the coloured noise associated with the numerical solution of the non-Markovian dynamics.

  19. A Spatial Discretization Scheme for Solving the Transport Equation on Unstructured Grids of Polyhedra

    SciTech Connect

    Thompson, Kelly Glen

    2000-11-01

    In this work, we develop a new spatial discretization scheme that may be used to numerically solve the neutron transport equation. This new discretization extends the family of corner balance spatial discretizations to include spatial grids of arbitrary polyhedra. This scheme enforces balance on subcell volumes called corners. It produces a lower triangular matrix for sweeping, is algebraically linear, is non-negative in a source-free absorber, and produces a robust and accurate solution in thick diffusive regions. Using an asymptotic analysis, we design the scheme so that in thick diffusive regions it will attain the same solution as an accurate polyhedral diffusion discretization. We then refine the approximations in the scheme to reduce numerical diffusion in vacuums, and we attempt to capture a second order truncation error. After we develop this Upstream Corner Balance Linear (UCBL) discretization we analyze its characteristics in several limits. We complete a full diffusion limit analysis showing that we capture the desired diffusion discretization in optically thick and highly scattering media. We review the upstream and linear properties of our discretization and then demonstrate that our scheme captures strictly non-negative solutions in source-free purely absorbing media. We then demonstrate the minimization of numerical diffusion of a beam and then demonstrate that the scheme is, in general, first order accurate. We also note that for slab-like problems our method actually behaves like a second-order method over a range of cell thicknesses that are of practical interest. We also discuss why our scheme is first order accurate for truly 3D problems and suggest changes in the algorithm that should make it a second-order accurate scheme. Finally, we demonstrate 3D UCBL's performance on several very different test problems. We show good performance in diffusive and streaming problems. We analyze truncation error in a 3D problem and demonstrate robustness in a

  20. A spatial discretization scheme for solving the transport equation on unstructured grids of polyhedra

    NASA Astrophysics Data System (ADS)

    Thompson, Kelly Glen

    In this work, we develop a new spatial discretization scheme that may be used to numerically solve the neutron transport equation. This new discretization extends the family of corner balance spatial discretizations to include spatial grids of arbitrary polyhedra. This scheme enforces balance on subcell volumes called corners. It produces a lower triangular matrix for sweeping, is algebraically linear, is non-negative in a source-free absorber, and produces a robust and accurate solution in thick diffusive regions. Using an asymptotic analysis, we design the scheme so that in thick diffusive regions it will attain the same solution as an accurate polyhedral diffusion discretization. We then refine the approximations in the scheme to reduce numerical diffusion in vacuums, and we attempt to capture a second order truncation error. After we develop this Upstream Comer Balance Linear (UCBL) discretization we analyze its characteristics in several limits. We complete a full diffusion limit analysis showing that we capture the desired diffusion discretization in optically thick and highly scattering media. We review the upstream and linear properties of our discretization and then demonstrate that our scheme captures strictly non-negative solutions in source-free purely absorbing media. We then demonstrate the minimization of numerical diffusion of a beam and then demonstrate that the scheme is, in general, first order accurate. We also note that for slab-like problems our method actually behaves like a second-order method over a range of cell thicknesses that are of practical interest. We also discuss why our scheme is first order accurate for truly 3D problems and suggest changes in the algorithm that should make it a second-order accurate scheme. Finally, we demonstrate 3D UCBL's performance on several very different test problems. We show good performance in diffusive and streaming problems. We analyze truncation error in a 3D problem and demonstrate robustness in a

  1. A one-equation turbulence transport model for high Reynolds number wall-bounded flows

    NASA Technical Reports Server (NTRS)

    Baldwin, Barrett S.; Barth, Timothy J.

    1990-01-01

    A one-equation turbulence model that avoids the need for an algebraic length scale is derived from a simplified form of the standard k-epsilon model equations. After calibration based on well established properties of the flow over a flat plate, predictions of several other flows are compared with experiment. The preliminary results presented indicate that the model has predictive and numerical properties of sufficient interest to merit further investigation and refinement. The one-equation model is also analyzed numerically and robust solution methods are presented.

  2. A time-asymptotic one equation non-equilibrium model for reactive transport in a two phase porous medium

    NASA Astrophysics Data System (ADS)

    Yohan, D.; Gerald, D.; Magali, G.; Michel, Q.

    2008-12-01

    The general problem of transport and reaction in multiphase porous media has been a subject of extensive studies during the last decades. For example, biologically mediated porous media have seen a long history of research from the environmental engineering point of view. Biofilms (aggregate of microorganisms coated in a polymer matrix generated by bacteria) have been particularly examined within the context of bioremediation in the subsurface zone. Five types of models may be used to describe these kinds of physical system: 1) one-equation local mass equilibrium models when the assumption of local mass equilibrium is valid 2) two equations models when the assumption of local mass equilibrium is not valid 3) one equation non-equilibrium models 4) mixed models coupling equations solved at two different scales 5) one equation time-asymptotic models. In this presentation, we use the method of volume averaging with closure to extend the time- asymptotic model at the Darcy scale to the reactive case. Closure problems are solved for simple unit cells, and the macro-scale model is validated against pore-scale simulations.

  3. A non-additive repulsive contribution in an equation of state: The development for homonuclear square well chains equation of state validated against Monte Carlo simulation.

    PubMed

    Trinh, Thi-Kim-Hoang; Passarello, Jean-Philippe; de Hemptinne, Jean-Charles; Lugo, Rafael; Lachet, Veronique

    2016-03-28

    This work consists of the adaptation of a non-additive hard sphere theory inspired by Malakhov and Volkov [Polym. Sci., Ser. A 49(6), 745-756 (2007)] to a square-well chain. Using the thermodynamic perturbation theory, an additional term is proposed that describes the effect of perturbing the chain of square well spheres by a non-additive parameter. In order to validate this development, NPT Monte Carlo simulations of thermodynamic and structural properties of the non-additive square well for a pure chain and a binary mixture of chains are performed. Good agreements are observed between the compressibility factors originating from the theory and those from molecular simulations.

  4. Calibration of Richards' and convection dispersion equations to field-scale water flow and solute transport under rainfall conditions

    NASA Astrophysics Data System (ADS)

    Jacques, Diederik; Šimůnek, Jirka; Timmerman, Anthony; Feyen, Jan

    2002-03-01

    In this paper, the applicability of Richards' equation for water flow and the convection-dispersion equation for solute transport is evaluated to model field-scale flow and transport under natural boundary conditions by using detailed experimental data and inverse optimization. The data consisted of depth-averaged time series of water content, pressure head and resident solute concentration data measured several times a day during 384 d. In a first approach, effective parameters are estimated using the time series for one depth and assuming a homogeneous soil profile. In a second approach, all time series were used simultaneously to estimate the parameters of a multi-layered soil profile. Water flow was described by the Richards' equation and solute transport either by the equilibrium convection-dispersion (CDE) or the physical non-equilibrium convection-dispersion (MIM) equation. To represent the dynamics of the water content and pressure head data, the multi-layered soil profile approach gave better results. Fitted soil hydraulic parameters were comparable with parameters obtained with other methods on the same soil. At larger depths, both the CDE- and MIM-models gave acceptable descriptions of the observed breakthrough data, although the MIM performed somewhat better in the tailing part. Both models underestimated significantly the fast breakthrough. To describe the breakthrough curves at the first depth, only the MIM with a mixing layer close to the soil surface gave acceptable results. Starting from an initial value problem with solutes homogeneously distributed over the mobile and immobile water phase was preferable compared to the incorporation of a small layer with only mobile water near the soil surface.

  5. Turbulence measurements over immobile gravel with additions of sand from supply limited to capacity transport conditions

    Technology Transfer Automated Retrieval System (TEKTRAN)

    Measurement of the turbulence that drives sand transport over and through immobile gravels is relevant to efforts to model sediment movement downstream of dams, where fine sediments are eroded from coarse substrates and are not replaced due to the presence of the upstream dam. The relative elevatio...

  6. Predictions of Separated and Transitional Boundary Layers Under Low-Pressure Turbine Airfoil Conditions Using an Intermittency Transport Equation

    NASA Technical Reports Server (NTRS)

    Suzen, Y. Bora; Huang, P. G.; Hultgren, Lennart S.; Ashpis, David E.

    2001-01-01

    A new transport equation for the intermittency factor was proposed to predict separated and transitional boundary layers under low-pressure turbine airfoil conditions. The intermittent behavior of the transitional flows is taken into account and incorporated into computations by modifying the eddy viscosity, mu(sub t), with the intermittency factor, gamma. Turbulent quantities are predicted by using Menter's two-equation turbulence model (SST). The intermittency factor is obtained from a transport equation model, which not only can reproduce the experimentally observed streamwise variation of the intermittency in the transition zone, but also can provide a realistic cross-stream variation of the intermittency profile. In this paper, the intermittency model is used to predict a recent separated and transitional boundary layer experiment under low pressure turbine airfoil conditions. The experiment provides detailed measurements of velocity, turbulent kinetic energy and intermittency profiles for a number of Reynolds numbers and freestream turbulent intensity conditions and is suitable for validation purposes. Detailed comparisons of computational results with experimental data are presented and good agreements between the experiments and predictions are obtained.

  7. Predictions of Separated and Transitional Boundary Layers Under Low-Pressure Turbine Airfoil Conditions Using an Intermittency Transport Equation

    NASA Technical Reports Server (NTRS)

    Suzen, Y. B.; Huang, P. G.; Hultgren, Lennart S.; Ashpis, David E.

    2003-01-01

    A new transport equation for the intermittency factor was proposed to predict separated and transitional boundary layers under low-pressure turbine airfoil conditions. The intermittent behavior of the transitional flows is taken into account and incorporated into computations by modifying the eddy viscosity, t , with the intermittency factor, y. Turbulent quantities are predicted by using Menter s two-equation turbulence model (SST). The intermittency factor is obtained from a transport equation model, which not only can reproduce the experimentally observed streamwise variation of the intermittency in the transition zone, but also can provide a realistic cross-stream variation of the intermittency profile. In this paper, the intermittency model is used to predict a recent separated and transitional boundary layer experiment under low pressure turbine airfoil conditions. The experiment provides detailed measurements of velocity, turbulent kinetic energy and intermittency profiles for a number of Reynolds numbers and freestream turbulent intensity conditions and is suitable for validation purposes. Detailed comparisons of computational results with experimental data are presented and good agreements between the experiments and predictions are obtained.

  8. Implementation of the LAX-Wendroff Method in Cobra-TF for Solving Two-Phase Flow Transport Equations

    SciTech Connect

    Salko, Robert K; Wang, Dean; Ren, Kangyu

    2016-01-01

    COBRA-TF (Coolant Boiling in Rod Arrays Two Fluid), or CTF, is a subchannel code used to conduct the reactor core thermal hydraulic (T/H) solution in both standalone and coupled multi-physics applications. CTF applies the first-order upwind spatial discretization scheme for solving two-phase flow conservation equations. In this work, the second-order Lax-Wendroff (L-W) scheme has been implemented in CTF to solve the two-phase flow transport equations to improve numerical accuracy in both temporal and spatial discretization. To avoid the oscillation issue, a non-linear flux limiter VA (Van Albada) is employed for the convective terms in the transport equations. Assessments have been carried out to evaluate the performance and stability of the implemented second-order L-W scheme. It has been found that the L-W scheme performs better than the upwind scheme for the single-phase and two-phase flow problems in terms of numerical accuracy and computational efficiency.

  9. Hierarchical equations of motion approach to transport through an Anderson impurity coupled to interacting Luttinger liquid leads

    NASA Astrophysics Data System (ADS)

    Okamoto, Jun-ichi; Mathey, Ludwig; Härtle, Rainer

    2016-12-01

    We generalize the hierarchical equations of motion method to study electron transport through a quantum dot or molecule coupled to one-dimensional interacting leads that can be described as Luttinger liquids. Such leads can be realized, for example, by quantum wires or fractional quantum Hall edge states. In comparison to noninteracting metallic leads, Luttinger liquid leads involve many-body correlations and the single-particle tunneling density of states shows a power-law singularity at the chemical potential. Using the generalized hierarchical equations of motion method, we assess the importance of the singularity and the next-to-leading order many-body correlations. To this end, we compare numerically converged results with second- and first-order results of the hybridization expansion that is inherent to our method. As a test case, we study transport through a single-level quantum dot or molecule that can be described by an Anderson impurity model. Cotunneling effects turn out to be most pronounced for attractive interactions in the leads or repulsive ones if an excitonic coupling between the dot and the leads is realized. We also find that an interaction-induced negative differential conductance near the Coulomb blockade thresholds is slightly suppressed as compared to a first-order and/or rate equation result. Moreover, we find that the two-particle (n -particle) correlations enter as a second-order (n -order) effect and are, thus, not very pronounced at the high temperatures and parameters that we consider.

  10. Transport solutions of the Lamé equations and shock elastic waves

    NASA Astrophysics Data System (ADS)

    Alexeyeva, L. A.; Kaishybaeva, G. K.

    2016-07-01

    The Lamé system describing the dynamics of an isotropic elastic medium affected by a steady transport load moving at subsonic, transonic, or supersonic speed is considered. Its fundamental and generalized solutions in a moving frame of reference tied to the transport load are analyzed. Shock waves arising in the medium at supersonic speeds are studied. Conditions on the jump in the stress, displacement rate, and energy across the shock front are obtained using distribution theory. Numerical results concerning the dynamics of an elastic medium influenced by concentrated transport loads moving at sub-, tran- and supersonic speeds are presented.

  11. A posteriori error estimators for the discrete ordinates approximation of the one-speed neutron transport equation

    SciTech Connect

    O'Brien, S.; Azmy, Y. Y.

    2013-07-01

    When calculating numerical solutions of the neutron transport equation it is important to have a measure of the accuracy of the solution. As the true solution is generally not known, a suitable estimation of the error must be made. The steady state transport equation possesses discretization errors in all its independent variables: angle, energy and space. In this work only spatial discretization errors are considered. An exact transport solution, in which the degree of regularity of the exact flux across the singular characteristic is controlled, is manufactured to determine the numerical solutions true discretization error. This solution is then projected onto a Legendre polynomial space in order to form an exact solution on the same basis space as the numerical solution, Discontinuous Galerkin Finite Element Method (DGFEM), to enable computation of the true error. Over a series of test problems the true error is compared to the error estimated by: Ragusa and Wang (RW), residual source (LER) and cell discontinuity estimators (JD). The validity and accuracy of the considered estimators are primarily assessed by considering the effectivity index and global L2 norm of the error. In general RW excels at approximating the true error distribution but usually under-estimates its magnitude; the LER estimator emulates the true error distribution but frequently over-estimates the magnitude of the true error; the JD estimator poorly captures the true error distribution and generally under-estimates the error about singular characteristics but over-estimates it elsewhere. (authors)

  12. 41 CFR 302-10.6 - Are the allowances for transporting a mobile home in addition to the allowances for per diem...

    Code of Federal Regulations, 2014 CFR

    2014-07-01

    ... transporting a mobile home in addition to the allowances for per diem, mileage, and transportation expenses... Management Federal Travel Regulation System RELOCATION ALLOWANCES TRANSPORTATION AND STORAGE OF PROPERTY 10-ALLOWANCES FOR TRANSPORTATION OF MOBILE HOMES AND BOATS USED AS A PRIMARY RESIDENCE Eligibility...

  13. 41 CFR 302-10.6 - Are the allowances for transporting a mobile home in addition to the allowances for per diem...

    Code of Federal Regulations, 2011 CFR

    2011-07-01

    ... transporting a mobile home in addition to the allowances for per diem, mileage, and transportation expenses... Management Federal Travel Regulation System RELOCATION ALLOWANCES TRANSPORTATION AND STORAGE OF PROPERTY 10-ALLOWANCES FOR TRANSPORTATION OF MOBILE HOMES AND BOATS USED AS A PRIMARY RESIDENCE Eligibility...

  14. 41 CFR 302-10.401 - Are the allowances for transporting a mobile home in addition to the allowances for per diem...

    Code of Federal Regulations, 2014 CFR

    2014-07-01

    ... transporting a mobile home in addition to the allowances for per diem, mileage, and transportation expenses... Property Management Federal Travel Regulation System RELOCATION ALLOWANCES TRANSPORTATION AND STORAGE OF PROPERTY 10-ALLOWANCES FOR TRANSPORTATION OF MOBILE HOMES AND BOATS USED AS A PRIMARY RESIDENCE...

  15. 41 CFR 302-10.6 - Are the allowances for transporting a mobile home in addition to the allowances for per diem...

    Code of Federal Regulations, 2013 CFR

    2013-07-01

    ... transporting a mobile home in addition to the allowances for per diem, mileage, and transportation expenses... Management Federal Travel Regulation System RELOCATION ALLOWANCES TRANSPORTATION AND STORAGE OF PROPERTY 10-ALLOWANCES FOR TRANSPORTATION OF MOBILE HOMES AND BOATS USED AS A PRIMARY RESIDENCE Eligibility...

  16. 41 CFR 302-10.401 - Are the allowances for transporting a mobile home in addition to the allowances for per diem...

    Code of Federal Regulations, 2010 CFR

    2010-07-01

    ... transporting a mobile home in addition to the allowances for per diem, mileage, and transportation expenses... Property Management Federal Travel Regulation System RELOCATION ALLOWANCES TRANSPORTATION AND STORAGE OF PROPERTY 10-ALLOWANCES FOR TRANSPORTATION OF MOBILE HOMES AND BOATS USED AS A PRIMARY RESIDENCE...

  17. 41 CFR 302-10.6 - Are the allowances for transporting a mobile home in addition to the allowances for per diem...

    Code of Federal Regulations, 2010 CFR

    2010-07-01

    ... transporting a mobile home in addition to the allowances for per diem, mileage, and transportation expenses... Management Federal Travel Regulation System RELOCATION ALLOWANCES TRANSPORTATION AND STORAGE OF PROPERTY 10-ALLOWANCES FOR TRANSPORTATION OF MOBILE HOMES AND BOATS USED AS A PRIMARY RESIDENCE Eligibility...

  18. 41 CFR 302-10.401 - Are the allowances for transporting a mobile home in addition to the allowances for per diem...

    Code of Federal Regulations, 2011 CFR

    2011-07-01

    ... transporting a mobile home in addition to the allowances for per diem, mileage, and transportation expenses... Property Management Federal Travel Regulation System RELOCATION ALLOWANCES TRANSPORTATION AND STORAGE OF PROPERTY 10-ALLOWANCES FOR TRANSPORTATION OF MOBILE HOMES AND BOATS USED AS A PRIMARY RESIDENCE...

  19. 41 CFR 302-10.401 - Are the allowances for transporting a mobile home in addition to the allowances for per diem...

    Code of Federal Regulations, 2013 CFR

    2013-07-01

    ... transporting a mobile home in addition to the allowances for per diem, mileage, and transportation expenses... Property Management Federal Travel Regulation System RELOCATION ALLOWANCES TRANSPORTATION AND STORAGE OF PROPERTY 10-ALLOWANCES FOR TRANSPORTATION OF MOBILE HOMES AND BOATS USED AS A PRIMARY RESIDENCE...

  20. Generalized semi-analytical solutions to multispecies transport equation coupled with sequential first-order reaction network with spatially or temporally variable transport and decay coefficients

    NASA Astrophysics Data System (ADS)

    Suk, Heejun

    2016-08-01

    This paper presents a semi-analytical procedure for solving coupled the multispecies reactive solute transport equations, with a sequential first-order reaction network on spatially or temporally varying flow velocities and dispersion coefficients involving distinct retardation factors. This proposed approach was developed to overcome the limitation reported by Suk (2013) regarding the identical retardation values for all reactive species, while maintaining the extensive capability of the previous Suk method involving spatially variable or temporally variable coefficients of transport, general initial conditions, and arbitrary temporal variable inlet concentration. The proposed approach sequentially calculates the concentration distributions of each species by employing only the generalized integral transform technique (GITT). Because the proposed solutions for each species' concentration distributions have separable forms in space and time, the solution for subsequent species (daughter species) can be obtained using only the GITT without the decomposition by change-of-variables method imposing the limitation of identical retardation values for all the reactive species by directly substituting solutions for the preceding species (parent species) into the transport equation of subsequent species (daughter species). The proposed solutions were compared with previously published analytical solutions or numerical solutions of the numerical code of the Two-Dimensional Subsurface Flow, Fate and Transport of Microbes and Chemicals (2DFATMIC) in three verification examples. In these examples, the proposed solutions were well matched with previous analytical solutions and the numerical solutions obtained by 2DFATMIC model. A hypothetical single-well push-pull test example and a scale-dependent dispersion example were designed to demonstrate the practical application of the proposed solution to a real field problem.

  1. Dynamical equations and transport coefficients for the metals at high pulse electromagnetic fields

    NASA Astrophysics Data System (ADS)

    Volkov, N. B.; Chingina, E. A.; Yalovets, A. P.

    2016-11-01

    We offer a metal model suitable for the description of fast electrophysical processes in conductors under influence of powerful electronic and laser radiation of femto- and picosecond duration, and also high-voltage electromagnetic pulses with picosecond front and duration less than 1 ns. The obtained dynamic equations for metal in approximation of one quasineutral liquid are in agreement with the equations received by other authors formerly. New wide-range expressions for the electronic conduction in strong electromagnetic fields are obtained and analyzed.

  2. Transport Equation Based Wall Distance Computations Aimed at Flows With Time-Dependent Geometry

    NASA Technical Reports Server (NTRS)

    Tucker, Paul G.; Rumsey, Christopher L.; Bartels, Robert E.; Biedron, Robert T.

    2003-01-01

    Eikonal, Hamilton-Jacobi and Poisson equations can be used for economical nearest wall distance computation and modification. Economical computations may be especially useful for aeroelastic and adaptive grid problems for which the grid deforms, and the nearest wall distance needs to be repeatedly computed. Modifications are directed at remedying turbulence model defects. For complex grid structures, implementation of the Eikonal and Hamilton-Jacobi approaches is not straightforward. This prohibits their use in industrial CFD solvers. However, both the Eikonal and Hamilton-Jacobi equations can be written in advection and advection-diffusion forms, respectively. These, like the Poisson's Laplacian, are commonly occurring industrial CFD solver elements. Use of the NASA CFL3D code to solve the Eikonal and Hamilton-Jacobi equations in advective-based forms is explored. The advection-based distance equations are found to have robust convergence. Geometries studied include single and two element airfoils, wing body and double delta configurations along with a complex electronics system. It is shown that for Eikonal accuracy, upwind metric differences are required. The Poisson approach is found effective and, since it does not require offset metric evaluations, easiest to implement. The sensitivity of flow solutions to wall distance assumptions is explored. Generally, results are not greatly affected by wall distance traits.

  3. Transport Equation Based Wall Distance Computations Aimed at Flows With Time-Dependent Geometry

    NASA Technical Reports Server (NTRS)

    Tucker, Paul G.; Rumsey, Christopher L.; Bartels, Robert E.; Biedron, Robert T.

    2003-01-01

    Eikonal, Hamilton-Jacobi and Poisson equations can be used for economical nearest wall distance computation and modification. Economical computations may be especially useful for aeroelastic and adaptive grid problems for which the grid deforms, and the nearest wall distance needs to be repeatedly computed. Modifications are directed at remedying turbulence model defects. For complex grid structures, implementation of the Eikonal and Hamilton-Jacobi approaches is not straightforward. This prohibits their use in industrial CFD solvers. However, both the Eikonal and Hamilton-Jacobi equations can be written in advection and advection-diffusion forms, respectively. These, like the Poisson s Laplacian, are commonly occurring industrial CFD solver elements. Use of the NASA CFL3D code to solve the Eikonal and Hamilton-Jacobi equations in advective-based forms is explored. The advection-based distance equations are found to have robust convergence. Geometries studied include single and two element airfoils, wing body and double delta configurations along with a complex electronics system. It is shown that for Eikonal accuracy, upwind metric differences are required. The Poisson approach is found effective and, since it does not require offset metric evaluations, easiest to implement. The sensitivity of flow solutions to wall distance assumptions is explored. Generally, results are not greatly affected by wall distance traits.

  4. Approximate Equations for Transport Coefficients of Multicomponent Mixtures of Neutral Gases.

    DTIC Science & Technology

    1980-11-19

    Journal of Chemical Physics, 25, 360 (1956). 51. H. Gruss and H. Schmick, Wiss. Veroffentlich Siemens -Konzern, 7, 202 (1928). 52. Clingman, Brokaw, and...component i in quantum state ai , given by ia nx in (D.4) with V - i" (D.5) i-i a We have left the index i off a in all equations for brevity. Notice

  5. Comparison of solutions to bi-Maxwellian and Maxwellian transport equations for subsonic flows. [in terrestrial ionosphere

    NASA Technical Reports Server (NTRS)

    Demars, H. G.; Schunk, R. W.

    1987-01-01

    Conditions corresponding to the steady state subsonic flow of a fully ionized electron-proton plasma in the terrestrial ionosphere are presently characterized by systematically comparing the solutions to the bi-Maxwellian-based 16-moment and Maxwellian-based 13-moment transport equations. The former can account for large temperature anisotropies and the flow of both parallel and perpendicular thermal energy, while the latter account for small temperature anisotropies and only a total heat flow. The comparison is conducted for 2000-10,000 K lower boundary temperatures and 1-4-K/km temperature gradients, over the 1500-13,000-km altitude range.

  6. A Piecewise Linear Discontinuous Finite Element Spatial Discretization of the Transport Equation in 2D Cylindrical Geometry

    SciTech Connect

    Bailey, T S; Adams, M L; Chang, J H

    2008-10-01

    We present a new spatial discretization of the discrete-ordinates transport equation in two-dimensional cylindrical (RZ) geometry for arbitrary polygonal meshes. This discretization is a discontinuous finite element method that utilizes the piecewise linear basis functions developed by Stone and Adams. We describe an asymptotic analysis that shows this method to be accurate for many problems in the thick diffusion limit on arbitrary polygons, allowing this method to be applied to radiative transfer problems with these types of meshes. We also present numerical results for multiple problems on quadrilateral grids and compare these results to the well-known bi-linear discontinuous finite element method.

  7. A guide to properly select the defocusing distance for accurate solution of transport of intensity equation while testing aspheric surfaces

    NASA Astrophysics Data System (ADS)

    Soltani, Peyman; Darudi, Ahmad; Moradi, Ali Reza; Amiri, Javad; Nehmetallah, Georges

    2016-05-01

    In this paper, the Transport of Intensity Equation (TIE) for testing of an aspheric surface is verified experimentally. Using simulation, a proper defocus distance Δ𝑧 that leads to an accurate solution of TIE is estimated whenever the conic constant and configuration of the experiment are known. To verify this procedure a non-nulled experiment for testing an aspheric is used. For verification of the solution, the results are compared with the Shack-Hartmann sensor. The theoretical method and experimental results are compared to validate the results.

  8. A Hitch-hiker's Guide to Stochastic Differential Equations - Solution Methods for Energetic Particle Transport in Space Physics and Astrophysics

    NASA Astrophysics Data System (ADS)

    Strauss, R. Du Toit; Effenberger, Frederic

    2017-03-01

    In this review, an overview of the recent history of stochastic differential equations (SDEs) in application to particle transport problems in space physics and astrophysics is given. The aim is to present a helpful working guide to the literature and at the same time introduce key principles of the SDE approach via "toy models". Using these examples, we hope to provide an easy way for newcomers to the field to use such methods in their own research. Aspects covered are the solar modulation of cosmic rays, diffusive shock acceleration, galactic cosmic ray propagation and solar energetic particle transport. We believe that the SDE method, due to its simplicity and computational efficiency on modern computer architectures, will be of significant relevance in energetic particle studies in the years to come.

  9. Solution of Linearized Drift Kinetic Equations in Neoclassical Transport Theory by the Method of Matched Asymptotic Expansions

    NASA Astrophysics Data System (ADS)

    Wong, S. K.; Chan, V. S.; Hinton, F. L.

    2001-10-01

    The classic solution of the linearized drift kinetic equations in neoclassical transport theory for large-aspect-ratio tokamak flux-surfaces relies on the variational principle and the choice of ``localized" distribution functions as trialfunctions.(M.N. Rosenbluth, et al., Phys. Fluids 15) (1972) 116. Somewhat unclear in this approach are the nature and the origin of the ``localization" and whether the results obtained represent the exact leading terms in an asymptotic expansion int he inverse aspect ratio. Using the method of matched asymptotic expansions, we were able to derive the leading approximations to the distribution functions and demonstrated the asymptotic exactness of the existing results. The method is also applied to the calculation of angular momentum transport(M.N. Rosenbluth, et al., Plasma Phys. and Contr. Nucl. Fusion Research, 1970, Vol. 1 (IAEA, Vienna, 1971) p. 495.) and the current driven by electron cyclotron waves.

  10. Accurate testing of aspheric surfaces using the transport of intensity equation by properly selecting the defocusing distance.

    PubMed

    Soltani, Peyman; Darudi, Ahmad; Nehmetallah, George; Moradi, Ali Reza; Amiri, Javad

    2016-12-10

    In the last decade, the transport of intensity has been increasingly used in microscopy, wavefront sensing, and metrology. In this study, we verify by simulation and experiment the use of the transport of intensity equation (TIE) in the accurate testing of optical aspheric surfaces. Guided by simulation results and assuming that the experimental setup parameters and the conic constants are known, one can estimate an appropriate defocusing distance Δz that leads to an accurate solution of the TIE. In this paper, this method is verified through the construction of a non-nulled experiment for testing the 2D profile of an aspheric surface. The theoretical method and experimental results are compared to validate the results. Finally, to validate the TIE methodology, the phase distribution obtained by TIE is compared with the phase distribution obtained by a Shack-Hartmann sensor.

  11. Gliders Measure Western Boundary Current Transport from the South Pacific to the Equator

    NASA Astrophysics Data System (ADS)

    Davis, R. E.; Kessler, W. S.; Sherman, J. T.

    2011-12-01

    Since 2007, the Consortium on the Ocean's Role in Climate (CORC) has used repeated glider transects across the southern Solomon Sea to measure the previously nearly unsampled mass and heat transport from the South Pacific to the equatorial zone. Mean transport is dominated by the New Guinea Coastal Undercurrent (NGCUC). This low-latitude western boundary current is a major element of the shallow meridional overturning circulation, returning water from the subtropical South Pacific to the Equatorial Undercurrent (EUC) where it upwells. We find the mean NGCUC to be a jet less than 100 km wide, centered near 300 m depth, with equatorward velocities reaching 35 cm/s and salinity anomalies on isopycnals up to 0.05. Weaker poleward flow is found near the surface in the eastern basin. Equatorward transport above 700 m is typically 20 Sv, but nearly vanished during two La Niñas and reached 25 Sv during an El Niño. Within these events the seasonal cycle cannot yet be defined. Transport variability is strongest outside the boundary current and appears to consist of two independently moving layers with a boundary near 250 m. ENSO variability is predominantly in the upper layer. The relation of Solomon Sea mass and heat transport with ENSO indicators will be discussed The ability to initiate and maintain measurements that support such quantitative analyses with a small effort in a remote site far from research institutions demonstrates that gliders can be a productive part of the global ocean observing system.

  12. A solution of the monoenergetic neutral particle transport equation for adjacent half-spaces with anisotropic scattering

    SciTech Connect

    Ganapol, B.D.; Mostacci, D.; Previti, A.

    2016-07-01

    We present highly accurate solutions to the neutral particle transport equation in a half-space. While our initial motivation was in response to a recently published solution based on Chandrasekhar's H-function, the presentation to follow has taken on a more comprehensive tone. The solution by H-functions certainly did achieved high accuracy but was limited to isotropic scattering and emission from spatially uniform and linear sources. Moreover, the overly complicated nature of the H-function approach strongly suggests that its extension to anisotropic scattering and general sources is not at all practical. For this reason, an all encompassing theory for the determination of highly precise benchmarks, including anisotropic scattering for a variety of spatial source distributions, is presented for particle transport in a half-space. We illustrate the approach via a collection of cases including tables of 7-place flux benchmarks to guide transport methods developers. The solution presented can be applied to a considerable number of one and two half-space transport problems with variable sources and represents a state-of-the-art benchmark solution.

  13. Discontinuous Galerkin discretization of the Reynolds-averaged Navier-Stokes equations with the shear-stress transport model

    NASA Astrophysics Data System (ADS)

    Schoenawa, Stefan; Hartmann, Ralf

    2014-04-01

    In this article we consider the development of Discontinuous Galerkin (DG) methods for the numerical approximation of the Reynolds-averaged Navier-Stokes (RANS) equations with the shear-stress transport (SST) model by Menter. This turbulence model is based on a blending of the Wilcox k-ω model used near the wall and the k-ɛ model used in the rest of the domain where the blending functions depend on the distance to the nearest wall. For the computation of the distance of each quadrature point in the domain to the nearest of the curved, piecewise polynomial wall boundaries, we propose a stabilized continuous finite element (FE) discretization of the eikonal equation. Furthermore, we propose a new wall boundary condition for the dissipation rate ω based on the projection of the analytic near-wall behavior of ω onto the discrete ansatz space of the DG discretization. Finally, we introduce an artificial viscosity to the discretization of the turbulence kinetic energy (k-)equation to suppress oscillations of k near the underresolved boundary layer edge. The wall distance computation based on the continuous FE discretization of the eikonal equation is demonstrated for an internal and three external/aerodynamic flow geometries including a three-element high-lift configuration. The DG discretization of the RANS equations with the SST model is demonstrated for turbulent flows past a flat plate and the RAE2822 airfoil (Cases 9 and 10). The results are compared to the underlying k-ω model and experimental data.

  14. Screening of Potential O-Ring Swelling Additives for Ultraclean Transportation Fuels

    SciTech Connect

    Baltrus, J.P.; Link, D.D.; Zandhuis, P.H.; Gormley, R.J.; Anderson, R.R.

    2007-03-01

    Several classes of organic compounds and mixtures of organic compounds were evaluated as potential additives to Fischer-Tropsch fuels to promote swelling of nitrile rubber o-rings that come in contact with the fuels. Computational modeling studies were also carried out to predict which compounds might be best at promoting o-ring swelling. The combined experimental-theoretical approach showed that steric factors strongly influence the interactions between additives and the nitrile sites in the rubber that result in swelling. Select compounds incorporating both oxygenate and aromatic functionalities appear to be the best candidates for additives because of a "dual" interaction between complementary functionalities on these compounds and the nitrile rubber.

  15. Influence of Conducting Plate Boundary Conditions on the Transverse Envelope Equations Describing Intense Ion Beam Transport

    SciTech Connect

    Lund, S M; Bukh, B

    2003-07-23

    In typical diagnostic applications, intense ion beams are intercepted by a conducting plate associated with devices used to measure beam phase-space projections. This results in the transverse space-charge field near the plate being shorted out, rendering simple envelope models with constant space-charge strength inaccurate. Here we develop corrected envelope models based on analytical calculations to account for this effect on the space-charge term of the envelope equations, thereby removing a systematic source of error in the equations and enabling more accurate comparisons with experiment. For common intense beam parameters, we find that the correction occurs primarily in the envelope angles and that the effect can be large enough to degrade precision beam matching. Results are verified with 3D self-consistent PIC simulations based on intense beam experiments associated with driver developments for Heavy-Ion Fusion.

  16. Kershaw closures for linear transport equations in slab geometry I: Model derivation

    NASA Astrophysics Data System (ADS)

    Schneider, Florian

    2016-10-01

    This paper provides a new class of moment models for linear kinetic equations in slab geometry. These models can be evaluated cheaply while preserving the important realizability property, that is the fact that the underlying closure is non-negative. Several comparisons with the (expensive) state-of-the-art minimum-entropy models are made, showing the similarity in approximation quality of the two classes.

  17. Parameter Estimation Techniques for Transport Equations with Application to Population Dispersal and Tissue Bulk Flow Models.

    DTIC Science & Technology

    1982-07-01

    MODELSLDS#-1 7. AUTHOR(*)11.CNRCOGRNNUB(* H.T. Banks and P. Kareiva AFOSR-81-0198 93 PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT...parameters that predicted several consecutive recapture distributions. Because insects are ectotherms and are very sensitive to weather, their moveet...regression equations describing the density distribution of dispersing organisms , Nature, vol. 286, 53-55, 1980. tb 4J / • t

  18. Heat flux solutions of the 13-moment approximation transport equations in a multispecies gas

    SciTech Connect

    Jian Wu; Taieb, C.

    1993-09-01

    The authors study steady state heat flux equations by means of the 13-moment approximation for situations applicable to aeronomy and space plasmas. They compare their results with Fourier`s law applied to similar problems, to test validity conditions for it. They look at the flux of oxygen and hydrogen ions in the high-latitude ionosphere, and compare calculations with observations from EISCAT radar measurements. These plasma components are observed to have strongly non-Maxwellian distributions.

  19. New approach to the solution of the Boltzmann radiation transport equation

    NASA Astrophysics Data System (ADS)

    Boffi, Vinicio C.; Dunn, William L.

    1987-03-01

    Transport monodimensional stationary solutions for the angular space-energy neutron flux, of interest in radiation penetration problems, are studied by Green's function method. Explicit analytical results for the spatial moments of the sought solution are obtained for the case of an isotropically scattering slab of infinite thickness and of a continuous slowing down model in energy.

  20. A nonlinear positive method for solving the transport equation on course meshes

    SciTech Connect

    Walters, W.F.; Wareing, T.A.

    1994-02-01

    A new nonlinear S{sub n} transport differencing scheme for slab geometry is presented that is fourth order accurate for small meshes and is strictly positive. The new scheme has been coded into the existing ONELD code and tested. Numerical results to demonstrate the accuracy and positivity of this new scheme are presented.

  1. Using Modern C++ Idiom for the Discretisation of Sets of Coupled Transport Equations in Numerical Plasma Physics

    NASA Astrophysics Data System (ADS)

    van Dijk, Jan; Hartgers, Bart; van der Mullen, Joost

    2006-10-01

    Self-consistent modelling of plasma sources requires a simultaneous treatment of multiple physical phenomena. As a result plasma codes have a high degree of complexity. And with the growing interest in time-dependent modelling of non-equilibrium plasma in three dimensions, codes tend to become increasingly hard to explain-and-maintain. As a result of these trends there has been an increased interest in the software-engineering and implementation aspects of plasma modelling in our group at Eindhoven University of Technology. In this contribution we will present modern object-oriented techniques in C++ to solve an old problem: that of the discretisation of coupled linear(ized) equations involving multiple field variables on ortho-curvilinear meshes. The `LinSys' code has been tailored to the transport equations that occur in transport physics. The implementation has been made both efficient and user-friendly by using modern idiom like expression templates and template meta-programming. Live demonstrations will be given. The code is available to interested parties; please visit www.dischargemodelling.org.

  2. Numerical solution of the equation of neutrons transport on plane geometry by analytical schemes using acceleration by synthetic diffusion

    NASA Astrophysics Data System (ADS)

    Alonso-Vargas, G.

    A computer program has been developed which uses a technique of synthetic acceleration by diffusion by analytical schemes. Both in the diffusion equation as in that of transport, analytical schemes were used which allowed a substantial time saving in the number of iterations required by source iteration method to obtain the K(sub e)ff. The program developed ASD (Synthetic Diffusion Acceleration) by diffusion was written in FORTRAN and can be executed on a personal computer with a hard disc and mathematical O-processor. The program is unlimited as to the number of regions and energy groups. The results obtained by the ASD program for K(sub e)ff is nearly completely concordant with those obtained by utilizing the ANISN-PC code for different analytical type problems in this work. The ASD program allowed obtention of an approximate solution of the neutron transport equation with a relatively low number of internal reiterations with good precision. One of its applications would be in the direct determinations of axial distribution neutronic flow in a fuel assembly as well as in the obtention of the effective multiplication factor.

  3. Salicylic acid transport in Ricinus communis involves a pH-dependent carrier system in addition to diffusion.

    PubMed

    Rocher, Françoise; Chollet, Jean-François; Legros, Sandrine; Jousse, Cyril; Lemoine, Rémi; Faucher, Mireille; Bush, Daniel R; Bonnemain, Jean-Louis

    2009-08-01

    Despite its important functions in plant physiology and defense, the membrane transport mechanism of salicylic acid (SA) is poorly documented due to the general assumption that SA is taken up by plant cells via the ion trap mechanism. Using Ricinus communis seedlings and modeling tools (ACD LogD and Vega ZZ softwares), we show that phloem accumulation of SA and hydroxylated analogs is completely uncorrelated with the physicochemical parameters suitable for diffusion (number of hydrogen bond donors, polar surface area, and, especially, LogD values at apoplastic pHs and Delta LogD between apoplast and phloem sap pH values). These and other data (such as accumulation in phloem sap of the poorly permeant dissociated form of monohalogen derivatives from apoplast and inhibition of SA transport by the thiol reagent p-chloromercuribenzenesulfonic acid [pCMBS]) lead to the following conclusions. As in intestinal cells, SA transport in Ricinus involves a pH-dependent carrier system sensitive to pCMBS; this carrier can translocate monohalogen analogs in the anionic form; the efficiency of phloem transport of hydroxylated benzoic acid derivatives is tightly dependent on the position of the hydroxyl group on the aromatic ring (SA corresponds to the optimal position) but moderately affected by halogen addition in position 5, which is known to increase plant defense. Furthermore, combining time-course experiments and pCMBS used as a tool, we give information about the localization of the SA carrier. SA uptake by epidermal cells (i.e. the step preceding the symplastic transport to veins) insensitive to pCMBS occurs via the ion-trap mechanism, whereas apoplastic vein loading involves a carrier-mediated mechanism (which is targeted by pCMBS) in addition to diffusion.

  4. Rain water transport and storage in a model sandy soil with hydrogel particle additives.

    PubMed

    Wei, Y; Durian, D J

    2014-10-01

    We study rain water infiltration and drainage in a dry model sandy soil with superabsorbent hydrogel particle additives by measuring the mass of retained water for non-ponding rainfall using a self-built 3D laboratory set-up. In the pure model sandy soil, the retained water curve measurements indicate that instead of a stable horizontal wetting front that grows downward uniformly, a narrow fingered flow forms under the top layer of water-saturated soil. This rain water channelization phenomenon not only further reduces the available rain water in the plant root zone, but also affects the efficiency of soil additives, such as superabsorbent hydrogel particles. Our studies show that the shape of the retained water curve for a soil packing with hydrogel particle additives strongly depends on the location and the concentration of the hydrogel particles in the model sandy soil. By carefully choosing the particle size and distribution methods, we may use the swollen hydrogel particles to modify the soil pore structure, to clog or extend the water channels in sandy soils, or to build water reservoirs in the plant root zone.

  5. The addition of organic carbon and nitrate affects reactive transport of heavy metals in sandy aquifers.

    PubMed

    Satyawali, Yamini; Seuntjens, Piet; Van Roy, Sandra; Joris, Ingeborg; Vangeel, Silvia; Dejonghe, Winnie; Vanbroekhoven, Karolien

    2011-04-25

    Organic carbon introduction in the soil to initiate remedial measures, nitrate infiltration due to agricultural practices or sulphate intrusion owing to industrial usage can influence the redox conditions and pH, thus affecting the mobility of heavy metals in soil and groundwater. This study reports the fate of Zn and Cd in sandy aquifers under a variety of plausible in-situ redox conditions that were induced by introduction of carbon and various electron acceptors in column experiments. Up to 100% Zn and Cd removal (from the liquid phase) was observed in all the four columns, however the mechanisms were different. Metal removal in column K1 (containing sulphate), was attributed to biological sulphate reduction and subsequent metal precipitation (as sulphides). In the presence of both nitrate and sulphate (K2), the former dominated the process, precipitating the heavy metals as hydroxides and/or carbonates. In the presence of sulphate, nitrate and supplemental iron (Fe(OH)(3)) (K3), metal removal was also due to precipitation as hydroxides and/or carbonates. In abiotic column, K4, (with supplemental iron (Fe(OH)(3)), but no nitrate), cation exchange with soil led to metal removal. The results obtained were modeled using the reactive transport model PHREEQC-2 to elucidate governing processes and to evaluate scenarios of organic carbon, sulphate and nitrate inputs.

  6. Atmospheric transport and deposition, an additional input pathway for triazine herbicides to surface waters

    SciTech Connect

    Muir, D.C.G.; Rawn, D.F.

    1996-10-01

    Although surface runoff from treated fields is regarded as the major route of entry of triazine herbicides to surface waters, other pathways such as deposition via precipitation, gas absorption and dryfall may also be important. Triazine herbicides have been detected in precipitation but there has been only a very limited amount of work on gas phase and aerosols. To examine the importance of atmospheric inputs concentrations of atrazine, cyanazine and terbuthylazine in gas phase/aerosols, precipitation, and surface waters were determined (along with other herbicides) using selected ion GC-MS. Atrazine was detected at low ng/L concentrations in surface waters (<0.04-5.3 ng/L) and precipitation (0.1-53 ng/L), and at 0.02-0.1 ng/m{sup 3} in air. Cyanazine and terbuthylazine were detected in air and infrequently in water. Highest atrazine concentrations in air were found during June each year on both gas phase and particles. Concentrations of atrazine in surface waters at both locations increased during June, even in the absence of precipitation or overland flow, presumably due to inputs from dryfall and to gas areas and boreal forest lakes due to transport and deposition. Ecological risk assessment of triazines, especially for pristine aquatic environments should include consideration of this atmospheric pathway.

  7. Additional Development and Systems Analyses of Pneumatic Technology for High Speed Civil Transport Aircraft

    NASA Technical Reports Server (NTRS)

    Englar, Robert J.; Willie, F. Scott; Lee, Warren J.

    1999-01-01

    In the Task I portion of this NASA research grant, configuration development and experimental investigations have been conducted on a series of pneumatic high-lift and control surface devices applied to a generic High Speed Civil Transport (HSCT) model configuration to determine their potential for improved aerodynamic performance, plus stability and control of higher performance aircraft. These investigations were intended to optimize pneumatic lift and drag performance; provide adequate control and longitudinal stability; reduce separation flowfields at high angle of attack; increase takeoff/climbout lift-to-drag ratios; and reduce system complexity and weight. Experimental aerodynamic evaluations were performed on a semi-span HSCT generic model with improved fuselage fineness ratio and with interchangeable plain flaps, blown flaps, pneumatic Circulation Control Wing (CCW) high-lift configurations, plain and blown canards, a novel Circulation Control (CC) cylinder blown canard, and a clean cruise wing for reference. Conventional tail power was also investigated for longitudinal trim capability. Also evaluated was unsteady pulsed blowing of the wing high-lift system to determine if reduced pulsed mass flow rates and blowing requirements could be made to yield the same lift as that resulting from steady-state blowing. Depending on the pulsing frequency applied, reduced mass flow rates were indeed found able to provide lift augmentation at lesser blowing values than for the steady conditions. Significant improvements in the aerodynamic characteristics leading to improved performance and stability/control were identified, and the various components were compared to evaluate the pneumatic potential of each. Aerodynamic results were provided to the Georgia Tech Aerospace System Design Lab. to conduct the companion system analyses and feasibility study (Task 2) of theses concepts applied to an operational advanced HSCT aircraft. Results and conclusions from these

  8. Suppression of flow pulsation activity by relaxation process of additive effect on viscous media transport

    NASA Astrophysics Data System (ADS)

    Kharlamov, S.; Dedeyev, P.; Meucci, L.; Shenderova, I.; Manastirniy, A.; Usenko, M.

    2015-11-01

    The article presents the analysis of the processes occurring together with the turbulent transfer of impulse in mixture of hydrocarbon fluid and polymer solutions (anti-turbulent additives). The study evaluates complex shear flows by popular theoretical and practical methods. Understanding of hydrodynamic and dissipative effects of laminar-turbulent transition tightening and turbulence suppression is provided. The peculiarities of "thin" flow structure in pipeline zones with complex shape walls are evaluated. Recommendations to forecast the local flow parameters, calculation of hydraulic resistance are given.

  9. A continuum mechanical approach to the flow equations for membrane transport. I. Water flow.

    PubMed

    Mikulecky, D C

    1972-12-01

    A concept is presented for modeling flows through membranes using continuum mechanics. Viscous interactions (due to velocity gradients) are explicitly incorporated and position-dependent local water-membrane interactions are taken into account before obtaining slab averages. This is in distinction to other treatments where strictly one-dimensional force balance equations are written using slab average friction coefficients which are really composite functions of local interactions. It is shown that the viscous and other frictional interactions do not simply form linear combinations in the solutions to the equations of motion. Flow profiles for pressure-driven flows ranging from Poiseuille's flow to "diffusion" flow are obtained depending on the strength and extent of the water-membrane interaction. The model is also applied to self-diffusion flows and the measurement of "equivalent pore size." It is shown that for a fixed pore size the ratio of filtration flow to self-diffusion flow for equal driving forces is able to vary over a wide range depending on the water-membrane interaction.

  10. Parallel multigrid solver of radiative transfer equation for photon transport via graphics processing unit.

    PubMed

    Gao, Hao; Phan, Lan; Lin, Yuting

    2012-09-01

    A graphics processing unit-based parallel multigrid solver for a radiative transfer equation with vacuum boundary condition or reflection boundary condition is presented for heterogeneous media with complex geometry based on two-dimensional triangular meshes or three-dimensional tetrahedral meshes. The computational complexity of this parallel solver is linearly proportional to the degrees of freedom in both angular and spatial variables, while the full multigrid method is utilized to minimize the number of iterations. The overall gain of speed is roughly 30 to 300 fold with respect to our prior multigrid solver, which depends on the underlying regime and the parallelization. The numerical validations are presented with the MATLAB codes at https://sites.google.com/site/rtefastsolver/.

  11. Parallel multigrid solver of radiative transfer equation for photon transport via graphics processing unit

    PubMed Central

    Phan, Lan; Lin, Yuting

    2012-01-01

    Abstract. A graphics processing unit–based parallel multigrid solver for a radiative transfer equation with vacuum boundary condition or reflection boundary condition is presented for heterogeneous media with complex geometry based on two-dimensional triangular meshes or three-dimensional tetrahedral meshes. The computational complexity of this parallel solver is linearly proportional to the degrees of freedom in both angular and spatial variables, while the full multigrid method is utilized to minimize the number of iterations. The overall gain of speed is roughly 30 to 300 fold with respect to our prior multigrid solver, which depends on the underlying regime and the parallelization. The numerical validations are presented with the MATLAB codes at https://sites.google.com/site/rtefastsolver/. PMID:23085905

  12. Group additivity equations of state for calculating the standard molal thermodynamic properties of aqueous organic species at elevated temperatures and pressures

    NASA Astrophysics Data System (ADS)

    Amend, Jan P.; Helgeson, Harold C.

    1997-01-01

    Group additivity equations of state for aqueous organic molecules have been generated by combining the revised Helgeson-Kirkham-Flowers (HKF) equations of state ( Shock and Helgeson, 1988, 1990; Tanger and Helgeson, 1988; Shock et al., 1989, 1992) with experimental values of the standard molal properties of aqueous alkanes, alkanols, alkylbenzenes, car☐ylic acids, amides, and amines. Equations of state parameters for the groups represented by -CH 2-, -CH 3, -CHCH 3-, -C 6H 5, -CH 2OH, -COOH, -CONH 2, and -CH 2NH 2 were determined by regression of the experimental data. This procedure permits calculation of the standard molal thermodynamic properties of these groups at elevated temperatures and pressures. Although curves representing the apparent standard molal Gibbs free energies (Δ G°) and enthalpies (Δ H°) of formation, and the standard molal entropies ( S°) of the groups as a function of temperature and pressure are respectively similar for each of them, the temperature dependence of the standard molal heat capacities ( Cp°) and volumes ( V°) of a number of the groups are quite different from one another. For example, the standard molal heat capacities of the hydrocarbon groups minimize with increasing temperature, but those of -CH 2OH and -CH 2NH 2 maximize. Computed values of Δ G°, Δ H°, S°, Cp°, V°, and the equations of state parameters for the various groups were used together with group additivity relations to generate corresponding values of these properties for aqueous n-alkanes, 2-methylalkanes, n-alkylbenzenes, n-alkanols, n-car☐ylic acids, n-amides, and n-amines at temperatures ≤ 250°C and pressures ≤ 1 kbar. The validity and generality of the equations of state are supported by the fact that predicted equilibrium constants for liquid n-alkane solubility reactions in water compare favorably with experimental values reported in the literature for temperatures as high as 200°C. Furthermore, equilibrium constants for aqueous ethane

  13. A seamless hybrid RANS-LES model based on transport equations for the subgrid stresses and elliptic blending

    NASA Astrophysics Data System (ADS)

    Fadai-Ghotbi, Atabak; Friess, Christophe; Manceau, Rémi; Borée, Jacques

    2010-05-01

    The aim of the present work is to develop a seamless hybrid Reynolds-averaged Navier-Stokes (RANS) large-eddy simulation (LES) model based on transport equations for the subgrid stresses, using the elliptic-blending method to account for the nonlocal kinematic blocking effect of the wall. It is shown that the elliptic relaxation strategy of Durbin is valid in a RANS (steady) as well as a LES context (unsteady). In order to reproduce the complex production and redistribution mechanisms when the cutoff wavenumber is located in the productive zone of the turbulent energy spectrum, the model is based on transport equations for the subgrid-stress tensor. The partially integrated transport model (PITM) methodology offers a consistent theoretical framework for such a model, enabling to control the cutoff wavenumber κc, and thus the transition from RANS to LES, by making the Cɛ2 coefficient in the dissipation equation of a RANS model a function of κc. The equivalence between the PITM and the Smagorinsky model is shown when κc is in the inertial range of the energy spectrum. The extension of the underlying RANS model used in the present work, the elliptic-blending Reynolds-stress model, to the hybrid RANS-LES context, brings out some modeling issues. The different modeling possibilities are compared in a channel flow at Reτ=395. Finally, a dynamic procedure is proposed in order to adjust during the computation the dissipation rate necessary to drive the model toward the expected amount of resolved energy. The final model gives very encouraging results in comparison to the direct numerical simulation data. In particular, the turbulence anisotropy in the near-wall region is satisfactorily reproduced. The contribution of the resolved and modeled fields to the Reynolds stresses behaves as expected: the modeled part is dominant in the near-wall zones (RANS mode) and decreases toward the center of the channel, where the relative contribution of the resolved part increases

  14. Additive-Free Transparent Triarylamine-Based Polymeric Hole-Transport Materials for Stable Perovskite Solar Cells.

    PubMed

    Matsui, Taisuke; Petrikyte, Ieva; Malinauskas, Tadas; Domanski, Konrad; Daskeviciene, Maryte; Steponaitis, Matas; Gratia, Paul; Tress, Wolfgang; Correa-Baena, Juan-Pablo; Abate, Antonio; Hagfeldt, Anders; Grätzel, Michael; Nazeeruddin, Mohammad Khaja; Getautis, Vytautas; Saliba, Michael

    2016-09-22

    Triarylamine-based polymers with different functional groups were synthetized as hole-transport materials (HTMs) for perovskite solar cells (PSCs). The novel materials enabled efficient PSCs without the use of chemical doping (or additives) to enhance charge transport. Devices employing poly(triarylamine) with methylphenylethenyl functional groups (V873) showed a power conversion efficiency of 12.3 %, whereas widely used additive-free poly[bis(4-phenyl)(2,4,6-trimethylphenyl)amine] (PTAA) demonstrated 10.8 %. Notably, devices with V873 enabled stable PSCs under 1 sun illumination at maximum power point tracking for approximately 40 h at room temperature, and in the dark under elevated temperature (85 °C) for more than 140 h. This is in stark contrast to additive-containing devices, which degrade significantly within the same time frame. The results present remarkable progress towards stable PSC under real working conditions and industrial stress tests.

  15. High-order local maximum principle preserving (MPP) discontinuous Galerkin finite element method for the transport equation

    NASA Astrophysics Data System (ADS)

    Anderson, R.; Dobrev, V.; Kolev, Tz.; Kuzmin, D.; Quezada de Luna, M.; Rieben, R.; Tomov, V.

    2017-04-01

    In this work we present a FCT-like Maximum-Principle Preserving (MPP) method to solve the transport equation. We use high-order polynomial spaces; in particular, we consider up to 5th order spaces in two and three dimensions and 23rd order spaces in one dimension. The method combines the concepts of positive basis functions for discontinuous Galerkin finite element spatial discretization, locally defined solution bounds, element-based flux correction, and non-linear local mass redistribution. We consider a simple 1D problem with non-smooth initial data to explain and understand the behavior of different parts of the method. Convergence tests in space indicate that high-order accuracy is achieved. Numerical results from several benchmarks in two and three dimensions are also reported.

  16. Phase retrieval with the transport-of-intensity equation in an arbitrarily-shaped aperture by iterative discrete cosine transforms

    DOE PAGES

    Huang, Lei; Zuo, Chao; Idir, Mourad; ...

    2015-04-21

    A novel transport-of-intensity equation (TIE) based phase retrieval method is proposed with putting an arbitrarily-shaped aperture into the optical wavefield. In this arbitrarily-shaped aperture, the TIE can be solved under non-uniform illuminations and even non-homogeneous boundary conditions by iterative discrete cosine transforms with a phase compensation mechanism. Simulation with arbitrary phase, arbitrary aperture shape, and non-uniform intensity distribution verifies the effective compensation and high accuracy of the proposed method. Experiment is also carried out to check the feasibility of the proposed method in real measurement. Comparing to the existing methods, the proposed method is applicable for any types of phasemore » distribution under non-uniform illumination and non-homogeneous boundary conditions within an arbitrarily-shaped aperture, which enables the technique of TIE with hard aperture become a more flexible phase retrieval tool in practical measurements.« less

  17. Phase retrieval with the transport-of-intensity equation in an arbitrarily-shaped aperture by iterative discrete cosine transforms

    SciTech Connect

    Huang, Lei; Zuo, Chao; Idir, Mourad; Qu, Weijuan; Asundi, Anand

    2015-04-21

    A novel transport-of-intensity equation (TIE) based phase retrieval method is proposed with putting an arbitrarily-shaped aperture into the optical wavefield. In this arbitrarily-shaped aperture, the TIE can be solved under non-uniform illuminations and even non-homogeneous boundary conditions by iterative discrete cosine transforms with a phase compensation mechanism. Simulation with arbitrary phase, arbitrary aperture shape, and non-uniform intensity distribution verifies the effective compensation and high accuracy of the proposed method. Experiment is also carried out to check the feasibility of the proposed method in real measurement. Comparing to the existing methods, the proposed method is applicable for any types of phase distribution under non-uniform illumination and non-homogeneous boundary conditions within an arbitrarily-shaped aperture, which enables the technique of TIE with hard aperture become a more flexible phase retrieval tool in practical measurements.

  18. Beam characterization of FLASH from beam profile measurement by intensity transport equation and reconstruction of the Wigner distribution function

    NASA Astrophysics Data System (ADS)

    Schäfer, Bernd; Mey, Tobias; Mann, Klaus; Keitel, Barbara; Kreis, Svea; Kuhlmann, Marion; Plönjes, Elke; Tiedtke, Kai

    2013-05-01

    Beam parameters of the free-electron laser FLASH @13.5 nm in two different operation modes were determined from beam profile measurements and subsequent reconstruction of the Wigner distribution function behind the ellipsoidal focusing mirror at beamline BL2. 40 two-dimensional single pulse intensity distributions were recorded at each of 65 axial positions around the waist of the FEL beam with a magnifying EUV sensitized CCD camera. From these beam profile data the Wigner distribution function based on different levels of averaging could be reconstructed by an inverse Radon transform. For separable beams this yields the complete Wigner distribution, and for beams with zero twist the information is still sufficient for wavefront determination and beam propagation through stigmatic systems. The obtained results are compared to wavefront reconstructions based on the transport of intensity equation. A future setup for Wigner distribution measurements of general beams is discussed.

  19. Series integration of the diaphragm cell transport equation when the diffusion coefficient is a function of concentration

    NASA Technical Reports Server (NTRS)

    Cain, Judith B.; Baird, James K.

    1992-01-01

    An integral of the form, t = B0 + BL ln(Delta-c) + B1(Delta-c) + B2(Delta-c)-squared + ..., where t is the time and Delta-c is the concentration difference across the frit, is derived in the case of the diaphragm cell transport equation where the interdiffusion coefficient is a function of concentration. The coefficient, B0, is a constant of the integration, while the coefficients, BL, B1, B2,..., depend in general upon the constant, the compartment volumes, and the interdiffusion coefficient and various of its concentration derivatives evaluated at the mean concentration for the cell. Explicit formulas for BL, B1, B2,... are given.

  20. Least-Squares PN Formulation of the Transport Equation Using Self-Adjoint-Angular-Flux Consistent Boundary Conditions.

    SciTech Connect

    Vincent M. Laboure; Yaqi Wang; Mark D. DeHart

    2016-05-01

    In this paper, we study the Least-Squares (LS) PN form of the transport equation compatible with voids in the context of Continuous Finite Element Methods (CFEM).We first deriveweakly imposed boundary conditions which make the LS weak formulation equivalent to the Self-Adjoint Angular Flux (SAAF) variational formulation with a void treatment, in the particular case of constant cross-sections and a uniform mesh. We then implement this method in Rattlesnake with the Multiphysics Object Oriented Simulation Environment (MOOSE) framework using a spherical harmonics (PN) expansion to discretize in angle. We test our implementation using the Method of Manufactured Solutions (MMS) and find the expected convergence behavior both in angle and space. Lastly, we investigate the impact of the global non-conservation of LS by comparing the method with SAAF on a heterogeneous test problem.

  1. Fully automated, high speed, tomographic phase object reconstruction using the transport of intensity equation in transmission and reflection configurations.

    PubMed

    Nguyen, Thanh; Nehmetallah, George; Tran, Dat; Darudi, Ahmad; Soltani, Peyman

    2015-12-10

    While traditional transport of intensity equation (TIE) based phase retrieval of a phase object is performed through axial translation of the CCD, in this work a tunable lens TIE is employed in both transmission and reflection configurations. These configurations are extended to a 360° tomographic 3D reconstruction through multiple illuminations from different angles by a custom fabricated rotating assembly of the phase object. Synchronization circuitry is developed to control the CCD camera and the Arduino board, which in its turn controls the tunable lens and the stepper motor to automate the tomographic reconstruction process. Finally, a MATLAB based user friendly graphical user interface is developed to control the whole system and perform tomographic reconstruction using both multiplicative and inverse radon based techniques.

  2. Electrical transport limited by electron-phonon coupling from Boltzmann transport equation: An ab initio study of Si, Al, and MoS2

    NASA Astrophysics Data System (ADS)

    Li, Wu

    2015-08-01

    We demonstrate the ab initio electrical transport calculation limited by electron-phonon coupling by using the full solution of the Boltzmann transport equation (BTE), which applies equally to metals and semiconductors. Numerical issues are emphasized in this work. We show that the simple linear interpolation of the electron-phonon coupling matrix elements from a relatively coarse grid to an extremely fine grid can ease the calculational burden, which makes the calculation feasible in practice. For the Brillouin zone (BZ) integration of the transition probabilities involving one δ function, the Gaussian smearing method with a physical choice of locally adaptive broadening parameters is employed. We validate the calculation in the cases of n -type Si and Al. The calculated conductivity and mobility are in good agreement with experiments. In the metal case we also demonstrate that the Gaussian smearing method with locally adaptive broadening parameters works excellently for the BZ integration with double δ functions involved in the Eliashberg spectral function and its transport variant. The simpler implementation is the advantage of the Gaussian smearing method over the tetrahedron method. The accuracy of the relaxation time approximation and the approximation made by Allen [Phys. Rev. B 17, 3725 (1978), 10.1103/PhysRevB.17.3725] has been examined by comparing with the exact solution of BTE. We also apply our method to n -type monolayer MoS2, for which a mobility of 150 cm2 v-1 s-1 is obtained at room temperature. Moreover, the mean free paths are less than 9 nm, indicating that in the presence of grain boundaries the mobilities should not be effectively affected if the grain boundary size is tens of nanometers or larger. The ab initio approach demonstrated in this paper can be directly applied to other materials without the need for any a priori knowledge about the electron-phonon scattering processes, and can be straightforwardly extended to study cases with

  3. Transport in simple networks described by an integrable discrete nonlinear Schrödinger equation.

    PubMed

    Nakamura, K; Sobirov, Z A; Matrasulov, D U; Sawada, S

    2011-08-01

    We elucidate the case in which the Ablowitz-Ladik (AL)-type discrete nonlinear Schrödinger equation (NLSE) on simple networks (e.g., star graphs and tree graphs) becomes completely integrable just as in the case of a simple one-dimensional (1D) discrete chain. The strength of cubic nonlinearity is different from bond to bond, and networks are assumed to have at least two semi-infinite bonds with one of them working as an incoming bond. The present work is a nontrivial extension of our preceding one [Sobirov et al., Phys. Rev. E 81, 066602 (2010)] on the continuum NLSE to the discrete case. We find (1) the solution on each bond is a part of the universal (bond-independent) AL soliton solution on the 1D discrete chain, but it is multiplied by the inverse of the square root of bond-dependent nonlinearity; (2) nonlinearities at individual bonds around each vertex must satisfy a sum rule; and (3) under findings 1 and 2, there exist an infinite number of constants of motion. As a practical issue, with the use of an AL soliton injected through the incoming bond, we obtain transmission probabilities inversely proportional to the strength of nonlinearity on the outgoing bonds.

  4. Equation of state and transport properties of warm dense helium via quantum molecular dynamics simulations

    NASA Astrophysics Data System (ADS)

    Li, Zhi-Guo; Cheng, Yan; Chen, Qi-Feng; Chen, Xiang-Rong

    2016-05-01

    The equation of state, self-diffusion, and viscosity coefficients of helium have been investigated by quantum molecular dynamics (QMD) simulations in the warm dense matter regime. Our simulations are validated through the comparison with the reliable experimental data. The calculated principal and reshock Hugoniots of liquid helium are in good agreement with the gas-gun data. On this basis, we revisit the issue for helium, i.e., the possibility of the instabilities predicted by chemical models at around 2000 GPa and 10 g/cm3 along the pressure isotherms of 6309, 15 849, and 31 623 K. Our calculations show no indications of instability in this pressure-temperature region, which reconfirm the predictions of previous QMD simulations. The self-diffusion and viscosity coefficients of warm dense helium have been systematically investigated by the QMD simulations. We carefully test the finite-size effects and convergences of statistics, and obtain numerically converged self-diffusion and viscosity coefficients by using the Kubo-Green formulas. The present results have been used to evaluate the existing one component plasma models. Finally, the validation of the Stokes-Einstein relationship for helium in the warm dense regime is discussed.

  5. Fast Solutions of Maxwell's Equation for High Resolution Electromagnetic Imaging of Transport Pathways

    SciTech Connect

    DAY,DAVID M.; NEWMAN,GREGORY A.

    1999-10-01

    A fast precondition technique has been developed which accelerates the finite difference solutions of the 3D Maxwell's equations for geophysical modeling. The technique splits the electric field into its curl free and divergence free projections, and allows for the construction of an inverse operator. Test examples show an order of magnitude speed up compared with a simple Jacobi preconditioner. Using this preconditioner a low frequency Neumann series expansion is developed and used to compute responses at multiple frequencies very efficiently. Simulations requiring responses at multiple frequencies, show that the Neumann series is faster than the preconditioned solution, which must compute solutions at each discrete frequency. A Neumann series expansion has also been developed in the high frequency limit along with spectral Lanczos methods in both the high and low frequency cases for simulating multiple frequency responses with maximum efficiency. The research described in this report was to have been carried out over a two-year period. Because of communication difficulties, the project was funded for first year only. Thus the contents of this report are incomplete with respect to the original project objectives.

  6. Influence of nano-Cu additive on MgB2 phase formation, processing temperature, and transport properties

    NASA Astrophysics Data System (ADS)

    Varghese, Neson; Vinod, K.; Rahul, S.; Devadas, K. M.; Thomas, Syju; Pradhan, S.; Syamaprasad, U.

    2011-02-01

    Pure and nano-Cu doped MgB2/Fe superconducting wires were prepared by in situ powder-in-tube method at different temperatures (550-675 °C). The phase formation, microstructure, and transport critical current density of the wires were investigated as a function of the heat-treatment temperature. A small amount of nano-Cu addition (2.5 wt %) was found to dramatically decrease the reaction temperature of magnesium and boron, forming MgB2 without any degradation in the transport critical current. From x-ray diffraction and scanning electron microscopy analyses, it was found that the added Cu form a reacted phase Mg2Cu with Mg which melts at around 550 °C. This liquid phase helps the formation of MgB2 at a significant lower temperature with improved grain connectivity, grain size, and density. All Cu doped samples heat treated in the range of 550-650 °C exhibited a transport JC quite comparable to that of the pure sample processed at 650 °C, which shows that high quality MgB2 conductors can be produced even at 550 °C with minor Cu doping.

  7. Time-dependent quantum transport through an interacting quantum dot beyond sequential tunneling: second-order quantum rate equations.

    PubMed

    Dong, B; Ding, G H; Lei, X L

    2015-05-27

    A general theoretical formulation for the effect of a strong on-site Coulomb interaction on the time-dependent electron transport through a quantum dot under the influence of arbitrary time-varying bias voltages and/or external fields is presented, based on slave bosons and the Keldysh nonequilibrium Green's function (GF) techniques. To avoid the difficulties of computing double-time GFs, we generalize the propagation scheme recently developed by Croy and Saalmann to combine the auxiliary-mode expansion with the celebrated Lacroix's decoupling approximation in dealing with the second-order correlated GFs and then establish a closed set of coupled equations of motion, called second-order quantum rate equations (SOQREs), for an exact description of transient dynamics of electron correlated tunneling. We verify that the stationary solution of our SOQREs is able to correctly describe the Kondo effect on a qualitative level. Moreover, a comparison with other methods, such as the second-order von Neumann approach and Hubbard-I approximation, is performed. As illustrations, we investigate the transient current behaviors in response to a step voltage pulse and a harmonic driving voltage, and linear admittance as well, in the cotunneling regime.

  8. Derivation of Transport Equations for a Strongly Interacting Lagrangian in Powers of ħand 1/ Nc

    NASA Astrophysics Data System (ADS)

    Klevansky, S. P.; Ogura, A.; Hüfner, J.

    1997-11-01

    Transport theory for an interacting fermionic system is reviewed and applied to the chiral Lagrangian of the Nambu-Jona-Lasinio model. Two expansions must be applied: an expansion in the inverse number of colors, 1/Nc, due to the nature of the strong coupling theory, and a semiclassical expansion, in powers of ħ. The quasiparticle approximation is implemented at an early stage, and spin effects are omitted. The self-energy is evaluated, self-consistently only in the Hartree approximation, and semi-perturbatively in the collision integral. In the Hartree approximation,O((1/Nc)0), the Vlasov equation is recovered toO(ħ1), together with an on-mass shell constraint equation, that is automatically fulfilled by the quasiparticle ansatz. The expressions for the self-energy to orderO((1/Nc)) lead to the collision term. Here one sees explicitly that particle-antiparticle creation and annihilation processes are suppressed that would otherwise be present, should an off-shell energy spectral function be admitted. A clear identification of thes,tanduchannel scattering processes in connection with the self-energy graphs is made and the origin of the mixed terms is made evident. Finally, after ordering according to powers in ħ, a Boltzmann-like form for the collision integral is obtained.

  9. Effect of catalyst additives on the production of biofuels from palm oil cracking in a transport riser reactor.

    PubMed

    Chew, Thiam Leng; Bhatia, Subhash

    2009-05-01

    Catalytic cracking of crude palm oil (CPO) and used palm oil (UPO) were studied in a transport riser reactor for the production of biofuels at a reaction temperature of 450 degrees C, with residence time of 20s and catalyst-to-oil ratio (CTO) of 5 gg(-1). The effect of HZSM-5 (different Si/Al ratios), beta zeolite, SBA-15 and AlSBA-15 were studied as physically mixed additives with cracking catalyst Rare earth-Y (REY). REY catalyst alone gave 75.8 wt% conversion with 34.5 wt% of gasoline fraction yield using CPO, whereas with UPO, the conversion was 70.9 wt% with gasoline fraction yield of 33.0 wt%. HZSM-5, beta zeolite, SBA-15 and AlSBA-15 as additives with REY increased the conversion and the yield of organic liquid product. The transport riser reactor can be used for the continuous production of biofuels from cracking of CPO and UPO over REY catalyst.

  10. Multigroup discrete ordinates solution of Boltzmann-Fokker-Planck equations and cross section library development of ion transport

    SciTech Connect

    Prinja, A.K.

    1995-08-01

    We have developed and successfully implemented a two-dimensional bilinear discontinuous in space and time, used in conjunction with the S{sub N} angular approximation, to numerically solve the time dependent, one-dimensional, one-speed, slab geometry, (ion) transport equation. Numerical results and comparison with analytical solutions have shown that the bilinear-discontinuous (BLD) scheme is third-order accurate in the space ad time dimensions independently. Comparison of the BLD results with diamond-difference methods indicate that the BLD method is both quantitavely and qualitatively superior to the DD scheme. We note that the form of the transport operator is such that these conclusions carry over to energy dependent problems that include the constant-slowing-down-approximation term, and to multiple space dimensions or combinations thereof. An optimized marching or inversion scheme or a parallel algorithm should be investigated to determine if the increased accuracy can compensate for the extra overhead required for a BLD solution, and then could be compared to other discretization methods such as nodal or characteristic schemes.

  11. Finite difference numerical method for the superlattice Boltzmann transport equation and case comparison of CPU(C) and GPU(CUDA) implementations

    SciTech Connect

    Priimak, Dmitri

    2014-12-01

    We present a finite difference numerical algorithm for solving two dimensional spatially homogeneous Boltzmann transport equation which describes electron transport in a semiconductor superlattice subject to crossed time dependent electric and constant magnetic fields. The algorithm is implemented both in C language targeted to CPU and in CUDA C language targeted to commodity NVidia GPU. We compare performances and merits of one implementation versus another and discuss various software optimisation techniques.

  12. New concepts for Reynolds stress transport equation modeling of inhomogeneous flows

    NASA Technical Reports Server (NTRS)

    Perot, J. Blair; Moin, Parviz

    1993-01-01

    The ability to model turbulence near solid walls and other types of boundaries is important in predicting complex engineering flows. Most turbulence modeling has concentrated either on flows which are nearly homogeneous or isotropic, or on turbulent boundary layers. Boundary layer models usually rely very heavily on the presence of mean shear and the production of turbulence due to that mean shear. Most other turbulence models are based on the assumption of quasi-homogeneity. However, there are many situations of engineering interest which do not involve large shear rates and which are not quasi-homogeneous or isotropic. Shear-free turbulent boundary layers are the prototypical example of such flows, with practical situations being separation and reattachment, bluff body flow, high free-stream turbulence, and free surface flows. Although these situations are not as common as the variants of the flat plate turbulent boundary layer, they tend to be critical factors in complex engineering situations. The models developed are intended to extend classical quasi-homogeneous models into regions of large inhomogeneity. These models do not rely on the presence of mean shear or production, but are still applicable when those additional effects are included. Although the focus is on shear-free boundary layers as tests for these models, results for standard shearing boundary layers are also shown.

  13. Global ocean circulation and equator-pole heat transport as a function of ocean GCM resolution

    SciTech Connect

    Covey, C.

    1994-06-01

    To determine whether resolution of smaller scales is necessary to simulate large-scale ocean climate correctly, I examine results from a global ocean GCM run with horizontal grid spacings spanning a range from coarse resolutions traditionally used in climate modeling to nearly the highest resolution attained with today`s computers. The experiments include four cases employing 4{degrees}, 2{degrees}, 1{degrees} and 1/2{degrees} spacing in latitude and longitude, which were run with minimal differences among them, i.e., in a controlled experiment. Two additional cases-1/2{degrees} spacing with a more scale-selective sub-gridscale mixing of heat and momentum, and approximate 1/4{degrees} spacing-are also included. The 1/4{degrees} run resolves most of the observed mesoscale eddy energy in the ocean. Several artificial constraints on the model tend to minimize differences among the different resolution cases. Nevertheless, for quantities of interest to global climate studies,the simulations show significant changes as resolution increases.

  14. A cell-local finite difference discretization of the low-order quasidiffusion equations for neutral particle transport on unstructured quadrilateral meshes

    SciTech Connect

    Wieselquist, William A.; Anistratov, Dmitriy Y.; Morel, Jim E.

    2014-09-15

    We present a quasidiffusion (QD) method for solving neutral particle transport problems in Cartesian XY geometry on unstructured quadrilateral meshes, including local refinement capability. Neutral particle transport problems are central to many applications including nuclear reactor design, radiation safety, astrophysics, medical imaging, radiotherapy, nuclear fuel transport/storage, shielding design, and oil well-logging. The primary development is a new discretization of the low-order QD (LOQD) equations based on cell-local finite differences. The accuracy of the LOQD equations depends on proper calculation of special non-linear QD (Eddington) factors from a transport solution. In order to completely define the new QD method, a proper discretization of the transport problem is also presented. The transport equation is discretized by a conservative method of short characteristics with a novel linear approximation of the scattering source term and monotonic, parabolic representation of the angular flux on incoming faces. Analytic and numerical tests are used to test the accuracy and spatial convergence of the non-linear method. All tests exhibit O(h{sup 2}) convergence of the scalar flux on orthogonal, random, and multi-level meshes.

  15. Models for microtubule cargo transport coupling the Langevin equation to stochastic stepping motor dynamics: Caring about fluctuations

    NASA Astrophysics Data System (ADS)

    Bouzat, Sebastián

    2016-01-01

    One-dimensional models coupling a Langevin equation for the cargo position to stochastic stepping dynamics for the motors constitute a relevant framework for analyzing multiple-motor microtubule transport. In this work we explore the consistence of these models focusing on the effects of the thermal noise. We study how to define consistent stepping and detachment rates for the motors as functions of the local forces acting on them in such a way that the cargo velocity and run-time match previously specified functions of the external load, which are set on the base of experimental results. We show that due to the influence of the thermal fluctuations this is not a trivial problem, even for the single-motor case. As a solution, we propose a motor stepping dynamics which considers memory on the motor force. This model leads to better results for single-motor transport than the approaches previously considered in the literature. Moreover, it gives a much better prediction for the stall force of the two-motor case, highly compatible with the experimental findings. We also analyze the fast fluctuations of the cargo position and the influence of the viscosity, comparing the proposed model to the standard one, and we show how the differences on the single-motor dynamics propagate to the multiple motor situations. Finally, we find that the one-dimensional character of the models impede an appropriate description of the fast fluctuations of the cargo position at small loads. We show how this problem can be solved by considering two-dimensional models.

  16. Cross equator transport of 137Cs from North Pacific Ocean to South Pacific Ocean ( BEAGLE2003 cruises)

    NASA Astrophysics Data System (ADS)

    Aoyama, M.; Fukasawa, M.; Hirose, K.; Hamajima, Y.; Kawano, T.; Povinec, P. P.; Sanchez-Cabeza, J. A.

    2011-04-01

    The anthropogenic radionuclides such as 137Cs, 90Sr, 99Tc, 129I and some transuranics are important tracers of transport and biogeochemical processes in the ocean. 137Cs, with a half-life of 30 years, a major fission product present in a dissolved form in seawater, is a good tracer of oceanic circulation at a time scale of several decades. At WOCE P6 line along 30°S during the BEAGLE cruise in 2003, surface seawater (around 80 L) was collected a few meters below the ocean surface by a pumping system. Water column samples (from 5 to 20 L) were collected using a Rosette multisampling system and Niskin bottles. 137Cs was separated from seawater samples using ammonium phosphomolybdate (AMP) and analysed for 137Cs in low-level HPGe gamma-ray spectrometers. Results allowed to draw a detailed picture of the distribution of 137Cs in the South Pacific Ocean along P6 line. A 137Cs depth section was depicted from about 160 samples. 137Cs concentrations in the subsurface layers ranged from 0.07 ± 0.04 Bq m -3 to 1.85 ± 0.145 Bq m -3, high in the Tasman Sea and very low in the eastern region where upwelling occurs. Water column inventories of 137Cs from surface to 1000 dbar depth ranged from 270 ± 104 to 1048 ± 127 Bq m -2. It was concluded that the source of higher 137Cs concentration and inventories in the Tasman Sea was 137Cs deposited in the mid latitude of the North Pacific Ocean and transported across the equator during four decades.

  17. 41 CFR 302-10.6 - Are the allowances for transporting a mobile home in addition to the allowances for per diem...

    Code of Federal Regulations, 2012 CFR

    2012-07-01

    ... 41 Public Contracts and Property Management 4 2012-07-01 2012-07-01 false Are the allowances for transporting a mobile home in addition to the allowances for per diem, mileage, and transportation expenses, for me and my immediate family member(s)? 302-10.6 Section 302-10.6 Public Contracts and...

  18. 41 CFR 302-10.401 - Are the allowances for transporting a mobile home in addition to the allowances for per diem...

    Code of Federal Regulations, 2012 CFR

    2012-07-01

    ... 41 Public Contracts and Property Management 4 2012-07-01 2012-07-01 false Are the allowances for transporting a mobile home in addition to the allowances for per diem, mileage, and transportation expenses, for an employee and immediate family member(s)? 302-10.401 Section 302-10.401 Public Contracts...

  19. Thermal Investigation of Common 2d FETs and New Generation of 3d FETs Using Boltzmann Transport Equation in Nanoscale

    NASA Astrophysics Data System (ADS)

    Samian, R. S.; Abbassi, A.; Ghazanfarian, J.

    2013-09-01

    The thermal performance of two-dimensional (2D) field-effect transistors (FET) is investigated frequently by solving the Fourier heat diffusion law and the Boltzmann transport equation (BTE). With the introduction of the new generation of 3D FETs in which their thickness is less than the phonon mean-free-path it is necessary to carefully simulate the thermal performance of such devices. This paper numerically integrates the BTE in common 2D transistors including planar single layer and Silicon-On-Insulator (SOI) transistor, and the new generation of 3D transistors including FinFET and Tri-Gate devices. In order to decrease the directional dependency of results in 3D simulations; the Legendre equal-weight (PN-EW) quadrature set has been employed. It is found that if similar switching time is assumed for 3D and 2D FETs while the new generation of 3D FETs has less net energy consumption, they have higher hot-spot temperature. The results show continuous heat flux distribution normal to the silicon/oxide interface while the temperature jump is seen at the interface in double layer transistors.

  20. PHASE RETRIEVAL FROM TWO DEFOCUSED IMAGES BY THE TRANSPORT OF INTENSITY EQUATION FORMALISM WITH FAST FOURIER TRANSFORM.

    SciTech Connect

    VOLKOV,V.V.; ZHU,Y.

    2001-08-05

    The problem of phase retrieval from intensity measurements plays an important role in many fields of physical research, e.g. optics, electron and x-ray microscopy, crystallography, diffraction tomography and others. In practice the recorded images contain information only on the intensity distribution I(x,y) = {Psi}*{Psi} = {vert_bar}A{vert_bar}{sup 2} of the imaging wave function {Psi} = A*exp(-i{var_phi}) and the phase information {var_phi}(x,y) is usually lost. In general, the phase problem can be solved either by special holographic/interferometric methods, or by non-interferometric approaches based on intensity measurements in far Fraunhofer zone or in the Fresnel zone at two adjacent planes orthogonal to the optical axis. The latter approach uses the transport-of-intensity equation (TIE) formalism, introduced originally by Teague [1] and developed later in [2]. Applications of TIE to nonmagnetic materials and magnetic inductance mapping were successfully made in [3,4]. However, this approach still needs further improvement both in mathematics and in practical solutions, since the result is very sensitive to many experimental parameters.

  1. Review on measurement techniques of transport properties of nanowires Additions and Corrections. See DOI:10.1039/C3NR03242F Click here for additional data file.

    PubMed Central

    Rojo, Miguel Muñoz; Calero, Olga Caballero; Lopeandia, A. F.; Rodriguez-Viejo, J.

    2013-01-01

    Physical properties at the nanoscale are novel and different from those in bulk materials. Over the last few decades, there has been an ever growing interest in the fabrication of nanowire structures for a wide variety of applications including energy generation purposes. Nevertheless, the study of their transport properties, such as thermal conductivity, electrical conductivity or Seebeck coefficient, remains an experimental challenge. For instance, in the particular case of nanostructured thermoelectrics, theoretical calculations have shown that nanowires offer a promising way of enhancing the hitherto low efficiency of these materials in the conversion of temperature differences into electricity. Therefore, within the thermoelectrical community there has been a great experimental effort in the measurement of these quantities in actual nanowires. The measurements of these properties at the nanoscale are also of interest in fields other than energy, such as electrical components for microchips, field effect transistors, sensors, and other low scale devices. For all these applications, knowing the transport properties is mandatory. This review deals with the latest techniques developed to perform the measurement of these transport properties in nanowires. A thorough overview of the most important and modern techniques used for the characterization of different kinds of nanowires will be shown. PMID:24113712

  2. Semi-analytical solution to the frequency-dependent Boltzmann transport equation for cross-plane heat conduction in thin films

    SciTech Connect

    Hua, Chengyun; Minnich, Austin J.

    2015-05-07

    Cross-plane heat transport in thin films with thicknesses comparable to the phonon mean free paths is of both fundamental and practical interest for applications such as light-emitting diodes and quantum well lasers. However, physical insight is difficult to obtain for the cross-plane geometry due to the challenge of solving the Boltzmann equation in a finite domain. Here, we present a semi-analytical series expansion method to solve the transient, frequency-dependent Boltzmann transport equation that is valid from the diffusive to ballistic transport regimes and rigorously includes the frequency-dependence of phonon properties. Further, our method is more than three orders of magnitude faster than prior numerical methods and provides a simple analytical expression for the thermal conductivity as a function of film thickness. Our result enables a straightforward physical understanding of cross-plane heat conduction in thin films.

  3. The Coupled Photothermal Reaction and Transport in a Laser Additive Metal Nanolayer Simultaneous Synthesis and Pattering for Flexible Electronics.

    PubMed

    Tsai, Song-Ling; Liu, Yi-Kai; Pan, Heng; Liu, Chien-Hung; Lee, Ming-Tsang

    2016-01-08

    The Laser Direct Synthesis and Patterning (LDSP) technology has advantages in terms of processing time and cost compared to nanomaterials-based laser additive microfabrication processes. In LDSP, a scanning laser on the substrate surface induces chemical reactions in the reactive liquid solution and selectively deposits target material in a preselected pattern on the substrate. In this study, we experimentally investigated the effect of the processing parameters and type and concentration of the additive solvent on the properties and growth rate of the resulting metal film fabricated by this LDSP technology. It was shown that reactive metal ion solutions with substantial viscosity yield metal films with superior physical properties. A numerical analysis was also carried out the first time to investigate the coupled opto-thermo-fluidic transport phenomena and the effects on the metal film growth rate. To complete the simulation, the optical properties of the LDSP deposited metal film with a variety of thicknesses were measured. The characteristics of the temperature field and the thermally induced flow associated with the moving heat source are discussed. It was shown that the processing temperature range of the LDSP is from 330 to 390 K. A semi-empirical model for estimating the metal film growth rate using this process was developed based on these results. From the experimental and numerical results, it is seen that, owing to the increased reflectivity of the silver film as its thickness increases, the growth rate decreases gradually from about 40 nm at initial to 10 nm per laser scan after ten scans. This self-controlling effect of LDSP process controls the thickness and improves the uniformity of the fabricated metal film. The growth rate and resulting thickness of the metal film can also be regulated by adjustment of the processing parameters, and thus can be utilized for controllable additive nano/microfabrication.

  4. The Coupled Photothermal Reaction and Transport in a Laser Additive Metal Nanolayer Simultaneous Synthesis and Pattering for Flexible Electronics

    PubMed Central

    Tsai, Song-Ling; Liu, Yi-Kai; Pan, Heng; Liu, Chien-Hung; Lee, Ming-Tsang

    2016-01-01

    The Laser Direct Synthesis and Patterning (LDSP) technology has advantages in terms of processing time and cost compared to nanomaterials-based laser additive microfabrication processes. In LDSP, a scanning laser on the substrate surface induces chemical reactions in the reactive liquid solution and selectively deposits target material in a preselected pattern on the substrate. In this study, we experimentally investigated the effect of the processing parameters and type and concentration of the additive solvent on the properties and growth rate of the resulting metal film fabricated by this LDSP technology. It was shown that reactive metal ion solutions with substantial viscosity yield metal films with superior physical properties. A numerical analysis was also carried out the first time to investigate the coupled opto-thermo-fluidic transport phenomena and the effects on the metal film growth rate. To complete the simulation, the optical properties of the LDSP deposited metal film with a variety of thicknesses were measured. The characteristics of the temperature field and the thermally induced flow associated with the moving heat source are discussed. It was shown that the processing temperature range of the LDSP is from 330 to 390 K. A semi-empirical model for estimating the metal film growth rate using this process was developed based on these results. From the experimental and numerical results, it is seen that, owing to the increased reflectivity of the silver film as its thickness increases, the growth rate decreases gradually from about 40 nm at initial to 10 nm per laser scan after ten scans. This self-controlling effect of LDSP process controls the thickness and improves the uniformity of the fabricated metal film. The growth rate and resulting thickness of the metal film can also be regulated by adjustment of the processing parameters, and thus can be utilized for controllable additive nano/microfabrication.

  5. Time-dependent integral equations of neutron transport for calculating the kinetics of nuclear reactors by the Monte Carlo method

    NASA Astrophysics Data System (ADS)

    Davidenko, V. D.; Zinchenko, A. S.; Harchenko, I. K.

    2016-12-01

    Integral equations for the shape functions in the adiabatic, quasi-static, and improved quasi-static approximations are presented. The approach to solving these equations by the Monte Carlo method is described.

  6. Xylem-Transported Glucose as an Additional Carbon Source for Leaf Isoprene Formation in Quercus Robur L.

    NASA Astrophysics Data System (ADS)

    Graus, M.; Kreuzwieser, J.; Schnitzler, J.; Wisthaler, A.; Hansel, A.; Rennenberg, H.

    2003-04-01

    Isoprene is emitted from mature, photosynthesizing leaves of many plant species, particularly of trees. Current interest in understanding the biochemical and physiological mechanisms controlling isoprene formation is caused by the important role isoprene plays in atmospheric chemistry. Isoprene reacts with hydroxyl radicals (OH) thereby generating oxidizing agents such as ozone and organic peroxides. Ozone causes significant deterioration in air quality and can pose threats to human health therefore its control is a major goal in Europe and the United States. In recent years, much progress has been made in elucidating the pathways of isoprene biosynthesis. Nevertheless the regulatory mechanisms controlling isoprene emission are not completely understood. Light and temperature appear to be the main factors controlling short-term variations in isoprene emission. Exposure of plants to C-13 labeled carbon dioxide showed instantaneous assimilated carbon is the primary carbon source for isoprene formation. However, variations in diurnal and seasonal isoprene fluxes, which cannot be explained by temperature, light, and leaf development led to the suggestion that alternative carbon sources may exist contributing to isoprene emissions. The aim of the present study was to test whether xylem-transported carbohydrates act as additional sources for isoprene biosynthesis. For this purpose, [U-C-13] alpha-D-glucose was fed to photosynthesizing leaves via the xylem of Quercus robur L. seedlings and the incorporation of glucose derived C-13 into emitted isoprene was monitored in real time using Proton-Transfer-Reaction Mass Spectrometry (PTR-MS). A rapid incorporation of C-13 from xylem-fed glucose into single (mass 70) and double (mass 71) C-13 labeled isoprene molecules was observed after a lag phase of approximately 5 to 10 minutes. This incorporation was temperature dependent and was highest (up to 13% C-13 of total carbon emitted as isoprene) at the temperature optimum of

  7. Xylem-transported Glucose as an Additional Carbon Source for Leaf Isoprene Formation in Quercus Robur L.

    NASA Astrophysics Data System (ADS)

    Graus, M.; Wisthaler, A.; Hansel, A.; Kreuzwieser, J.; Rennenberg, H.; Schnitzler, J.

    2002-12-01

    Isoprene is emitted from mature, photosynthesizing leaves of many plant species, particularly of trees. Current interest in understanding the biochemical and physiological mechanisms controlling isoprene formation is caused by the important role isoprene plays in atmospheric chemistry. Isoprene reacts with hydroxyl radicals (OH) thereby generating oxidizing agents such as ozone and organic peroxides. Ozone causes significant deterioration in air quality and can pose threats to human health therefore its control is a major goal in Europe and the United States. In recent years, much progress has been made in elucidating the pathways of isoprene biosynthesis. Nevertheless the regulatory mechanisms controlling isoprene emission are not completely understood. Light and temperature appear to be the main factors controlling short-term variations in isoprene emission. Exposure of plants to 13CO2 showed instantaneous assimilated carbon is the primary carbon source for isoprene formation. However, variations in diurnal and seasonal isoprene fluxes, which cannot be explained by temperature, light, and leaf development led to the suggestion that alternative carbon sources may exist contributing to isoprene emissions. The aim of the present study was to test whether xylem-transported carbohydrates act as additional sources for isoprene biosynthesis. For this purpose, [U-13C]α-D-glucose was fed to photosynthesizing leaves via the xylem of {Quercus} {robur} L. seedlings and the incorporation of glucose derived 13C into emitted isoprene was monitored in real time using Proton-Transfer-Reaction Mass Spectrometry (PTR-MS). A rapid incorporation of 13C from xylem-fed glucose into single (mass 70) and double (mass 71) 13C-labeled isoprene molecules was observed after a lag phase of approximately 5 to 10 minutes. This incorporation was temperature dependent and was highest (up to 13 % 13C of total carbon emitted as isoprene) at the temperature optimum of isoprene emission (40 - 42

  8. The potential of oceanic transport and onshore leaching of additive-derived lead by marine macro-plastic debris.

    PubMed

    Nakashima, Etsuko; Isobe, Atsuhiko; Kako, Shin'ichiro; Itai, Takaaki; Takahashi, Shin; Guo, Xinyu

    2016-06-15

    The long-distance transport potential of toxic lead (Pb) by plastic marine debris was examined by pure water leaching experiments using plastic fishery floats containing high level of additive-Pb such as 5100±74.3mgkg(-1). The leaching of Pb ended after sequential 480-h leaching experiments, and the total leaching amount is equivalent to approximately 0.1% of total Pb in a float. But it recovered when the float was scratched using sandpaper. We propose that a "low-Pb layer," in which Pb concentration is negligibly small, be generated on the float surface by the initial leaching process. Thickness of the layer is estimated at 2.5±1.2μm, much shallower than flaws on floats scratched by sandpaper and floats littering beaches. The result suggests that the low-Pb layer is broken by physical abrasion when floats are washed ashore, and that Pb inside the floats can thereafter leach into beaches.

  9. Numerical Solution of 3D Poisson-Nernst-Planck Equations Coupled with Classical Density Functional Theory for Modeling Ion and Electron Transport in a Confined Environment

    SciTech Connect

    Meng, Da; Zheng, Bin; Lin, Guang; Sushko, Maria L.

    2014-08-29

    We have developed efficient numerical algorithms for the solution of 3D steady-state Poisson-Nernst-Planck equations (PNP) with excess chemical potentials described by the classical density functional theory (cDFT). The coupled PNP equations are discretized by finite difference scheme and solved iteratively by Gummel method with relaxation. The Nernst-Planck equations are transformed into Laplace equations through the Slotboom transformation. Algebraic multigrid method is then applied to efficiently solve the Poisson equation and the transformed Nernst-Planck equations. A novel strategy for calculating excess chemical potentials through fast Fourier transforms is proposed which reduces computational complexity from O(N2) to O(NlogN) where N is the number of grid points. Integrals involving Dirac delta function are evaluated directly by coordinate transformation which yields more accurate result compared to applying numerical quadrature to an approximated delta function. Numerical results for ion and electron transport in solid electrolyte for Li ion batteries are shown to be in good agreement with the experimental data and the results from previous studies.

  10. Additively manufactured metallic porous biomaterials based on minimal surfaces: A unique combination of topological, mechanical, and mass transport properties.

    PubMed

    Bobbert, F S L; Lietaert, K; Eftekhari, A A; Pouran, B; Ahmadi, S M; Weinans, H; Zadpoor, A A

    2017-02-16

    Porous biomaterials that simultaneously mimic the topological, mechanical, and mass transport properties of bone are in great demand but are rarely found in the literature. In this study, we rationally designed and additively manufactured (AM) porous metallic biomaterials based on four different types of triply periodic minimal surfaces (TPMS) that mimic the properties of bone to an unprecedented level of multi-physics detail. Sixteen different types of porous biomaterials were rationally designed and fabricated using selective laser melting (SLM) from a titanium alloy (Ti-6Al-4V). The topology, quasi-static mechanical properties, fatigue resistance, and permeability of the developed biomaterials were then characterized. In terms of topology, the biomaterials resembled the morphological properties of trabecular bone including mean surface curvatures close to zero. The biomaterials showed a favorable but rare combination of relatively low elastic properties in the range of those observed for trabecular bone and high yield strengths exceeding those reported for cortical bone. This combination allows for simultaneously avoiding stress shielding, while providing ample mechanical support for bone tissue regeneration and osseointegration. Furthermore, as opposed to other AM porous biomaterials developed to date for which the fatigue endurance limit has been found to be ≈20% of their yield (or plateau) stress, some of the biomaterials developed in the current study show extremely high fatigue resistance with endurance limits up to 60% of their yield stress. It was also found that the permeability values measured for the developed biomaterials were in the range of values reported for trabecular bone. In summary, the developed porous metallic biomaterials based on TPMS mimic the topological, mechanical, and physical properties of trabecular bone to a great degree. These properties make them potential candidates to be applied as parts of orthopedic implants and/or as bone

  11. Analytical insights into the partially integrated transport modeling method for hybrid Reynolds averaged Navier-Stokes equations-large eddy simulations of turbulent flows

    NASA Astrophysics Data System (ADS)

    Chaouat, Bruno; Schiestel, Roland

    2012-08-01

    The basis of the partially integrated transport modeling (PITM) method was introduced by Schiestel and Dejoan ["Towards a new partially integrated transport model for coarse grid and unsteady turbulent flow simulations," Theor. Comput. Fluid Dyn. 18, 443 (2005)], 10.1007/s00162-004-0155-z and Chaouat and Schiestel ["A new partially integrated transport model for subgrid-scale stresses and dissipation rate for turbulent developing flows," Phys. Fluids 17, 065106 (2005)], 10.1063/1.1928607. This method provides a continuous approach for hybrid RANS-LES (Reynolds averaged Navier-Stokes equations-large eddy simulations) simulations with seamless coupling between RANS and LES regions. The main ingredient of the method is the new dissipation-rate equation that can be applied as a subfilter scale turbulence model. Then, it becomes easy to convert almost any usual RANS transport model into a subfilter scale model. In particular, the method can be applied to two equation models and to stress transport models as well. In the derivation of the method, the partial integration technique allows to keep a link between the spectral space and the physical space of the resulting model. The physical turbulent processes involving the production, dissipation, and flux transfer of the turbulent energy are introduced in the equations. The present work, after recalling the main building steps of the PITM method, brings further insight into the physical interpretation of the method, its underlying hypotheses and its internal acting mechanisms. In particular, the finiteness of the coefficients used in the dissipation-rate equation is discussed in detail from a theoretical point of view. Then, we consider the analytical example of self-similar turbulent flow for analyzing the dissipation-rate equation. From an analytical solution obtained by Taylor series expansions taking into account the Kovasznay hypothesis for evaluating the transfer term, we compute the functional coefficients c

  12. TRANSPORT

    EPA Science Inventory

    Presentation outline: transport principles, effective solubility; gasoline composition; and field examples (plume diving).
    Presentation conclusions: MTBE transport follows from - phyiscal and chemical properties and hydrology. Field examples show: MTBE plumes > benzene plu...

  13. Application of the Stefan-Maxwell Equations to determine limitations of Fick's law when modeling organic vapor transport in sand columns

    USGS Publications Warehouse

    Baehr, Arthur L.; Bruell, Clifford J.

    1990-01-01

    The organic component of the vapor phase of a porous medium contaminated by an immiscible organic liquid can be significant enough to violate the condition of a dilute species diffusing in a bulk phase assumed by Fick's law. The Stefan-Maxwell equations provide a more comprehensive model for quantifying steady state transport for a vapor phase composed of arbitrary proportions of its constituents. The application of both types of models to the analysis of column experiments demonstrates that use of a Fickian-based transport model can lead to significant overestimates of soil tortuosity constants. Further, the physical displacement of naturally occurring gases (e.g., O2), predicted by the Stefan-Maxwell model but not by application of Fick's Law, can be attributed improperly to a sink term such as microbial degradation in a Fickian-based transport model.

  14. Stability analysis of phonon transport equations derived via the Chapman-Enskog method and transformation of variables.

    PubMed

    Banach, Zbigniew; Larecki, Wieslaw; Zajaczkowski, Wojciech

    2009-10-01

    Under the assumption of Callaway's model of the Boltzmann-Peierls equation, the Chapman-Enskog method for a phonon gas forms the basis to derive various hydrodynamic equations for the energy density and the drift velocity of interest when normal processes dominate over resistive ones. The first three levels of the expansion (i.e., the zeroth-, first-, and second-order approximations) are satisfactory in that they are entropy consistent and ensure linear stability of the rest state. However, the entropy density contains a weakly nonlocal term, the entropy production is a degenerate function of variables, and the next order in the Chapman-Enskog expansion gives the equations with linearly unstable rest solutions. In the context of Burnett and super-Burnett equations, a similar type of problem was recognized by several authors who proposed different ways to deal with it. Here we report on yet another possible device for obtaining more satisfactory equations. Namely, inspired by the fact that there exists no unique way to truncate the Chapman-Enskog expansion, we combine the Chapman-Enskog procedure with the method of variable transformation and subsequently find a class of epsilon -dependent transformations through which it is possible to derive the second-order equations possessing a local entropy density and nondegenerate expression for the entropy production. Regardless of this result, we also show that although the method cannot be used to construct linearly stable third-order equations, it can be used to make the originally stable first-order equations asymptotically stable.

  15. A fractal Richards’ equation to capture the non-Boltzmann scaling of water transport in unsaturated media

    PubMed Central

    Sun, HongGuang; Meerschaert, Mark M.; Zhang, Yong; Zhu, Jianting; Chen, Wen

    2013-01-01

    The traditional Richards’ equation implies that the wetting front in unsaturated soil follows Boltzmann scaling, with travel distance growing as the square root of time. This study proposes a fractal Richards’ equation (FRE), replacing the integer-order time derivative of water content by a fractal derivative, using a power law ruler in time. FRE solutions exhibit anomalous non-Boltzmann scaling, attributed to the fractal nature of heterogeneous media. Several applications are presented, fitting the FRE to water content curves from previous literature. PMID:23794783

  16. Penetration equations

    SciTech Connect

    Young, C.W.

    1997-10-01

    In 1967, Sandia National Laboratories published empirical equations to predict penetration into natural earth materials and concrete. Since that time there have been several small changes to the basic equations, and several more additions to the overall technique for predicting penetration into soil, rock, concrete, ice, and frozen soil. The most recent update to the equations was published in 1988, and since that time there have been changes in the equations to better match the expanding data base, especially in concrete penetration. This is a standalone report documenting the latest version of the Young/Sandia penetration equations and related analytical techniques to predict penetration into natural earth materials and concrete. 11 refs., 6 tabs.

  17. Stochastic uncertainty analysis for solute transport in randomly heterogeneous media using a Karhunen-Loève-based moment equation approach

    USGS Publications Warehouse

    Liu, Gaisheng; Lu, Zhiming; Zhang, Dongxiao

    2007-01-01

    A new approach has been developed for solving solute transport problems in randomly heterogeneous media using the Karhunen-Loève-based moment equation (KLME) technique proposed by Zhang and Lu (2004). The KLME approach combines the Karhunen-Loève decomposition of the underlying random conductivity field and the perturbative and polynomial expansions of dependent variables including the hydraulic head, flow velocity, dispersion coefficient, and solute concentration. The equations obtained in this approach are sequential, and their structure is formulated in the same form as the original governing equations such that any existing simulator, such as Modular Three-Dimensional Multispecies Transport Model for Simulation of Advection, Dispersion, and Chemical Reactions of Contaminants in Groundwater Systems (MT3DMS), can be directly applied as the solver. Through a series of two-dimensional examples, the validity of the KLME approach is evaluated against the classical Monte Carlo simulations. Results indicate that under the flow and transport conditions examined in this work, the KLME approach provides an accurate representation of the mean concentration. For the concentration variance, the accuracy of the KLME approach is good when the conductivity variance is 0.5. As the conductivity variance increases up to 1.0, the mismatch on the concentration variance becomes large, although the mean concentration can still be accurately reproduced by the KLME approach. Our results also indicate that when the conductivity variance is relatively large, neglecting the effects of the cross terms between velocity fluctuations and local dispersivities, as done in some previous studies, can produce noticeable errors, and a rigorous treatment of the dispersion terms becomes more appropriate.

  18. Nonlinear heat-transport equation beyond Fourier law: application to heat-wave propagation in isotropic thin layers

    NASA Astrophysics Data System (ADS)

    Sellitto, A.; Tibullo, V.; Dong, Y.

    2017-03-01

    By means of a nonlinear generalization of the Maxwell-Cattaneo-Vernotte equation, on theoretical grounds we investigate how nonlinear effects may influence the propagation of heat waves in isotropic thin layers which are not laterally isolated from the external environment. A comparison with the approach of the Thermomass Theory is made as well.

  19. Improved fully-implicit spherical harmonics methods for first and second order forms of the transport equation using Galerkin Finite Element

    NASA Astrophysics Data System (ADS)

    Laboure, Vincent Matthieu

    In this dissertation, we focus on solving the linear Boltzmann equation -- or transport equation -- using spherical harmonics (PN) expansions with fully-implicit time-integration schemes and Galerkin Finite Element spatial discretizations within the Multiphysics Object Oriented Simulation Environment (MOOSE) framework. The presentation is composed of two main ensembles. On one hand, we study the first-order form of the transport equation in the context of Thermal Radiation Transport (TRT). This nonlinear application physically necessitates to maintain a positive material temperature while the PN approximation tends to create oscillations and negativity in the solution. To mitigate these flaws, we provide a fully-implicit implementation of the Filtered PN (FPN) method and investigate local filtering strategies. After analyzing its effect on the conditioning of the system and showing that it improves the convergence properties of the iterative solver, we numerically investigate the error estimates derived in the linear setting and observe that they hold in the non-linear case. Then, we illustrate the benefits of the method on a standard test problem and compare it with implicit Monte Carlo (IMC) simulations. On the other hand, we focus on second-order forms of the transport equation for neutronics applications. We mostly consider the Self-Adjoint Angular Flux (SAAF) and Least-Squares (LS) formulations, the former being globally conservative but void incompatible and the latter having -- in all generality -- the opposite properties. We study the relationship between these two methods based on the weakly-imposed LS boundary conditions. Equivalences between various parity-based PN methods are also established, in particular showing that second-order filters are not an appropriate fix to retrieve void compatibility. The importance of global conservation is highlighted on a heterogeneous multigroup k-eigenvalue test problem. Based on these considerations, we propose a new

  20. Parallelization of the Red-Black Algorithm on Solving the Second-Order PN Transport Equation with the Hybrid Finite Element Method

    SciTech Connect

    Yaqi Wang; Cristian Rabiti; Giuseppe Palmiotti

    2011-06-01

    The Red-Black algorithm has been successfully applied on solving the second-order parity transport equation with the PN approximation in angle and the Hybrid Finite Element Method (HFEM) in space, i.e., the Variational Nodal Method (VNM) [1,2,3,4,5]. Any transport solving techniques, including the Red-Black algorithm, need to be parallelized in order to take the advantage of the development of supercomputers with multiple processors for the advanced modeling and simulation. To our knowledge, an attempt [6] was done to parallelize it, but it was devoted only to the z axis plans in three-dimensional calculations. General parallelization of the Red-Black algorithm with the spatial domain decomposition has not been reported in the literature. In this summary, we present our implementation of the parallelization of the Red-Black algorithm and its efficiency results.

  1. A non-linear discontinuous Petrov-Galerkin method for removing oscillations in the solution of the time-dependent transport equation

    SciTech Connect

    Merton, S. R.; Smedley-Stevenson, R. P.; Pain, C. C.

    2012-07-01

    This paper describes a Non-Linear Discontinuous Petrov-Galerkin method and its application to the one-speed Boltzmann Transport Equation (BTE) for space-time problems. The purpose of the method is to remove unwanted oscillations in the transport solution which occur in the vicinity of sharp flux gradients, while improving computational efficiency and numerical accuracy. This is achieved by applying artificial dissipation in the solution gradient direction, internal to an element using a novel finite element (FE) Riemann approach. The added dissipation is calculated at each node of the finite element mesh based on local behaviour of the transport solution on both the spatial and temporal axes of the problem. Thus a different dissipation is used in different elements. The magnitude of dissipation that is used is obtained from a gradient-informed scaling of the advection velocities in the stabilisation term. This makes the method in its most general form non-linear. The method is implemented within a very general finite element Riemann framework. This makes it completely independent of choice of angular basis function allowing one to use different descriptions of the angular variation. Results show the non-linear scheme performs consistently well in demanding time-dependent multi-dimensional neutron transport problems. (authors)

  2. Conservative finite volume solutions of a linear hyperbolic transport equation in two and three dimensions using multiple grids

    NASA Technical Reports Server (NTRS)

    Tiwari, Surendra N.; Kathong, Monchai

    1987-01-01

    The feasibility of the multiple grid technique is investigated by solving linear hyperbolic equations for simple two- and three-dimensional cases. The results are compared with exact solutions and those obtained from the single grid calculations. It is demonstrated that the technique works reasonably well when two grid systems contain grid cells of comparative sizes. The study indicates that use of the multiple grid does not introduce any significant error and that it can be used to attack more complex problems.

  3. Computational transport phenomena in bioprocessing with the approach of the optimized source term in the governing equations

    NASA Astrophysics Data System (ADS)

    De Bonis, Maria Valeria; Ruocco, Gianpaolo

    2012-09-01

    Progress in the modeling of bio and food industry processes can be achieved by developing robust and efficient codes. Even complex configurations can be tackled, featuring multiphysics mechanisms that are interdependent or even competing with each other. In this paper the use of optimized "source terms" of the governing partial differential equations are discussed, reporting on simulation results. The related framework is addressed, as well as the potential of the adopted approach.

  4. Analytical and Numerical Problems Associtated with Extending the Use of the Second order Even-parity Transport Equation.

    DTIC Science & Technology

    1981-06-01

    including the ground was demonstrated by Straker (Ref. 2) who showed a significant effect on the atmospheric neutron distribution due to the presence of...regions of the spatial domain. This set of equations was solved by finite difference methods. The angular dependence of the neutron distribution in...known as flux synthesis (Refs. 19-22) and provides a method of intro- ducing a priori knowledge of the particle distribution into the trial solution

  5. Interaction of Dopamine Transporter Gene and Observed Parenting Behaviors on Attention-Deficit/Hyperactivity Disorder: A Structural Equation Modeling Approach

    ERIC Educational Resources Information Center

    Li, James J.; Lee, Steve S.

    2013-01-01

    Emerging evidence suggests that some individuals may be simultaneously more responsive to the effects from environmental adversity "and" enrichment (i.e., differential susceptibility). Given that parenting behavior and a variable number tandem repeat polymorphism in the 3'untranslated region of the dopamine transporter (DAT1) gene are…

  6. Intercontinental Transport of Tropical Ozone from Biomass Burning: Views from Satellite and SHADOZ (Southern Hemisphere Additional Ozonesondes)

    NASA Technical Reports Server (NTRS)

    Thompson, A. M.; Witte, J. C.; Chatfield, R. B.; Guam, H.

    2003-01-01

    There has been interest in the connection between tropical fires and ozone since about 1980. Photochemically reactive gases released by fires (e.g. NO, CO, volatile organic carbon) interact as they do in an urban environment to form ozone. Interacting with chemical sources, tropical meteorology plays a part in tropospheric ozone distributions in the tropics, through large-scale circulation, deep convection, and regional phenomena like the West African and Asian monsoons. An overview of observations, taken from satellite and from ozone soundings, illustrates regional influences and intercontinental- range ozone transport in the tropics. One of the most striking findings is evidence for impacts of Indian Ocean pollution on the south Atlantic ozone maximum referred to as the "ozone paradox" [Thompson et al., GRL, 2000; JGR, 2003; Chatfield et al., GRL, 20031.

  7. Intercontinental Transport of Tropical Ozone from Biomass Burning: Views from Satellite and SHADOZ (Southern Hemisphere Additional Ozonesondes) Soundings

    NASA Technical Reports Server (NTRS)

    Thompson, Anne M.

    2003-01-01

    The atmospheric impacts of tropical fires came to attention in the 1970's and there has been interest in the connection between these fires and ozone since about 1980. Photochemically reactive gases released by fires (e.g. NO, CO, volatile organic carbon) interact as they do in an urban environment to form ozone. Tropical meteorology also plays a part in tropospheric ozone distributions in the tropics - through large-scale circulation, deep convection, regional phenomena (West African and Asian monsoon) - and variations associated with El-Nino and the Quasi- biennial Oscillation have been reported. This Poster is an overview of observations, taken from satellite and from ozone soundings, that illustrate regional influences and intercontinental-range ozone transport in the tropics.

  8. A Novel Multigrid Method for Sn Discretizations of the Mono-Energetic Boltzmann Transport Equation in the Optically Thick and Thin Regimes with Anisotropic Scattering, Part I

    SciTech Connect

    Lee, Barry

    2010-05-01

    This paper presents a new multigrid method applied to the most common Sn discretizations (Petrov-Galerkin, diamond-differenced, corner-balanced, and discontinuous Galerkin) of the mono-energetic Boltzmann transport equation in the optically thick and thin regimes, and with strong anisotropic scattering. Unlike methods that use scalar DSA diffusion preconditioners for the source iteration, this multigrid method is applied directly to an integral equation for the scalar flux. Thus, unlike the former methods that apply a multigrid strategy to the scalar DSA diffusion operator, this method applies a multigrid strategy to the integral source iteration operator, which is an operator for 5 independent variables in spatial 3-d (3 in space and 2 in angle) and 4 independent variables in spatial 2-d (2 in space and 2 in angle). The core smoother of this multigrid method involves applications of the integral operator. Since the kernel of this integral operator involves the transport sweeps, applying this integral operator requires a transport sweep (an inversion of an upper triagular matrix) for each of the angles used. As the equation is in 5-space or 4-space, the multigrid approach in this paper coarsens in both angle and space, effecting efficient applications of the coarse integral operators. Although each V-cycle of this method is more expensive than a V-cycle for the DSA preconditioner, since the DSA equation does not have angular dependence, the overall computational efficiency is about the same for problems where DSA preconditioning {\\it is} effective. This new method also appears to be more robust over all parameter regimes than DSA approaches. Moreover, this new method is applicable to a variety of Sn spatial discretizations, to problems involving a combination of optically thick and thin regimes, and more importantly, to problems with anisotropic scattering cross-sections, all of which DSA approaches perform poorly or not applicable at all. This multigrid approach

  9. 14 CFR 61.63 - Additional aircraft ratings (other than for ratings at the airline transport pilot certification...

    Code of Federal Regulations, 2013 CFR

    2013-01-01

    ... airship rating at that pilot certificate level. (c) Additional aircraft class rating. A person who applies...-than-air category rating with a balloon class rating and is seeking an airship class rating, then that..., rotorcraft, powered-lift, weight-shift-control aircraft, powered parachute, or airship rating at that...

  10. 14 CFR 61.63 - Additional aircraft ratings (other than for ratings at the airline transport pilot certification...

    Code of Federal Regulations, 2011 CFR

    2011-01-01

    ... airship rating at that pilot certificate level. (c) Additional aircraft class rating. A person who applies...-than-air category rating with a balloon class rating and is seeking an airship class rating, then that..., rotorcraft, powered-lift, weight-shift-control aircraft, powered parachute, or airship rating at that...

  11. 14 CFR 61.63 - Additional aircraft ratings (other than for ratings at the airline transport pilot certification...

    Code of Federal Regulations, 2012 CFR

    2012-01-01

    ... airship rating at that pilot certificate level. (c) Additional aircraft class rating. A person who applies...-than-air category rating with a balloon class rating and is seeking an airship class rating, then that..., rotorcraft, powered-lift, weight-shift-control aircraft, powered parachute, or airship rating at that...

  12. 14 CFR 61.63 - Additional aircraft ratings (other than for ratings at the airline transport pilot certification...

    Code of Federal Regulations, 2014 CFR

    2014-01-01

    ... airship rating at that pilot certificate level. (c) Additional aircraft class rating. A person who applies...-than-air category rating with a balloon class rating and is seeking an airship class rating, then that..., rotorcraft, powered-lift, weight-shift-control aircraft, powered parachute, or airship rating at that...

  13. Time-dependent quantum transport: an efficient method based on Liouville-von-Neumann equation for single-electron density matrix.

    PubMed

    Xie, Hang; Jiang, Feng; Tian, Heng; Zheng, Xiao; Kwok, Yanho; Chen, Shuguang; Yam, ChiYung; Yan, YiJing; Chen, Guanhua

    2012-07-28

    Basing on our hierarchical equations of motion for time-dependent quantum transport [X. Zheng, G. H. Chen, Y. Mo, S. K. Koo, H. Tian, C. Y. Yam, and Y. J. Yan, J. Chem. Phys. 133, 114101 (2010)], we develop an efficient and accurate numerical algorithm to solve the Liouville-von-Neumann equation. We solve the real-time evolution of the reduced single-electron density matrix at the tight-binding level. Calculations are carried out to simulate the transient current through a linear chain of atoms, with each represented by a single orbital. The self-energy matrix is expanded in terms of multiple Lorentzian functions, and the Fermi distribution function is evaluated via the Padè spectrum decomposition. This Lorentzian-Padè decomposition scheme is employed to simulate the transient current. With sufficient Lorentzian functions used to fit the self-energy matrices, we show that the lead spectral function and the dynamics response can be treated accurately. Compared to the conventional master equation approaches, our method is much more efficient as the computational time scales cubically with the system size and linearly with the simulation time. As a result, the simulations of the transient currents through systems containing up to one hundred of atoms have been carried out. As density functional theory is also an effective one-particle theory, the Lorentzian-Padè decomposition scheme developed here can be generalized for first-principles simulation of realistic systems.

  14. Pollutant transport by shallow water equations on unstructured meshes: Hyperbolization of the model and numerical solution via a novel flux splitting scheme

    NASA Astrophysics Data System (ADS)

    Vanzo, Davide; Siviglia, Annunziato; Toro, Eleuterio F.

    2016-09-01

    The purpose of this paper is twofold. First, using the Cattaneo's relaxation approach, we reformulate the system of governing equations for the pollutant transport by shallow water flows over non-flat topography and anisotropic diffusion as hyperbolic balance laws with stiff source terms. The proposed relaxation system circumvents the infinite wave speed paradox which is inherent in standard advection-diffusion models. This turns out to give a larger stability range for the choice of the time step. Second, following a flux splitting approach, we derive a novel numerical method to discretise the resulting problem. In particular, we propose a new flux splitting and study the associated two systems of differential equations, called the ;hydrodynamic; and the ;relaxed diffusive; system, respectively. For the presented splitting we analyse the resulting two systems of differential equations and propose two discretisation schemes of the Godunov-type. These schemes are simple to implement, robust, accurate and fast when compared with existing methods. The resulting method is implemented on unstructured meshes and is systematically assessed for accuracy, robustness and efficiency on a carefully selected suite of test problems including non-flat topography and wetting and drying problems. Formal second order accuracy is assessed through convergence rates studies.

  15. Optimization of municipal solid waste transportation by integrating GIS analysis, equation-based, and agent-based model.

    PubMed

    Nguyen-Trong, Khanh; Nguyen-Thi-Ngoc, Anh; Nguyen-Ngoc, Doanh; Dinh-Thi-Hai, Van

    2017-01-01

    The amount of municipal solid waste (MSW) has been increasing steadily over the last decade by reason of population rising and waste generation rate. In most of the urban areas, disposal sites are usually located outside of the urban areas due to the scarcity of land. There is no fixed route map for transportation. The current waste collection and transportation are already overloaded arising from the lack of facilities and insufficient resources. In this paper, a model for optimizing municipal solid waste collection will be proposed. Firstly, the optimized plan is developed in a static context, and then it is integrated into a dynamic context using multi-agent based modelling and simulation. A case study related to Hagiang City, Vietnam, is presented to show the efficiency of the proposed model. From the optimized results, it has been found that the cost of the MSW collection is reduced by 11.3%.

  16. Structure, equation of state and transport properties of molten calcium carbonate (CaCO3) by atomistic simulations

    NASA Astrophysics Data System (ADS)

    Vuilleumier, Rodolphe; Seitsonen, Ari; Sator, Nicolas; Guillot, Bertrand

    2014-09-01

    First-principle molecular dynamics (FPMD) calculations have been performed to evaluate the physical properties of liquid calcium carbonate (CaCO3), which are up to now poorly known. The liquid structure, the density, the atomic vibration motions, the diffusion coefficients of calcium and carbonate ions and the electrical conductivity have been evaluated. As compared with silicate melts, molten CaCO3 is characterized by a low density (∼2.25 g/cm3 at 1623 K and 0.5 GPa), a viscosity almost as low as that of water (∼5 mPa s), and a high conductivity (∼200 S/m). In using the FPMD calculations for benchmark, an empirical force field has been developed for predicting the properties of molten CaCO3 at any state point in the liquid stability field. This force field is implemented into a classical molecular dynamics (MD) code, much cheaper in computer time, and the equation of state and the phase diagram of the liquid phase have been obtained. The evolutions of the self diffusion coefficients, viscosity, and the electrical conductivity with pressure and temperature have been investigated and the results fitted with analytical forms. It is shown that the Stokes-Einstein equation, expressing the viscosity as a function of diffusion motion, is well followed, and that the Nernst-Einstein equation relating the electrical conductivity to the diffusion coefficients of charge carriers leads to an accurate prediction of the conductivity, provided that a constant correcting factor is applied. Consequently, viscosity and electrical conductivity of the liquid are found to be anticorrelated with each other and can be described by a simple law; λ = A/η0.9 (where A = 1.905, λ is in S/m, and η in Pa s).

  17. Equation of State and Transport Measurements on Expanded Liquid Metals up to 8000 K and 0.4 GPa

    DTIC Science & Technology

    1978-05-01

    It is hoped that, although the trans-ort properties are strongly a function of the alloying , the measured equation of state parameters will bear some... Properties of Liquid Pb, Pt, AuCu, U, Nb, and NbHf 63 Lead 63 Platinum 83 Gold-Copper 94 Uranium 103 Niobium 115 Niobium-Hafnium 123 5. Electrical Resistivity...Potential Calculations 144 41. T-Matrix Calculations on Uranium 152 viii List of Tables 1. Measured Properties of Liquid Lead 66 2. L_•ad Emissivity

  18. Discontinuous finite element space-angle treatment of the first order linear Boltzmann transport equation with magnetic fields: Application to MRI-guided radiotherapy

    SciTech Connect

    St Aubin, J.; Keyvanloo, A.; Fallone, B. G.

    2016-01-15

    Purpose: The advent of magnetic resonance imaging (MRI) guided radiotherapy systems demands the incorporation of the magnetic field into dose calculation algorithms of treatment planning systems. This is due to the fact that the Lorentz force of the magnetic field perturbs the path of the relativistic electrons, hence altering the dose deposited by them. Building on the previous work, the authors have developed a discontinuous finite element space-angle treatment of the linear Boltzmann transport equation to accurately account for the effects of magnetic fields on radiotherapy doses. Methods: The authors present a detailed description of their new formalism and compare its accuracy to GEANT4 Monte Carlo calculations for magnetic fields parallel and perpendicular to the radiation beam at field strengths of 0.5 and 3 T for an inhomogeneous 3D slab geometry phantom comprising water, bone, and air or lung. The accuracy of the authors’ new formalism was determined using a gamma analysis with a 2%/2 mm criterion. Results: Greater than 98.9% of all points analyzed passed the 2%/2 mm gamma criterion for the field strengths and orientations tested. The authors have benchmarked their new formalism against Monte Carlo in a challenging radiation transport problem with a high density material (bone) directly adjacent to a very low density material (dry air at STP) where the effects of the magnetic field dominate collisions. Conclusions: A discontinuous finite element space-angle approach has been proven to be an accurate method for solving the linear Boltzmann transport equation with magnetic fields for cases relevant to MRI guided radiotherapy. The authors have validated the accuracy of this novel technique against GEANT4, even in cases of strong magnetic field strengths and low density air.

  19. Radiation Transport

    SciTech Connect

    Urbatsch, Todd James

    2015-06-15

    We present an overview of radiation transport, covering terminology, blackbody raditation, opacities, Boltzmann transport theory, approximations to the transport equation. Next we introduce several transport methods. We present a section on Caseology, observing transport boundary layers. We briefly broach topics of software development, including verification and validation, and we close with a section on high energy-density experiments that highlight and support radiation transport.

  20. Opioids and efflux transporters. Part 3: P-glycoprotein substrate activity of 3-hydroxyl addition to meperidine analogs.

    PubMed

    Mercer, Susan L; Cunningham, Christopher W; Eddington, Natalie D; Coop, Andrew

    2008-06-15

    Numerous studies have shown that many clinically employed opioid analgesics are substrates for P-glycoprotein (P-gp), suggesting that up-regulation of P-gp may contribute to the development of central tolerance to opioids. The studies herein focus on the development of SAR for P-gp substrate activity in the meperidine series of opioids. Addition of a 3-OH to meperidine and the ketone analog of meperidine yielding bemidone and ketobemidone, respectively, significantly increased P-gp substrate affinity. The results of this study have implications in the development of novel analgesics to be utilized as tools to study the contribution of P-gp on the development of central tolerance to opioids.

  1. Transportation of high-current ion and electron beams in the accelerator drift gap in the presence of an additional electron background

    SciTech Connect

    Karas’, V. I. Kornilov, E. A.; Manuilenko, O. V.; Tarakanov, V. P.; Fedorovskaya, O. V.

    2015-12-15

    The dynamics of a high-current ion beam propagating in the drift gap of a linear induction accelerator with collective focusing is studied using 3D numerical simulations in the framework of the full system of the Vlasov–Maxwell equations (code KARAT). The ion beam is neutralized by a comoving electron beam in the current density and, partially, in space charge, since the velocities of electrons and ions differ substantially. The dynamics of the high-current ion beam is investigated for different versions of additional neutralization of its space charge. It is established that, for a given configuration of the magnetic field and in the presence of a specially programmed injection of additional electrons from the boundary opposite to the ion injection boundary, the angular divergence of the ion beam almost vanishes, whereas the current of the ion beam at the exit from the accelerator drift gap changes insignificantly and the beam remains almost monoenergetic.

  2. Transportation of high-current ion and electron beams in the accelerator drift gap in the presence of an additional electron background

    NASA Astrophysics Data System (ADS)

    Karas', V. I.; Kornilov, E. A.; Manuilenko, O. V.; Tarakanov, V. P.; Fedorovskaya, O. V.

    2015-12-01

    The dynamics of a high-current ion beam propagating in the drift gap of a linear induction accelerator with collective focusing is studied using 3D numerical simulations in the framework of the full system of the Vlasov-Maxwell equations (code KARAT). The ion beam is neutralized by a comoving electron beam in the current density and, partially, in space charge, since the velocities of electrons and ions differ substantially. The dynamics of the high-current ion beam is investigated for different versions of additional neutralization of its space charge. It is established that, for a given configuration of the magnetic field and in the presence of a specially programmed injection of additional electrons from the boundary opposite to the ion injection boundary, the angular divergence of the ion beam almost vanishes, whereas the current of the ion beam at the exit from the accelerator drift gap changes insignificantly and the beam remains almost monoenergetic.

  3. Quantum transport equation for systems with rough surfaces and its application to ultracold neutrons in a quantizing gravity field

    SciTech Connect

    Escobar, M.; Meyerovich, A. E.

    2014-12-15

    We discuss transport of particles along random rough surfaces in quantum size effect conditions. As an intriguing application, we analyze gravitationally quantized ultracold neutrons in rough waveguides in conjunction with GRANIT experiments (ILL, Grenoble). We present a theoretical description of these experiments in the biased diffusion approximation for neutron mirrors with both one- and two-dimensional (1D and 2D) roughness. All system parameters collapse into a single constant which determines the depletion times for the gravitational quantum states and the exit neutron count. This constant is determined by a complicated integral of the correlation function (CF) of surface roughness. The reliable identification of this CF is always hindered by the presence of long fluctuation-driven correlation tails in finite-size samples. We report numerical experiments relevant for the identification of roughness of a new GRANIT waveguide and make predictions for ongoing experiments. We also propose a radically new design for the rough waveguide.

  4. Equation of state and transport properties of warm dense aluminum by ab initio and chemical model simulations

    NASA Astrophysics Data System (ADS)

    Fu, Zhijian; Quan, Weilong; Zhang, Wei; Li, Zhiguo; Zheng, Jun; Gu, Yunjun; Chen, Qifeng

    2017-01-01

    We have performed the ab initio molecular dynamics (AIMD) simulations for aluminum in the density and temperature range of 2.35-7.00 g cm-3 and 1000-70 000 K, respectively. The equation-of-state data obtained from the AIMD simulations are consistent with the available experimental and theoretical results. The electrical conductivity and thermal conductivity obtained by combining the Kubo-Greenwood formula with the AIMD simulations are also in agreement with the available experimental and theoretical results. The electrical conductivity calculated by a linear mixing rule (LMR) in the chemical picture provides appropriate although relatively underestimated values compared to those based on AIMD simulation. Both LMR and AIMD simulations demonstrate that a metal to nonmetal transition takes place at a temperature less than 30 000 K. The thermal power calculated shows not the direct signal connecting with the metal-nonmetal transition. The coupling parameter, degeneracy parameter, and fractions of warm dense aluminum are discussed systematically. Comparison of the simulation results with currently available theoretical and experimental data for warm dense aluminum is employed to evaluate the appropriate scope for currently available theoretical models, which will provide a useful guide for future experiments.

  5. Numerical Solution of the Electron Heat Transport Equation and Physics-Constrained Modeling of the Thermal Conductivity via Sequential Quadratic Programming Optimization in Nuclear Fusion Plasmas

    NASA Astrophysics Data System (ADS)

    Paloma, Cynthia S.

    The plasma electron temperature (Te) plays a critical role in a tokamak nu- clear fusion reactor since temperatures on the order of 108K are required to achieve fusion conditions. Many plasma properties in a tokamak nuclear fusion reactor are modeled by partial differential equations (PDE's) because they depend not only on time but also on space. In particular, the dynamics of the electron temperature is governed by a PDE referred to as the Electron Heat Transport Equation (EHTE). In this work, a numerical method is developed to solve the EHTE based on a custom finite-difference technique. The solution of the EHTE is compared to temperature profiles obtained by using TRANSP, a sophisticated plasma transport code, for specific discharges from the DIII-D tokamak, located at the DIII-D National Fusion Facility in San Diego, CA. The thermal conductivity (also called thermal diffusivity) of the electrons (Xe) is a plasma parameter that plays a critical role in the EHTE since it indicates how the electron temperature diffusion varies across the minor effective radius of the tokamak. TRANSP approximates Xe through a curve-fitting technique to match experimentally measured electron temperature profiles. While complex physics-based model have been proposed for Xe, there is a lack of a simple mathematical model for the thermal diffusivity that could be used for control design. In this work, a model for Xe is proposed based on a scaling law involving key plasma variables such as the electron temperature (Te), the electron density (ne), and the safety factor (q). An optimization algorithm is developed based on the Sequential Quadratic Programming (SQP) technique to optimize the scaling factors appearing in the proposed model so that the predicted electron temperature and magnetic flux profiles match predefined target profiles in the best possible way. A simulation study summarizing the outcomes of the optimization procedure is presented to illustrate the potential of the

  6. Equations of state, transport properties, and compositions of argon plasma: combination of self-consistent fluid variation theory and linear response theory.

    PubMed

    Quan, W L; Chen, Q F; Fu, Z J; Sun, X W; Zheng, J; Gu, Y J

    2015-02-01

    A consistent theoretical model that can be applied in a wide range of densities and temperatures is necessary for understanding the variation of a material's properties during compression and heating. Taking argon as an example, we show that the combination of self-consistent fluid variational theory and linear response theory is a promising route for studying warm dense matter. Following this route, the compositions, equations of state, and transport properties of argon plasma are calculated in a wide range of densities (0.001-20 g/cm(3)) and temperatures (5-100 kK). The obtained equations of state and electrical conductivities are found in good agreement with available experimental data. The plasma phase transition of argon is observed at temperatures below 30 kK and density about 2-6g/cm(3). The minimum density for the metallization of argon is found to be about 5.8 g/cm(3), occurring at 30-40 kK. The effects of many-particle correlations and dynamic screening on the electrical conductivity are also discussed through the effective potentials.

  7. Compendium of NASA data base for the global tropospheric experiment's Transport and Atmospheric Chemistry Near the Equator-Atlantic (TRACE-A)

    NASA Technical Reports Server (NTRS)

    Gregory, Gerald L.; Scott, A. Donald, Jr.

    1995-01-01

    This compendium describes aircraft data that are available from NASA's Transport and Atmospheric Chemistry near the Equator - Atlantic (TRACE-A) conducted in September/October 1992. The broad objectives of TRACE-A were to study chemical processes and long-range transport associated with South American and African continental outflow during periods of widespread vegetation burning, and to understand the ozone enhancements observed from satellite data measured over the southern tropical Atlantic Ocean during the September/October time period. Flight experiments were conducted from Brazil, South Africa, Namibia, and the Ascension Island. This document provides a representation of aircraft data that are available from NASA Langley's Distributed Active Archive Center (DAAC). The data format of time series and altitude profile plots is not intended to support original analyses, but to assist the reader in identifying data that are of interest. This compendium is for only the NASA aircraft data. The DAAC data base includes numerous supporting data-meteorological products, results from surface studies, satellite observations, and data from sonde releases.

  8. Wind-Tunnel Investigation of the Effects of Wing Bodies, Fences, Flaps, and a Fuselage Addition on the Wing Buffet Response of a Transonic-Transport Model

    NASA Technical Reports Server (NTRS)

    Cornette, Elden S.

    1961-01-01

    The experimental wing buffet response of a transport-type airplane model with and without wing bodies, fences, flaps, and a fuselage addition has been investigated at Mach numbers from 0.20 to 1.03. The wing had NACA 64A-series airfoil sections inclined 5 degrees to the free-stream direction. The quarter-chord line of the wing was swept back 45 degrees, the aspect ratio was 7, the taper ratio was 0.3, and the thickness ratio varied from 0.115 at the root to 0.074 at the midsemispan and was constant from that station to the tip. The wing was twisted and cambered for a design lift coefficient of 0.3. The results of the investigation indicated that a marked reduction of buffet intensity and a delay of buffet onset at transonic speeds were achieved by the addition to the wing of special bodies designed to reduce shock-induced separation. The further addition of wing fences and wing trailing-edge flaps deflected 30 degrees increased the lift coefficients at which low-speed stall buffeting occurred. An addition to the fuselage near the upper forward portion produced no consistent change in the buffet characteristics.

  9. Transportability

    DTIC Science & Technology

    2013-04-25

    length, with additional track in order to reverse the test railcar/ buffer car(s) for impacting in the opposite direction. To provide distance to...into the buffer car(s). Buffer car(s) (1 to 5) with total weight of 113,400 kg (250,000 lb), with the first buffer car equipped with standard...friction) draft gear and remaining buffer cars (if any) equipped with either standard draft gear or cushioned draft gear, with the draft gear

  10. FAA Smoke Transport Code

    SciTech Connect

    Domino, Stefan; Luketa-Hanlin, Anay; Gallegos, Carlos

    2006-10-27

    FAA Smoke Transport Code, a physics-based Computational Fluid Dynamics tool, which couples heat, mass, and momentum transfer, has been developed to provide information on smoke transport in cargo compartments with various geometries and flight conditions. The software package contains a graphical user interface for specification of geometry and boundary conditions, analysis module for solving the governing equations, and a post-processing tool. The current code was produced by making substantial improvements and additions to a code obtained from a university. The original code was able to compute steady, uniform, isothermal turbulent pressurization. In addition, a preprocessor and postprocessor were added to arrive at the current software package.

  11. Fractional chemotaxis diffusion equations.

    PubMed

    Langlands, T A M; Henry, B I

    2010-05-01

    We introduce mesoscopic and macroscopic model equations of chemotaxis with anomalous subdiffusion for modeling chemically directed transport of biological organisms in changing chemical environments with diffusion hindered by traps or macromolecular crowding. The mesoscopic models are formulated using continuous time random walk equations and the macroscopic models are formulated with fractional order differential equations. Different models are proposed depending on the timing of the chemotactic forcing. Generalizations of the models to include linear reaction dynamics are also derived. Finally a Monte Carlo method for simulating anomalous subdiffusion with chemotaxis is introduced and simulation results are compared with numerical solutions of the model equations. The model equations developed here could be used to replace Keller-Segel type equations in biological systems with transport hindered by traps, macromolecular crowding or other obstacles.

  12. An investigation on the effect of second-order additional thickness distributions to the upper surface of an NACA 64 sub 1-212 airfoil. [using flow equations and a CDC 7600 digital computer

    NASA Technical Reports Server (NTRS)

    Hague, D. S.; Merz, A. W.

    1975-01-01

    An investigation was conducted on a CDC 7600 digital computer to determine the effects of additional thickness distributions to the upper surface of an NACA 64 sub 1 - 212 airfoil. Additional thickness distributions employed were in the form of two second-order polynomial arcs which have a specified thickness at a given chordwise location. The forward arc disappears at the airfoil leading edge, the aft arc disappears at the airfoil trailing edge. At the juncture of the two arcs, x = x, continuity of slope is maintained. The effect of varying the maximum additional thickness and its chordwise location on airfoil lift coefficient, pitching moment, and pressure distribution was investigated. Results were obtained at a Mach number of 0.2 with an angle-of-attack of 6 degrees on the basic NACA 64 sub 1 - 212 airfoil, and all calculations employ the full potential flow equations for two dimensional flow. The relaxation method of Jameson was employed for solution of the potential flow equations.

  13. Theoretical effect of modifications to the upper surface of two NACA airfoils using smooth polynomial additional thickness distributions which emphasize leading edge profile and which vary quadratically at the trailing edge. [using flow equations and a CDC 7600 computer

    NASA Technical Reports Server (NTRS)

    Merz, A. W.; Hague, D. S.

    1975-01-01

    An investigation was conducted on a CDC 7600 digital computer to determine the effects of additional thickness distributions to the upper surface of the NACA 64-206 and 64 sub 1 - 212 airfoils. The additional thickness distribution had the form of a continuous mathematical function which disappears at both the leading edge and the trailing edge. The function behaves as a polynomial of order epsilon sub 1 at the leading edge, and a polynomial of order epsilon sub 2 at the trailing edge. Epsilon sub 2 is a constant and epsilon sub 1 is varied over a range of practical interest. The magnitude of the additional thickness, y, is a second input parameter, and the effect of varying epsilon sub 1 and y on the aerodynamic performance of the airfoil was investigated. Results were obtained at a Mach number of 0.2 with an angle-of-attack of 6 degrees on the basic airfoils, and all calculations employ the full potential flow equations for two dimensional flow. The relaxation method of Jameson was employed for solution of the potential flow equations.

  14. An investigation on the effect of second-order additional thickness distributions to the upper surface of an NACA 64-206 airfoil. [using flow equations and a CDC 7600 digital computer

    NASA Technical Reports Server (NTRS)

    Merz, A. W.; Hague, D. S.

    1975-01-01

    An investigation was conducted on a CDC 7600 digital computer to determine the effects of additional thickness distributions to the upper surface of an NACA 64-206 airfoil. Additional thickness distributions employed were in the form of two second-order polynomial arcs which have a specified thickness at a given chordwise location. The forward arc disappears at the airfoil leading edge, the aft arc disappears at the airfoil trailing edge. At the juncture of the two arcs, x = x, continuity of slope is maintained. The effect of varying the maximum additional thickness and its chordwise location on airfoil lift coefficient, pitching moment, and pressure distribution was investigated. Results were obtained at a Mach number of 0.2 with an angle-of-attack of 6 degrees on the basic NACA 64-206 airfoil, and all calculations employ the full potential flow equations for two dimensional flow. The relaxation method of Jameson was employed for solution of the potential flow equations.

  15. A WENO-solver combined with adaptive momentum discretization for the Wigner transport equation and its application to resonant tunneling diodes

    SciTech Connect

    Dorda, Antonius Schürrer, Ferdinand

    2015-03-01

    We present a novel numerical scheme for the deterministic solution of the Wigner transport equation, especially suited to deal with situations in which strong quantum effects are present. The unique feature of the algorithm is the expansion of the Wigner function in local basis functions, similar to finite element or finite volume methods. This procedure yields a discretization of the pseudo-differential operator that conserves the particle density on arbitrarily chosen grids. The high flexibility in refining the grid spacing together with the weighted essentially non-oscillatory (WENO) scheme for the advection term allows for an accurate and well-resolved simulation of the phase space dynamics. A resonant tunneling diode is considered as test case and a detailed convergence study is given by comparing the results to a non-equilibrium Green's functions calculation. The impact of the considered domain size and of the grid spacing is analyzed. The obtained convergence of the results towards a quasi-exact agreement of the steady state Wigner and Green's functions computations demonstrates the accuracy of the scheme, as well as the high flexibility to adjust to different physical situations.

  16. A WENO-solver combined with adaptive momentum discretization for the Wigner transport equation and its application to resonant tunneling diodes.

    PubMed

    Dorda, Antonius; Schürrer, Ferdinand

    2015-03-01

    We present a novel numerical scheme for the deterministic solution of the Wigner transport equation, especially suited to deal with situations in which strong quantum effects are present. The unique feature of the algorithm is the expansion of the Wigner function in local basis functions, similar to finite element or finite volume methods. This procedure yields a discretization of the pseudo-differential operator that conserves the particle density on arbitrarily chosen grids. The high flexibility in refining the grid spacing together with the weighted essentially non-oscillatory (WENO) scheme for the advection term allows for an accurate and well-resolved simulation of the phase space dynamics. A resonant tunneling diode is considered as test case and a detailed convergence study is given by comparing the results to a non-equilibrium Green's functions calculation. The impact of the considered domain size and of the grid spacing is analyzed. The obtained convergence of the results towards a quasi-exact agreement of the steady state Wigner and Green's functions computations demonstrates the accuracy of the scheme, as well as the high flexibility to adjust to different physical situations.

  17. A WENO-solver combined with adaptive momentum discretization for the Wigner transport equation and its application to resonant tunneling diodes

    PubMed Central

    Dorda, Antonius; Schürrer, Ferdinand

    2015-01-01

    We present a novel numerical scheme for the deterministic solution of the Wigner transport equation, especially suited to deal with situations in which strong quantum effects are present. The unique feature of the algorithm is the expansion of the Wigner function in local basis functions, similar to finite element or finite volume methods. This procedure yields a discretization of the pseudo-differential operator that conserves the particle density on arbitrarily chosen grids. The high flexibility in refining the grid spacing together with the weighted essentially non-oscillatory (WENO) scheme for the advection term allows for an accurate and well-resolved simulation of the phase space dynamics. A resonant tunneling diode is considered as test case and a detailed convergence study is given by comparing the results to a non-equilibrium Green's functions calculation. The impact of the considered domain size and of the grid spacing is analyzed. The obtained convergence of the results towards a quasi-exact agreement of the steady state Wigner and Green's functions computations demonstrates the accuracy of the scheme, as well as the high flexibility to adjust to different physical situations. PMID:25892748

  18. Discontinuous isogeometric analysis methods for the first-order form of the neutron transport equation with discrete ordinate (SN) angular discretisation

    NASA Astrophysics Data System (ADS)

    Owens, A. R.; Welch, J. A.; Kópházi, J.; Eaton, M. D.

    2016-06-01

    In this paper two discontinuous Galerkin isogeometric analysis methods are developed and applied to the first-order form of the neutron transport equation with a discrete ordinate (SN) angular discretisation. The discontinuous Galerkin projection approach was taken on both an element level and the patch level for a given Non-Uniform Rational B-Spline (NURBS) patch. This paper describes the detailed dispersion analysis that has been used to analyse the numerical stability of both of these schemes. The convergence of the schemes for both smooth and non-smooth solutions was also investigated using the method of manufactured solutions (MMS) for multidimensional problems and a 1D semi-analytical benchmark whose solution contains a strongly discontinuous first derivative. This paper also investigates the challenges posed by strongly curved boundaries at both the NURBS element and patch level with several algorithms developed to deal with such cases. Finally numerical results are presented both for a simple pincell test problem as well as the C5G7 quarter core MOX/UOX small Light Water Reactor (LWR) benchmark problem. These numerical results produced by the isogeometric analysis (IGA) methods are compared and contrasted against linear and quadratic discontinuous Galerkin finite element (DGFEM) SN based methods.

  19. Kinetics of solute adsorption at solid/solution interfaces: a theoretical development of the empirical pseudo-first and pseudo-second order kinetic rate equations, based on applying the statistical rate theory of interfacial transport.

    PubMed

    Rudzinski, Wladyslaw; Plazinski, Wojciech

    2006-08-24

    For practical applications of solid/solution adsorption processes, the kinetics of these processes is at least as much essential as their features at equilibrium. Meanwhile, the general understanding of this kinetics and its corresponding theoretical description are far behind the understanding and the level of theoretical interpretation of adsorption equilibria in these systems. The Lagergren empirical equation proposed at the end of 19th century to describe the kinetics of solute sorption at the solid/solution interfaces has been the most widely used kinetic equation until now. This equation has also been called the pseudo-first order kinetic equation because it was intuitively associated with the model of one-site occupancy adsorption kinetics governed by the rate of surface reaction. More recently, its generalization for the two-sites-occupancy adsorption was proposed and called the pseudo-second-order kinetic equation. However, the general use and the wide applicability of these empirical equations during more than one century have not resulted in a corresponding fundamental search for their theoretical origin. Here the first theoretical development of these equations is proposed, based on applying the new fundamental approach to kinetics of interfacial transport called the Statistical Rate Theory. It is shown that these empirical equations are simplified forms of a more general equation developed here, for the case when the adsorption kinetics is governed by the rate of surface reactions. The features of that general equation are shown by presenting exhaustive model investigations, and the applicability of that equation is tested by presenting a quantitative analysis of some experimental data reported in the literature.

  20. Niflumic acid activates additional currents of the human glial L-glutamate transporter EAAT1 in a substrate-dependent manner.

    PubMed

    Takahashi, Kanako; Ishii-Nozawa, Reiko; Takeuchi, Koichi; Nakazawa, Ken; Sekino, Yuko; Sato, Kaoru

    2013-01-01

    The astrocytic L-glutamate (L-Glu) transporter EAAT1 participates in the removal of L-Glu from the synaptic cleft and maintenance of non-toxic concentrations in the extracellular fluid. We have shown that niflumic acid (NFA), a non-steroidal anti-inflammatory drug (NSAIDs), alters L-Glu-induced EAAT1 currents in a voltage-dependent manner using the two-electrode voltage clamp technique in Xenopus oocytes expressing EAAT1. In this study, we characterised the effects of NFA on each type of ion-flux through EAAT1. NFA modulated currents induced by both L-Glu and L-aspartate (L-Asp) in a voltage-dependent manner. Ion-substitution experiments revealed that the activation of additional H(+) conductance was involved in the modulation of currents induced by L-Asp and L-Glu, but Cl(-) was involved only with the L-Asp currents. NFA activated additional currents of EAAT1 in a substrate-dependent manner.

  1. Transport Phenomena.

    ERIC Educational Resources Information Center

    Shah, D. B.

    1984-01-01

    Describes a course designed to achieve a balance between exposing students to (1) advanced topics in transport phenomena, pointing out similarities and differences between three transfer processes and (2) common methods of solving differential equations. (JN)

  2. Effective equations governing an active poroelastic medium.

    PubMed

    Collis, J; Brown, D L; Hubbard, M E; O'Dea, R D

    2017-02-01

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

  3. Effective equations governing an active poroelastic medium

    PubMed Central

    2017-01-01

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

  4. Additional Cover/Cap Scenario Streamtube Fate and Transport Modeling for the Old Radioactive Waste Burial Ground, Savannah River Site, Aiken, South Carolina

    SciTech Connect

    Brewer, K.

    2000-10-17

    The modeling described in this report is an extension of previous fate and transport modeling for the Old Radioactive Waste Burial Ground (ORWBG) Corrective Measures Study/Feasibility Study (CMS/FS). The purpose of this and the previous modeling is to provide quantitative input to the screening of remedial alternatives for the CMS/FS for this site.

  5. A simple recipe for setting up the flux equations of cyclic and linear reaction schemes of ion transport with a high number of states: The arrow scheme.

    PubMed

    Hansen, Ulf-Peter; Rauh, Oliver; Schroeder, Indra

    2016-01-01

    The calculation of flux equations or current-voltage relationships in reaction kinetic models with a high number of states can be very cumbersome. Here, a recipe based on an arrow scheme is presented, which yields a straightforward access to the minimum form of the flux equations and the occupation probability of the involved states in cyclic and linear reaction schemes. This is extremely simple for cyclic schemes without branches. If branches are involved, the effort of setting up the equations is a little bit higher. However, also here a straightforward recipe making use of so-called reserve factors is provided for implementing the branches into the cyclic scheme, thus enabling also a simple treatment of such cases.

  6. A simple recipe for setting up the flux equations of cyclic and linear reaction schemes of ion transport with a high number of states: The arrow scheme

    PubMed Central

    Hansen, Ulf-Peter; Rauh, Oliver; Schroeder, Indra

    2016-01-01

    abstract The calculation of flux equations or current-voltage relationships in reaction kinetic models with a high number of states can be very cumbersome. Here, a recipe based on an arrow scheme is presented, which yields a straightforward access to the minimum form of the flux equations and the occupation probability of the involved states in cyclic and linear reaction schemes. This is extremely simple for cyclic schemes without branches. If branches are involved, the effort of setting up the equations is a little bit higher. However, also here a straightforward recipe making use of so-called reserve factors is provided for implementing the branches into the cyclic scheme, thus enabling also a simple treatment of such cases. PMID:26646356

  7. Pavement-Transportation Computer Assisted Structural Engineering (PCASE) Implementation of the Modified Berggren (ModBerg) Equation for Computing the Frost Penetration Depth within Pavement Structures

    DTIC Science & Technology

    2012-04-01

    thermal conductivity is expressed by Equations 1 and 2. . .. ( ) . ( )é ù +ë û= 0 013 0 01460 076 10 0 032 10 12 d dγ γ f w K (1) ERDC/GSL TR-12-15...7 ( ) .( . log . )é ù +ë û= 0 010 7 0 4 10 12 dγ u w K (2) where γd = soil dry unit weight w = soil water content in percentage For fine...grained soils, such as silt and clay, the thermal conductivity is given by Equations 3 and 4. . .. ( ) . ( )é ù +ë û= 0 022 0 0080 01 10 0 085 10

  8. A Course in Transport Phenomena in Multicomponent, Multiphase, Reacting Systems.

    ERIC Educational Resources Information Center

    Carbonell, R. G.; Whitaker, S.

    1978-01-01

    This course concentrates on a rigorous development of the multicomponent transport equations, boundary conditions at phase interfaces, and volume-averaged transport equations for multiphase reacting systems. (BB)

  9. Conservational PDF Equations of Turbulence

    NASA Technical Reports Server (NTRS)

    Shih, Tsan-Hsing; Liu, Nan-Suey

    2010-01-01

    Recently we have revisited the traditional probability density function (PDF) equations for the velocity and species in turbulent incompressible flows. They are all unclosed due to the appearance of various conditional means which are modeled empirically. However, we have observed that it is possible to establish a closed velocity PDF equation and a closed joint velocity and species PDF equation through conditions derived from the integral form of the Navier-Stokes equations. Although, in theory, the resulted PDF equations are neither general nor unique, they nevertheless lead to the exact transport equations for the first moment as well as all higher order moments. We refer these PDF equations as the conservational PDF equations. This observation is worth further exploration for its validity and CFD application

  10. Pointwise Energy Solution of the Boltzmann Transport Equation for Thermal Neutrons - Final Report - 07/01/1999 - 06/30/2001

    SciTech Connect

    Williams, Mark L.

    2001-06-30

    In July of 1999 Louisiana State University (LSU) was awarded a two year research grant by the D.O.E. NEER program to develop a methodology for neutron transport calculations using pointwise (PW) nuclear data in the thermal energy range, and to implement the method into the CENTRM transport code being developed at LSU for Oak Ridge National Laboratory (ORNL). This work has extended CENTRM's current epithermal PW calculation to encompass the thermal range, providing a continuous-energy deterministic transport code that can address problems that may not be adequately treated using multigroup methods. The new version of the CENTRM code was completed, and provided to ORNL for inclusion in the next release of the SCALE code system. The new thermal calculation developed by the NEER project is a significant improvement in the CENTRM capability, and should have an impact on criticality and shipping cask analysis done by numerous organizations who use this code system.

  11. Albumin and Uptake of Drugs in Cells: Additional Validation Exercises of a Recently Published Equation that Quantifies the Albumin-Facilitated Uptake Mechanism(s) in Physiologically Based Pharmacokinetic and Pharmacodynamic Modeling Research.

    PubMed

    Poulin, Patrick; Haddad, Sami

    2015-12-01

    The impact of albumin concentration on the uptake of drugs in cells might involve mechanisms going beyond the free drug concentration hypothesis. Proceeding from the assumption that both the unbound and protein-bound drug fractions can be available for uptake, several authors have argued that the uptake of highly bound drugs in cells might be driven mainly by the albumin-facilitated uptake mechanism(s). Hence, a novel approach quantifying the additional contribution of the protein-bound drug complex and pH gradient effect in diverse in vitro-to-in vivo extrapolation (IVIVE) procedures of drug uptake and clearance has been proposed and extensively validated by Poulin et al. (2015. J Pharm Sci. Epub ahead of print); this approach consisted of replacing the unbound fraction in plasma (fup ) with an adjusted fup value (fup-adjusted ). After a second review of literature, the objective of the present study was to perform further validation exercises of the concept of fup-adjusted by using additional case examples of IVIVEs that covered diverse drug properties and experimental settings with varied albumin concentrations (e.g., perfused liver, isolated and suspended hepatocytes, and cultured cells overexpressing transporters). Again, the novel IVIVE method based on fup-adjusted was the best-performing prediction method of the uptake rate (or clearance) as a function of protein binding compared with the conventional method based on the fup theory (absolute average fold error of 1.4 vs. 7.4). Therefore, the present study confirms the utility of fup-adjusted compared with fup in IVIVE procedures for drugs highly bound to albumin, and the improvement was observed particularly in the higher range of albumin concentrations. From these findings, we may conclude that uptake of these drugs in cells is primarily driven by the albumin-bound form. Consequently, it is suggested to estimate the uptake kinetic parameters with cell-based assays incubated in 100% human serum or to make a

  12. Additive electroplating technology as a post-CMOS process for the production of MEMS acceleration-threshold switches for transportation applications

    NASA Astrophysics Data System (ADS)

    Michaelis, Sven; Timme, Hans-Jörg; Wycisk, Michael; Binder, Josef

    2000-06-01

    This paper presents an acceleration-threshold sensor fabricated with an electroplating technology which can be integrated on top of a pre-processed CMOS signal processing circuit. The device can be manufactured using a standard low-cost CMOS production line and then adding the mechanical sensor elements via a specialized back-end process. This makes the system especially interesting for automotive applications, such as airbag safety systems or transportation shock monitoring systems, where smaller size, improved functionality, high reliability and low costs are important.

  13. The Effective Equation Method

    NASA Astrophysics Data System (ADS)

    Kuksin, Sergei; Maiocchi, Alberto

    In this chapter we present a general method of constructing the effective equation which describes the behavior of small-amplitude solutions for a nonlinear PDE in finite volume, provided that the linear part of the equation is a hamiltonian system with a pure imaginary discrete spectrum. The effective equation is obtained by retaining only the resonant terms of the nonlinearity (which may be hamiltonian, or may be not); the assertion that it describes the limiting behavior of small-amplitude solutions is a rigorous mathematical theorem. In particular, the method applies to the three- and four-wave systems. We demonstrate that different possible types of energy transport are covered by this method, depending on whether the set of resonances splits into finite clusters (this happens, e.g. in case of the Charney-Hasegawa-Mima equation), or is connected (this happens, e.g. in the case of the NLS equation if the space-dimension is at least two). For equations of the first type the energy transition to high frequencies does not hold, while for equations of the second type it may take place. Our method applies to various weakly nonlinear wave systems, appearing in plasma, meteorology and oceanography.

  14. 49 CFR 1108.12 - Additional matters.

    Code of Federal Regulations, 2010 CFR

    2010-10-01

    ... 49 Transportation 8 2010-10-01 2010-10-01 false Additional matters. 1108.12 Section 1108.12 Transportation Other Regulations Relating to Transportation (Continued) SURFACE TRANSPORTATION BOARD, DEPARTMENT... JURISDICTION OF THE SURFACE TRANSPORTATION BOARD § 1108.12 Additional matters. Where an arbitration demand...

  15. 49 CFR 1108.12 - Additional matters.

    Code of Federal Regulations, 2012 CFR

    2012-10-01

    ... 49 Transportation 8 2012-10-01 2012-10-01 false Additional matters. 1108.12 Section 1108.12 Transportation Other Regulations Relating to Transportation (Continued) SURFACE TRANSPORTATION BOARD, DEPARTMENT... JURISDICTION OF THE SURFACE TRANSPORTATION BOARD § 1108.12 Additional matters. Where an arbitration demand...

  16. 49 CFR 1108.12 - Additional matters.

    Code of Federal Regulations, 2011 CFR

    2011-10-01

    ... 49 Transportation 8 2011-10-01 2011-10-01 false Additional matters. 1108.12 Section 1108.12 Transportation Other Regulations Relating to Transportation (Continued) SURFACE TRANSPORTATION BOARD, DEPARTMENT... JURISDICTION OF THE SURFACE TRANSPORTATION BOARD § 1108.12 Additional matters. Where an arbitration demand...

  17. Exact momentum conservation laws for the gyrokinetic Vlasov-Poisson equations

    SciTech Connect

    Brizard, Alain J.; Tronko, Natalia

    2011-08-15

    The exact momentum conservation laws for the nonlinear gyrokinetic Vlasov-Poisson equations are derived by applying the Noether method on the gyrokinetic variational principle [A. J. Brizard, Phys. Plasmas 7, 4816 (2000)]. From the gyrokinetic Noether canonical-momentum equation derived by the Noether method, the gyrokinetic parallel momentum equation and other gyrokinetic Vlasov-moment equations are obtained. In addition, an exact gyrokinetic toroidal angular-momentum conservation law is derived in axisymmetric tokamak geometry, where the transport of parallel-toroidal momentum is related to the radial gyrocenter polarization, which includes contributions from the guiding-center and gyrocenter transformations.

  18. Equation poems

    NASA Astrophysics Data System (ADS)

    Prentis, Jeffrey J.

    1996-05-01

    One of the most challenging goals of a physics teacher is to help students see that the equations of physics are connected to each other, and that they logically unfold from a small number of basic ideas. Derivations contain the vital information on this connective structure. In a traditional physics course, there are many problem-solving exercises, but few, if any, derivation exercises. Creating an equation poem is an exercise to help students see the unity of the equations of physics, rather than their diversity. An equation poem is a highly refined and eloquent set of symbolic statements that captures the essence of the derivation of an equation. Such a poetic derivation is uncluttered by the extraneous details that tend to distract a student from understanding the essential physics of the long, formal derivation.

  19. Anomalous transport

    NASA Astrophysics Data System (ADS)

    Cheverry, Christophe

    2017-02-01

    This article is concerned with the relativistic Vlasov equation, for collisionless axisymmetric plasmas immersed in a strong magnetic field, like in tokamaks. It provides a consistent kinetic treatment of the microscopic particle phase-space dynamics. It shows that the turbulent transport can be completely described through WKB expansions.

  20. Nonlinear ordinary difference equations

    NASA Technical Reports Server (NTRS)

    Caughey, T. K.

    1979-01-01

    Future space vehicles will be relatively large and flexible, and active control will be necessary to maintain geometrical configuration. While the stresses and strains in these space vehicles are not expected to be excessively large, their cumulative effects will cause significant geometrical nonlinearities to appear in the equations of motion, in addition to the nonlinearities caused by material properties. Since the only effective tool for the analysis of such large complex structures is the digital computer, it will be necessary to gain a better understanding of the nonlinear ordinary difference equations which result from the time discretization of the semidiscrete equations of motion for such structures.

  1. Food additives

    PubMed Central

    Spencer, Michael

    1974-01-01

    Food additives are discussed from the food technology point of view. The reasons for their use are summarized: (1) to protect food from chemical and microbiological attack; (2) to even out seasonal supplies; (3) to improve their eating quality; (4) to improve their nutritional value. The various types of food additives are considered, e.g. colours, flavours, emulsifiers, bread and flour additives, preservatives, and nutritional additives. The paper concludes with consideration of those circumstances in which the use of additives is (a) justified and (b) unjustified. PMID:4467857

  2. Energy-Dependent Scintillation Pulse Shape and Proportionality of Decay Components for CsI:Tl: Modeling with Transport and Rate Equations

    NASA Astrophysics Data System (ADS)

    Lu, X.; Gridin, S.; Williams, R. T.; Mayhugh, M. R.; Gektin, A.; Syntfeld-Kazuch, A.; Swiderski, L.; Moszynski, M.

    2017-01-01

    Relatively recent experiments on the scintillation response of CsI:Tl have found that there are three main decay times of about 730 ns, 3 μ s , and 16 μ s , i.e., one more principal decay component than had been previously reported; that the pulse shape depends on gamma-ray energy; and that the proportionality curves of each decay component are different, with the energy-dependent light yield of the 16 -μ s component appearing to be anticorrelated with that of the 0.73 -μ s component at room temperature. These observations can be explained by the described model of carrier transport and recombination in a particle track. This model takes into account processes of hot and thermalized carrier diffusion, electric-field transport, trapping, nonlinear quenching, and radiative recombination. With one parameter set, the model reproduces multiple observables of CsI:Tl scintillation response, including the pulse shape with rise and three decay components, its energy dependence, the approximate proportionality, and the main trends in proportionality of different decay components. The model offers insights on the spatial and temporal distributions of carriers and their reactions in the track.

  3. Computing generalized Langevin equations and generalized Fokker-Planck equations.

    PubMed

    Darve, Eric; Solomon, Jose; Kia, Amirali

    2009-07-07

    The Mori-Zwanzig formalism is an effective tool to derive differential equations describing the evolution of a small number of resolved variables. In this paper we present its application to the derivation of generalized Langevin equations and generalized non-Markovian Fokker-Planck equations. We show how long time scales rates and metastable basins can be extracted from these equations. Numerical algorithms are proposed to discretize these equations. An important aspect is the numerical solution of the orthogonal dynamics equation which is a partial differential equation in a high dimensional space. We propose efficient numerical methods to solve this orthogonal dynamics equation. In addition, we present a projection formalism of the Mori-Zwanzig type that is applicable to discrete maps. Numerical applications are presented from the field of Hamiltonian systems.

  4. Modeling acute respiratory illness during the 2007 San Diego wildland fires using a coupled emissions-transport system and generalized additive modeling

    PubMed Central

    2013-01-01

    Background A study of the impacts on respiratory health of the 2007 wildland fires in and around San Diego County, California is presented. This study helps to address the impact of fire emissions on human health by modeling the exposure potential of proximate populations to atmospheric particulate matter (PM) from vegetation fires. Currently, there is no standard methodology to model and forecast the potential respiratory health effects of PM plumes from wildland fires, and in part this is due to a lack of methodology for rigorously relating the two. The contribution in this research specifically targets that absence by modeling explicitly the emission, transmission, and distribution of PM following a wildland fire in both space and time. Methods Coupled empirical and deterministic models describing particulate matter (PM) emissions and atmospheric dispersion were linked to spatially explicit syndromic surveillance health data records collected through the San Diego Aberration Detection and Incident Characterization (SDADIC) system using a Generalized Additive Modeling (GAM) statistical approach. Two levels of geographic aggregation were modeled, a county-wide regional level and division of the county into six sub regions. Selected health syndromes within SDADIC from 16 emergency departments within San Diego County relevant for respiratory health were identified for inclusion in the model. Results The model captured the variability in emergency department visits due to several factors by including nine ancillary variables in addition to wildfire PM concentration. The model coefficients and nonlinear function plots indicate that at peak fire PM concentrations the odds of a person seeking emergency care is increased by approximately 50% compared to non-fire conditions (40% for the regional case, 70% for a geographically specific case). The sub-regional analyses show that demographic variables also influence respiratory health outcomes from smoke. Conclusions The

  5. Transport properties of uranium dioxide

    SciTech Connect

    Fink, J.K.; Chasanov, M.G.; Leibowitz, L.

    1981-04-01

    In order to provide reliable and consistent data on the thermophysical properties of reactor materials for reactor safety studies, this revision is prepared for the transport properties of the uranium dioxide portion of the fuel property section of the report Properties for LMFBR Safety Analysis. Since the original report was issued in 1976, measurements of thermal diffusivity and emissivity have been made. In addition to incorporating this new data, new equations have been derived to fit the thermal diffusivity and thermal conductivity data. This analysis is consistent with the analysis of enthalpy and heat capacity. A new form of equation for the emissivity is also given. The present report comprises the transport part of the UO/sub 2/ portion of section A of the planned complete revision of Properties for LMFBR Safety Analysis.

  6. Classical non-Markovian Boltzmann equation

    SciTech Connect

    Alexanian, Moorad

    2014-08-01

    The modeling of particle transport involves anomalous diffusion, (x²(t) ) ∝ t{sup α} with α ≠ 1, with subdiffusive transport corresponding to 0 < α < 1 and superdiffusive transport to α > 1. These anomalies give rise to fractional advection-dispersion equations with memory in space and time. The usual Boltzmann equation, with only isolated binary collisions, is Markovian and, in particular, the contributions of the three-particle distribution function are neglected. We show that the inclusion of higher-order distribution functions give rise to an exact, non-Markovian Boltzmann equation with resulting transport equations for mass, momentum, and kinetic energy with memory in both time and space. The two- and the three-particle distribution functions are considered under the assumption that the two- and the three-particle correlation functions are translationally invariant that allows us to obtain advection-dispersion equations for modeling transport in terms of spatial and temporal fractional derivatives.

  7. Classical non-Markovian Boltzmann equation

    NASA Astrophysics Data System (ADS)

    Alexanian, Moorad

    2014-08-01

    The modeling of particle transport involves anomalous diffusion, ⟨x2(t) ⟩ ∝ tα with α ≠ 1, with subdiffusive transport corresponding to 0 < α < 1 and superdiffusive transport to α > 1. These anomalies give rise to fractional advection-dispersion equations with memory in space and time. The usual Boltzmann equation, with only isolated binary collisions, is Markovian and, in particular, the contributions of the three-particle distribution function are neglected. We show that the inclusion of higher-order distribution functions give rise to an exact, non-Markovian Boltzmann equation with resulting transport equations for mass, momentum, and kinetic energy with memory in both time and space. The two- and the three-particle distribution functions are considered under the assumption that the two- and the three-particle correlation functions are translationally invariant that allows us to obtain advection-dispersion equations for modeling transport in terms of spatial and temporal fractional derivatives.

  8. Food additives

    MedlinePlus

    ... or natural. Natural food additives include: Herbs or spices to add flavor to foods Vinegar for pickling ... Certain colors improve the appearance of foods. Many spices, as well as natural and man-made flavors, ...

  9. The role of nuclear physics in supernovae and the evolution of neutron stars Neutrino Opacities, Equation of State, Transport Coefficients, and Dark Matter Production

    NASA Astrophysics Data System (ADS)

    Rrapaj, Ermal

    A massive star, of at least eight solar masses, end their life cycle in a sudden, catastrophic collapse under its own gravity. In a thousandth of a second, it can shrink from thousands of kilometers across to a ball of ultra-condensed matter just a few kilometers across. Ultimately, it all ends in a cataclysmic explosion known as a supernova, and for a few short weeks it burns as brightly as several billion suns, briefly outshining the star's entire home galaxy. The visible light of a supernova, though, represents only about 1% of the released energy, the vast majority being in the form of ultraviolet light, x-rays, gamma rays and, especially neutrinos. In the first chapter of work, I study neutrino - nucleon interactions and their role in the nucleosynthesis of heavy elements. Another key ingredient is the equation of state, which relates the thermodynamic properties of these extreme environments to the micro physics of nuclear interactions, explored in the second chapter. As a supernova cools, a new neutron star is born. The thermal, electric properties and the shear viscosity of this object are analyzed in terms of a newly discovered interaction, among electrons and neutrons, in the third chapter. Given the enormous amount of energy released during the explosion, I study the possibility of producing light massive particles, candidates for what is commonly called dark matter, in the last chapter of this work. I find that supernovae are ideal environments where the interplay of all forces in nature can be observed, nuclear forces playing a paramount role.

  10. SAM-CE; A Three Dimensional Monte Carlo Code for the Dolution of the Forward Neutron and Forward and Adjoint Gamma Ray Transport Equations. Revision C

    DTIC Science & Technology

    1974-07-31

    Phase Shift for Values of k From 0 to 3 . . . . . . . . . .. *. . . 24 2.2 Values of w Used for Integration of Neutron -Width Distributions with One...associated with multi-group codes, which use flux -averaged cross sections based on assumed flux distributions which may or may not be appropriate. By use of...providing the output is in the specified format. SAM-F then calculates and provides an edit of the desired neutron fluxes and flux -functionals. in addition

  11. Computer algebra and transport theory.

    SciTech Connect

    Warsa, J. S.

    2004-01-01

    Modern symbolic algebra computer software augments and complements more traditional approaches to transport theory applications in several ways. The first area is in the development and enhancement of numerical solution methods for solving the Boltzmann transport equation. Typically, special purpose computer codes are designed and written to solve specific transport problems in particular ways. Different aspects of the code are often written from scratch and the pitfalls of developing complex computer codes are numerous and well known. Software such as MAPLE and MATLAB can be used to prototype, analyze, verify and determine the suitability of numerical solution methods before a full-scale transport application is written. Once it is written, the relevant pieces of the full-scale code can be verified using the same tools I that were developed for prototyping. Another area is in the analysis of numerical solution methods or the calculation of theoretical results that might otherwise be difficult or intractable. Algebraic manipulations are done easily and without error and the software also provides a framework for any additional numerical calculations that might be needed to complete the analysis. We will discuss several applications in which we have extensively used MAPLE and MATLAB in our work. All of them involve numerical solutions of the S{sub N} transport equation. These applications encompass both of the two main areas in which we have found computer algebra software essential.

  12. Beautiful equations

    NASA Astrophysics Data System (ADS)

    Viljamaa, Panu; Jacobs, J. Richard; Chris; JamesHyman; Halma, Matthew; EricNolan; Coxon, Paul

    2014-07-01

    In reply to a Physics World infographic (part of which is given above) about a study showing that Euler's equation was deemed most beautiful by a group of mathematicians who had been hooked up to a functional magnetic-resonance image (fMRI) machine while viewing mathematical expressions (14 May, http://ow.ly/xHUFi).

  13. An upscaled approach for transport in media with extended tailing due to back-diffusion using analytical and numerical solutions of the advection dispersion equation.

    PubMed

    Parker, Jack C; Kim, Ungtae

    2015-11-01

    The mono-continuum advection-dispersion equation (mADE) is commonly regarded as unsuitable for application to media that exhibit rapid breakthrough and extended tailing associated with diffusion between high and low permeability regions. This paper demonstrates that the mADE can be successfully used to model such conditions if certain issues are addressed. First, since hydrodynamic dispersion, unlike molecular diffusion, cannot occur upstream of the contaminant source, models must be formulated to prevent "back-dispersion." Second, large variations in aquifer permeability will result in differences between volume-weighted average concentration (resident concentration) and flow-weighted average concentration (flux concentration). Water samples taken from wells may be regarded as flux concentrations, while soil samples may be analyzed to determine resident concentrations. While the mADE is usually derived in terms of resident concentration, it is known that a mADE of the same mathematical form may be written in terms of flux concentration. However, when solving the latter, the mathematical transformation of a flux boundary condition applied to the resident mADE becomes a concentration type boundary condition for the flux mADE. Initial conditions must also be consistent with the form of the mADE that is to be solved. Thus, careful attention must be given to the type of concentration data that is available, whether resident or flux concentrations are to be simulated, and to boundary and initial conditions. We present 3-D analytical solutions for resident and flux concentrations, discuss methods of solving numerical models to obtain resident and flux concentrations, and compare results for hypothetical problems. We also present an upscaling method for computing "effective" dispersivities and other mADE model parameters in terms of physically meaningful parameters in a diffusion-limited mobile-immobile model. Application of the latter to previously published studies of

  14. BHR equations re-derived with immiscible particle effects

    SciTech Connect

    Schwarzkopf, John Dennis; Horwitz, Jeremy A.

    2015-05-01

    Compressible and variable density turbulent flows with dispersed phase effects are found in many applications ranging from combustion to cloud formation. These types of flows are among the most challenging to simulate. While the exact equations governing a system of particles and fluid are known, computational resources limit the scale and detail that can be simulated in this type of problem. Therefore, a common method is to simulate averaged versions of the flow equations, which still capture salient physics and is relatively less computationally expensive. Besnard developed such a model for variable density miscible turbulence, where ensemble-averaging was applied to the flow equations to yield a set of filtered equations. Besnard further derived transport equations for the Reynolds stresses, the turbulent mass flux, and the density-specific volume covariance, to help close the filtered momentum and continuity equations. We re-derive the exact BHR closure equations which include integral terms owing to immiscible effects. Physical interpretations of the additional terms are proposed along with simple models. The goal of this work is to extend the BHR model to allow for the simulation of turbulent flows where an immiscible dispersed phase is non-trivially coupled with the carrier phase.

  15. Analytical solution of the simplified spherical harmonics equations in spherical turbid media

    NASA Astrophysics Data System (ADS)

    Edjlali, Ehsan; Bérubé-Lauzière, Yves

    2016-10-01

    We present for the first time an analytical solution for the simplified spherical harmonics equations (so-called SPN equations) in the case of a steady-state isotropic point source inside a spherical homogeneous absorbing and scattering medium. The SPN equations provide a reliable approximation to the radiative transfer equation for describing light transport inside turbid media. The SPN equations consist of a set of coupled partial differential equations and the eigen method is used to obtain a set of decoupled equations, each resembling the heat equation in the Laplace domain. The equations are solved for the realistic partial reflection boundary conditions accounting for the difference in refractive indices between the turbid medium and its environment (air) as occurs in practical cases of interest in biomedical optics. Specifically, we provide the complete solution methodology for the SP3, which is readily applicable to higher orders as well, and also give results for the SP5. This computationally easy to obtain solution is investigated for different optical properties of the turbid medium. For validation, the solution is also compared to the analytical solution of the diffusion equation and to gold standard Monte Carlo simulation results. The SP3 and SP5 analytical solutions prove to be in good agreement with the Monte Carlo results. This work provides an additional tool for validating numerical solutions of the SPN equations for curved geometries.

  16. Potlining Additives

    SciTech Connect

    Rudolf Keller

    2004-08-10

    In this project, a concept to improve the performance of aluminum production cells by introducing potlining additives was examined and tested. Boron oxide was added to cathode blocks, and titanium was dissolved in the metal pool; this resulted in the formation of titanium diboride and caused the molten aluminum to wet the carbonaceous cathode surface. Such wetting reportedly leads to operational improvements and extended cell life. In addition, boron oxide suppresses cyanide formation. This final report presents and discusses the results of this project. Substantial economic benefits for the practical implementation of the technology are projected, especially for modern cells with graphitized blocks. For example, with an energy savings of about 5% and an increase in pot life from 1500 to 2500 days, a cost savings of $ 0.023 per pound of aluminum produced is projected for a 200 kA pot.

  17. Phosphazene additives

    DOEpatents

    Harrup, Mason K; Rollins, Harry W

    2013-11-26

    An additive comprising a phosphazene compound that has at least two reactive functional groups and at least one capping functional group bonded to phosphorus atoms of the phosphazene compound. One of the at least two reactive functional groups is configured to react with cellulose and the other of the at least two reactive functional groups is configured to react with a resin, such as an amine resin of a polycarboxylic acid resin. The at least one capping functional group is selected from the group consisting of a short chain ether group, an alkoxy group, or an aryloxy group. Also disclosed are an additive-resin admixture, a method of treating a wood product, and a wood product.

  18. Marcus equation

    DOE R&D Accomplishments Database

    1998-09-21

    In the late 1950s to early 1960s Rudolph A. Marcus developed a theory for treating the rates of outer-sphere electron-transfer reactions. Outer-sphere reactions are reactions in which an electron is transferred from a donor to an acceptor without any chemical bonds being made or broken. (Electron-transfer reactions in which bonds are made or broken are referred to as inner-sphere reactions.) Marcus derived several very useful expressions, one of which has come to be known as the Marcus cross-relation or, more simply, as the Marcus equation. It is widely used for correlating and predicting electron-transfer rates. For his contributions to the understanding of electron-transfer reactions, Marcus received the 1992 Nobel Prize in Chemistry. This paper discusses the development and use of the Marcus equation. Topics include self-exchange reactions; net electron-transfer reactions; Marcus cross-relation; and proton, hydride, atom and group transfers.

  19. The thermal-vortex equations

    NASA Technical Reports Server (NTRS)

    Shebalin, John V.

    1987-01-01

    The Boussinesq approximation is extended so as to explicitly account for the transfer of fluid energy through viscous action into thermal energy. Ideal and dissipative integral invariants are discussed, in addition to the general equations for thermal-fluid motion.

  20. A Time Dependent Transport Equation Solver

    DTIC Science & Technology

    1991-05-01

    Using TWIGL Mesh Spacing ............. 63 11 Initial FEMP2D Flux Using 2X TWIGL Mesh Spacing ........ .. 64 12 Time Dependent Thermal Absorption...energy group, and g = G is the lowest ( thermal ) energy group. ?oo(r, E, t) the coefficient in the P approximation that phys- ically r’iDresents the total...than these MrPs. This suggest that the thermal flux calculations could be suspect. Indeed, both the FEMP2D and FMP2DT calculations showed that the

  1. Evaluation of pier-scour equations for coarse-bed streams

    USGS Publications Warehouse

    Chase, Katherine J.; Holnbeck, Stephen R.

    2004-01-01

    Streambed scour at bridge piers is among the leading causes of bridge failure in the United States. Several pier-scour equations have been developed to calculate potential scour depths at existing and proposed bridges. Because many pier-scour equations are based on data from laboratory flumes and from cohesionless silt- and sand-bottomed streams, they tend to overestimate scour for piers in coarse-bed materials. Several equations have been developed to incorporate the mitigating effects of large particle sizes on pier scour, but further investigations are needed to evaluate how accurately pier-scour depths calculated by these equations match measured field data. This report, prepared in cooperation with the Montana Department of Transportation, describes the evaluation of five pier-scour equations for coarse-bed streams. Pier-scour and associated bridge-geometry, bed-material, and streamflow-measurement data at bridges over coarse-bed streams in Montana, Alaska, Maryland, Ohio, and Virginia were selected from the Bridge Scour Data Management System. Pier scour calculated using the Simplified Chinese equation, the Froehlich equation, the Froehlich design equation, the HEC-18/Jones equation and the HEC-18/Mueller equation for flood events with approximate recurrence intervals of less than 2 to 100 years were compared to 42 pier-scour measurements. Comparison of results showed that pier-scour depths calculated with the HEC-18/Mueller equation were seldom smaller than measured pier-scour depths. In addition, pier-scour depths calculated using the HEC-18/Mueller equation were closer to measured scour than for the other equations that did not underestimate pier scour. However, more data are needed from coarse-bed streams and from less frequent flood events to further evaluate pier-scour equations.

  2. A semi-discrete finite element method for a class of time-fractional diffusion equations.

    PubMed

    Sun, HongGuang; Chen, Wen; Sze, K Y

    2013-05-13

    As fractional diffusion equations can describe the early breakthrough and the heavy-tail decay features observed in anomalous transport of contaminants in groundwater and porous soil, they have been commonly used in the related mathematical descriptions. These models usually involve long-time-range computation, which is a critical obstacle for their application; improvement of computational efficiency is of great significance. In this paper, a semi-discrete method is presented for solving a class of time-fractional diffusion equations that overcome the critical long-time-range computation problem. In the procedure, the spatial domain is discretized by the finite element method, which reduces the fractional diffusion equations to approximate fractional relaxation equations. As analytical solutions exist for the latter equations, the burden arising from long-time-range computation can effectively be minimized. To illustrate its efficiency and simplicity, four examples are presented. In addition, the method is used to solve the time-fractional advection-diffusion equation characterizing the bromide transport process in a fractured granite aquifer. The prediction closely agrees with the experimental data, and the heavy-tail decay of the anomalous transport process is well represented.

  3. Taxis equations for amoeboid cells.

    PubMed

    Erban, Radek; Othmer, Hans G

    2007-06-01

    The classical macroscopic chemotaxis equations have previously been derived from an individual-based description of the tactic response of cells that use a "run-and-tumble" strategy in response to environmental cues [17,18]. Here we derive macroscopic equations for the more complex type of behavioral response characteristic of crawling cells, which detect a signal, extract directional information from a scalar concentration field, and change their motile behavior accordingly. We present several models of increasing complexity for which the derivation of population-level equations is possible, and we show how experimentally measured statistics can be obtained from the transport equation formalism. We also show that amoeboid cells that do not adapt to constant signals can still aggregate in steady gradients, but not in response to periodic waves. This is in contrast to the case of cells that use a "run-and-tumble" strategy, where adaptation is essential.

  4. Stability analysis of ecomorphodynamic equations

    NASA Astrophysics Data System (ADS)

    Bärenbold, F.; Crouzy, B.; Perona, P.

    2016-02-01

    In order to shed light on the influence of riverbed vegetation on river morphodynamics, we perform a linear stability analysis on a minimal model of vegetation dynamics coupled with classical one- and two-dimensional Saint-Venant-Exner equations of morphodynamics. Vegetation is modeled as a density field of rigid, nonsubmerged cylinders and affects flow via a roughness change. Furthermore, vegetation is assumed to develop following a logistic dependence and may be uprooted by flow. First, we perform the stability analysis of the reduced one-dimensional framework. As a result of the competitive interaction between vegetation growth and removal through uprooting, we find a domain in the parameter space where originally straight rivers are unstable toward periodic longitudinal patterns. For realistic values of the sediment transport parameter, the dominant longitudinal wavelength is determined by the parameters of the vegetation model. Bed topography is found to adjust to the spatial pattern fixed by vegetation. Subsequently, the stability analysis is repeated for the two-dimensional framework, where the system may evolve toward alternate or multiple bars. On a fixed bed, we find instability toward alternate bars due to flow-vegetation interaction, but no multiple bars. Both alternate and multiple bars are present on a movable, vegetated bed. Finally, we find that the addition of vegetation to a previously unvegetated riverbed favors instability toward alternate bars and thus the development of a single course rather than braiding.

  5. Lattice Boltzmann method for the fractional advection-diffusion equation.

    PubMed

    Zhou, J G; Haygarth, P M; Withers, P J A; Macleod, C J A; Falloon, P D; Beven, K J; Ockenden, M C; Forber, K J; Hollaway, M J; Evans, R; Collins, A L; Hiscock, K M; Wearing, C; Kahana, R; Villamizar Velez, M L

    2016-04-01

    Mass transport, such as movement of phosphorus in soils and solutes in rivers, is a natural phenomenon and its study plays an important role in science and engineering. It is found that there are numerous practical diffusion phenomena that do not obey the classical advection-diffusion equation (ADE). Such diffusion is called abnormal or superdiffusion, and it is well described using a fractional advection-diffusion equation (FADE). The FADE finds a wide range of applications in various areas with great potential for studying complex mass transport in real hydrological systems. However, solution to the FADE is difficult, and the existing numerical methods are complicated and inefficient. In this study, a fresh lattice Boltzmann method is developed for solving the fractional advection-diffusion equation (LabFADE). The FADE is transformed into an equation similar to an advection-diffusion equation and solved using the lattice Boltzmann method. The LabFADE has all the advantages of the conventional lattice Boltzmann method and avoids a complex solution procedure, unlike other existing numerical methods. The method has been validated through simulations of several benchmark tests: a point-source diffusion, a boundary-value problem of steady diffusion, and an initial-boundary-value problem of unsteady diffusion with the coexistence of source and sink terms. In addition, by including the effects of the skewness β, the fractional order α, and the single relaxation time τ, the accuracy and convergence of the method have been assessed. The numerical predictions are compared with the analytical solutions, and they indicate that the method is second-order accurate. The method presented will allow the FADE to be more widely applied to complex mass transport problems in science and engineering.

  6. Lattice Boltzmann method for the fractional advection-diffusion equation

    NASA Astrophysics Data System (ADS)

    Zhou, J. G.; Haygarth, P. M.; Withers, P. J. A.; Macleod, C. J. A.; Falloon, P. D.; Beven, K. J.; Ockenden, M. C.; Forber, K. J.; Hollaway, M. J.; Evans, R.; Collins, A. L.; Hiscock, K. M.; Wearing, C.; Kahana, R.; Villamizar Velez, M. L.

    2016-04-01

    Mass transport, such as movement of phosphorus in soils and solutes in rivers, is a natural phenomenon and its study plays an important role in science and engineering. It is found that there are numerous practical diffusion phenomena that do not obey the classical advection-diffusion equation (ADE). Such diffusion is called abnormal or superdiffusion, and it is well described using a fractional advection-diffusion equation (FADE). The FADE finds a wide range of applications in various areas with great potential for studying complex mass transport in real hydrological systems. However, solution to the FADE is difficult, and the existing numerical methods are complicated and inefficient. In this study, a fresh lattice Boltzmann method is developed for solving the fractional advection-diffusion equation (LabFADE). The FADE is transformed into an equation similar to an advection-diffusion equation and solved using the lattice Boltzmann method. The LabFADE has all the advantages of the conventional lattice Boltzmann method and avoids a complex solution procedure, unlike other existing numerical methods. The method has been validated through simulations of several benchmark tests: a point-source diffusion, a boundary-value problem of steady diffusion, and an initial-boundary-value problem of unsteady diffusion with the coexistence of source and sink terms. In addition, by including the effects of the skewness β , the fractional order α , and the single relaxation time τ , the accuracy and convergence of the method have been assessed. The numerical predictions are compared with the analytical solutions, and they indicate that the method is second-order accurate. The method presented will allow the FADE to be more widely applied to complex mass transport problems in science and engineering.

  7. TH-E-BRE-01: A 3D Solver of Linear Boltzmann Transport Equation Based On a New Angular Discretization Method with Positivity for Photon Dose Calculation Benchmarked with Geant4

    SciTech Connect

    Hong, X; Gao, H

    2014-06-15

    Purpose: The Linear Boltzmann Transport Equation (LBTE) solved through statistical Monte Carlo (MC) method provides the accurate dose calculation in radiotherapy. This work is to investigate the alternative way for accurately solving LBTE using deterministic numerical method due to its possible advantage in computational speed from MC. Methods: Instead of using traditional spherical harmonics to approximate angular scattering kernel, our deterministic numerical method directly computes angular scattering weights, based on a new angular discretization method that utilizes linear finite element method on the local triangulation of unit angular sphere. As a Result, our angular discretization method has the unique advantage in positivity, i.e., to maintain all scattering weights nonnegative all the time, which is physically correct. Moreover, our method is local in angular space, and therefore handles the anisotropic scattering well, such as the forward-peaking scattering. To be compatible with image-guided radiotherapy, the spatial variables are discretized on the structured grid with the standard diamond scheme. After discretization, the improved sourceiteration method is utilized for solving the linear system without saving the linear system to memory. The accuracy of our 3D solver is validated using analytic solutions and benchmarked with Geant4, a popular MC solver. Results: The differences between Geant4 solutions and our solutions were less than 1.5% for various testing cases that mimic the practical cases. More details are available in the supporting document. Conclusion: We have developed a 3D LBTE solver based on a new angular discretization method that guarantees the positivity of scattering weights for physical correctness, and it has been benchmarked with Geant4 for photon dose calculation.

  8. Exact Averaging of Stochastic Equations for Flow in Porous Media

    SciTech Connect

    Karasaki, Kenzi; Shvidler, Mark; Karasaki, Kenzi

    2008-03-15

    It is well known that at present, exact averaging of the equations for flow and transport in random porous media have been proposed for limited special fields. Moreover, approximate averaging methods--for example, the convergence behavior and the accuracy of truncated perturbation series--are not well studied, and in addition, calculation of high-order perturbations is very complicated. These problems have for a long time stimulated attempts to find the answer to the question: Are there in existence some, exact, and sufficiently general forms of averaged equations? Here, we present an approach for finding the general exactly averaged system of basic equations for steady flow with sources in unbounded stochastically homogeneous fields. We do this by using (1) the existence and some general properties of Green's functions for the appropriate stochastic problem, and (2) some information about the random field of conductivity. This approach enables us to find the form of the averaged equations without directly solving the stochastic equations or using the usual assumption regarding any small parameters. In the common case of a stochastically homogeneous conductivity field we present the exactly averaged new basic nonlocal equation with a unique kernel-vector. We show that in the case of some type of global symmetry (isotropy, transversal isotropy, or orthotropy), we can for three-dimensional and two-dimensional flow in the same way derive the exact averaged nonlocal equations with a unique kernel-tensor. When global symmetry does not exist, the nonlocal equation with a kernel-tensor involves complications and leads to an ill-posed problem.

  9. Quantum transport through hierarchical structures.

    PubMed

    Boettcher, S; Varghese, C; Novotny, M A

    2011-04-01

    The transport of quantum electrons through hierarchical lattices is of interest because such lattices have some properties of both regular lattices and random systems. We calculate the electron transmission as a function of energy in the tight-binding approximation for two related Hanoi networks. HN3 is a Hanoi network with every site having three bonds. HN5 has additional bonds added to HN3 to make the average number of bonds per site equal to five. We present a renormalization group approach to solve the matrix equation involved in this quantum transport calculation. We observe band gaps in HN3, while no such band gaps are observed in linear networks or in HN5. We provide a detailed scaling analysis near the edges of these band gaps.

  10. Friedmann equation with quantum potential

    SciTech Connect

    Siong, Ch'ng Han; Radiman, Shahidan; Nikouravan, Bijan

    2013-11-27

    Friedmann equations are used to describe the evolution of the universe. Solving Friedmann equations for the scale factor indicates that the universe starts from an initial singularity where all the physical laws break down. However, the Friedmann equations are well describing the late-time or large scale universe. Hence now, many physicists try to find an alternative theory to avoid this initial singularity. In this paper, we generate a version of first Friedmann equation which is added with an additional term. This additional term contains the quantum potential energy which is believed to play an important role at small scale. However, it will gradually become negligible when the universe evolves to large scale.

  11. Effect of phosphorus additions on the sintering and transport properties of proton conducting BaZr{sub 0.85}Y{sub 0.15}O{sub 3-{delta}}

    SciTech Connect

    Soares, H.S.; Zhang, X.; Antunes, I.; Frade, J.R.; Mather, G.C.; Fagg, D.P.

    2012-07-15

    The influence of phosphorous additions on the sintering and electrical transport properties of the proton-conducting perovskite BaZr{sub 0.85}Y{sub 0.15}O{sub 3-{delta}} (BZY) has been studied with a view to the use of phosphates as typical dispersants for the formation of stabilised solid suspensions or as possible sintering aids. P{sub 2}O{sub 5} additions, (1-x)BZY{center_dot}xP{sub 2}O{sub 5}, monotonously promote densification in the intermediate compositional range 0.04{<=}x{<=}0.08. Nonetheless, BZY reacts with phosphorous forming the phase Ba{sub 3}(PO{sub 4}){sub 2} at temperatures as low as 600 Degree-Sign C. The associated loss of Ba from the perovskite, leads to a decrease in the perovskite lattice parameter, the formation of yttria-based impurity phases and impaired grain growth. Such reaction has an extremely detrimental effect on bulk and grain boundary conductivities. It is, therefore, vital that the current results are taken into account by the protonics community when attempting to prepare the stabilised solid suspensions of BZY nanopowders required for thin ceramic applications. Alternative dispersants to phosphate esters must be found. - Graphical Abstract: Sintering experiments performed at 1500 Degree-Sign C for 5 h and at 1400 Degree-Sign C for 24 h of (1-x)BaZr{sub 0.85}Y{sub 0.15}O{sub 3-{delta}}{center_dot}xP{sub 2}O{sub 5} in the range x=0-0.10. Highlights: Black-Right-Pointing-Pointer P{sub 2}O{sub 5} additions, (1-x)BZY{center_dot}xP{sub 2}O{sub 5}, promote densification in the intermediate compositional range 0.04{<=}x{<=}0.08. Black-Right-Pointing-Pointer BZY reacts with phosphorous forming the phase Ba{sub 3}(PO{sub 4}){sub 2} at temperatures as low as 600 Degree-Sign C. Black-Right-Pointing-Pointer Detrimental effects on bulk and grain boundary conductivities are shown. Black-Right-Pointing-Pointer Alternative dispersants to phosphate esters must be found.

  12. Hydrogen Sorption and Transport

    NASA Astrophysics Data System (ADS)

    McNeece, C. J.; Hesse, M. A.

    2015-12-01

    Hydrogen is unique among aqueous ions, both in its importance for geochemical reactions, and in its complex transport behavior through reactive media. The structure of hydrogen reaction fronts can be analyzed in the advective limit of the transport equation. At local chemical equilibrium, sorption of hydrogen onto the media surface (sorption isotherm) controls reaction front morphology. Transport modeling thus necessitates accurate knowledge of surface chemistry. Though motivated by transport, sorption models are often parameterized against batch titration experiments. The validity of these parameterizations, in a transport setting, are seldom tested. The analytic solution to the transport equation gives an algebraic relationship between concentration velocity and equilibrium sorption behavior. In this study, we conduct a suite of column flow experiments through quartz sand. Hydrogen concentration breakthrough curves at the column outlet are used to infer the "transport sorption isotherm." These results are compared to the batch titration derived sorption isotherm. We find excellent agreement between the datasets. Our findings suggest that, for aqueous hydrogen, local chemical equilibrium is a valid assumption. With the goal of a predictive transport model, we parameterize various sorption models against this dataset. Models which incorporate electrostatic effects at the surface predict transport well. Nonelectrostatic models such as the Kd, Langmuir, and Freundlich models fail. These results are particularly compelling as nonelectrostatic models are often employed to predict hydrogen transport in many reactive transport code.

  13. Diffusive and dynamical radiating stars with realistic equations of state

    NASA Astrophysics Data System (ADS)

    Brassel, Byron P.; Maharaj, Sunil D.; Goswami, Rituparno

    2017-03-01

    We model the dynamics of a spherically symmetric radiating dynamical star with three spacetime regions. The local internal atmosphere is a two-component system consisting of standard pressure-free, null radiation and an additional string fluid with energy density and nonzero pressure obeying all physically realistic energy conditions. The middle region is purely radiative which matches to a third region which is the Schwarzschild exterior. A large family of solutions to the field equations are presented for various realistic equations of state. We demonstrate that it is possible to obtain solutions via a direct integration of the second order equations resulting from the assumption of an equation of state. A comparison of our solutions with earlier well known results is undertaken and we show that all these solutions, including those of Husain, are contained in our family. We then generalise our class of solutions to higher dimensions. Finally we consider the effects of diffusive transport and transparently derive the specific equations of state for which this diffusive behaviour is possible.

  14. Modelling of solid polymer and direct methanol fuel cells: Phenomenological equations and analytical solutions

    NASA Astrophysics Data System (ADS)

    Kauranen, P. S.

    1993-04-01

    In the solid state concept of a direct methanol fuel cell (DMFC), methanol is directly oxidized at the anode of a solid polymer electrolyte fuel cell (SPEFC). Mathematical modelling of the transport and reaction phenomena within the electrodes and the electrolyte membrane is needed in order to get a closer insight into the operation of the fuel cell. In the work, macro-homogenous porous electrode and dilute solution theories are used to derive the phenomenological equations describing the transport and reaction mechanisms in a SPEFC single cell. The equations are first derived for a conventional H2/air SPEFC, and then extended for a DMFC. The basic model is derived in a one dimensional form in which it is assumed that species transport take place only in the direction crossing the cell sandwich. In addition, two dimensional descriptions of the catalyst layer are reviewed.

  15. An extended and total flux normalized correlation equation for predicting single-collector efficiency.

    PubMed

    Messina, Francesca; Marchisio, Daniele Luca; Sethi, Rajandrea

    2015-05-15

    In this study a novel total flux normalized correlation equation is proposed for predicting single-collector efficiency under a broad range of parameters. The correlation equation does not exploit the additivity approach introduced by Yao et al. (1971), but includes mixed terms that account for the mutual interaction of concomitant transport mechanisms (i.e., advection, gravity and Brownian motion) and of finite size of the particles (steric effect). The correlation equation is based on a combination of Eulerian and Lagrangian simulations performed, under Smoluchowski-Levich conditions, in a geometry which consists of a sphere enveloped by a cylindrical control volume. The normalization of the deposited flux is performed accounting for all of the particles entering into the control volume through all transport mechanisms (not just the upstream convective flux as conventionally done) to provide efficiency values lower than one over a wide range of parameters. In order to guarantee the independence of each term, the correlation equation is derived through a rigorous hierarchical parameter estimation process, accounting for single and mutual interacting transport mechanisms. The correlation equation, valid both for point and finite-size particles, is extended to include porosity dependency and it is compared with previous models. Reduced forms are proposed by elimination of the less relevant terms.

  16. Complex quantum Hamilton-Jacobi equation with Bohmian trajectories: application to the photodissociation dynamics of NOCl.

    PubMed

    Chou, Chia-Chun

    2014-03-14

    The complex quantum Hamilton-Jacobi equation-Bohmian trajectories (CQHJE-BT) method is introduced as a synthetic trajectory method for integrating the complex quantum Hamilton-Jacobi equation for the complex action function by propagating an ensemble of real-valued correlated Bohmian trajectories. Substituting the wave function expressed in exponential form in terms of the complex action into the time-dependent Schrödinger equation yields the complex quantum Hamilton-Jacobi equation. We transform this equation into the arbitrary Lagrangian-Eulerian version with the grid velocity matching the flow velocity of the probability fluid. The resulting equation describing the rate of change in the complex action transported along Bohmian trajectories is simultaneously integrated with the guidance equation for Bohmian trajectories, and the time-dependent wave function is readily synthesized. The spatial derivatives of the complex action required for the integration scheme are obtained by solving one moving least squares matrix equation. In addition, the method is applied to the photodissociation of NOCl. The photodissociation dynamics of NOCl can be accurately described by propagating a small ensemble of trajectories. This study demonstrates that the CQHJE-BT method combines the considerable advantages of both the real and the complex quantum trajectory methods previously developed for wave packet dynamics.

  17. Complex quantum Hamilton-Jacobi equation with Bohmian trajectories: Application to the photodissociation dynamics of NOCl

    SciTech Connect

    Chou, Chia-Chun

    2014-03-14

    The complex quantum Hamilton-Jacobi equation-Bohmian trajectories (CQHJE-BT) method is introduced as a synthetic trajectory method for integrating the complex quantum Hamilton-Jacobi equation for the complex action function by propagating an ensemble of real-valued correlated Bohmian trajectories. Substituting the wave function expressed in exponential form in terms of the complex action into the time-dependent Schrödinger equation yields the complex quantum Hamilton-Jacobi equation. We transform this equation into the arbitrary Lagrangian-Eulerian version with the grid velocity matching the flow velocity of the probability fluid. The resulting equation describing the rate of change in the complex action transported along Bohmian trajectories is simultaneously integrated with the guidance equation for Bohmian trajectories, and the time-dependent wave function is readily synthesized. The spatial derivatives of the complex action required for the integration scheme are obtained by solving one moving least squares matrix equation. In addition, the method is applied to the photodissociation of NOCl. The photodissociation dynamics of NOCl can be accurately described by propagating a small ensemble of trajectories. This study demonstrates that the CQHJE-BT method combines the considerable advantages of both the real and the complex quantum trajectory methods previously developed for wave packet dynamics.

  18. Basic lubrication equations

    NASA Technical Reports Server (NTRS)

    Hamrock, B. J.; Dowson, D.

    1981-01-01

    Lubricants, usually Newtonian fluids, are assumed to experience laminar flow. The basic equations used to describe the flow are the Navier-Stokes equation of motion. The study of hydrodynamic lubrication is, from a mathematical standpoint, the application of a reduced form of these Navier-Stokes equations in association with the continuity equation. The Reynolds equation can also be derived from first principles, provided of course that the same basic assumptions are adopted in each case. Both methods are used in deriving the Reynolds equation, and the assumptions inherent in reducing the Navier-Stokes equations are specified. Because the Reynolds equation contains viscosity and density terms and these properties depend on temperature and pressure, it is often necessary to couple the Reynolds with energy equation. The lubricant properties and the energy equation are presented. Film thickness, a parameter of the Reynolds equation, is a function of the elastic behavior of the bearing surface. The governing elasticity equation is therefore presented.

  19. Decision-Making, Science and Gasoline Additives

    NASA Astrophysics Data System (ADS)

    Weaver, J. W.; Small, M. C.

    2001-12-01

    Methyl-tert butyl ether (MTBE) has been used as a gasoline additive to serve two major purposes. The first use was as an octane-enhancer to replace organic lead, beginning in 1979. The second use, which began about 1992, was as a oxygenated additive to meet requirements of the Clean Air Act Amendments (CAAA) of 1990. Generally, the amount of MTBE used for octane enhancement was lower than that required to meet CAAA requirements. An unintended consequence of MTBE use has been widespread groundwater contamination. The decision to use certain amounts of MTBE or other chemcials as gasoline additives is the outcome of economic, regulatory, policy, political, and scientific considerations. Decision makers ask questions such as "How do ground water impacts change with changing MTBE content? How many wells would be impacted? and What are the associated costs?" These are best answered through scientific inquiry, but many different approaches could be developed. Decision criteria include time, money, comprehensiveness, and complexity of the approach. Because results must be communicated to a non-technical audience, there is a trade off between the complexity of the approach and the ability to convince economists, lawyers and policy makers that results make sense. The question on MTBE content posed above was investigated using transport models, a release scenario and gasoline composition. Because of the inability of transport models to predict future concentrations, an approach was chosen to base comparative assessment on a calibrated model. By taking this approach, "generic" modeling with arbitrarily selected parameters was avoided and the validity of the simulation results rests upon relatively small extrapolations from the original calibrated models. A set of simulations was performed that assumed 3% (octane enhancement) and 11% (CAAA) MTBE in gasoline. The results were that ground water concentrations would be reduced in proportion to the reduction of MTBE in the fuel

  20. Variational Derivation of Dissipative Equations

    NASA Astrophysics Data System (ADS)

    Sogo, Kiyoshi

    2017-03-01

    A new variational principle is formulated to derive various dissipative equations. Model equations considered are the damping equation, Bloch equation, diffusion equation, Fokker-Planck equation, Kramers equation and Smoluchowski equation. Each equation and its time reversal equation are simultaneously obtained in our variational principle.

  1. Iterative solution of the semiconductor device equations

    SciTech Connect

    Bova, S.W.; Carey, G.F.

    1996-12-31

    Most semiconductor device models can be described by a nonlinear Poisson equation for the electrostatic potential coupled to a system of convection-reaction-diffusion equations for the transport of charge and energy. These equations are typically solved in a decoupled fashion and e.g. Newton`s method is used to obtain the resulting sequences of linear systems. The Poisson problem leads to a symmetric, positive definite system which we solve iteratively using conjugate gradient. The transport equations lead to nonsymmetric, indefinite systems, thereby complicating the selection of an appropriate iterative method. Moreover, their solutions exhibit steep layers and are subject to numerical oscillations and instabilities if standard Galerkin-type discretization strategies are used. In the present study, we use an upwind finite element technique for the transport equations. We also evaluate the performance of different iterative methods for the transport equations and investigate various preconditioners for a few generalized gradient methods. Numerical examples are given for a representative two-dimensional depletion MOSFET.

  2. Thermoelectric transport in nanoscale materials

    NASA Astrophysics Data System (ADS)

    Small, Joshua P.

    Measurements of thermoelectric transport coefficients yield important information regarding fundamental properties of a system in addition to the information supplied from the electronic transport measurements. In this thesis we re port gate dependent and temperature dependent conductance ( G) and thermo-electric power (TEP) measurements made in three different basic nanomaterials: single-walled nanotubes (SWNTs), multi-walled nanotubes (MWNTs), and silicon nanowires (SiNWs). There are two means of generating a thermoelectric voltage: carrier diffusion and phonon drag. Gate dependent measurements of metallic SWNTs verified the use of the mesoscopic Mott formula, the equation governing diffusive thermoelectric voltage, used to relate TEP with the conductance. We find phonon drag negligible in graphene based systems. In the semi-conducting SWNT we observed high valued and variable TEP. In addition, the TEP behaves according to a simple Schottky barrier (SB) controlled transport model where transport takes place by quantum mechanical tunneling through the barrier, or thermal activation over it, depending on the value of the gate electric field. We also observe saw-tooth oscillations of the TEP in weakly contacted SWNTs at temperatures below the charging energy, indicative of Coulomb blockade transport. Importantly, we made quantitative measurements of the TEP oscillation amplitude, agreeing well with theory. In the MWNT, the Mott formula describes well the TEP within a framework of multiple parallel channels. We observe TEP weighting in this parallel system. In conjunction with conductance measurements, by probing the TEP in SWNTs we are able to extract the number of shells participating in electrical transport. These results agree well with figures obtained independently in controlled breakdown experiments, and the temperature dependent results may prove useful for investigation of the intershell interaction energy. We also investigate TEP in the SiNW, where TEP

  3. Turbulent kinetic energy equation and free mixing

    NASA Technical Reports Server (NTRS)

    Morel, T.; Torda, T. P.; Bradshaw, P.

    1973-01-01

    Calculation of free shear flows was carried out to investigate the usefulness of several concepts which were previously successfully applied to wall flows. The method belongs to the class of differential approaches. The turbulence is taken into account by the introduction of one additional partial differential equation, the transport equation for the turbulent shear stress. The structure of turbulence is modeled after Bradshaw et al. This model was used successfully in boundary layers and its applicability to other flows is demonstrated. The work reported differs substantially from that of an earlier attempt to use this approach for calculation of free flows. The most important difference is that the region around the center line is treated by invoking the interaction hypothesis (concerning the structure of turbulence in the regions separated by the velocity extrema). The compressibility effects on shear layer spreading at low and moderate Mach numbers were investigated. In the absence of detailed experiments in free flows, the evidence from boundary layers that at low Mach numbers the structure of turbulence is unaffected by the compressibility was relied on. The present model was tested over a range of self-preserving and developing flows including pressure gradients using identical empirical input. The dependence of the structure of turbulence on the spreading rate of the shear layer was established.

  4. VIRUS TRANSPORT IN PHYSICALLY AND GEOCHEMICALLY HETEROGENEOUS SUBSURFACE POROUS MEDIA. (R826179)

    EPA Science Inventory

    A two-dimensional model for virus transport in physically and geochemically heterogeneous subsurface porous media is presented. The model involves solution of the advection–dispersion equation, which additionally considers virus inactivation in the solution, as well as ...

  5. Structural equation models of VMT growth in US urbanised areas.

    USGS Publications Warehouse

    Ewing, Reid; Hamidi, Shima; Gallivan, Frank; Nelson, Arthur C.; Grace, James B.

    2014-01-01

    Vehicle miles travelled (VMT) is a primary performance indicator for land use and transportation, bringing with it both positive and negative externalities. This study updates and refines previous work on VMT in urbanised areas, using recent data, additional metrics and structural equation modelling (SEM). In a cross-sectional model for 2010, population, income and freeway capacity are positively related to VMT, while gasoline prices, development density and transit service levels are negatively related. Findings of the cross-sectional model are generally confirmed in a more tightly controlled longitudinal study of changes in VMT between 2000 and 2010, the first model of its kind. The cross-sectional and longitudinal models together, plus the transportation literature generally, give us a basis for generalising across studies to arrive at elasticity values of VMT with respect to different urban variables.

  6. Chemical Equation Balancing.

    ERIC Educational Resources Information Center

    Blakley, G. R.

    1982-01-01

    Reviews mathematical techniques for solving systems of homogeneous linear equations and demonstrates that the algebraic method of balancing chemical equations is a matter of solving a system of homogeneous linear equations. FORTRAN programs using this matrix method to chemical equation balancing are available from the author. (JN)

  7. Finite scale equations for compressible fluid flow

    SciTech Connect

    Margolin, Len G

    2008-01-01

    Finite-scale equations (FSE) describe the evolution of finite volumes of fluid over time. We discuss the FSE for a one-dimensional compressible fluid, whose every point is governed by the Navier-Stokes equations. The FSE contain new momentum and internal energy transport terms. These are similar to terms added in numerical simulation for high-speed flows (e.g. artificial viscosity) and for turbulent flows (e.g. subgrid scale models). These similarities suggest that the FSE may provide new insight as a basis for computational fluid dynamics. Our analysis of the FS continuity equation leads to a physical interpretation of the new transport terms, and indicates the need to carefully distinguish between volume-averaged and mass-averaged velocities in numerical simulation. We make preliminary connections to the other recent work reformulating Navier-Stokes equations.

  8. Non-Fickian mass transport in fractured porous media

    NASA Astrophysics Data System (ADS)

    Fomin, Sergei A.; Chugunov, Vladimir A.; Hashida, Toshiyuki

    2011-02-01

    The paper provides an introduction to fundamental concepts of mathematical modeling of mass transport in fractured porous heterogeneous rocks. Keeping aside many important factors that can affect mass transport in subsurface, our main concern is the multi-scale character of the rock formation, which is constituted by porous domains dissected by the network of fractures. Taking into account the well-documented fact that porous rocks can be considered as a fractal medium and assuming that sizes of pores vary significantly (i.e. have different characteristic scales), the fractional-order differential equations that model the anomalous diffusive mass transport in such type of domains are derived and justified analytically. Analytical solutions of some particular problems of anomalous diffusion in the fractal media of various geometries are obtained. Extending this approach to more complex situation when diffusion is accompanied by advection, solute transport in a fractured porous medium is modeled by the advection-dispersion equation with fractional time derivative. In the case of confined fractured porous aquifer, accounting for anomalous non-Fickian diffusion in the surrounding rock mass, the adopted approach leads to introduction of an additional fractional time derivative in the equation for solute transport. The closed-form solutions for concentrations in the aquifer and surrounding rocks are obtained for the arbitrary time-dependent source of contamination located in the inlet of the aquifer. Based on these solutions, different regimes of contamination of the aquifers with different physical properties can be readily modeled and analyzed.

  9. The transepithelial transport mechanism of polybrominated diphenyl ethers in human intestine determined using a Caco-2 cell monolayer.

    PubMed

    Yu, Yingxin; Wang, Mengmeng; Zhang, Kaiqiong; Yang, Dan; Zhong, Yufang; An, Jing; Lei, Bingli; Zhang, Xinyu

    2017-04-01

    Oral ingestion plays an important role in human exposure to polybrominated diphenyl ethers (PBDEs). The uptake of PBDEs primarily occurs in the small intestine. The aim of the present study is to investigate the transepithelial transport characteristics and mechanisms of PBDEs in the small intestine using a Caco-2 cell monolayer model. The apparent permeability coefficients of PBDEs indicated that tri- to hepta-BDEs were poorly absorbed compounds. A linear increase in transepithelial transport was observed with various concentrations of PBDEs, which suggested that passive diffusion dominated their transport at the concentration range tested. In addition, the pseudo-first-order kinetics equation can be applied to the transepithelial transport of PBDEs. The rate-determining step in transepithelial transport of PBDEs was trans-cell transport including the trans-pore process. The significantly lower transepithelial transport rates at low temperature for bidirectional transepithelial transport suggested that an energy-dependent transport mechanism was involved. The efflux transporters (P-glycoprotein, multidrug resistance-associated protein, and breast cancer resistance protein) and influx transporters (organic cation transporters) participated in the transepithelial transport of PBDEs. In addition, the transepithelial transport of PBDEs was pH sensitive; however, more information is required to understand the influence of pH.

  10. One-Dimensional Transport with Inflow and Storage (OTIS): A Solute Transport Model for Streams and Rivers

    USGS Publications Warehouse

    Runkel, Robert L.

    1998-01-01

    OTIS is a mathematical simulation model used to characterize the fate and transport of water-borne solutes in streams and rivers. The governing equation underlying the model is the advection-dispersion equation with additional terms to account for transient storage, lateral inflow, first-order decay, and sorption. This equation and the associated equations describing transient storage and sorption are solved using a Crank-Nicolson finite-difference solution. OTIS may be used in conjunction with data from field-scale tracer experiments to quantify the hydrologic parameters affecting solute transport. This application typically involves a trial-and-error approach wherein parameter estimates are adjusted to obtain an acceptable match between simulated and observed tracer concentrations. Additional applications include analyses of nonconservative solutes that are subject to sorption processes or first-order decay. OTIS-P, a modified version of OTIS, couples the solution of the governing equation with a nonlinear regression package. OTIS-P determines an optimal set of parameter estimates that minimize the squared differences between the simulated and observed concentrations, thereby automating the parameter estimation process. This report details the development and application of OTIS and OTIS-P. Sections of the report describe model theory, input/output specifications, sample applications, and installation instructions.

  11. Hypersonic three-dimensional nonequilibrium boundary-layer equations in generalized curvilinear coordinates

    NASA Technical Reports Server (NTRS)

    Lee, Jong-Hun

    1993-01-01

    The basic governing equations for the second-order three-dimensional hypersonic thermal and chemical nonequilibrium boundary layer are derived by means of an order-of-magnitude analysis. A two-temperature concept is implemented into the system of boundary-layer equations by simplifying the rather complicated general three-temperature thermal gas model. The equations are written in a surface-oriented non-orthogonal curvilinear coordinate system, where two curvilinear coordinates are non-orthogonial and a third coordinate is normal to the surface. The equations are described with minimum use of tensor expressions arising from the coordinate transformation, to avoid unnecessary confusion for readers. The set of equations obtained will be suitable for the development of a three-dimensional nonequilibrium boundary-layer code. Such a code could be used to determine economically the aerodynamic/aerothermodynamic loads to the surfaces of hypersonic vehicles with general configurations. In addition, the basic equations for three-dimensional stagnation flow, of which solution is required as an initial value for space-marching integration of the boundary-layer equations, are given along with the boundary conditions, the boundary-layer parameters, and the inner-outer layer matching procedure. Expressions for the chemical reaction rates and the thermodynamic and transport properties in the thermal nonequilibrium environment are explicitly given.

  12. Cable equation for general geometry.

    PubMed

    López-Sánchez, Erick J; Romero, Juan M

    2017-02-01

    The cable equation describes the voltage in a straight cylindrical cable, and this model has been employed to model electrical potential in dendrites and axons. However, sometimes this equation might give incorrect predictions for some realistic geometries, in particular when the radius of the cable changes significantly. Cables with a nonconstant radius are important for some phenomena, for example, discrete swellings along the axons appear in neurodegenerative diseases such as Alzheimers, Parkinsons, human immunodeficiency virus associated dementia, and multiple sclerosis. In this paper, using the Frenet-Serret frame, we propose a generalized cable equation for a general cable geometry. This generalized equation depends on geometric quantities such as the curvature and torsion of the cable. We show that when the cable has a constant circular cross section, the first fundamental form of the cable can be simplified and the generalized cable equation depends on neither the curvature nor the torsion of the cable. Additionally, we find an exact solution for an ideal cable which has a particular variable circular cross section and zero curvature. For this case we show that when the cross section of the cable increases the voltage decreases. Inspired by this ideal case, we rewrite the generalized cable equation as a diffusion equation with a source term generated by the cable geometry. This source term depends on the cable cross-sectional area and its derivates. In addition, we study different cables with swelling and provide their numerical solutions. The numerical solutions show that when the cross section of the cable has abrupt changes, its voltage is smaller than the voltage in the cylindrical cable. Furthermore, these numerical solutions show that the voltage can be affected by geometrical inhomogeneities on the cable.

  13. Cable equation for general geometry

    NASA Astrophysics Data System (ADS)

    López-Sánchez, Erick J.; Romero, Juan M.

    2017-02-01

    The cable equation describes the voltage in a straight cylindrical cable, and this model has been employed to model electrical potential in dendrites and axons. However, sometimes this equation might give incorrect predictions for some realistic geometries, in particular when the radius of the cable changes significantly. Cables with a nonconstant radius are important for some phenomena, for example, discrete swellings along the axons appear in neurodegenerative diseases such as Alzheimers, Parkinsons, human immunodeficiency virus associated dementia, and multiple sclerosis. In this paper, using the Frenet-Serret frame, we propose a generalized cable equation for a general cable geometry. This generalized equation depends on geometric quantities such as the curvature and torsion of the cable. We show that when the cable has a constant circular cross section, the first fundamental form of the cable can be simplified and the generalized cable equation depends on neither the curvature nor the torsion of the cable. Additionally, we find an exact solution for an ideal cable which has a particular variable circular cross section and zero curvature. For this case we show that when the cross section of the cable increases the voltage decreases. Inspired by this ideal case, we rewrite the generalized cable equation as a diffusion equation with a source term generated by the cable geometry. This source term depends on the cable cross-sectional area and its derivates. In addition, we study different cables with swelling and provide their numerical solutions. The numerical solutions show that when the cross section of the cable has abrupt changes, its voltage is smaller than the voltage in the cylindrical cable. Furthermore, these numerical solutions show that the voltage can be affected by geometrical inhomogeneities on the cable.

  14. Bending equation for a quasianisotropic plate

    NASA Astrophysics Data System (ADS)

    Shachnev, V. A.

    2010-10-01

    In the framework of the linear theory of elasticity, an exact bending equation is obtained for the median plane of a plate whose material is a monoclinic system with the axis of symmetry perpendicular to the plate plane. As an example, the equation of the median plane of an isotropic plate is considered; the operator of this equation coincides with the operator of Sophie Germain's approximate equation. As the plate thickness tends to zero, the right-hand side of the equation is asymptotically equivalent to the right-hand side of the approximate equation. In addition, equations relating the median plane transverse stresses and the total stresses in the plate boundary planes to the median plane deflexions are obtained.

  15. Nonlinear gyrokinetic equations for tokamak microturbulence

    SciTech Connect

    Hahm, T.S.

    1988-05-01

    A nonlinear electrostatic gyrokinetic Vlasov equation, as well as Poisson equation, has been derived in a form suitable for particle simulation studies of tokamak microturbulence and associated anomalous transport. This work differs from the existing nonlinear gyrokinetic theories in toroidal geometry, since the present equations conserve energy while retaining the crucial linear and nonlinear polarization physics. In the derivation, the action-variational Lie perturbation method is utilized in order to preserve the Hamiltonian structure of the original Vlasov-Poisson system. Emphasis is placed on the dominant physics of the collective fluctuations in toroidal geometry, rather than on details of particle orbits. 13 refs.

  16. On Coupled Rate Equations with Quadratic Nonlinearities

    PubMed Central

    Montroll, Elliott W.

    1972-01-01

    Rate equations with quadratic nonlinearities appear in many fields, such as chemical kinetics, population dynamics, transport theory, hydrodynamics, etc. Such equations, which may arise from basic principles or which may be phenomenological, are generally solved by linearization and application of perturbation theory. Here, a somewhat different strategy is emphasized. Alternative nonlinear models that can be solved exactly and whose solutions have the qualitative character expected from the original equations are first searched for. Then, the original equations are treated as perturbations of those of the solvable model. Hence, the function of the perturbation theory is to improve numerical accuracy of solutions, rather than to furnish the basic qualitative behavior of the solutions of the equations. PMID:16592013

  17. Turbulence kinetic energy equation for dilute suspensions

    NASA Technical Reports Server (NTRS)

    Abou-Arab, T. W.; Roco, M. C.

    1989-01-01

    A multiphase turbulence closure model is presented which employs one transport equation, namely the turbulence kinetic energy equation. The proposed form of this equation is different from the earlier formulations in some aspects. The power spectrum of the carrier fluid is divided into two regions, which interact in different ways and at different rates with the suspended particles as a function of the particle-eddy size ratio and density ratio. The length scale is described algebraically. A mass/time averaging procedure for the momentum and kinetic energy equations is adopted. The resulting turbulence correlations are modeled under less retrictive assumptions comparative to previous work. The closures for the momentum and kinetic energy equations are given. Comparisons of the predictions with experimental results on liquid-solid jet and gas-solid pipe flow show satisfactory agreement.

  18. Single wall penetration equations

    NASA Technical Reports Server (NTRS)

    Hayashida, K. B.; Robinson, J. H.

    1991-01-01

    Five single plate penetration equations are compared for accuracy and effectiveness. These five equations are two well-known equations (Fish-Summers and Schmidt-Holsapple), two equations developed by the Apollo project (Rockwell and Johnson Space Center (JSC), and one recently revised from JSC (Cour-Palais). They were derived from test results, with velocities ranging up to 8 km/s. Microsoft Excel software was used to construct a spreadsheet to calculate the diameters and masses of projectiles for various velocities, varying the material properties of both projectile and target for the five single plate penetration equations. The results were plotted on diameter versus velocity graphs for ballistic and spallation limits using Cricket Graph software, for velocities ranging from 2 to 15 km/s defined for the orbital debris. First, these equations were compared to each other, then each equation was compared with various aluminum projectile densities. Finally, these equations were compared with test results performed at JSC for the Marshall Space Flight Center. These equations predict a wide variety of projectile diameters at a given velocity. Thus, it is very difficult to choose the 'right' prediction equation. The thickness of a single plate could have a large variation by choosing a different penetration equation. Even though all five equations are empirically developed with various materials, especially for aluminum alloys, one cannot be confident in the shield design with the predictions obtained by the penetration equations without verifying by tests.

  19. Numerical optimization using flow equations.

    PubMed

    Punk, Matthias

    2014-12-01

    We develop a method for multidimensional optimization using flow equations. This method is based on homotopy continuation in combination with a maximum entropy approach. Extrema of the optimizing functional correspond to fixed points of the flow equation. While ideas based on Bayesian inference such as the maximum entropy method always depend on a prior probability, the additional step in our approach is to perform a continuous update of the prior during the homotopy flow. The prior probability thus enters the flow equation only as an initial condition. We demonstrate the applicability of this optimization method for two paradigmatic problems in theoretical condensed matter physics: numerical analytic continuation from imaginary to real frequencies and finding (variational) ground states of frustrated (quantum) Ising models with random or long-range antiferromagnetic interactions.

  20. Numerical optimization using flow equations

    NASA Astrophysics Data System (ADS)

    Punk, Matthias

    2014-12-01

    We develop a method for multidimensional optimization using flow equations. This method is based on homotopy continuation in combination with a maximum entropy approach. Extrema of the optimizing functional correspond to fixed points of the flow equation. While ideas based on Bayesian inference such as the maximum entropy method always depend on a prior probability, the additional step in our approach is to perform a continuous update of the prior during the homotopy flow. The prior probability thus enters the flow equation only as an initial condition. We demonstrate the applicability of this optimization method for two paradigmatic problems in theoretical condensed matter physics: numerical analytic continuation from imaginary to real frequencies and finding (variational) ground states of frustrated (quantum) Ising models with random or long-range antiferromagnetic interactions.

  1. Reflections on Chemical Equations.

    ERIC Educational Resources Information Center

    Gorman, Mel

    1981-01-01

    The issue of how much emphasis balancing chemical equations should have in an introductory chemistry course is discussed. The current heavy emphasis on finishing such equations is viewed as misplaced. (MP)

  2. Classical Boltzmann equation and high-temperature QED

    NASA Astrophysics Data System (ADS)

    Brandt, F. T.; Ferreira, R. B.; Thuorst, J. F.

    2015-02-01

    The equivalence between thermal field theory and the Boltzmann transport equation is investigated at higher orders in the context of quantum electrodynamics. We compare the contributions obtained from the collisionless transport equation with the high temperature limit of the one-loop thermal Green's function. Our approach employs the representation of the thermal Green's functions in terms of forward scattering amplitudes. The general structure of these amplitudes clearly indicates that the physics described by the leading high temperature limit of quantum electrodynamics can be obtained from the Boltzman transport equation. We also present some explicit examples of this interesting equivalence.

  3. Parametrically defined differential equations

    NASA Astrophysics Data System (ADS)

    Polyanin, A. D.; Zhurov, A. I.

    2017-01-01

    The paper deals with nonlinear ordinary differential equations defined parametrically by two relations. It proposes techniques to reduce such equations, of the first or second order, to standard systems of ordinary differential equations. It obtains the general solution to some classes of nonlinear parametrically defined ODEs dependent on arbitrary functions. It outlines procedures for the numerical solution of the Cauchy problem for parametrically defined differential equations.

  4. Morphogen transport in epithelia

    NASA Astrophysics Data System (ADS)

    Bollenbach, T.; Kruse, K.; Pantazis, P.; González-Gaitán, M.; Jülicher, F.

    2007-01-01

    We present a general theoretical framework to discuss mechanisms of morphogen transport and gradient formation in a cell layer. Trafficking events on the cellular scale lead to transport on larger scales. We discuss in particular the case of transcytosis where morphogens undergo repeated rounds of internalization into cells and recycling. Based on a description on the cellular scale, we derive effective nonlinear transport equations in one and two dimensions which are valid on larger scales. We derive analytic expressions for the concentration dependence of the effective diffusion coefficient and the effective degradation rate. We discuss the effects of a directional bias on morphogen transport and those of the coupling of the morphogen and receptor kinetics. Furthermore, we discuss general properties of cellular transport processes such as the robustness of gradients and relate our results to recent experiments on the morphogen Decapentaplegic (Dpp) that acts in the wing disk of the fruit fly Drosophila.

  5. The Pendulum Equation

    ERIC Educational Resources Information Center

    Fay, Temple H.

    2002-01-01

    We investigate the pendulum equation [theta] + [lambda][squared] sin [theta] = 0 and two approximations for it. On the one hand, we suggest that the third and fifth-order Taylor series approximations for sin [theta] do not yield very good differential equations to approximate the solution of the pendulum equation unless the initial conditions are…

  6. Renormalization of tracer turbulence leading to fractional differential equations.

    PubMed

    Sánchez, R; Carreras, B A; Newman, D E; Lynch, V E; van Milligen, B Ph

    2006-07-01

    For many years quasilinear renormalization has been applied to numerous problems in turbulent transport. This scheme relies on the localization hypothesis to derive a linear transport equation from a simplified stochastic description of the underlying microscopic dynamics. However, use of the localization hypothesis narrows the range of transport behaviors that can be captured by the renormalized equations. In this paper, we construct a renormalization procedure that manages to avoid the localization hypothesis completely and produces renormalized transport equations, expressed in terms of fractional differential operators, that exhibit much more of the transport phenomenology observed in nature. This technique provides a first step toward establishing a rigorous link between the microscopic physics of turbulence and the fractional transport models proposed phenomenologically for a wide variety of turbulent systems such as neutral fluids or plasmas.

  7. 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.

  8. Vibrational energy flow in the villin headpiece subdomain: Master equation simulations

    SciTech Connect

    Leitner, David M. E-mail: stock@physik.uni-freiburg.de; Buchenberg, Sebastian; Brettel, Paul; Stock, Gerhard E-mail: stock@physik.uni-freiburg.de

    2015-02-21

    We examine vibrational energy flow in dehydrated and hydrated villin headpiece subdomain HP36 by master equation simulations. Transition rates used in the simulations are obtained from communication maps calculated for HP36. In addition to energy flow along the main chain, we identify pathways for energy transport in HP36 via hydrogen bonding between residues quite far in sequence space. The results of the master equation simulations compare well with all-atom non-equilibrium simulations to about 1 ps following initial excitation of the protein, and quite well at long times, though for some residues we observe deviations between the master equation and all-atom simulations at intermediate times from about 1–10 ps. Those deviations are less noticeable for hydrated than dehydrated HP36 due to energy flow into the water.

  9. Transportation and public health.

    PubMed

    Litman, Todd

    2013-01-01

    This article investigates various ways that transportation policy and planning decisions affect public health and better ways to incorporate public health objectives into transport planning. Conventional planning tends to consider some public health impacts, such as crash risk and pollution emissions measured per vehicle-kilometer, but generally ignores health problems resulting from less active transport (reduced walking and cycling activity) and the additional crashes and pollution caused by increased vehicle mileage. As a result, transport agencies tend to undervalue strategies that increase transport system diversity and reduce vehicle travel. This article identifies various win-win strategies that can help improve public health and other planning objectives.

  10. Iterative solvers for Navier-Stokes equations: Experiments with turbulence model

    SciTech Connect

    Page, M.; Garon, A.

    1994-12-31

    In the framework of developing software for the prediction of flows in hydraulic turbine components, Reynolds averaged Navier-Stokes equations coupled with {kappa}-{omega} two-equation turbulence model are discretized by finite element method. Since the resulting matrices are large, sparse and nonsymmetric, strategies based on CG-type iterative methods must be devised. A segregated solution strategy decouples the momentum equation, the {kappa} transport equation and the {omega} transport equation. These sets of equations must be solved while satisfying constraint equations. Experiments with orthogonal projection method are presented for the imposition of essential boundary conditions in a weak sense.

  11. BRIEF REPORT: The colour relaxation equation

    NASA Astrophysics Data System (ADS)

    Xiaofei, Zhang; Jiarong, Li

    1996-03-01

    Colour diffusion in quark - gluon plasma (QGP) is investigated from the transport equations of QGP. The pure non-Abelian collision term describing the colour diffusion in QGP is obtained, the expression for colour relaxation time is derived and the physical picture of the colour diffusion in QGP is shown.

  12. 14 CFR 29.927 - Additional tests.

    Code of Federal Regulations, 2014 CFR

    2014-01-01

    ... 14 Aeronautics and Space 1 2014-01-01 2014-01-01 false Additional tests. 29.927 Section 29.927... STANDARDS: TRANSPORT CATEGORY ROTORCRAFT Powerplant Rotor Drive System § 29.927 Additional tests. (a) Any additional dynamic, endurance, and operational tests, and vibratory investigations necessary to...

  13. 14 CFR 29.927 - Additional tests.

    Code of Federal Regulations, 2010 CFR

    2010-01-01

    ... 14 Aeronautics and Space 1 2010-01-01 2010-01-01 false Additional tests. 29.927 Section 29.927... STANDARDS: TRANSPORT CATEGORY ROTORCRAFT Powerplant Rotor Drive System § 29.927 Additional tests. (a) Any additional dynamic, endurance, and operational tests, and vibratory investigations necessary to...

  14. 14 CFR 29.927 - Additional tests.

    Code of Federal Regulations, 2013 CFR

    2013-01-01

    ... 14 Aeronautics and Space 1 2013-01-01 2013-01-01 false Additional tests. 29.927 Section 29.927... STANDARDS: TRANSPORT CATEGORY ROTORCRAFT Powerplant Rotor Drive System § 29.927 Additional tests. (a) Any additional dynamic, endurance, and operational tests, and vibratory investigations necessary to...

  15. A few remarks on ordinary differential equations

    SciTech Connect

    Desjardins, B.

    1996-12-31

    We present in this note existence and uniqueness results for solutions of ordinary differential equations and linear transport equations with discontinuous coefficients in a bounded open subset {Omega} of R{sup N} or in the whole space R{sup N} (N {ge} 1). R.J. Di Perna and P.L. Lions studied the case of vector fields b with coefficients in Sobolev spaces and bounded divergence. We want to show that similar results hold for more general b: we assume in the bounded autonomous case that b belongs to W{sup 1,1}({Omega}), b.n = 0 on {partial_derivative}{Omega}, and that there exists T{sub o} > O such that exp(T{sub o}{vert_bar}div b{vert_bar}) {element_of} L{sup 1}({Omega}). Furthermore, we establish results on transport equations with initial values in L{sup p} spaces (p > 1). 9 refs.

  16. Correlation Equation for Predicting the Single-Collector Contact Efficiency of Colloids in a Horizontal Flow.

    PubMed

    Li, Jing; Xie, Xiaohu; Ghoshal, Subhasis

    2015-07-07

    The single-collector contact efficiency (η0) for physicochemical colloid filtration under horizontal flow in saturated porous media was calculated using trajectory analysis in three dimensions. Past studies have developed correlation equations for colloids with densities close to that of water, such as bacteria and latex particles. A new correlation equation was developed for predicting η0 based on a large number of trajectory simulations to account for higher-density particles representative of metal colloids. The correlation equation was developed by assuming Brownian diffusion, interception, and gravitational sedimentation contributed to η0 in an additive manner. Numerical simulations for colloid trajectory analysis used for calculating η0 were based on horizontal flow around a collector under the action of van der Waals attractive forces, gravity, and hydrodynamic forces as well as Brownian motion. The derived correlation equation shows excellent agreement with existing correlation equations for particles with density close to that of water. However, the correlation equation presented in this study shows that η0 of high-density colloids, such as metal particles, transported under horizontal flow deviates from that predicted by existing correlations for colloids larger than 4 μm and under low approach velocities. Simulations of trajectory paths show that a significantly reduced contact of high-density colloids larger than 4 μm in size with a collector is due to gravity forces causing trajectory paths to deviate away from the underside of collectors. The new correlation equation is suitable for predicting the single collector efficiency of large particles (several hundred nanometers to several micrometers) and with a large amount of density transport in the horizontal flow mode but is unsuitable for particles with a quite small size (several to tens of nanometers) and for the particle with a large amount of density flow in the vertical flow mode. The

  17. Analysis of electron transport in the plasma of thermionic converters

    SciTech Connect

    Stoenescu, M.L.; Heinicke, P.H.

    1980-03-01

    Electron transport coefficients of a gaseous ensemble are expressed analytically as function of density, and are expressed analytically as function of temperature up to an unknown function which has to be evaluated for each specific electron-neutral atom cross section. In order to complete the analytical temperature dependence one may introduce a polynomial expansion of the function or one may derive the temperature dependence of a set of coefficients, numbering thirteen for a third approximation transport evaluation, which completely determine the transport coefficients. The latter approach is used for determining the electron transport coefficients of a cesium plasma for any ion neutral composition and any temperature between 500/sup 0/K and 3500/sup 0/K. The relation between the transport coefficients of a fully and partly ionized gas is readily available and shows that, in the classical formalism, electron-ion and electron-neutral resistivities are not additive. The present form of the transport coefficients makes possible an accurate numerical integration of transport equations eliminating lengthy computations which are frequently inaccessible. It thus provides a detailed knowledge of spatial distribution of particle and energy transport and makes possible the determination of one of the three internal voltage drops, surface barrier, sheath and plasma, which are linked together experimentally by current density versus voltage characteristics of thermionic converters.

  18. Imaging and quantification of preferential solute transport in soil macropores

    NASA Astrophysics Data System (ADS)

    Koestel, John; Larsbo, Mats

    2014-05-01

    Despite significant advances during the last decades, there are still many processes related to nonequilibrium flow and transport in macroporous soil that are far from completely understood. The use of X-rays for imaging time-lapse 3-D solute transport has a large potential to help advance the knowledge in this field. We visualized the transport of potassium iodide (20 g iodide l-1 H2O) through a small undisturbed soil column (height 3.8 cm, diameter 6.8 cm) under steady state hydraulic conditions using an industrial X-ray scanner. In addition, the electrical conductivity was measured in the effluent solution during the experiment. We attained a series of seventeen 3-D difference images which we related to iodide concentrations using a linear calibration relationship. The solute transport through the soil mainly took place in two cylindrical macropores, by-passing more than 90% of the bulk soil volume during the entire experiment. From these macropores the solute diffused into the surrounding soil matrix. We illustrated the properties of the investigated solute transport by comparing it to a 1-D convective-dispersive transport and by calculating the temporal evolution of the dilution index. We furthermore showed that the tracer diffusion from one of the macropores into the surrounding soil matrix could not be exactly fitted with the cylindrical diffusion equation. We believe that similar studies will help establish links between soil structure and solute transport processes and lead to improvements in models for solute transport through undisturbed soil.

  19. Implementing Parquet equations using HPX

    NASA Astrophysics Data System (ADS)

    Kellar, Samuel; Wagle, Bibek; Yang, Shuxiang; Tam, Ka-Ming; Kaiser, Hartmut; Moreno, Juana; Jarrell, Mark

    A new C++ runtime system (HPX) enables simulations of complex systems to run more efficiently on parallel and heterogeneous systems. This increased efficiency allows for solutions to larger simulations of the parquet approximation for a system with impurities. The relevancy of the parquet equations depends upon the ability to solve systems which require long runs and large amounts of memory. These limitations, in addition to numerical complications arising from stability of the solutions, necessitate running on large distributed systems. As the computational resources trend towards the exascale and the limitations arising from computational resources vanish efficiency of large scale simulations becomes a focus. HPX facilitates efficient simulations through intelligent overlapping of computation and communication. Simulations such as the parquet equations which require the transfer of large amounts of data should benefit from HPX implementations. Supported by the the NSF EPSCoR Cooperative Agreement No. EPS-1003897 with additional support from the Louisiana Board of Regents.

  20. Inclined, collisional sediment transport

    NASA Astrophysics Data System (ADS)

    Berzi, Diego; Fraccarollo, Luigi

    2013-10-01

    We apply the constitutive relations of kinetic theory of granular gases to the transport of cohesionless sediments driven by a gravitational liquid turbulent stream in steady uniform conditions. The sediment-laden flow forms self-equilibrated mechanisms of resistance at the bed surface, below which the sediments are at rest. This geo-physical process takes place quite often in streams at moderate slope and may be interpreted through tools common to fluid mechanics and particle physics. Taking into account the viscous dissipation of the fluctuation energy of the particles, and using approximate methods of integration of the governing differential equations, permit to obtain a set of simple formulas for predicting how depths and flow rates adjust to the angle of inclination of the bed, without requiring additional tuning parameters besides the particle and fluid properties. The agreement with laboratory experiments performed with either plastic cylinders or gravel in water is remarkable. We also provide quantitative criteria to determine the range of validity of the theory, i.e., the values of the Shields number and the angle of inclination of the bed for which the particle stresses can be mostly ascribed to collisional exchange of momentum.

  1. Transport of inertial anisotropic particles under surface gravity waves

    NASA Astrophysics Data System (ADS)

    Dibenedetto, Michelle; Koseff, Jeffrey; Ouellette, Nicholas

    2016-11-01

    The motion of neutrally and almost-neutrally buoyant particles under surface gravity waves is relevant to the transport of microplastic debris and other small particulates in the ocean. Consequently, a number of studies have looked at the transport of spherical particles or mobile plankton in these conditions. However, the effects of particle-shape anisotropy on the trajectories and behavior of irregularly shaped particles in this type of oscillatory flow are still relatively unknown. To better understand these issues, we created an idealized numerical model which simulates the three-dimensional behavior of anisotropic spheroids in flow described by Airy wave theory. The particle's response is calculated using a simplified Maxey-Riley equation coupled with Jeffery's equation for particle rotation. We show that the particle dynamics are strongly dependent on their initial conditions and shape, with some some additional dependence on Stokes number.

  2. Interface area transport of monodispersed spherical particulates

    SciTech Connect

    Chang, Chong H.

    2016-08-05

    We present an interface area transport model required in tracking of mass, momentum, and energy exchange between dispersed and background materials. The basic transport equation has been rigorously derived from the volume fraction evolution equation. Interface area changes due to mass transport and local compression/expansion are included. The model is then simplified for the case in which the dispersed phase is composed of spheres of locally uniform size. A procedure for calculating advective flux with interface reconstruction has been suggested.

  3. 49 CFR 172.402 - Additional labeling requirements.

    Code of Federal Regulations, 2014 CFR

    2014-10-01

    ... 49 Transportation 2 2014-10-01 2014-10-01 false Additional labeling requirements. 172.402 Section 172.402 Transportation Other Regulations Relating to Transportation PIPELINE AND HAZARDOUS MATERIALS SAFETY ADMINISTRATION, DEPARTMENT OF TRANSPORTATION HAZARDOUS MATERIALS REGULATIONS HAZARDOUS...

  4. 49 CFR 223.8 - Additional requirements for passenger equipment.

    Code of Federal Regulations, 2014 CFR

    2014-10-01

    ... 49 Transportation 4 2014-10-01 2014-10-01 false Additional requirements for passenger equipment. 223.8 Section 223.8 Transportation Other Regulations Relating to Transportation (Continued) FEDERAL RAILROAD ADMINISTRATION, DEPARTMENT OF TRANSPORTATION SAFETY GLAZING STANDARDS-LOCOMOTIVES, PASSENGER...

  5. Users manual for the UEDGE edge-plasma transport code

    SciTech Connect

    Rognlien, T D; Rensink, M E; Smith, G R

    2000-01-10

    Operational details are given for the two-dimensional UEDGE edge-plasma transport code. The model applies to nearly fully-ionized plasmas in a strong magnetic field. Equations are solved for the plasma density, velocity along the magnetic field, electron temperature, ion temperature, and electrostatic potential. In addition, fluid models of neutrals species are included or the option to couple to a Monte Carlo code description of the neutrals. Multi-species ion mixtures can be simulated. The physical equations are discretized by a finite-difference procedure, and the resulting system of algebraic equations are solved by fully-implicit techniques. The code can be used to follow time-dependent solutions or to find steady-state solutions by direct iteration.

  6. Functional BES equation

    NASA Astrophysics Data System (ADS)

    Kostov, Ivan; Serban, Didina; Volin, Dmytro

    2008-08-01

    We give a realization of the Beisert, Eden and Staudacher equation for the planar Script N = 4 supersymetric gauge theory which seems to be particularly useful to study the strong coupling limit. We are using a linearized version of the BES equation as two coupled equations involving an auxiliary density function. We write these equations in terms of the resolvents and we transform them into a system of functional, instead of integral, equations. We solve the functional equations perturbatively in the strong coupling limit and reproduce the recursive solution obtained by Basso, Korchemsky and Kotański. The coefficients of the strong coupling expansion are fixed by the analyticity properties obeyed by the resolvents.

  7. Coupled electron-photon radiation transport

    SciTech Connect

    Lorence, L.; Kensek, R.P.; Valdez, G.D.; Drumm, C.R.; Fan, W.C.; Powell, J.L.

    2000-01-17

    Massively-parallel computers allow detailed 3D radiation transport simulations to be performed to analyze the response of complex systems to radiation. This has been recently been demonstrated with the coupled electron-photon Monte Carlo code, ITS. To enable such calculations, the combinatorial geometry capability of ITS was improved. For greater geometrical flexibility, a version of ITS is under development that can track particles in CAD geometries. Deterministic radiation transport codes that utilize an unstructured spatial mesh are also being devised. For electron transport, the authors are investigating second-order forms of the transport equations which, when discretized, yield symmetric positive definite matrices. A novel parallelization strategy, simultaneously solving for spatial and angular unknowns, has been applied to the even- and odd-parity forms of the transport equation on a 2D unstructured spatial mesh. Another second-order form, the self-adjoint angular flux transport equation, also shows promise for electron transport.

  8. A parametric determination of transport aircraft price

    NASA Technical Reports Server (NTRS)

    Anderson, J. L.

    1975-01-01

    Cost per unit weight and other airframe and engine cost relations are given. Power equations representing these relations are presented for six airplane groups: general aircraft, turboprop transports, small jet transports, conventional jet transports, wide-body transports, supersonic transports, and for reciprocating, turboshaft, and turbothrust engines. Market prices calculated for a number of aircraft by use of the equations together with the aircraft characteristics are in reasonably good agreement with actual prices. Such price analyses are of value in the assessment of new aircraft devices and designs and potential research and development programs.

  9. Solving Ordinary Differential Equations

    NASA Technical Reports Server (NTRS)

    Krogh, F. T.

    1987-01-01

    Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.

  10. Lagrangian Sediment Transport Model

    NASA Astrophysics Data System (ADS)

    Maderych, V.; Brovchenko, I.; Fenical, S.; Shepsis, V.

    2004-12-01

    A new two-dimensional Lagrangian sediment transport model was developed to simulate a wide-range of sediment transport processes, including sediment mobility under combined current and wave action, sediment transport and bed change under wave and currents effects, sediment transport patterns at nearshore coastal and offshore structures, and turbidity and sediment motion during dredging and dredged material placement. The Lagrangian technique was used to simulate transport of sediments, deposition, and re-suspension. The model can be applied to cohesive, non-cohesive, or mixed sediments. The sediment transport is simulated using bathymetry data, bed resistance characteristics, wave height and period, depth-averaged current velocity and bed material type, size and gradation, which vary throughout the model domain.The non-cohesive sediment transport model is based on a solution of two-dimensional mass conservation equations for the bed layer material and 2D equations for movement of sediment fractions either bed load or suspended load. The water column and bottom are divided into a set of layers: water layer, active layer, several active bed layers, and the bed layer. The model also takes into account the effects of armoring and changes in the bed composition. Cohesive sediments move entirely as suspended load in the water layer and sediment transport computations are based on a solution of the two-dimensional mass conservation equations for the bed layer material and two-dimensional equations for movement of sediment as suspended load. The water column and bed, as for non-cohesive sediments, was divided into a set of layers. Following the approach of Van Ledden (2002), the erosion of sediments made up of mud and sand mixtures is non-cohesive if the mud content is below a critical level. Above a critical mud content, the bed behaves cohesively. Deposition fluxes of mud and sand are independent. The sediment concentration in the water and active layer is represented by

  11. The impact of charge transfer and structural disorder on the thermoelectric properties of cobalt intercalated TiS2 † †Electronic supplementary information (ESI) available: Powder X-ray diffraction data, thermal analysis data and additional magnetic and transport property data. See DOI: 10.1039/c5tc04217h Click here for additional data file.

    PubMed Central

    Guélou, Gabin; Vaqueiro, Paz; Prado-Gonjal, Jesús; Barbier, Tristan; Hébert, Sylvie; Guilmeau, Emmanuel; Kockelmann, Winfried

    2016-01-01

    A family of phases, CoxTiS2 (0 ≤ x ≤ 0.75) has been prepared and characterised by powder X-ray and neutron diffraction, electrical and thermal transport property measurements, thermal analysis and SQUID magnetometry. With increasing cobalt content, the structure evolves from a disordered arrangement of cobalt ions in octahedral sites located in the van der Waals' gap (x ≤ 0.2), through three different ordered vacancy phases, to a second disordered phase at x ≥ 0.67. Powder neutron diffraction reveals that both octahedral and tetrahedral inter-layer sites are occupied in Co0.67TiS2. Charge transfer from the cobalt guest to the TiS2 host affords a systematic tuning of the electrical and thermal transport properties. At low levels of cobalt intercalation (x < 0.1), the charge transfer increases the electrical conductivity sufficiently to offset the concomitant reduction in |S|. This, together with a reduction in the overall thermal conductivity leads to thermoelectric figures of merit that are 25% higher than that of TiS2, ZT reaching 0.30 at 573 K for CoxTiS2 with 0.04 ≤ x ≤ 0.08. Whilst the electrical conductivity is further increased at higher cobalt contents, the reduction in |S| is more marked due to the higher charge carrier concentration. Furthermore both the charge carrier and lattice contributions to the thermal conductivity are increased in the electrically conductive ordered-vacancy phases, with the result that the thermoelectric performance is significantly degraded. These results illustrate the competition between the effects of charge transfer from guest to host and the disorder generated when cobalt cations are incorporated in the inter-layer space. PMID:27774151

  12. A New Algorithm for Supernova Neutrino Transport and Some Applications

    NASA Astrophysics Data System (ADS)

    Burrows, Adam; Young, Timothy; Pinto, Philip; Eastman, Ron; Thompson, Todd A.

    2000-08-01

    We have developed an implicit, multigroup, time-dependent, spherical neutrino transport code based on the Feautrier variables, the tangent-ray method, and accelerated Λ iteration. The code achieves high angular resolution, is good to O(v/c), is equivalent to a Boltzmann solver (without gravitational redshifts), and solves the transport equation at all optical depths with precision. In this paper, we present our formulation of the relevant numerics and microphysics and explore protoneutron star atmospheres for snapshot postbounce models. Our major focus is on spectra, neutrino-matter heating rates, Eddington factors, angular distributions, and phase-space occupancies. In addition, we investigate the influence on neutrino spectra and heating of final-state electron blocking, stimulated absorption, velocity terms in the transport equation, neutrino-nucleon scattering asymmetry, and weak magnetism and recoil effects. Furthermore, we compare the emergent spectra and heating rates obtained using full transport with those obtained using representative flux-limited transport formulations to gauge their accuracy and viability. Finally, we derive useful formulae for the neutrino source strength due to nucleon-nucleon bremsstrahlung and determine bremsstrahlung's influence on the emergent νμ and ντ neutrino spectra. These studies are in preparation for new calculations of spherically symmetric core-collapse supernovae, proto-neutron star winds, and neutrino signals.

  13. Proton Transport

    NASA Technical Reports Server (NTRS)

    Pohorille, Andrew; DeVincenzi, Donald L. (Technical Monitor)

    2001-01-01

    channel is large enough to contain water molecules. and is normally filled with water. In analogy to the mechanism of proton transfer in some other channels, it has been postulated that protons are translocated along the network of water molecules filling the pore of the channel. This mechanism, however, must involve an additional important step because the channel contains four histidine amino acid residues, one from each of the helices, which are sufficiently large to occlude the pore and interrupt the water network. The histidine residues ensure channel selectivity by blocking transport of small ions, such as sodium or potassium. They have been also implicated in gating protons due to the ability of each histidine to become positively charged by accepting an additional proton. Two mechanisms of gating have been proposed. In one mechanism, all four histidines acquire an additional proton and, due to repulsion between their positive charges, move away from one another, thus opening the channel. The alternative mechanism relies of the ability of protons to move between different atoms in a molecule (tautomerization). Thus, a proton is captured on one side of the gate while another proton is released from the opposite side, and the molecule returns to the initial state through tautomerization. The simulations were designed to test these two mechanisms. Large-scale, atomic-level molecular dynamics simulations of the channel with the histidine residues in different protonation states revealed that all intermediate states of the system involved in the tautomerization mechanism are structurally stable and the arrangement of water molecules in the channel is conducive to the proton transport. In contrast, in the four-protonated state, postulated to exist in the gate-opening mechanism, the electrostatic repulsion between the histidine residues appears to be so large that the channel loses its structural integrity and one helix moves away from the remaining three. Additional

  14. Turning Equations Into Stories: Using "Equation Dictionaries" in an Introductory Geophysics Class

    NASA Astrophysics Data System (ADS)

    Caplan-Auerbach, J.

    2008-12-01

    To students with math fear, equations can be intimidating and overwhelming. This discomfort is reflected in some of the frequent questions heard in introductory geophysics: "which equation should I use?" and "does T stand for travel time or period?" Questions such as these indicate that many students view equations as a series of variables and operators rather than as a representation of a physical process. To solve a problem they may simply look for an equation with the correct variables and assume that it meets their needs, rather than selecting an equation that represents the appropriate physical process. These issues can be addressed by encouraging students to think of equations as stories, and to describe them in prose. This is the goal of the Equation Dictionary project, used in Western Washington University's introductory geophysics course. Throughout the course, students create personal equation dictionaries, adding an entry each time an equation is introduced. Entries consist of (a) the equation itself, (b) a brief description of equation variables, (c) a prose description of the physical process described by the equation, and (d) any additional notes that help them understand the equation. Thus, rather than simply writing down the equations for the velocity of body waves, a student might write "The speed of a seismic body wave is controlled by the material properties of the medium through which it passes." In a study of gravity a student might note that the International Gravity Formula describes "the expected value of g at a given latitude, correcting for Earth's shape and rotation." In writing these definitions students learn that equations are simplified descriptions of physical processes, and that understanding the process is more useful than memorizing a sequence of variables. Dictionaries also serve as formula sheets for exams, which encourages students to write definitions that are meaningful to them, and to organize their thoughts clearly. Finally

  15. Uniqueness of Maxwell's Equations.

    ERIC Educational Resources Information Center

    Cohn, Jack

    1978-01-01

    Shows that, as a consequence of two feasible assumptions and when due attention is given to the definition of charge and the fields E and B, the lowest-order equations that these two fields must satisfy are Maxwell's equations. (Author/GA)

  16. Linear Equations: Equivalence = Success

    ERIC Educational Resources Information Center

    Baratta, Wendy

    2011-01-01

    The ability to solve linear equations sets students up for success in many areas of mathematics and other disciplines requiring formula manipulations. There are many reasons why solving linear equations is a challenging skill for students to master. One major barrier for students is the inability to interpret the equals sign as anything other than…

  17. Reduced Braginskii equations

    SciTech Connect

    Yagi, M.; Horton, W. )

    1994-07-01

    A set of reduced Braginskii equations is derived without assuming flute ordering and the Boussinesq approximation. These model equations conserve the physical energy. It is crucial at finite [beta] that the perpendicular component of Ohm's law be solved to ensure [del][center dot][bold j]=0 for energy conservation.

  18. Functional Cantor equation

    NASA Astrophysics Data System (ADS)

    Shabat, A. B.

    2016-12-01

    We consider the class of entire functions of exponential type in relation to the scattering theory for the Schrödinger equation with a finite potential that is a finite Borel measure. These functions have a special self-similarity and satisfy q-difference functional equations. We study their asymptotic behavior and the distribution of zeros.

  19. Mars surface transportation options

    NASA Technical Reports Server (NTRS)

    Leitner, Jeffrey M.; Alred, John W.

    1986-01-01

    As the number of scientific experiments for the surface of Mars grows, the need for effective surface transportation becomes critical. Because of the diversity of the experiments proposed, as well as the desire to explore Mars from the equator to the poles, the optimum surface vehicle configuration is not obvious. Five candidate vehicles are described, with an estimate of their size and performance. In order to maximize the success of a manned Mars mission, it appears that two vehicles should be designed for surface transportation: an advanced long-range rover, and a remotely-piloted airplane.

  20. Almost periodic solutions to difference equations

    NASA Technical Reports Server (NTRS)

    Bayliss, A.

    1975-01-01

    The theory of Massera and Schaeffer relating the existence of unique almost periodic solutions of an inhomogeneous linear equation to an exponential dichotomy for the homogeneous equation was completely extended to discretizations by a strongly stable difference scheme. In addition it is shown that the almost periodic sequence solution will converge to the differential equation solution. The preceding theory was applied to a class of exponentially stable partial differential equations to which one can apply the Hille-Yoshida theorem. It is possible to prove the existence of unique almost periodic solutions of the inhomogeneous equation (which can be approximated by almost periodic sequences) which are the solutions to appropriate discretizations. Two methods of discretizations are discussed: the strongly stable scheme and the Lax-Wendroff scheme.

  1. Transport analysis in toroidal helical plasmas using the integrated code: TASK3D

    NASA Astrophysics Data System (ADS)

    Wakasa, A.; Fukuyama, A.; Murakami, S.; Beidler, C. D.; Maassberg, H.; Yokoyama, M.; Sato, M.

    2009-11-01

    The integrated simulation code in helical plasmas, TASK3D, is being developed on the basis of an integrated modeling code for tokamak plasma, TASK. In helical systems, the neoclassical transport is one of the important issues in addition to the anomalous transport, because of strong temperature dependence of heat conductivity and an important role in determining the radial electric field. We have already constructed the neoclassical transport database in LHD, DGN/LHD. The mono-energetic diffusion coefficients are evaluated based on the Monte Carlo method by DCOM code and the mono-energetic diffusion coefficients database is constructed using a neural network technique. Also we apply GSRAKE code, which solves the ripple-averaged drift kinetic equation, to obtain transport coefficients in highly collisionless regime. We have newly incorporated the DGN/LHD module into TASK3D. We will present several results of transport simulation in typical LHD plasmas.

  2. 46 CFR 308.502 - Additional insurance.

    Code of Federal Regulations, 2013 CFR

    2013-10-01

    ... 46 Shipping 8 2013-10-01 2013-10-01 false Additional insurance. 308.502 Section 308.502 Shipping MARITIME ADMINISTRATION, DEPARTMENT OF TRANSPORTATION EMERGENCY OPERATIONS WAR RISK INSURANCE War Risk Cargo Insurance I-Introduction § 308.502 Additional insurance. The assured may place increased value...

  3. 46 CFR 308.502 - Additional insurance.

    Code of Federal Regulations, 2012 CFR

    2012-10-01

    ... 46 Shipping 8 2012-10-01 2012-10-01 false Additional insurance. 308.502 Section 308.502 Shipping MARITIME ADMINISTRATION, DEPARTMENT OF TRANSPORTATION EMERGENCY OPERATIONS WAR RISK INSURANCE War Risk Cargo Insurance I-Introduction § 308.502 Additional insurance. The assured may place increased value...

  4. 46 CFR 308.502 - Additional insurance.

    Code of Federal Regulations, 2014 CFR

    2014-10-01

    ... 46 Shipping 8 2014-10-01 2014-10-01 false Additional insurance. 308.502 Section 308.502 Shipping MARITIME ADMINISTRATION, DEPARTMENT OF TRANSPORTATION EMERGENCY OPERATIONS WAR RISK INSURANCE War Risk Cargo Insurance Introduction § 308.502 Additional insurance. The assured may place increased value...

  5. 10 CFR 71.65 - Additional requirements.

    Code of Federal Regulations, 2010 CFR

    2010-01-01

    ... 10 Energy 2 2010-01-01 2010-01-01 false Additional requirements. 71.65 Section 71.65 Energy NUCLEAR REGULATORY COMMISSION (CONTINUED) PACKAGING AND TRANSPORTATION OF RADIOACTIVE MATERIAL Package Approval Standards § 71.65 Additional requirements. The Commission may, by rule, regulation, or...

  6. 46 CFR 308.502 - Additional insurance.

    Code of Federal Regulations, 2010 CFR

    2010-10-01

    ... 46 Shipping 8 2010-10-01 2010-10-01 false Additional insurance. 308.502 Section 308.502 Shipping MARITIME ADMINISTRATION, DEPARTMENT OF TRANSPORTATION EMERGENCY OPERATIONS WAR RISK INSURANCE War Risk Cargo Insurance I-Introduction § 308.502 Additional insurance. The assured may place increased value...

  7. 46 CFR 308.502 - Additional insurance.

    Code of Federal Regulations, 2011 CFR

    2011-10-01

    ... 46 Shipping 8 2011-10-01 2011-10-01 false Additional insurance. 308.502 Section 308.502 Shipping MARITIME ADMINISTRATION, DEPARTMENT OF TRANSPORTATION EMERGENCY OPERATIONS WAR RISK INSURANCE War Risk Cargo Insurance I-Introduction § 308.502 Additional insurance. The assured may place increased value...

  8. Energetic Particle Transport in Strong Compressive Wave Turbulence Near Shocks

    SciTech Connect

    Le Roux, J.A.; Zank, G.P.; Li, G.; Webb, G.M.

    2005-08-01

    Strong interplanetary coronal mass ejection driven shocks are often accompanied by high levels of low frequency compressive wave turbulence. This might require a non-linear kinetic theory approach to properly describe energetic particle transport in their vicinity. We present a non-linear diffusive kinetic theory for suprathermal particle transport and stochastic acceleration along the background magnetic field in strong compressive dynamic wave turbulence to which small-scale Alfven waves are coupled. Our theory shows that the standard cosmic-ray transport equation must be revised for low suprathermal particle energies to accommodate fundamental changes in spatial diffusion (standard diffusion becomes turbulent diffusion) as well as modifications to particle convection, and adiabatic energy changes. In addition, a momentum diffusion term, which generates accelerated suprathermal particle spectra with a hard power law, must be added. Such effective first stage acceleration possibly leads to efficient injection of particles into second stage diffusive shock acceleration as described by standard theory.

  9. Dissipative particle dynamics model for colloid transport in porous media

    SciTech Connect

    Pan, W.; Tartakovsky, A. M.

    2013-08-01

    We present that the transport of colloidal particles in porous media can be effectively modeled with a new formulation of dissipative particle dynamics, which augments standard DPD with non-central dissipative shear forces between particles while preserving angular momentum. Our previous studies have demonstrated that the new formulation is able to capture accurately the drag forces as well as the drag torques on colloidal particles that result from the hydrodynamic retardation effect. In the present work, we use the new formulation to study the contact efficiency in colloid filtration in saturated porous media. Note that the present model include all transport mechanisms simultaneously, including gravitational sedimentation, interception and Brownian diffusion. Our results of contact efficiency show a good agreement with the predictions of the correlation equation proposed by Tufenkji and EliMelech, which also incorporate all transport mechanisms simultaneously without the additivity assumption.

  10. Grey transport acceleration method for time-dependent radiative transfer problems

    SciTech Connect

    Larsen, E.

    1988-10-01

    A new iterative method for solving hte time-dependent multifrequency radiative transfer equations is described. The method is applicable to semi-implicit time discretizations that generate a linear steady-state multifrequency transport problem with pseudo-scattering within each time step. The standard ''lambda'' iteration method is shown to often converge slowly for such problems, and the new grey transport acceleration (GTA) method, based on accelerating the lambda method by employing a grey, or frequency-independent transport equation, is developed. The GTA method is shown, theoretically by an iterative Fourier analysis, and experimentally by numerical calculations, to converge significantly faster than the lambda method. In addition, the GTA method is conceptually simple to implement for general differencing schemes, on either Eulerian or Lagrangian meshes. copyright 1988 Academic Press, Inc.

  11. Payload transportation system study

    NASA Technical Reports Server (NTRS)

    1976-01-01

    A standard size set of shuttle payload transportation equipment was defined that will substantially reduce the cost of payload transportation and accommodate a wide range of payloads with minimum impact on payload design. The system was designed to accommodate payload shipments between the level 4 payload integration sites and the launch site during the calendar years 1979-1982. In addition to defining transportation multi-use mission support equipment (T-MMSE) the mode of travel, prime movers, and ancillary equipment required in the transportation process were also considered. Consistent with the STS goals of low cost and the use of standardized interfaces, the transportation system was designed to commercial grade standards and uses the payload flight mounting interfaces for transportation. The technical, cost, and programmatic data required to permit selection of a baseline system of MMSE for intersite movement of shuttle payloads were developed.

  12. Consistent transport coefficients in astrophysics

    NASA Technical Reports Server (NTRS)

    Fontenla, Juan M.; Rovira, M.; Ferrofontan, C.

    1986-01-01

    A consistent theory for dealing with transport phenomena in stellar atmospheres starting with the kinetic equations and introducing three cases (LTE, partial LTE, and non-LTE) was developed. The consistent hydrodynamical equations were presented for partial-LTE, the transport coefficients defined, and a method shown to calculate them. The method is based on the numerical solution of kinetic equations considering Landau, Boltzmann, and Focker-Planck collision terms. Finally a set of results for the transport coefficients derived for a partially ionized hydrogen gas with radiation was shown, considering ionization and recombination as well as elastic collisions. The results obtained imply major changes is some types of theoretical model calculations and can resolve some important current problems concerning energy and mass balance in the solar atmosphere. It is shown that energy balance in the lower solar transition region can be fully explained by means of radiation losses and conductive flux.

  13. Nonlinear gyrokinetic equations

    SciTech Connect

    Dubin, D.H.E.; Krommes, J.A.; Oberman, C.; Lee, W.W.

    1983-03-01

    Nonlinear gyrokinetic equations are derived from a systematic Hamiltonian theory. The derivation employs Lie transforms and a noncanonical perturbation theory first used by Littlejohn for the simpler problem of asymptotically small gyroradius. For definiteness, we emphasize the limit of electrostatic fluctuations in slab geometry; however, there is a straight-forward generalization to arbitrary field geometry and electromagnetic perturbations. An energy invariant for the nonlinear system is derived, and various of its limits are considered. The weak turbulence theory of the equations is examined. In particular, the wave kinetic equation of Galeev and Sagdeev is derived from an asystematic truncation of the equations, implying that this equation fails to consider all gyrokinetic effects. The equations are simplified for the case of small but finite gyroradius and put in a form suitable for efficient computer simulation. Although it is possible to derive the Terry-Horton and Hasegawa-Mima equations as limiting cases of our theory, several new nonlinear terms absent from conventional theories appear and are discussed.

  14. The Ffowcs Williams-Hawkings equation - Fifteen years of research

    NASA Technical Reports Server (NTRS)

    Farassat, F.

    1986-01-01

    The Ffowcs Williams-Hawkings equation governs the generation of sound in fluids in the presence of solid boundaries in motion. This equation is reviewed for situations where the linearization of the governing equations is allowed. In addition, research on the application of this equation to problems of aeroacoustic is briefly surveyed. Particular attention is given to the formulation of supersonic sources moving in uniform propeller-like motion.

  15. Magneto-transport properties of La0.75Ca0.15Sr0.1MnO3 with YBa2Cu3O7-δ addition

    NASA Astrophysics Data System (ADS)

    Zghal, E.; Koubaa, M.; Berthet, P.; Sicard, L.; Cheikhrouhou-Koubaa, W.; Decorse-Pascanut, C.; Cheikhrouhou, A.; Ammar-Merah, S.

    2016-09-01

    We report the structural, magnetic, electrical and magentoresistance properties of (La0.75Ca0.15Sr0.1MnO3)1-x(YBa2Cu3O7-δ)x (with x=0, 0.025, 0.05, 0.075, 0.1, 0.2, and 0.3) composites synthesized through sol-gel method. The powder X-ray diffraction patterns indicate no evidence of reaction between La0.75Ca0.15Sr0.1MnO3 (LCSMO) and YBa2Cu3O7-δ (YBCO). The addition of YBCO induces a reduction of the total magnetization while the Curie temperature remains almost constant (∼312 K). The behavior of the electrical resistivity evolves differently depending on the doping level. Above the paramagnetic-insulating transition temperature the resistivity data were best-fitted by using the adiabatic small polaron and variable range hopping models. Ferromagnetic-metallic regime in the composites seems to emanate from the electron-phonon or/and electron-magnon scattering processes. With increasing the YBCO doping content (until x=0.1), the positive magnetoresistance (MR) of YBCO phase dominates the negative MR of LCSMO one, which gives rise to the decreasing of MR of the composites.

  16. Smoothed MHD equations for numerical simulations of ideal quasi-neutral gas dynamic flows

    NASA Astrophysics Data System (ADS)

    Popov, Mikhail V.; Elizarova, Tatiana G.

    2015-11-01

    We introduce a mathematical model and related numerical method for numerical modeling of ideal magnetohydrodynamic (MHD) gas flows as an extension of previously known quasi-gasdynamic (QGD) equations. This approach is based on smoothing, or averaging of the original MHD equation system over a small time interval that leads to a new equation system, named quasi-MHD, or QMHD system. The QMHD equations are closely related to the original MHD system except for additional strongly non-linear dissipative τ-terms with a small parameter τ as a factor. The τ-terms depend on the solution itself and decrease in regions with the small space gradients of the solution. In this sense the QMHD system could be regarded as an approach with adaptive artificial dissipation. The QMHD is a generalization of regularized (or quasi-) gas dynamic equation system suggested in last three decades. In the QMHD numerical method the evolution of all physical variables is presented in a non-split divergence form. Divergence-free evolution of the magnetic field provides by using a constrained transport method based on Faraday's law of induction. Accuracy and convergence of the QMHD method is verified on a wide set of standard MHD tests including the 3D Orszag-Tang vortex flow.

  17. Klein-Gordon Equation in Hydrodynamical Form

    SciTech Connect

    Wong, Cheuk-Yin

    2010-01-01

    We follow and modify the Feshbach-Villars formalism by separating the Klein-Gordon equation into two coupled time-dependent Schroedinger equations for the particle and antiparticle wave functions with positive probability densities. We find that the equation of motion for the probability densities is in the form of relativistic hydrodynamics where various forces have their physical and classical counterparts. An additional element is the presence of the quantum stress tensor that depends on the derivatives of the amplitude of the wave function.

  18. The Quadrature Master Equations

    NASA Astrophysics Data System (ADS)

    Hassan, N. J.; Pourdarvish, A.; Sadeghi, J.; Olaomi, J. O.

    2017-04-01

    In this paper, we derive the non-Markovian stochastic equation of motion (SEM) and master equations (MEs) for the open quantum system by using the non-Markovian stochastic Schrödinger equations (SSEs) for the quadrature unraveling in linear and nonlinear cases. The SSEs for quadrature unraveling arise as a special case of a quantum system. Also we derive the Markovian SEM and ME by using linear and nonlinear Itô SSEs for the measurement probabilities. In linear non-Markovian case, we calculate the convolutionless linear quadrature non-Markovian SEM and ME. We take advantage from example and show that corresponding theory.

  19. A Fundamental Equation of State for Ethanol

    NASA Astrophysics Data System (ADS)

    Schroeder, J. A.; Penoncello, S. G.; Schroeder, J. S.

    2014-12-01

    The existing fundamental equation for ethanol demonstrates undesirable behavior in several areas and especially in the critical region. In addition, new experimental data have become available in the open literature since the publication of the current correlation. The development of a new fundamental equation for ethanol, in the form of Helmholtz energy as a function of temperature and density, is presented. New, nonlinear fitting techniques, along with the new experimental data, are shown to improve the behavior of the fundamental equation. Ancillary equations are developed, including equations for vapor pressure, saturated liquid density, saturated vapor density, and ideal gas heat capacity. Both the fundamental and ancillary equations are compared to experimental data. The fundamental equation can compute densities to within ±0.2%, heat capacities to within ±1%-2%, and speed of sound to within ±1%. Values of the vapor pressure and saturated vapor densities are represented to within ±1% at temperatures of 300 K and above, while saturated liquid densities are represented to within ±0.3% at temperatures of 200 K and above. The uncertainty of all properties is higher in the critical region and near the triple point. The equation is valid for pressures up to 280 MPa and temperatures from 160 to 650 K.

  20. Riparian seed dispersal: transport and depositional processes

    NASA Astrophysics Data System (ADS)

    Cunnings, A.; Johnson, E. A.; Martin, Y. E.

    2012-04-01

    Riparian tree population dynamics are linked to the physical processes controlled by the hydrogeomorphic setting. In particular, fluvial seed dispersal is influenced by a combination of factors including the hydrology, fluvial geomorphology, and seed dispersal traits. This study examines the influence of stream flow patterns on the transportation and deposition of buoyant seeds by applying a one dimensional transport model. Conceptually, the model separates the stream into two components: the main channel and transient storage /deposition zones. The hydrologic processes are governed by an advection-dispersion equation and numerically solved using the Crank-Nicolson method. Additional terms in the equation allow for model variation in the flow regime (lateral inflow and outflow) and the incorporation of a transient storage/deposition component where seeds may be detained. The model parameters are based on a bedrock-gravel bed river with pool-riffle morphology where we conducted field experimentation in Coastal Northern California. The riparian zone of the study reach is inhabited by White Alder (Alnus rhombifolia) which disperses buoyant seeds in late winter/early spring coinciding with the latter part of the wet, Mediterranean climate. Artificial seeds with similar characteristic traits of buoyancy, density and Bond Number to White Alder seeds were used to quantify transport times and identify storage areas. The model output captures a greater number of seeds during a receding hydrograph due to the increase in transient storage. Typically, this is found in shallow stream margins where the flow is divergent such as areas with back-eddies. In the field, this is associated with the ends of gravel bars or riffles where flow expansion causes secondary flows. The results demonstrate the importance of transient storage for seed transport and depositional processes and emphasize the need for improved measurement techniques, in lieu of empirical coefficients, to advance the