Science.gov

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. Langevin equation approach to reactor noise analysis: stochastic transport equation

    SciTech Connect

    Akcasu, A.Z. ); Stolle, A.M. )

    1993-01-01

    The application of the Langevin equation method to the study of fluctuations in the space- and velocity-dependent neutron density as well as in the detector outputs in nuclear reactors is presented. In this case, the Langevin equation is the stochastic linear neutron transport equation with a space- and velocity-dependent random neutron source, often referred to as the noise equivalent source (NES). The power spectral densities (PSDs) of the NESs in the transport equation, as well as in the accompanying detection rate equations, are obtained, and the cross- and auto-power spectral densities of the outputs of pairs of detectors are explicitly calculated. The transport-level expression for the R([omega]) ratio measured in the [sup 252]Cf source-driven noise analysis method is also derived. Finally, the implementation of the Langevin equation approach at different levels of approximation is discussed, and the stochastic one-speed transport and one-group P[sub 1] equations are derived by first integrating the stochastic transport equation over speed and then eliminating the angular dependence by a spherical harmonics expansion. By taking the large transport rate limit in the P[sub 1] description, the stochastic diffusion equation is obtained as well as the PSD of the NES in it. This procedure also leads directly to the stochastic Fick's law.

  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. Fractional transport equation on random fractals

    NASA Astrophysics Data System (ADS)

    Zeng, Qiuhua; Li, Houqiang; Fang, Yaquan

    1998-12-01

    According to the ways of H.E. Roman and M. Giona with the constitutive equation of diffusive particles in isotropic and homogeneous three dimensions and the Laplace transform we derive the multiscaling fractional transport equation in disordered fractal media, whose solution is consistent with literature results.

  7. Dual Diagonalization of Reactive Transport Equations

    NASA Astrophysics Data System (ADS)

    Yeh, G.; Tsai, C.

    2013-12-01

    One solves a system of species transport equations in the primitive approach to reactive transport modeling. This approach is not able to decouple equilibrium reaction rates from species concentrations. This problem has been overcome with the approach to diagonalizing the reaction matrix since mid 1990's, which yields the same number of transport equations for reaction-extents. In the diagonalization approach, first, a subset of reaction- extent transport equations is solved for concentrations of components and kinetic-variables. Then, the component, kinetic-variable, and mass action equations are solved for all species concentrations. Finally, the equilibrium reaction rates are posterior computed. The difficulty in this approach is that the solution of species concentrations in the second step is a stiff problem when the concentrations of master species are small compared to those of equilibrium species. To overcome the problem of stiffness, we propose a dual diagonalization approach. Here, a second diagonalization is performed on the decomposed unit matrix to yield species concentrations, each as a linear function of reaction extents. In this dual diagonalization approach, four steps are needed to complete the modeling. First, component and kinetic-variable transport equations are solved for the concentrations of components (a subset of reaction-extents) and kinetic-variables (another subset of reaction-extents). Second, the set of mass action equations written in terms of reaction extents are solved for equilibrium-variables (yet another subset of reaction-extents). Third, species concentrations are posterior obtained by solving the set of linear equations defining reaction-extents. Fourth, equilibrium rates are posterior calculated with transport equations for equilibrium-variables. Several example problems will be used to demonstrate the efficiency of this approach. Keywords: Reactive Transport, Reaction-Extent, Component, Kinetic-Variable, Equilibrium

  8. The telegraph equation in charged particle transport

    NASA Technical Reports Server (NTRS)

    Gombosi, T. I.; Jokipii, J. R.; Kota, J.; Lorencz, K.; Williams, L. L.

    1993-01-01

    We present a new derivation of the telegraph equation which modifies its coefficients. First, an infinite order partial differential equation is obtained for the velocity space solid angle-averaged phase-space distribution of particles which underwent at least a few collisions. It is shown that, in the lowest order asymptotic expansion, this equation simplifies to the well-known diffusion equation. The second-order asymptotic expansion for isotropic small-angle scattering results in a modified telegraph equation with a signal propagation speed of v(5/11) exp 1/2 instead of the usual v/3 exp 1/2. Our derivation of a modified telegraph equation follows from an expansion of the Boltzmann equation in the relevant smallness parameters and not from a truncation of an eigenfunction expansion. This equation is consistent with causality. It is shown that, under steady state conditions in a convecting plasma, the telegraph equation may be regarded as a diffusion equation with a modified transport coefficient, which describes a combination of diffusion and cosmic-ray inertia.

  9. Alternative formulation of the monokinetic transport equation

    SciTech Connect

    Coppa, G.; Ravetto, P.; Sumini, M.

    1985-03-01

    After recalling a technique already exploited in stationary neutron transport, the dynamic linear monokinetic equation for general geometry is cast into an integro-differential form where a second order space Laplace operator and both a second and first time derivatives appear. The introduced unknowns are given a physical interpretation for plane geometry and their relations with the total flux and current are derived.

  10. 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.

  11. Dispersion in tidally averaged transport equation

    USGS Publications Warehouse

    Cheng, R.T.; Casulli, V.

    1992-01-01

    A general governing inter-tidal transport equation for conservative solutes has been derived without invoking the weakly nonlinear approximation. The governing inter-tidal transport equation is a convection-dispersion equation in which the convective velocity is a mean Lagrangian residual current, and the inter-tidal dispersion coefficient is defined by a dispersion patch. When the weakly nonlinear condition is violated, the physical significance of the Stokes' drift, as used in tidal dynamics, becomes questionable. For nonlinear problems, analytical solutions for the mean Lagrangian residual current and for the inter-tidal dispersion coefficient do not exist, they must be determined numerically. A rectangular tidal inlet with a constriction is used in the first example. The solutions of the residual currents and the computed properties of the inter-tidal dispersion coefficient are used to illuminate the mechanisms of the inter-tidal transport processes. Then, the present formulation is tested in a geometrically complex tidal estuary – San Francisco Bay, California. The computed inter-tidal dispersion coefficients are in the range between 5×104 and 5×106 cm2/sec., which are consistent with the values reported in the literature

  12. 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.

  13. 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.

  14. One-dimensional transport equation models for sound energy propagation in long spaces: simulations and experiments.

    PubMed

    Jing, Yun; Xiang, Ning

    2010-04-01

    In this paper, the accuracy and efficiency of the previously discussed one-dimensional transport equation models [Y. Jing et al., J. Acoust. Soc. Am. 127, 2312-2322 (2010)] are examined both numerically and experimentally. The finite element method is employed to solve the equations. Artificial diffusion is applied in the numerical implementation to suppress oscillations of the solution. The transport equation models are then compared with the ray-tracing based method for different scenarios. In general, they are in good agreement, and the transport equation models are substantially less time consuming. In addition, the two-group model is found to yield more accurate results than the one-group model for the tested cases. Lastly, acoustic experimental results obtained from a 1:10 long room scale-model are used to verify the transport equation models. The results suggest that the transport equation models are able to accurately model the sound field in a long space. PMID:20370014

  15. Cable Connected Spinning Spacecraft, 1. the Canonical Equations, 2. Urban Mass Transportation, 3

    NASA Technical Reports Server (NTRS)

    Sitchin, A.

    1972-01-01

    Work on the dynamics of cable-connected spinning spacecraft was completed by formulating the equations of motion by both the canonical equations and Lagrange's equations and programming them for numerical solution on a digital computer. These energy-based formulations will permit future addition of the effect of cable mass. Comparative runs indicate that the canonical formulation requires less computer time. Available literature on urban mass transportation was surveyed. Areas of the private rapid transit concept of urban transportation are also studied.

  16. On diagonalization of coupled hydrologic transport and geochemical reaction equations

    SciTech Connect

    Yeh, Gour-Tsyh; Cheng, Hwai-Ping

    1996-12-31

    Two basic ingredients present in modeling the transport of reactive multi-components: the transport is described by a set of advection-dispersion-reactive partial differential equations (PDEs) based on the principle of mass balance; the chemical reactions, under the assumptions of local equilibrium, are described by a set of highly nonlinear algebraic equations (AEs) base on the principles of mole balance and mass action. For a typical application, the complete set of nonlinear PDEs and AEs consist of more than one hundred simultaneous equations. Thus, it is impractical to solve this set of equations simultaneously. General practice is to divide this set of equations into two subsets: one is the primary governing equations (PGEs) consisting of mainly the transport equations and the other one is the secondary governing equations consisting of mainly the geochemical reaction equations. The PGEs are solved for the chosen primary dependent variables (PDVs) and the SGEs are used to compute for the secondary dependent variables (SDVs). The major difficulties in simulating the reactive transport is the numerical solution of PGEs. From the computational point of view, the solution of the set of highly nonlinear PDEs are solved either with the direct substitution approach (DSA) or with the sequential iteration approach (SIA). For DSA, geochemical equilibrium reaction equations are substituted into the hydrologic transport equations to results in a set of nonlinear partial differential equations.

  17. Stable Difference Schemes for the Neutron Transport Equation

    SciTech Connect

    Ashyralyev, Allaberen; Taskin, Abdulgafur

    2011-09-22

    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.

  18. 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

  19. Strongly asymmetric discrete Painlevé equations: The additive case

    SciTech Connect

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

    2014-05-15

    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. 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.

  1. 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.

  2. 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.

  3. 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)

  4. Relativistic transport equations for electromagnetic scalar, and pseudoscalar potentials

    SciTech Connect

    Shin, G.R.; Rafelski, J.

    1995-10-01

    The authors propose a particular form of relativistic transport equations arising from the classical limit of single-time Wigner function for Dirac particles evolving in the presence of scalar, pseudoscalar, and electromagnetic fields. These relativistic Vlasov-type equations for the particle and the antiparticle sector of the Fock space can be also obtained assuming the validity of the Liouville`s equation given a suitable classical Hamiltonian and the associated force. 11 refs.

  5. Onsager's-principle-consistent 13-moment transport equations

    NASA Astrophysics Data System (ADS)

    Singh, Narendra; Agrawal, Amit

    2016-06-01

    A new set of generalized transport equations is derived for higher-order moments which are generated in evolution equation for stress tensor and heat flux vector in 13-moment equations. The closure we employ satisfies Onsager's symmetry principle. In the derivation, we do not employ a phase density function based on Hermite polynomial series in terms of higher-order moments, unlike Grad's approach. The distribution function is rather chosen to satisfy collision invariance, and H-theorem and capture relatively strong deviations from equilibrium. The phase density function satisfies the linearized Boltzmann equation and provides the correct value of the Prandtl number for monatomic gas. The derived equations are compared with Grad's 13-moments equations for gas modeled as Maxwellian molecule. The merits of the proposed equations against Grad's and R13 equations are discussed. In particular, it is noted that the proposed equations contain higher-order terms compared to these equations but require a fewer number of boundary conditions as compared to the R13 equations. The Knudsen number envelope which can be covered to describe flows with these equations is therefore expected to be larger as compared to the earlier equations.

  6. A discrete formulation of the Wigner transport equation

    NASA Astrophysics Data System (ADS)

    Kim, Kyoung-Youm

    2007-12-01

    A discrete formulation of the Wigner distribution function (WDF) and the Wigner transport equation (WTE) is proposed, where the "discreteness" of the WDF and WTE is not just a practical, mathematical feature of discretization for the possible computations, but reveals a fundamental physics regarding the maximum correlation length of potentials (an essential quantum-mechanical feature of the WTE): it is set by the positional uncertainty due to the discrete values of momentum in evaluating the discrete WDF. Our formulation also shows that the weighting function to the potential-correlation term can be derived naturally from a mathematical necessity related to the antiperiodicity of the discrete density operator. In addition, we propose a mutually independent discretization scheme for the diagonal and cross-diagonal coordinates of the density operator, which results in a numerically effective discrete WTE in that it requires much less computational resources without significant loss in accuracy.

  7. Transport equations for linear surface waves with random underlying flows

    NASA Astrophysics Data System (ADS)

    Bal, Guillaume; Chou, Tom

    1999-11-01

    We define the Wigner distribution and use it to develop equations for linear surface capillary-gravity wave propagation in the transport regime. The energy density a(r, k) contained in waves propagating with wavevector k at field point r is given by dota(r,k) + nabla_k[U_⊥(r,z=0) \\cdotk + Ω(k)]\\cdotnabla_ra [13pt] \\: hspace1in - (nabla_r\\cdotU_⊥)a - nabla_r(k\\cdotU_⊥)\\cdotnabla_ka = Σ(δU^2) where U_⊥(r, z=0) is a slowly varying surface current, and Ω(k) = √(k^3+k)tanh kh is the free capillary-gravity dispersion relation. Note that nabla_r\\cdotU_⊥(r,z=0) neq 0, and that the surface currents exchange energy density with the propagating waves. When an additional weak random current √\\varepsilon δU(r/\\varepsilon) varying on the scale of k-1 is included, we find an additional scattering term Σ(δU^2) as a function of correlations in δU. Our results can be applied to the study of surface wave energy transport over a turbulent ocean.

  8. 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. PMID:11461346

  9. 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.

  10. Volume transport and generalized hydrodynamic equations for monatomic fluids.

    PubMed

    Eu, Byung Chan

    2008-10-01

    In this paper, the effects of volume transport on the generalized hydrodynamic equations for a pure simple fluid are examined from the standpoint of statistical mechanics and, in particular, kinetic theory of fluids. First, we derive the generalized hydrodynamic equations, namely, the constitutive equations for the stress tensor and heat flux for a single-component monatomic fluid, from the generalized Boltzmann equation in the presence of volume transport. Then their linear steady-state solutions are derived and examined with regard to the effects of volume transport on them. The generalized hydrodynamic equations and linear constitutive relations obtained for nonconserved variables make it possible to assess Brenner's proposition [Physica A 349, 11 (2005); Physica A 349, 60 (2005)] for volume transport and attendant mass and volume velocities as well as the effects of volume transport on the Newtonian law of viscosity, compression/dilatation (bulk viscosity) phenomena, and Fourier's law of heat conduction. On the basis of study made, it is concluded that the notion of volume transport is sufficiently significant to retain in irreversible thermodynamics of fluids and fluid mechanics. PMID:19045107

  11. The transport exponent in percolation models with additional loops

    NASA Astrophysics Data System (ADS)

    Babalievski, F.

    1994-10-01

    Several percolation models with additional loops were studied. The transport exponents for these models were estimated numerically by means of a transfer-matrix approach. It was found that the transport exponent has a drastically changed value for some of the models. This result supports some previous numerical studies on the vibrational properties of similar models (with additional loops).

  12. 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.

  13. Magnetohydrodynamic transport equations for high current propagation in overdense plasmas

    NASA Astrophysics Data System (ADS)

    Zha, Xuejun; Wang, Yan; Han, Shensheng

    2008-10-01

    In this paper, it is presented that the full set of magnetohydrodynamic (MHD) equations which may be used to study the transport mechanism for the high current relativistic electron beams (current intensity 100˜1000 MA, electron energy ˜ MeV) by the laser in background overdense plasma (1022-1026cm). The transport of intense relativistic electron beams (REB) has two basic characteristics: the first is that the forward current is a giga-ampere and the forward current density is about 10 14 A/cm 2 which exceeds the Alfven current limit [M. Tabak et al., Phys. Plasmas 12, 057305 (2005)]; the second is the propagation of the intense forward current in the presence of a background overdense plasma which may have very strong MHD instability. The transport problem can be solved by MHD equations that describe the dynamic, self consistent collisional and electromagnetic interaction of REB with overdense hydrogenic plasmas or arbitrary atomic-number plasmas. The full set of equations consists of the REB transport equations which are coupled to Maxwell's equations through the electromagnetic-field terms and two-fluid plasma dynamical equations for the background overdense plasma through the collision term.

  14. Transport equations for superconductors in the presence of spin interaction

    NASA Astrophysics Data System (ADS)

    Konschelle, François

    2014-05-01

    Quasi-classical theory of superconductivity provides a powerful and yet simple description of the superconductivity phenomenology. In particular, the Eilenberger and Usadel equations provide a neat simplification of the description of the superconducting state in the presence of disorder and electromagnetic interaction. However, the modern aspects of superconductivity require a correct description of the spin interaction as well. Here, we generalize the transport equations of superconductivity in order to take into account space-time dependent electromagnetic and spin interactions on equal footing. Using a gauge-covariant Wigner transformation for the Green-Gor'kov correlation functions, we establish the correspondence between the Dyson-Gor'kov equation and the quasi-classical transport equation in the time-dependent phase-space. We give the expressions for the gauge-covariant current and charge densities (quasi-particle, electric and spin) in the transport formulation. The generalized Eilenberger and Usadel limits of the transport equation are given, too. This study is devoted to the formal derivation of the equations of motion in the electromagnetic plus spin plus particle-hole space. The studies of some specific systems are postponed to future works.

  15. 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.

  16. Quantum Non-Markovian Langevin Equations and Transport Coefficients

    SciTech Connect

    Sargsyan, V.V.; Antonenko, N.V.; Kanokov, Z.; Adamian, G.G.

    2005-12-01

    Quantum diffusion equations featuring explicitly time-dependent transport coefficients are derived from generalized non-Markovian Langevin equations. Generalized fluctuation-dissipation relations and analytic expressions for calculating the friction and diffusion coefficients in nuclear processes are obtained. The asymptotic behavior of the transport coefficients and correlation functions for a damped harmonic oscillator that is linearly coupled in momentum to a heat bath is studied. The coupling to a heat bath in momentum is responsible for the appearance of the diffusion coefficient in coordinate. The problem of regression of correlations in quantum dissipative systems is analyzed.

  17. 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.

  18. Multilevel methods for transport equations in diffusive regimes

    NASA Technical Reports Server (NTRS)

    Manteuffel, Thomas A.; Ressel, Klaus

    1993-01-01

    We consider the numerical solution of the single-group, steady state, isotropic transport equation. An analysis by means of the moment equations shows that a discrete ordinate S(sub N) discretization in direction (angle) with a least squares finite element discretization in space does not behave properly in the diffusion limit. A scaling of the S(sub N) equations is introduced so that the least squares discretization has the correct diffusion limit. For the resulting discrete system a full multigrid algorithm was developed.

  19. 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.

  20. 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.

  1. Singular perturbation analysis of the neutron transport equation

    SciTech Connect

    Losey, D.C.; Lee, J.C.

    1996-07-01

    A singular perturbation technique is applied to the one-speed, one- dimensional neutron transport equation with isotropic scattering. Our technique extends previous singular perturbation applications to higher-order and reduces the transport problem to a series of diffusion theory problems in the interior medium and a series of analytically solvable transport problems in the boundary layers. Asymptotic matching links the two solutions, yielding boundary conditions and a composite expansion valid throughout the media. Our formulation generates an accurate correction for the material interface condition used in global diffusion theory calculations.

  2. 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.

  3. 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.

  4. 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.

  5. 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.

  6. 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"

  7. 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}.

  8. A transport equation for reaction rate in turbulent flows

    NASA Astrophysics Data System (ADS)

    Sabelnikov, V. A.; Lipatnikov, A. N.; Chakraborty, N.; Nishiki, S.; Hasegawa, T.

    2016-08-01

    New transport equations for chemical reaction rate and its mean value in turbulent flows have been derived and analyzed. Local perturbations of the reaction zone by turbulent eddies are shown to play a pivotal role even for weakly turbulent flows. The mean-reaction-rate transport equation is shown to involve two unclosed dominant terms and a joint closure relation for the sum of these two terms is developed. Obtained analytical results and, in particular, the closure relation are supported by processing two widely recognized sets of data obtained from earlier direct numerical simulations of statistically planar 1D premixed flames associated with both weak large-scale and intense small-scale turbulence.

  9. Transport equations for lower hybrid waves in a turbulent plasma

    NASA Astrophysics Data System (ADS)

    Mendonca, J. T.; Horton, W.; Galvao, R. M. O.; Elskens, Y.

    2014-10-01

    Injection and control of intense lower hybrid (LH) wave spectra is required to achieve steady state tokamak operation in the new WEST tokamak at CEA France. The tungsten [W] environment [E] steadytstate [S] tokamak [T] has two high-power [20 MW] lower hybrid antennas launching 3.7 GHz polarized waves for steady fusion-grade plasmas control. The wave propagation and scattering is described in by ray equations in the presence of the drift wave turbulence. Theory for the wave transport equations for propagation of the wave momentum and energy densities are derived from the Wigner function method of QM. The limits of the diffraction and scattering for ray transport theory are established. Comparisons are made between the wave propagation in WEST and ITER tokamaks. Supported by the University of Texas at Austin; PIIM/CNRS at Aix-Marseille University and University of Sao Paulo.

  10. Lorentz force correction to the Boltzmann radiation transport equation and its implications for Monte Carlo algorithms

    NASA Astrophysics Data System (ADS)

    Bouchard, Hugo; Bielajew, Alex

    2015-07-01

    To establish a theoretical framework for generalizing Monte Carlo transport algorithms by adding external electromagnetic fields to the Boltzmann radiation transport equation in a rigorous and consistent fashion. Using first principles, the Boltzmann radiation transport equation is modified by adding a term describing the variation of the particle distribution due to the Lorentz force. The implications of this new equation are evaluated by investigating the validity of Fano’s theorem. Additionally, Lewis’ approach to multiple scattering theory in infinite homogeneous media is redefined to account for the presence of external electromagnetic fields. The equation is modified and yields a description consistent with the deterministic laws of motion as well as probabilistic methods of solution. The time-independent Boltzmann radiation transport equation is generalized to account for the electromagnetic forces in an additional operator similar to the interaction term. Fano’s and Lewis’ approaches are stated in this new equation. Fano’s theorem is found not to apply in the presence of electromagnetic fields. Lewis’ theory for electron multiple scattering and moments, accounting for the coupling between the Lorentz force and multiple elastic scattering, is found. However, further investigation is required to develop useful algorithms for Monte Carlo and deterministic transport methods. To test the accuracy of Monte Carlo transport algorithms in the presence of electromagnetic fields, the Fano cavity test, as currently defined, cannot be applied. Therefore, new tests must be designed for this specific application. A multiple scattering theory that accurately couples the Lorentz force with elastic scattering could improve Monte Carlo efficiency. The present study proposes a new theoretical framework to develop such algorithms.

  11. Lorentz force correction to the Boltzmann radiation transport equation and its implications for Monte Carlo algorithms.

    PubMed

    Bouchard, Hugo; Bielajew, Alex

    2015-07-01

    To establish a theoretical framework for generalizing Monte Carlo transport algorithms by adding external electromagnetic fields to the Boltzmann radiation transport equation in a rigorous and consistent fashion. Using first principles, the Boltzmann radiation transport equation is modified by adding a term describing the variation of the particle distribution due to the Lorentz force. The implications of this new equation are evaluated by investigating the validity of Fano's theorem. Additionally, Lewis' approach to multiple scattering theory in infinite homogeneous media is redefined to account for the presence of external electromagnetic fields. The equation is modified and yields a description consistent with the deterministic laws of motion as well as probabilistic methods of solution. The time-independent Boltzmann radiation transport equation is generalized to account for the electromagnetic forces in an additional operator similar to the interaction term. Fano's and Lewis' approaches are stated in this new equation. Fano's theorem is found not to apply in the presence of electromagnetic fields. Lewis' theory for electron multiple scattering and moments, accounting for the coupling between the Lorentz force and multiple elastic scattering, is found. However, further investigation is required to develop useful algorithms for Monte Carlo and deterministic transport methods. To test the accuracy of Monte Carlo transport algorithms in the presence of electromagnetic fields, the Fano cavity test, as currently defined, cannot be applied. Therefore, new tests must be designed for this specific application. A multiple scattering theory that accurately couples the Lorentz force with elastic scattering could improve Monte Carlo efficiency. The present study proposes a new theoretical framework to develop such algorithms. PMID:26061045

  12. Numerical solution of the radiation transport equation in disk geometry

    NASA Technical Reports Server (NTRS)

    Spagna, George F., Jr.; Leung, Chun Ming

    1987-01-01

    An efficient numerical method for solving the problem of radiation transport in a dusty medium with two dimensional (2-D) disk geometry is described. It is a generalization of the one-dimensional quasi-diffusion method in which the transport equation is cast in diffusion form and then solved as a boundary value problem. The method should be applicable to a variety of astronomical sources, the dynamics of which are angular-momentum dominated and hence not accurately treated by spherical geometry, e.g., protoplanetary nebulae, circumstellar disks, interstellar molecular clouds, accretion disks, and disk galaxies. The computational procedure and practical considerations for implementing the method are described in detail. To illustrate the effects of 2-D radiation transport, some model results (dust temperature distributions and IR flux spectra) for externally heated, interstellar dust clouds with spherically symmetric and disk geometry are compared.

  13. Inverse problems for homogeneous transport equations: II. The multidimensional case

    NASA Astrophysics Data System (ADS)

    Bal, Guillaume

    2000-08-01

    A companion paper by Bal (Bal G 2000 Inverse Problems 16 997) and this paper are parts I and II of a series dealing with the reconstruction from boundary measurements of the scattering operator of homogeneous linear transport equations. This part II deals with the case of convex bounded domains in dimensions higher than one. We distinguish the analysis of smooth boundaries from that of boundaries with discontinuities such as corners. We propose a reconstruction in the case of degenerate symmetric scattering operators and show the well-posedness of the inverse problem. The proof of well-posedness is based on a decomposition of angular moments of the transport solution into unbounded and bounded components. This decomposition allows us to show the linear independence of a sufficiently large number of angular moments of the transport solution that are used to construct an invertible system for the scattering coefficients to be reconstructed.

  14. Application of the Broyden method to stiff transport equations

    NASA Astrophysics Data System (ADS)

    Carlsson, Johan; Cary, John R.; Cohen, Ron

    2002-11-01

    Plasma turbulence generates fluxes (of particles, energy, etc.) that are said to be stiff, that is a small change in temperature, density, or some other quantity, can lead to a large change in flux. The dependence of the diffusivities on the temperature and density profiles, and their gradients, also introduces nonlinearity. Irrespective of whether the fluxes are given by transport models, such as IFS/PPPL, GLF23, or MMM95, or are directly calculated, the resulting system of transport equations is thus numerically challenging to solve. Efficient transport solvers must also take into account that the evaluation of the diffusivities (or their gradients: the fluxes) is numerically costly. We have developed a new iterative transport solver that combines the stability of a relaxation scheme with the fast convergence of a Newton solver. The new solver uses a gradually decreasing relaxation parameter for the first few iterations and once it is inside the radius of convergence it switches over to a quasi-Newton method where a Broyden-like scheme is used to approximate the Jacobian. By taking advantage of the structure of the matrix (tri-diagonal if a second-order spatial finite differencing is used) the Broyden algorithm[1] gives a good approximation of the Jacobian after only a few iterations. We have implemented the new transport solver in the form of a C++ library called the Transport Analysis Tool. To make the library easy to access from codes written in other languages, a C interface is also provided. We will present the new transport solver in detail, as well as benchmark results and examples of how to use the Transport Analysis Tool library. [1] C. G. Broyden, in Mathematics of Computation, vol. 19, 1965, pp. 577--593.

  15. Optimal Transport, Convection, Magnetic Relaxation and Generalized Boussinesq Equations

    NASA Astrophysics Data System (ADS)

    Brenier, Yann

    2009-10-01

    We establish a connection between optimal transport theory (see Villani in Topics in optimal transportation. Graduate studies in mathematics, vol. 58, AMS, Providence, 2003, for instance) and classical convection theory for geophysical flows (Pedlosky, in Geophysical fluid dynamics, Springer, New York, 1979). Our starting point is the model designed few years ago by Angenent, Haker, and Tannenbaum (SIAM J. Math. Anal. 35:61-97, 2003) to solve some optimal transport problems. This model can be seen as a generalization of the Darcy-Boussinesq equations, which is a degenerate version of the Navier-Stokes-Boussinesq (NSB) equations. In a unified framework, we relate different variants of the NSB equations (in particular what we call the generalized hydrostatic-Boussinesq equations) to various models involving optimal transport (and the related Monge-Ampère equation, Brenier in Commun. Pure Appl. Math. 64:375-417, 1991; Caffarelli in Commun. Pure Appl. Math. 45:1141-1151, 1992). This includes the 2D semi-geostrophic equations (Hoskins in Annual review of fluid mechanics, vol. 14, pp. 131-151, Palo Alto, 1982; Cullen et al. in SIAM J. Appl. Math. 51:20-31, 1991, Arch. Ration. Mech. Anal. 185:341-363, 2007; Benamou and Brenier in SIAM J. Appl. Math. 58:1450-1461, 1998; Loeper in SIAM J. Math. Anal. 38:795-823, 2006) and some fully nonlinear versions of the so-called high-field limit of the Vlasov-Poisson system (Nieto et al. in Arch. Ration. Mech. Anal. 158:29-59, 2001) and of the Keller-Segel for Chemotaxis (Keller and Segel in J. Theor. Biol. 30:225-234, 1971; Jäger and Luckhaus in Trans. Am. Math. Soc. 329:819-824, 1992; Chalub et al. in Mon. Math. 142:123-141, 2004). Mathematically speaking, we establish some existence theorems for local smooth, global smooth or global weak solutions of the different models. We also justify that the inertia terms can be rigorously neglected under appropriate scaling assumptions in the generalized Navier-Stokes-Boussinesq equations

  16. Implicitly causality enforced solution of multidimensional transient photon transport equation.

    PubMed

    Handapangoda, Chintha C; Premaratne, Malin

    2009-12-21

    A novel method for solving the multidimensional transient photon transport equation for laser pulse propagation in biological tissue is presented. A Laguerre expansion is used to represent the time dependency of the incident short pulse. Owing to the intrinsic causal nature of Laguerre functions, our technique automatically always preserve the causality constrains of the transient signal. This expansion of the radiance using a Laguerre basis transforms the transient photon transport equation to the steady state version. The resulting equations are solved using the discrete ordinates method, using a finite volume approach. Therefore, our method enables one to handle general anisotropic, inhomogeneous media using a single formulation but with an added degree of flexibility owing to the ability to invoke higher-order approximations of discrete ordinate quadrature sets. Therefore, compared with existing strategies, this method offers the advantage of representing the intensity with a high accuracy thus minimizing numerical dispersion and false propagation errors. The application of the method to one, two and three dimensional geometries is provided. PMID:20052050

  17. 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.

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

    NASA Astrophysics Data System (ADS)

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

    1989-03-01

    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.

  19. 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.

  20. 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.

  1. 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.

  2. 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.

  3. Proton transport model in the ionosphere 1. Multistream approach of the transport equations

    NASA Astrophysics Data System (ADS)

    Galand, M.; Lilensten, J.; Kofman, W.; Sidje, R. B.

    1997-09-01

    The suprathermal particles, electrons and protons, coming from the magnetosphere and precipitating into the high-latitude atmosphere are an energy source of the Earth's ionosphere. They interact with ambient thermal gas through inelastic and elastic collisions. The physical quantities perturbed by these precipitations, such as the heating rate, the electron production rate, or the emission intensities, can be provided in solving the kinetic stationary Boltzmann equation. This equation yields particle fluxes as a function of altitude, energy, and pitch angle. While this equation has been solved through different ways for the electron transport and fully tested, the proton transport is more complicated. Because of charge-changing reactions, the latter is a set of two-coupled transport equations that must be solved: one for protons and the other for H atoms. We present here a new approach that solves the multistream proton/hydrogen transport equations encompassing the collision angular redistributions and the magnetic mirroring effect. In order to validate our model we discuss the energy conservation and we compare with another model under the same inputs and with rocket observations. The influence of the angular redistributions is discussed in a forthcoming paper.

  4. Geometric Correction for Diffusive Expansion of Steady Neutron Transport Equation

    NASA Astrophysics Data System (ADS)

    Wu, Lei; Guo, Yan

    2015-06-01

    We revisit the diffusive limit of a steady neutron transport equation in a two-dimensional unit disk with one-speed velocity. A classical theorem by Bensoussan et al. (Publ Res Inst Math Sci 15(1):53-157, 1979) states that its solution can be approximated in L ∞ by the leading order interior solution plus the Knudsen layer in the diffusive limit. In this paper, we construct a counterexample to this result via a different boundary layer expansion with geometric correction.

  5. A stochastic multi-symplectic scheme for stochastic Maxwell equations with additive noise

    SciTech Connect

    Hong, Jialin; Zhang, Liying

    2014-07-01

    In this paper we investigate a stochastic multi-symplectic method for stochastic Maxwell equations with additive noise. Based on the stochastic version of variational principle, we find a way to obtain the stochastic multi-symplectic structure of three-dimensional (3-D) stochastic Maxwell equations with additive noise. We propose a stochastic multi-symplectic scheme and show that it preserves the stochastic multi-symplectic conservation law and the local and global stochastic energy dissipative properties, which the equations themselves possess. Numerical experiments are performed to verify the numerical behaviors of the stochastic multi-symplectic scheme.

  6. 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.

  7. 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. PMID:21231274

  8. Modeling tracer transport in randomly heterogeneous porous media by nonlocal moment equations: Anomalous transport

    NASA Astrophysics Data System (ADS)

    Morales-Casique, E.; Lezama-Campos, J. L.; Guadagnini, A.; Neuman, S. P.

    2013-05-01

    Modeling tracer transport in geologic porous media suffers from the corrupt characterization of the spatial distribution of hydrogeologic properties of the system and the incomplete knowledge of processes governing transport at multiple scales. Representations of transport dynamics based on a Fickian model of the kind considered in the advection-dispersion equation (ADE) fail to capture (a) the temporal variation associated with the rate of spreading of a tracer, and (b) the distribution of early and late arrival times which are often observed in field and/or laboratory scenarios and are considered as the signature of anomalous transport. Elsewhere we have presented exact stochastic moment equations to model tracer transport in randomly heterogeneous aquifers. We have also developed a closure scheme which enables one to provide numerical solutions of such moment equations at different orders of approximations. The resulting (ensemble) average and variance of concentration fields were found to display a good agreement against Monte Carlo - based simulation results for mildly heterogeneous (or well-conditioned strongly heterogeneous) media. Here we explore the ability of the moment equations approach to describe the distribution of early arrival times and late time tailing effects which can be observed in Monte-Carlo based breakthrough curves (BTCs) of the (ensemble) mean concentration. We show that BTCs of mean resident concentration calculated at a fixed space location through higher-order approximations of moment equations display long tailing features of the kind which is typically associated with anomalous transport behavior and are not represented by an ADE model with constant dispersive parameter, such as the zero-order approximation.

  9. 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. PMID:16494340

  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. 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.

  12. A unified transport equation for both cosmic rays and thermal particles

    NASA Technical Reports Server (NTRS)

    Williams, L. L.; Schwadron, N.; Jokipii, J. R.; Gombosi, T. I.

    1993-01-01

    We present a unified transport equation that is valid for particles of all energies if the particle mean free paths are much smaller than macroscopic fluid length scales. If restricted to particles with random speeds much greater than fluid flow speeds, this equation reduces to the previously discussed extended cosmic-ray transport equation. It is significant that this allows one to describe the acceleration of particles from thermal energies to cosmic-ray energies using one transport equation. This is in contrast to previous transport equations (the Parker equation and the extended cosmic-ray transport equation), which were restricted to fast particles. The close connection to the extended cosmic-ray transport equation is demonstrated.

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

    NASA Astrophysics Data System (ADS)

    Davey, K.; Darvizeh, R.

    2016-03-01

    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.

  14. 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)

  15. Taylor's hypothesis in turbulent channel flow considered using a transport equation analysis

    NASA Astrophysics Data System (ADS)

    Wallace, James; Geng, Chenhui; He, Guowei; Wang, Yinshan; Xu, Chunxiao

    2014-11-01

    A DNS of turbulent channel flow was carried out to examine Taylor's ``frozen turbulence'' hypothesis, i.e. the simple time-space transformation that allows (1 / Ū) ∂ / ∂ t to approximate streamwise derivatives, ∂ / ∂x , of velocity fluctuations. These terms in Taylor's hypothesis appear in the transport equation for instantaneous momentum for this flow. The additional terms, i.e. the additional convective acceleration and the pressure gradient and viscous force terms, act to diminish the validity of Taylor's hypothesis when they are relatively large compared to the Taylor's hypothesis terms and are not in balance. A similar analysis also has been applied to the transport equation for instantaneous vorticity. There the additional terms, namely the additional convective rates of change, the stretching/compression/rotation and the viscous diffusion of vorticity terms, similarly act to diminish the validity of Taylor's hypothesis when they also are relatively large compared to the terms in the hypothesis and are not in balance. Where in the channel flow this diminishment occurs, and to what degree, and which of the non-Taylor's hypothesis terms in the momentum and vorticity equations contribute most to this diminishment will be presented. Supported by National Natural Sci. Found. and the National Basic Res. Progr. of China and the Burgers Progr. for Fluid Dynamics.

  16. Variational Phase Imaging Using the Transport-of-Intensity Equation.

    PubMed

    Bostan, Emrah; Froustey, Emmanuel; Nilchian, Masih; Sage, Daniel; Unser, Michael

    2016-02-01

    We introduce a variational phase retrieval algorithm for the imaging of transparent objects. Our formalism is based on the transport-of-intensity equation (TIE), which relates the phase of an optical field to the variation of its intensity along the direction of propagation. TIE practically requires one to record a set of defocus images to measure the variation of intensity. We first investigate the effect of the defocus distance on the retrieved phase map. Based on our analysis, we propose a weighted phase reconstruction algorithm yielding a phase map that minimizes a convex functional. The method is nonlinear and combines different ranges of spatial frequencies - depending on the defocus value of the measurements - in a regularized fashion. The minimization task is solved iteratively via the alternating-direction method of multipliers. Our simulations outperform commonly used linear and nonlinear TIE solvers. We also illustrate and validate our method on real microscopy data of HeLa cells. PMID:26685242

  17. 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.

  18. 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.

  19. Averaging of Stochastic Equations for Flow and Transport in PorousMedia

    SciTech Connect

    Shvidler, Mark; Karasaki, Kenzi

    2005-01-07

    It is well known that at present exact averaging of theequations of flow and transport in random porous media have been realizedfor only a small number of special fields. Moreover, the approximateaveraging methods are not yet fully understood. For example, theconvergence behavior and the accuracy of truncated perturbation seriesare not well known; and in addition, the calculation of the high-orderperturbations is very complicated. These problems for a long time havestimulated attempts to find the answer for the question: Are there inexistence some exact general and sufficiently universal forms of averagedequations? If the answer is positive, there arises the problem of theconstruction of these equations and analyzing them. There are manypublications on different applications of this problem to various fields,including: Hydrodynamics, flow and transport in porous media, theory ofelasticity, acoustic and electromagnetic waves in random fields, etc.Here, we present a method of finding some general form of exactlyaveraged equations for flow and transport in random fields by using (1)some general properties of the Green s functions for appropriatestochastic problems, and (2) some basic information about the randomfields of the conductivity, porosity and flow velocity. We presentgeneral forms of exactly averaged non-local equations for the followingcases: (1) steady-state flow with sources in porous media with randomconductivity, (2) transient flow with sources in compressible media withrandom conductivity and porosity; and (3) Nonreactive solute transport inrandom porous media. We discuss the problem of uniqueness and theproperties of the non-local averaged equations for cases with some typeof symmetry (isotropic, transversal isotropic and orthotropic), and weanalyze the structure of the nonlocal equations in the general case ofstochastically homogeneous fields.

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

    NASA Astrophysics Data System (ADS)

    Maassen, Jesse; Lundstrom, Mark

    2015-04-01

    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. 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.

  2. Generalized parallel heat transport equations in collisional to weakly collisional plasmas

    NASA Astrophysics Data System (ADS)

    Zawaideh, Emad; Kim, N. S.; Najmabadi, Farrokh

    1988-11-01

    A new set of two-fluid heat-transport equations for heat conduction in collisional to weakly collisional plasmas was derived on the basis of gyrokinetic equations in flux coordinates. In these equations, no restrictions on the anisotropy of the ion distribution function or the collisionality are imposed. In the highly collisional limit, these equations reduce to the classical heat conduction equation of Spitzer and Haerm (1953), while in the weakly collisional limit, they describe a saturated heat flux. Numerical examples comparing these equations with conventional heat transport equations are presented.

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

    SciTech Connect

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

    2011-01-01

    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{sub 3}{sup -}, SO{sub 4}{sup 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.

  4. Ab initio electronic transport model with explicit solution to the linearized Boltzmann transport equation

    NASA Astrophysics Data System (ADS)

    Faghaninia, Alireza; Ager, Joel W.; Lo, Cynthia S.

    2015-06-01

    Accurate models of carrier transport are essential for describing the electronic properties of semiconductor materials. To the best of our knowledge, the current models following the framework of the Boltzmann transport equation (BTE) either rely heavily on experimental data (i.e., semiempirical), or utilize simplifying assumptions, such as the constant relaxation time approximation (BTE-cRTA). While these models offer valuable physical insights and accurate calculations of transport properties in some cases, they often lack sufficient accuracy—particularly in capturing the correct trends with temperature and carrier concentration. We present here a transport model for calculating low-field electrical drift mobility and Seebeck coefficient of n -type semiconductors, by explicitly considering relevant physical phenomena (i.e., elastic and inelastic scattering mechanisms). We first rewrite expressions for the rates of elastic scattering mechanisms, in terms of ab initio properties, such as the band structure, density of states, and polar optical phonon frequency. We then solve the linear BTE to obtain the perturbation to the electron distribution—resulting from the dominant scattering mechanisms—and use this to calculate the overall mobility and Seebeck coefficient. Therefore, we have developed an ab initio model for calculating mobility and Seebeck coefficient using the Boltzmann transport (aMoBT) equation. Using aMoBT, we accurately calculate electrical transport properties of the compound n -type semiconductors, GaAs and InN, over various ranges of temperature and carrier concentration. aMoBT is fully predictive and provides high accuracy when compared to experimental measurements on both GaAs and InN, and vastly outperforms both semiempirical models and the BTE-cRTA. Therefore, we assert that this approach represents a first step towards a fully ab initio carrier transport model that is valid in all compound semiconductors.

  5. Transport in the spatially tempered, fractional Fokker-Planck equation

    NASA Astrophysics Data System (ADS)

    Kullberg, A.; del-Castillo-Negrete, D.

    2012-06-01

    A study of truncated Lévy flights in super-diffusive transport in the presence of an external potential is presented. The study is based on the spatially tempered, fractional Fokker-Planck (TFFP) equation in which the fractional diffusion operator is replaced by a tempered fractional diffusion (TFD) operator. We focus on harmonic (quadratic) potentials and periodic potentials with broken spatial symmetry. The main objective is to study the dependence of the steady-state probability density function (PDF), and the current (in the case of periodic potentials) on the level of tempering, λ, and on the order of the fractional derivative in space, α. An expansion of the TFD operator for large λ is presented, and the corresponding equation for the coarse grained PDF is obtained. The steady-state PDF solution of the TFFP equation for a harmonic potential is computed numerically. In the limit λ → ∞, the PDF approaches the expected Boltzmann distribution. However, nontrivial departures from this distribution are observed for finite (λ > 0) truncations, and α ≠ 2. In the study of periodic potentials, we use two complementary numerical methods: a finite-difference scheme based on the Grunwald-Letnikov discretization of the truncated fractional derivatives and a Fourier-based spectral method. In the limit λ → ∞, the PDFs converges to the Boltzmann distribution and the current vanishes. However, for α ≠ 2, the PDF deviates from the Boltzmann distribution and a finite non-equilibrium ratchet current appears for any λ > 0. The current is observed to converge exponentially in time to the steady-state value. The steady-state current exhibits algebraical decay with λ, as J ˜ λ-ζ, for α ⩾ 1.75. However, for α ⩽ 1.5, the steady-state current decays exponentially with λ, as J ˜ e-ξλ. In the presence of an asymmetry in the TFD operator, the tempering can lead to a current reversal. A detailed numerical study is presented on the dependence of the

  6. Transport in the spatially tempered, fractional Fokker-Planck equation

    SciTech Connect

    Kullberg, A.; Del-Castillo-Negrete, Diego B

    2012-01-01

    A study of truncated Levy flights in super-diffusive transport in the presence of an external potential is presented. The study is based on the spatially tempered, fractional Fokker-Planck (TFFP) equation in which the fractional diffusion operator is replaced by a tempered fractional diffusion (TFD) operator. We focus on harmonic (quadratic) potentials and periodic potentials with broken spatial symmetry. The main objective is to study the dependence of the steady-state probability density function (PDF), and the current (in the case of periodic potentials) on the level of tempering, lambda, and on the order of the fractional derivative in space, alpha. An expansion of the TFD operator for large lambda is presented, and the corresponding equation for the coarse grained PDF is obtained. The steady-state PDF solution of the TFFP equation for a harmonic potential is computed numerically. In the limit lambda -> infinity, the PDF approaches the expected Boltzmann distribution. However, nontrivial departures from this distribution are observed for finite (lambda > 0) truncations, and alpha not equal 2. In the study of periodic potentials, we use two complementary numerical methods: a finite-difference scheme based on the Grunwald-Letnikov discretization of the truncated fractional derivatives and a Fourier-based spectral method. In the limit lambda -> infinity, the PDFs converges to the Boltzmann distribution and the current vanishes. However, for alpha not equal 2, the PDF deviates from the Boltzmann distribution and a finite non-equilibrium ratchet current appears for any lambda > 0. The current is observed to converge exponentially in time to the steady-state value. The steady-state current exhibits algebraical decay with lambda, as J similar to lambda(-zeta), for alpha >= 1.75. However, for alpha <= 1.5, the steady-state current decays exponentially with lambda, as J similar to e(-xi lambda). In the presence of an asymmetry in the TFD operator, the tempering can lead

  7. Drift-diffusion equation for ballistic transport in nanoscale metal-oxide-semiconductor field effect transistors

    NASA Astrophysics Data System (ADS)

    Rhew, Jung-Hoon; Lundstrom, Mark S.

    2002-11-01

    We develop a drift-diffusion equation that describes ballistic transport in a nanoscale metal-oxide-semiconductor field effect transistor (MOSFET). We treat injection from different contacts separately, and describe each injection with a set of extended McKelvey one-flux equations [Phys. Rev. 123, 51 (1961); 125, 1570 (1962)] that include hierarchy closure approximations appropriate for high-field ballistic transport and degenerate carrier statistics. We then reexpress the extended one-flux equations in a drift-diffusion form with a properly defined Einstein relationship. The results obtained for a nanoscale MOSFET show excellent agreement with the solution of the ballistic Boltzmann transport equation with no fitting parameters. These results show that a macroscopic transport model based on the moments of the Boltzmann transport equation can describe ballistic transport.

  8. 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.

  9. Exact solution of Smoluchowski's continuous multi-component equation with an additive kernel

    NASA Astrophysics Data System (ADS)

    Fernández-Díaz, J. M.; Gómez-García, G. J.

    2007-06-01

    Smoluchowski's equation is used to analyse the dynamics of particulate systems under aggregation processes in aerosol physics, atmospheric physics, astrophysics, polymer chemistry, colloidal chemistry, etc. Here we provide an exact analytical solution for Smoluchowski's general, continuous, multi-component equation with additive kernel, for any initial particle size distribution (PSD). Once obtained the general solution, we apply it to a case with initial gamma PSD, which can be used to test numerical methods developed for solving more general cases. We have analysed the behaviour for large sizes and time, and a scaling approximation has been obtained as Vigil and Ziff conjectured. For bi-component mixtures we prove that as time increases, for the additive kernel, we cannot use the scaling solution to describe the behaviour of the number PSD on the whole. This fact contradicts a recent affirmation on the subject done by Matsoukas et al.

  10. Phonon-limited low-field mobility in silicon: Quantum transport vs. linearized Boltzmann Transport Equation

    NASA Astrophysics Data System (ADS)

    Rhyner, Reto; Luisier, Mathieu

    2013-12-01

    We propose to check and validate the approximations made in dissipative quantum transport (QT) simulations solved in the Non-equilibrium Green's Function formalism by comparing them with the exact solution of the linearized Boltzmann Transport Equation (LB) in the stationary regime. For that purpose, we calculate the phonon-limited electron and hole mobility in bulk Si and ultra-scaled Si nanowires for different crystal orientations ⟨100⟩, ⟨110⟩, and ⟨111⟩. In both QT and LB simulations, we use the same sp3d5s* tight-binding model to describe the electron/hole properties and the same valence-force-field approach to account for the phonon properties. It is found that the QT simplifications work well for electrons, but are less accurate for holes, where a renormalization of the phonon scattering strength is proved useful to improve the results.

  11. Moment-based effective transport equations for energy straggling.

    SciTech Connect

    Prinja, A. K.; Klein, V.; Hughes, H. G.

    2002-01-01

    Ion energy straggling is accomodated in condensed history (CH) Monte Carlo simulation by sampling energy-losses at the end of a fixed spatial step from precomputed, pathlength dependent energy-loss distributions. These distributions are essentially solutions to a straight ahead transport equation given by {partial_derivative}{psi}(s,E)/{partial_derivative}s = {integral}{sub Q{sub min}}{sup Q{sub max}} dQ {sigma}{sub e}(E,Q){psi}(s, E + Q) - {sigma}{sub e}(E){psi}(s,E), 8 {ge} 0, with monoenergetic incidence {psi}(0, E) = {delta}(E{sub 0} - E). In Eq.(1), s is the pathlength variable, {sigma}{sub e}(E,Q) is the differential cross section for energy loss Q, typically given by the relativistic Rutherford cross section for hard collisions, {sigma}{sub e}(E) is the total ion-electron scattering cross section, and Q{sub min} and Q{sub max} are, respectively, the minimum and maximum energy transfer per collision. Direct solution of Eq.( 1) by stochastic or deterministic numerical techniques is not feasible because of the very small energy transfers and very small mean free paths that characterize charged particle interactions. Condensed history codes typically employ an approximate solution due to Vavilov, obtained assuming a constant mean free path and thus restricted to short step sizes. This solution is formal and its numerical evaluation can be computationally laborious, especially for small step sizes. In practice, Monte Carlo codes have incorporated the Vavilov theory through elaborate numerical approximations, such as truncated Edgeworth expansions, curve-fitting approximations using Moyal functions for small penetration depths or higher energies, and special treatments for the large energy-loss tail of the distribution. In this paper we propose an alternative approach which is also valid under the conditions of the Vavilov theory but has the potential of being computationally more efficient.

  12. Cardiovascular risk assessment: addition of CKD and race to the Framingham equation

    PubMed Central

    Drawz, Paul E.; Baraniuk, Sarah; Davis, Barry R.; Brown, Clinton D.; Colon, Pedro J.; Cujyet, Aloysius B.; Dart, Richard A.; Graumlich, James F.; Henriquez, Mario A.; Moloo, Jamaluddin; Sakalayen, Mohammed G.; Simmons, Debra L.; Stanford, Carol; Sweeney, Mary Ellen; Wong, Nathan D.; Rahman, Mahboob

    2012-01-01

    Background/Aims The value of the Framingham equation in predicting cardiovascular risk in African Americans and patients with chronic kidney disease (CKD) is unclear. The purpose of the study was to evaluate whether the addition of CKD and race to the Framingham equation improves risk stratification in hypertensive patients. Methods Participants in the Antihypertensive and Lipid-Lowering Treatment to Prevent Heart Attack Trial (ALLHAT) were studied. Those randomized to doxazosin, age greater than 74 years, and those with a history of coronary heart disease (CHD) were excluded. Two risk stratification models were developed using Cox proportional hazards models in a two-thirds developmental sample. The first model included the traditional Framingham risk factors. The second model included the traditional risk factors plus CKD, defined by eGFR categories, and stratification by race (Black vs. Non-Black). The primary outcome was a composite of fatal CHD, nonfatal MI, coronary revascularization, and hospitalized angina. Results There were a total of 19,811 eligible subjects. In the validation cohort, there was no difference in C-statistics between the Framingham equation and the ALLHAT model including CKD and race. This was consistent across subgroups by race and gender and among those with CKD. One exception was among Non-Black women where the C-statistic was higher for the Framingham equation (0.68 vs 0.65, P=0.02). Additionally, net reclassification improvement was not significant for any subgroup based on race and gender, ranging from −5.5% to 4.4%. Conclusion The addition of CKD status and stratification by race does not improve risk prediction in high-risk hypertensive patients. PMID:23194494

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

    Code of Federal Regulations, 2014 CFR

    2014-10-01

    ... 49 Transportation 2 2014-10-01 2014-10-01 false Additional planning requirements for transportation by rail. 172.820 Section 172.820 Transportation Other Regulations Relating to Transportation PIPELINE AND HAZARDOUS MATERIALS SAFETY ADMINISTRATION, DEPARTMENT OF TRANSPORTATION HAZARDOUS MATERIALS REGULATIONS HAZARDOUS MATERIALS TABLE,...

  14. 49 CFR 172.820 - Additional planning requirements for transportation by rail.

    Code of Federal Regulations, 2013 CFR

    2013-10-01

    ... 49 Transportation 2 2013-10-01 2013-10-01 false Additional planning requirements for transportation by rail. 172.820 Section 172.820 Transportation Other Regulations Relating to Transportation PIPELINE AND HAZARDOUS MATERIALS SAFETY ADMINISTRATION, DEPARTMENT OF TRANSPORTATION HAZARDOUS MATERIALS REGULATIONS HAZARDOUS MATERIALS TABLE,...

  15. Temperature-dependent thermal conductivity in silicon nanostructured materials studied by the Boltzmann transport equation

    NASA Astrophysics Data System (ADS)

    Romano, Giuseppe; Esfarjani, Keivan; Strubbe, David A.; Broido, David; Kolpak, Alexie M.

    2016-01-01

    Nanostructured materials exhibit low thermal conductivity because of the additional scattering due to phonon-boundary interactions. As these interactions are highly sensitive to the mean free path (MFP) of phonons, MFP distributions in nanostructures can be dramatically distorted relative to bulk. Here we calculate the MFP distribution in periodic nanoporous Si for different temperatures, using the recently developed MFP-dependent Boltzmann transport equation. After analyzing the relative contribution of each phonon branch to thermal transport in nanoporous Si, we find that at room temperature optical phonons contribute 17 % to heat transport, compared to 5 % in bulk Si. Interestingly, we observe a constant thermal conductivity over the range 200 K transport of acoustic phonons with long intrinsic MFP and the temperature dependence of the heat capacity. Our findings, which are in qualitative agreement with the temperature trend of thermal conductivities measured in nanoporous Si-based systems, shed light on the origin of the reduction of thermal conductivity in nanostructured materials and demonstrate the necessity of multiscale heat transport engineering, in which the bulk material and geometry are optimized concurrently.

  16. On the derivation of vector radiative transfer equation for polarized radiative transport in graded index media

    NASA Astrophysics Data System (ADS)

    Zhao, J. M.; Tan, J. Y.; Liu, L. H.

    2012-02-01

    Light transport in graded index media follows a curved trajectory determined by Fermat's principle. Besides the effect of variation of the refractive index on the transport of radiative intensity, the curved ray trajectory will induce geometrical effects on the transport of polarization ellipse. This paper presents a complete derivation of vector radiative transfer equation for polarized radiation transport in absorption, emission and scattering graded index media. The derivation is based on the analysis of the conserved quantities for polarized light transport along curved trajectory and a novel approach. The obtained transfer equation can be considered as a generalization of the classic vector radiative transfer equation that is only valid for uniform refractive index media. Several variant forms of the transport equation are also presented, which include the form for Stokes parameters defined with a fixed reference and the Eulerian forms in the ray coordinate and in several common orthogonal coordinate systems.

  17. 2D/1D approximations to the 3D neutron transport equation. II: Numerical comparisons

    SciTech Connect

    Kelley, B. W.; Collins, B.; Larsen, E. W.

    2013-07-01

    In a companion paper [1], (i) several new '2D/1D equations' are introduced as accurate approximations to the 3D Boltzmann transport equation, (ii) the simplest of these approximate equations is systematically discretized, and (iii) a theoretically stable iteration scheme is developed to solve the discrete equations. In this paper, numerical results are presented that confirm the theoretical predictions made in [1]. (authors)

  18. Velocity-Field Theory, Boltzmann's Transport Equation and Geometry

    NASA Astrophysics Data System (ADS)

    Ichinose, Shoichi

    Boltzmann equation describes the time development of the velocity distribution in the continuum fluid matter. We formulate the equation using the field theory where the velocity-field plays the central role. The matter (constituent particles) fields appear as the density and the viscosity. Fluctuation is examined, and is clearly discriminated from the quantum effect. The time variable is emergently introduced through the computational process step. The collision term, for the (velocity)**4 potential (4-body interaction), is explicitly obtained and the (statistical) fluctuation is closely explained. The present field theory model does not conserve energy and is an open-system model. (One dimensional) Navier-Stokes equation or Burger's equation, appears. In the latter part, we present a way to directly define the distribution function by use of the geometry, appearing in the mechanical dynamics, and Feynman's path-integral.

  19. Time-Dependent Ginzburg-Landau Equation and Boltzmann Transport Equation for Charge-Density-Wave Conductors

    NASA Astrophysics Data System (ADS)

    Takane, Yositake; Hayashi, Masahiko; Ebisawa, Hiromichi

    2016-08-01

    The time-dependent Ginzburg-Landau equation and the Boltzmann transport equation for charge-density-wave (CDW) conductors are derived from a microscopic one-dimensional model by applying the Keldysh Green's function approach under a quasiclassical approximation. The effects of an external electric field and impurity pinning of the CDW are fully taken into account without relying on a phenomenological argument. These equations simultaneously describe the spatiotemporal dynamics of both the CDW and quasiparticles; thus, they serve as a starting point to develop a general framework to analyze various nonequilibrium phenomena, such as current conversion between the CDW condensate and quasiparticles, in realistic CDW conductors. It is shown that, in typical situations, the equations correctly describe the nonlinear behavior of electric conductivity in a simpler manner.

  20. 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.

  1. The radiative transport equation in flatland with separation of variables

    NASA Astrophysics Data System (ADS)

    Machida, Manabu

    2016-07-01

    The linear Boltzmann equation can be solved with separation of variables in one dimension, i.e., in three-dimensional space with planar symmetry. In this method, solutions are given by superpositions of eigenmodes which are sometimes called singular eigenfunctions. In this paper, we explore the singular-eigenfunction approach in flatland or two-dimensional space.

  2. Gluon transport equations with condensate in the small angle approximation

    NASA Astrophysics Data System (ADS)

    Blaizot, Jean-Paul; Liao, Jinfeng

    2016-05-01

    We derive the set of kinetic equations that control the evolution of gluons in the presence of a condensate. We show that the dominant singularities remain logarithmic when the scattering involves particles in the condensate. This allows us to define a consistent small angle approximation.

  3. Solving parallel transport equations in the higher-dimensional Kerr-NUT-(A)dS spacetimes

    SciTech Connect

    Connell, Patrick; Frolov, Valeri P.; Kubiznak, David

    2008-07-15

    We obtain and study the equations describing the parallel transport of orthonormal frames along geodesics in a spacetime admitting a nondegenerate, principal, conformal Killing-Yano tensor h. We demonstrate that the operator F, obtained by a projection of h to a subspace orthogonal to the velocity, has in a generic case eigenspaces of dimension not greater than 2. Each of these eigenspaces is independently parallel propagated. This allows one to reduce the parallel transport equations to a set of first order, ordinary, differential equations for the angles of rotation in the 2D eigenspaces. General analysis is illustrated by studying the equations of the parallel transport in the Kerr-NUT-(A)dS metrics. Examples of three-, four-, and five-dimensional Kerr-NUT-(A)dS are considered, and it is shown that the obtained first order equations can be solved by a separation of variables.

  4. Solving parallel transport equations in the higher-dimensional Kerr-NUT-(A)dS spacetimes

    NASA Astrophysics Data System (ADS)

    Connell, Patrick; Frolov, Valeri P.; Kubizňák, David

    2008-07-01

    We obtain and study the equations describing the parallel transport of orthonormal frames along geodesics in a spacetime admitting a nondegenerate, principal, conformal Killing-Yano tensor h. We demonstrate that the operator F, obtained by a projection of h to a subspace orthogonal to the velocity, has in a generic case eigenspaces of dimension not greater than 2. Each of these eigenspaces is independently parallel propagated. This allows one to reduce the parallel transport equations to a set of first order, ordinary, differential equations for the angles of rotation in the 2D eigenspaces. General analysis is illustrated by studying the equations of the parallel transport in the Kerr-NUT-(A)dS metrics. Examples of three-, four-, and five-dimensional Kerr-NUT-(A)dS are considered, and it is shown that the obtained first order equations can be solved by a separation of variables.

  5. Differential equation of exospheric lateral transport and its application to terrestrial hydrogen

    NASA Technical Reports Server (NTRS)

    Hodges, R. R., Jr.

    1973-01-01

    The differential equation description of exospheric lateral transport of Hodges and Johnson is reformulated to extend its utility to light gases. Accuracy of the revised equation is established by applying it to terrestrial hydrogen. The resulting global distributions for several static exobase models are shown to be essentially the same as those that have been computed by Quessette using an integral equation approach. The present theory is subsequently used to elucidate the effects of nonzero lateral flow, exobase rotation, and diurnal tidal winds on the hydrogen distribution. Finally it is shown that the differential equation of exospheric transport is analogous to a diffusion equation. Hence it is practical to consider exospheric transport as a continuation of thermospheric diffusion, a concept that alleviates the need for an artificial exobase dividing thermosphere and exosphere.

  6. 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...

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

    PubMed

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

    2014-04-01

    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

  8. 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.

  9. General solution of a fractional diffusion-advection equation for solar cosmic-ray transport

    NASA Astrophysics Data System (ADS)

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

    2016-04-01

    In this effort we exactly solve the fractional diffusion-advection equation for solar cosmic-ray transport and give its general solution in terms of hypergeometric distributions. Numerical analysis of this equation shows that its solutions resemble power-laws.

  10. Numerical evaluation of the intensity transport equation for well-known wavefronts and intensity distributions

    NASA Astrophysics Data System (ADS)

    Campos-García, Manuel; Granados-Agustín, Fermín.; Cornejo-Rodríguez, Alejandro; Estrada-Molina, Amilcar; Avendaño-Alejo, Maximino; Moreno-Oliva, Víctor Iván.

    2013-11-01

    In order to obtain a clearer interpretation of the Intensity Transport Equation (ITE), in this work, we propose an algorithm to solve it for some particular wavefronts and its corresponding intensity distributions. By simulating intensity distributions in some planes, the ITE is turns into a Poisson equation with Neumann boundary conditions. The Poisson equation is solved by means of the iterative algorithm SOR (Simultaneous Over-Relaxation).

  11. Electrophoretic transport equations - Electrophoretic models based on migration only and their interrelationships

    NASA Technical Reports Server (NTRS)

    Thormann, Wolfgang; Mosher, Richard A.

    1985-01-01

    The general equations which describe the electrophoretic transport of components in solution are restated using Newman's general concept of mobilities. A concise derivation of the moving boundary equation and the regulating function from the continuity equation is presented. Various other regulating principles across moving and stationary boundaries are also discussed, which permits a review of the features and interrelationships of the electrophoretic models based on electromigration only. The effect of considering an interactive (dissociating) solvent on the mathematical treatment is discussed.

  12. Variable order spherical harmonic expansion scheme for the radiative transport equation using finite elements

    SciTech Connect

    Surya Mohan, P.; Tarvainen, Tanja; Schweiger, Martin; Pulkkinen, Aki; Arridge, Simon R.

    2011-08-10

    Highlights: {yields} We developed a variable order global basis scheme to solve light transport in 3D. {yields} Based on finite elements, the method can be applied to a wide class of geometries. {yields} It is computationally cheap when compared to the fixed order scheme. {yields} Comparisons with local basis method and other models demonstrate its accuracy. {yields} Addresses problems encountered n modeling of light transport in human brain. - Abstract: We propose the P{sub N} approximation based on a finite element framework for solving the radiative transport equation with optical tomography as the primary application area. The key idea is to employ a variable order spherical harmonic expansion for angular discretization based on the proximity to the source and the local scattering coefficient. The proposed scheme is shown to be computationally efficient compared to employing homogeneously high orders of expansion everywhere in the domain. In addition the numerical method is shown to accurately describe the void regions encountered in the forward modeling of real-life specimens such as infant brains. The accuracy of the method is demonstrated over three model problems where the P{sub N} approximation is compared against Monte Carlo simulations and other state-of-the-art methods.

  13. Surface harmonics method equations for solving the time-dependent neutron transport problems and their verification

    SciTech Connect

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

    2012-07-01

    Finite-difference time-dependent equations of Surface Harmonics method have been obtained for plane geometry. Verification of these equations has been carried out by calculations of tasks from 'Benchmark Problem Book ANL-7416'. The capacity and efficiency of the Surface Harmonics method have been demonstrated by solution of the time-dependent neutron transport equation in diffusion approximation. The results of studies showed that implementation of Surface Harmonics method for full-scale calculations will lead to a significant progress in the efficient solution of the time-dependent neutron transport problems in nuclear reactors. (authors)

  14. A two-equation integral model for particle transport in renewal statistical media

    SciTech Connect

    Zuchuat, O.; Sanchez, R.

    1995-12-31

    The authors consider the problem of particle transport including scattering in renewal statistical media. The general description of this problem leads to an infinite hierarchy of equations. A new closure scheme is developed to obtain a more tractable set of equations. Numerical results in planar geometry are given which compare the predictions of this new closure with exact benchmark results as well as with a previous model available in the literature. The development of the new closure and the comparisons the authors make underline the importance of having a physical basis in the elaboration of closure schemes for the hierarchy of equations describing the transport of particle with collisions in stochastic mixtures.

  15. 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.

  16. A Hybrid FE-FV Discontinuous Method to Solve Flow and Transport Equations in Heterogeneous Porous Media

    NASA Astrophysics Data System (ADS)

    Nick, H. M.; Matthai, S. K.

    2009-05-01

    In heterogeneous porous media material discontinuities affect single phase flow as well as multiphase flow. The finite-element method allows to represent such boundaries using piecewise constant or linear material property variations from finite element to element. However, when a node-centered complementary finite volume method is used to model transport across these material interfaces, this discretization can not represent jump discontinuities in concentration or saturation. To overcome this dilemma there are two options, one can either enrich the nodes at the interfaces by additional degrees of freedom or explode the model along the interfaces. This technique, is another way of resolving this problem. Interface nodes are multiplicated so that they match in number the material domains which they join. Here, we use this latter approach, developing an IMPES transport model that can evolve discontinuities at material interfaces in a heterogeneous porous medium. To achieve pressure continuity across the exploded material interfaces, we implement a new implicit algorithm. For the transport equation, we develop a higher-order-accurate scheme which captures jump discontinuity of the transport variable. We use operator-splitting to solve the transport equation after the pressure equation, with the finite volume method, modeling diffusion implicitly employing the finite element method. We verify the new method by a comparison between its results and those of the continuous one. The main advantage of the discontinuous scheme is the resolution of the effects of the material discontinuities. The first order discretization dependency is removed.

  17. FRACTIONAL SOLUTE TRANSPORT EQUATION EVALUATED WITH THE MISCIBLE DISPLACEMENT EXPERIMENTAL DATA

    Technology Transfer Automated Retrieval System (TEKTRAN)

    A new solute transport model has been recently developed assuming that the movements of solute particles in hierarchically-structured porous media belongs to the family of Lévy motions rather than to the Brownian motion. The one-dimensional fractional advective-dispersive transport equation, or FADE...

  18. Fractional Advective-Dispersive Equation as a Model of Solute Transport in Porous Media

    Technology Transfer Automated Retrieval System (TEKTRAN)

    Understanding and modeling transport of solutes in porous media is a critical issue in the environmental protection. The common model is the advective-dispersive equation (ADE) describing the superposition of the advective transport and the Brownian motion in water-filled pore space. Deviations from...

  19. 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.

  20. 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.

  1. Radiative or neutron transport modeling using a lattice Boltzmann equation framework

    NASA Astrophysics Data System (ADS)

    Bindra, H.; Patil, D. V.

    2012-07-01

    In this paper, the lattice Boltzmann equation (LBE)-based framework is used to obtain the solution for the linear radiative or neutron transport equation. The LBE framework is devised for the integrodifferential forms of these equations which arise due to the inclusion of the scattering terms. The interparticle collisions are neglected, hence omitting the nonlinear collision term. Furthermore, typical representative examples for one-dimensional or two-dimensional geometries and inclusion or exclusion of the scattering term (isotropic and anisotropic) in the Boltzmann transport equation are illustrated to prove the validity of the method. It has been shown that the solution from the LBE methodology is equivalent to the well-known Pn and Sn methods. This suggests that the LBE can potentially provide a more convenient and easy approach to solve the physical problems of neutron and radiation transport.

  2. 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.

  3. Stability of a general mixed additive-cubic functional equation in non-Archimedean fuzzy normed spaces

    SciTech Connect

    Xu Tianzhou; Rassias, John Michael; Xu Wanxin

    2010-09-15

    We establish some stability results concerning the general mixed additive-cubic functional equation in non-Archimedean fuzzy normed spaces. In addition, we establish some results of approximately general mixed additive-cubic mappings in non-Archimedean fuzzy normed spaces. The results improve and extend some recent results.

  4. General analytic methods for solving coupled transport equations: From cosmology to beyond

    NASA Astrophysics Data System (ADS)

    White, G. A.

    2016-02-01

    We propose a general method to analytically solve transport equations during a phase transition without making approximations based on the assumption that any transport coefficient is large. Using a cosmic phase transition in the minimal supersymmetric standard model as a pedagogical example, we derive the solutions to a set of 3 transport equations derived under the assumption of supergauge equilibrium and the diffusion approximation. The result is then rederived efficiently using a technique we present involving a parametrized ansatz which turns the process of deriving a solution into an almost elementary problem. We then show how both the derivation and the parametrized ansatz technique can be generalized to solve an arbitrary number of transport equations. Finally we derive a perturbative series that relaxes the usual approximation that inactivates vacuum-expectation-value dependent relaxation and C P -violating source terms at the bubble wall and through the symmetric phase. Our analytical methods are able to reproduce a numerical calculation in the literature.

  5. Generalized parallel heat transport equations in collisional to weakly collisional plasmas

    SciTech Connect

    Zawaideh, E.; Kim, N.S.; Najmabadi, F.

    1988-11-01

    A new set of two-fluid heat transport equations that is valid from collisional to weakly collisional limits is derived. Starting from gyrokinetic equations in flux coordinates, a set of moment equations describing plasma energy transport along the field lines of a space- and time-dependent magnetic field is derived. No restrictions on the anisotropy of the ion distribution function or collisionality are imposed. In the highly collisional limit, these equations reduce to the classical heat conduction equation (e.g., Spitzer and Haerm or Braginskii), while in the weakly collisional limit, they describe a saturated heat flux (flux limited). Numerical examples comparing these equations with conventional heat transport equations show that in the limit where the ratio of the mean free path lambda to the scale length of the temperature gradient L/sub T/ approaches zero, there is no significant difference between the solutions of the new and conventional heat transport equations. As lambda/L/sub T/..-->..1, the conventional heat conduction equation contains a significantly larger error than (lambda/L/sub T/)/sup 2/. The error is found to be O(lambda/L)/sup 2/, where L is the smallest of the scale lengths of the gradient in the magnetic field, or the macroscopic plasma parameters (e.g., velocity scale length, temperature scale length, and density scale length). The accuracy of the flux-limited model depends significantly on the value of the flux limit parameter which, in general, is not known. The new set of equations shows that the flux-limited parameter is a function of the magnetic field and plasma parameter profiles.

  6. 2D/1D approximations to the 3D neutron transport equation. I: Theory

    SciTech Connect

    Kelley, B. W.; Larsen, E. W.

    2013-07-01

    A new class of '2D/1D' approximations is proposed for the 3D linear Boltzmann equation. These approximate equations preserve the exact transport physics in the radial directions x and y and diffusion physics in the axial direction z. Thus, the 2D/1D equations are more accurate approximations of the 3D Boltzmann equation than the conventional 3D diffusion equation. The 2D/1D equations can be systematically discretized, to yield accurate simulation methods for 3D reactor core problems. The resulting solutions will be more accurate than 3D diffusion solutions, and less expensive to generate than standard 3D transport solutions. In this paper, we (i) show that the simplest 2D/1D equation has certain desirable properties, (ii) systematically discretize this equation, and (iii) derive a stable iteration scheme for solving the discrete system of equations. In a companion paper [1], we give numerical results that confirm the theoretical predictions of accuracy and iterative stability. (authors)

  7. Molecular representation of molar domain (volume), evolution equations, and linear constitutive relations for volume transport.

    PubMed

    Eu, Byung Chan

    2008-09-01

    In the traditional theories of irreversible thermodynamics and fluid mechanics, the specific volume and molar volume have been interchangeably used for pure fluids, but in this work we show that they should be distinguished from each other and given distinctive statistical mechanical representations. In this paper, we present a general formula for the statistical mechanical representation of molecular domain (volume or space) by using the Voronoi volume and its mean value that may be regarded as molar domain (volume) and also the statistical mechanical representation of volume flux. By using their statistical mechanical formulas, the evolution equations of volume transport are derived from the generalized Boltzmann equation of fluids. Approximate solutions of the evolution equations of volume transport provides kinetic theory formulas for the molecular domain, the constitutive equations for molar domain (volume) and volume flux, and the dissipation of energy associated with volume transport. Together with the constitutive equation for the mean velocity of the fluid obtained in a previous paper, the evolution equations for volume transport not only shed a fresh light on, and insight into, irreversible phenomena in fluids but also can be applied to study fluid flow problems in a manner hitherto unavailable in fluid dynamics and irreversible thermodynamics. Their roles in the generalized hydrodynamics will be considered in the sequel. PMID:19044872

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

    NASA Technical Reports Server (NTRS)

    Kennedy, Christopher A.; Carpenter, Mark H.

    2002-01-01

    Additive Runge-Kutta (ARK) methods are investigated for application to the spatially discretized one- dimensional convection-diffusion-reaction (CDR) equations. Accuracy, stability, conservation, and dense-output are first 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 (ARK(sub 2)) 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 of the partitioned method are of equal order to those of the elemental methods. Derived ARK(sub 2) methods have vanishing stability functions for very large values of the stiff scaled eigenvalue, z['] yields -infinity, and retain high stability efficiency in the absence of stiffness, z['] yield 0. Extrapolation-type stage- value predictors are provided based on dense-output formulae. Optimized methods minimize both leading order ARK(sub 2) 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 ARK(sub 2) methods.

  9. 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.

  10. Modeling ballistic effects in frequency-dependent transient thermal transport using diffusion equations

    NASA Astrophysics Data System (ADS)

    Maassen, Jesse; Lundstrom, Mark

    2016-03-01

    Understanding ballistic phonon transport effects in transient thermoreflectance experiments and explaining the observed deviations from classical theory remains a challenge. Diffusion equations are simple and computationally efficient but are widely believed to break down when the characteristic length scale is similar or less than the phonon mean-free-path. Building on our prior work, we demonstrate how well-known diffusion equations, namely, the hyperbolic heat equation and the Cattaneo equation, can be used to model ballistic phonon effects in frequency-dependent periodic steady-state thermal transport. Our analytical solutions are found to compare excellently to rigorous numerical results of the phonon Boltzmann transport equation. The correct physical boundary conditions can be different from those traditionally used and are paramount for accurately capturing ballistic effects. To illustrate the technique, we consider a simple model problem using two different, commonly used heating conditions. We demonstrate how this framework can easily handle detailed material properties, by considering the case of bulk silicon using a full phonon dispersion and mean-free-path distribution. This physically transparent approach provides clear insights into the nonequilibrium physics of quasi-ballistic phonon transport and its impact on thermal transport properties.

  11. Comparing the results of bed load transport equations to field measurements in an Alpine river

    NASA Astrophysics Data System (ADS)

    Rascher, E.; Baewert, H.; Schmidt, K.-H.; Morche, D.

    2012-04-01

    Transport processes play a decisive role in fluvial systems when sediment is carried from source to sink. In a mountain river reach the morphologic development is basically determined by the bed load transport. Attempts to observe bed load entrainment and movement directly in the field are often complicated through difficulties in spatial and temporal variability and a necessary field effort. For this reason the development of sediment transport equations has a long history. A variety of such formulae has appeared since the first "modern" equation of DU BOYS (1879) was presented. Each of them is based on one of the following approaches: shear stress, stream discharge, stochastic function for sediment movement or stream power. Many of these equations have been developed on the basis of flume data or field data sets from specific river reaches. Therefore a critical consideration of their application to other natural streams is essential. A lack of available field data is undoubtedly the cause for a deficiency of such testing. (GOMEZ & CHURCH 1989; HABERSACK & LARONNE 2002; MARTIN 2003) In this study a selection of sediment transport equations is tested against data sets of 50 field observations from the Partnach River, in the Reintal Valley, Germany, in the years 2008-2011. At the outlet of this alpine catchment the channel bed is characterized by a gradient of 2 % and a median grain size of 24 mm. Bed load samples were taken using the Helley-Smith sampler at flow rates ranging from 1.0 - 5.9 m3/s. According to these data evaluations performance and feasibility of transport equations for field applications are checked. Up to now the results between observed and calculated transport rates show a large scatter of more than several orders of magnitude. This underlines the statements from GOMEZ AND CHURCH (1989) that most equations under/over predict transport rates if the basic requirements (steady flow, equilibrium load), which are usually assumed, are not fulfilled.

  12. 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

  13. Solution and Study of the Two-Dimensional Nodal Neutron Transport Equation

    SciTech Connect

    Panta Pazos, Ruben; Biasotto Hauser, Eliete; Tullio de Vilhena, Marco

    2002-07-01

    In the last decade Vilhena and coworkers reported an analytical solution to the two-dimensional nodal discrete-ordinates approximations of the neutron transport equation in a convex domain. The key feature of these works was the application of the combined collocation method of the angular variable and nodal approach in the spatial variables. By nodal approach we mean the transverse integration of the SN equations. This procedure leads to a set of one-dimensional S{sub N} equations for the average angular fluxes in the variables x and y. These equations were solved by the old version of the LTS{sub N} method, which consists in the application of the Laplace transform to the set of nodal S{sub N} equations and solution of the resulting linear system by symbolic computation. It is important to recall that this procedure allow us to increase N the order of S{sub N} up to 16. To overcome this drawback we step forward performing a spectral painstaking analysis of the nodal S{sub N} equations for N up to 16 and we begin the convergence of the S{sub N} nodal equations defining an error for the angular flux and estimating the error in terms of the truncation error of the quadrature approximations of the integral term. Furthermore, we compare numerical results of this approach with those of other techniques used to solve the two-dimensional discrete approximations of the neutron transport equation. (authors)

  14. One-dimensional transport equation models for sound energy propagation in long spaces: theory.

    PubMed

    Jing, Yun; Larsen, Edward W; Xiang, Ning

    2010-04-01

    In this paper, a three-dimensional transport equation model is developed to describe the sound energy propagation in a long space. Then this model is reduced to a one-dimensional model by approximating the solution using the method of weighted residuals. The one-dimensional transport equation model directly describes the sound energy propagation in the "long" dimension and deals with the sound energy in the "short" dimensions by prescribed functions. Also, the one-dimensional model consists of a coupled set of N transport equations. Only N=1 and N=2 are discussed in this paper. For larger N, although the accuracy could be improved, the calculation time is expected to significantly increase, which diminishes the advantage of the model in terms of its computational efficiency. PMID:20370013

  15. 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.

  16. Variance estimates for transport in stochastic media by means of the master equation

    SciTech Connect

    Pautz, S. D.; Franke, B. C.; Prinja, A. K.

    2013-07-01

    The master equation has been used to examine properties of transport in stochastic media. It has been shown previously that not only may the Levermore-Pomraning (LP) model be derived from the master equation for a description of ensemble-averaged transport quantities, but also that equations describing higher-order statistical moments may be obtained. We examine in greater detail the equations governing the second moments of the distribution of the angular fluxes, from which variances may be computed. We introduce a simple closure for these equations, as well as several models for estimating the variances of derived transport quantities. We revisit previous benchmarks for transport in stochastic media in order to examine the error of these new variance models. We find, not surprisingly, that the errors in these variance estimates are at least as large as the corresponding estimates of the average, and sometimes much larger. We also identify patterns in these variance estimates that may help guide the construction of more accurate models. (authors)

  17. Iterative solution of the multistream electron transport equation. I - Comparison with laboratory beam injection experiments

    NASA Technical Reports Server (NTRS)

    Porter, H. S.; Varosi, F.; Mayr, H. G.

    1987-01-01

    The Neumann iteration method presently used for solving the electron transport equation in which energy, attitude, and pitch angle are independent variables is fast, and can compute numerical point-response-function solutions of the electron transport equation. Because both the inelastic cross sections and angular elastic cross sections of the model are empirically based, the solutions obtained represent a test of compatibility between various sets of cross sections and energy deposition measurements. The use of a numerical quadrature based on analytic phase function forms yields accurate phase function integrals at low computational cost.

  18. 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.

  19. Numerical Analysis of Quantum Transport Equation for Bose Gas in One Dimensional Optical Lattice

    NASA Astrophysics Data System (ADS)

    Kuwahara, Yukiro; Nakamura, Yusuke; Yamanaka, Yoshiya

    The quantum transport equation and the correction of the quasiparticle energy are derived by imposing the renormalization conditions on the improved time-dependent on-shell self-energy in nonequilibrium Thermo Field Dynamics. They are numerically analyzed for the one dimensional system of cold neutral atomic Bose gas confined by a combined harmonic and optical lattice potentials. The analysis indicates that the correction of the quaisparticle energy plays a crucial role in the thermal relaxation processes described by the quantum transport equation.

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

    NASA Astrophysics Data System (ADS)

    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.

  1. 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.

  2. Variational approach to solving the spectral Boltzmann transport equation in transient thermal grating for thin films

    NASA Astrophysics Data System (ADS)

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

    2016-07-01

    The phonon Boltzmann transport equation (BTE) is widely utilized to study non-diffusive thermal transport. We find a solution of the BTE in the thin film transient thermal grating (TTG) experimental geometry by using a recently developed variational approach with a trial solution supplied by the Fourier heat conduction equation. We obtain an analytical expression for the thermal decay rate that shows excellent agreement with Monte Carlo simulations. We also obtain a closed form expression for the effective thermal conductivity that demonstrates the full material property and heat transfer geometry dependence, and recovers the limits of the one-dimensional TTG expression for very thick films and the Fuchs-Sondheimer expression for very large grating spacings. The results demonstrate the utility of the variational technique for analyzing non-diffusive phonon-mediated heat transport for nanostructures in multi-dimensional transport geometries, and will assist the probing of the mean free path distribution of materials via transient grating experiments.

  3. 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)

  4. 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.

  5. 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.

  6. Modeling scalar dissipation and scalar variance in large eddy simulation: Algebraic and transport equation closures

    NASA Astrophysics Data System (ADS)

    Knudsen, E.; Richardson, E. S.; Doran, E. M.; Pitsch, H.; Chen, J. H.

    2012-05-01

    Scalar dissipation rates and subfilter scalar variances are important modeling parameters in large eddy simulations (LES) of reacting flows. Currently available models capture the general behavior of these parameters, but these models do not always perform with the degree of accuracy that is needed for predictive LES. Here, two direct numerical simulations (DNS) are used to analyze LES dissipation rate and variance models, and to propose a new model for the dissipation rate that is based on a transport equation. The first DNS that is considered is a non-premixed auto-igniting C2H4 jet flame simulation originally performed by Yoo et al. [Proc. Combust. Inst. 33, 1619-1627 (2011)], 10.1016/j.proci.2010.06.147. A LES of this case is run using algebraic models for the dissipation rate and subfilter variance. It is shown that the algebraic models fail to adequately reproduce the DNS results. This motivates the introduction of a transport equation model for the LES dissipation rate. Closure of the equation is addressed by formulating a new adapted dynamic approach. This approach borrows dynamically computed information from LES quantities that, unlike the dissipation rate, do not reside on the smallest flow length scales. The adapted dynamic approach is analyzed by considering a second DNS of scalar mixing in homogeneous isotropic turbulence. Data from this second DNS are used to confirm that the adapted dynamic approach successfully closes the dissipation rate equation over a wide range of LES filter widths. The first reacting jet case is then returned to and used to test the LES transport equation models. The transport equation model for the dissipation rate is shown to be more accurate than its algebraic counterpoint, and the dissipation rate is eliminated as a source of error in the transported variance model.

  7. Exactly averaged stochastic equations for flow and transport in random media

    SciTech Connect

    Shvidler, Mark; Karasaki, Kenzi

    2001-11-30

    It is well known that exact averaging of the equations of flow and transport in random porous media are at present realized only for a small number of special, occasionally exotic, fields. On the other hand, the properties of approximate averaging methods are not yet fully understood. For example, the convergence behavior and the accuracy of truncated perturbation series are not well known. Furthermore, the calculation of the high-order perturbations is very complicated. These problems for a long time have stimulated attempts to find the answer for the question: Are there in existence some exact general and sufficiently universal forms of averaged equations? If the answer is positive, there arises the problem of the construction of these equations and analyzing them. There exist many publications related to these problems and oriented on different applications: hydrodynamics, flow and transport in porous media, theory of elasticity, acoustic and electromagnetic waves in random fields, etc. We present a method of finding some general forms of exactly averaged equations for flow and transport in random fields by using (1) an assumption of the existence of Green's functions for appropriate stochastic problems, (2 ) some general properties of the Green's functions, and (3) the some basic information about the random fields of the conductivity, porosity and flow velocity. We present some general forms of the exactly averaged non-local equations for the following cases. 1. Steady-state flow with sources in porous media with random conductivity. 2. Transient flow with sources in compressible media with random conductivity and porosity. 3. Non-reactive solute transport in random porous media. We discuss the problem of uniqueness and the properties of the non-local averaged equations, for the cases with some types of symmetry (isotropic, transversal isotropic, orthotropic) and we analyze the hypothesis of the structure of non-local equations in a general case of

  8. A Reynolds-averaged turbulence modeling approach using three transport equations for the turbulent viscosity, kinetic energy, and dissipation rate

    NASA Astrophysics Data System (ADS)

    Yoshizawa, Akira; Abe, Hiroyuki; Matsuo, Yuichi; Fujiwara, Hitoshi; Mizobuchi, Yasuhiro

    2012-07-01

    A Reynolds-averaged approach to turbulent shear flows is sought with resort to a three-equation method. Its novelty is the introduction of a turbulent-viscosity transport equation through the transport equation for the Reynolds stress in addition to those for the turbulent kinetic energy and the dissipation rate. The latter two equations are used for evaluating the dimensional coefficients in the former. The aim of this model is to enhance the capability to cope with nonstationary and advection effects in various turbulent flows. The adaptability to them is confirmed through the application to homogeneous-shear and supersonic free-shear flows. In particular, the reasonable prediction is obtained in the latter where the growth rate of the shear layer is suppressed with the increase in the convective Mach number. The present model is also applied to a three-dimensional flow past a wing tip as an instance of complex aeronautical flows, and the excessive diffusion of the trailing vortices is shown to be suppressed. The turbulent-viscosity representation for the Reynolds stress is systematically supplemented with nonlinear effects of mean-velocity gradient tensors, and its adequacy is verified in a channel flow.

  9. 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...

  10. Modeling Solute Transport in Soil Columns Using Advective-Dispersive Equation with Fractional Spatial Derivatives

    Technology Transfer Automated Retrieval System (TEKTRAN)

    It has been reported that this model cannot take into account several important features of solute movement through soil. Recently, a new model has been suggested that results in a solute transport equation with fractional spatial derivatives, or FADE. We have assembled a database on published solu...

  11. Parallel algorithms for 2-D cylindrical transport equations of Eigenvalue problem

    SciTech Connect

    Wei, J.; Yang, S.

    2013-07-01

    In this paper, aimed at the neutron transport equations of eigenvalue problem under 2-D cylindrical geometry on unstructured grid, the discrete scheme of Sn discrete ordinate and discontinuous finite is built, and the parallel computation for the scheme is realized on MPI systems. Numerical experiments indicate that the designed parallel algorithm can reach perfect speedup, it has good practicality and scalability. (authors)

  12. Moment-equation methods for calculating neoclassical transport coefficients in general toroidal plasmas

    SciTech Connect

    Sugama, H.; Nishimura, S.

    2008-04-15

    A detailed comparison is made between moment-equation methods presented by H. Sugama and S. Nishimura [Phys. Plasmas 9, 4637 (2002)] and by M. Taguchi [Phys. Fluids B 4, 3638 (1992)] for calculating neoclassical transport coefficients in general toroidal plasmas including nonsymmetric systems. It is shown that these methods can be derived from the drift kinetic equation with the same collision model used for correctly taking account of collisional momentum conservation. In both methods, the Laguerre polynomials of the energy variable are employed to expand the guiding-center distribution function and to obtain the moment equations, by which the radial neoclassical transport fluxes and the parallel flows are related to the thermodynamic forces. The methods are given here in the forms applicable for an arbitrary truncation number of the Laguerre-polynomial expansion so that their accuracies can be improved by increasing the truncation number. Differences between results from the two methods appear when the Laguerre-polynomial expansion is truncated up to a finite order because different weight functions are used in them to derive the moment equations. At each order of the truncation, the neoclassical transport coefficients obtained from the Sugama-Nishimura method show the Onsager symmetry and satisfy the ambipolar-diffusion condition intrinsically for symmetric systems. Also, numerical examples are given to show how the transport coefficients converge with the truncation number increased for the two methods.

  13. 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...

  14. 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.

  15. Exact PDF equations and closure approximations for advective-reactive transport

    SciTech Connect

    Venturi, D.; Tartakovsky, Daniel M.; Tartakovsky, Alexandre M.; Karniadakis, George E.

    2013-06-01

    Mathematical models of advection–reaction phenomena rely on advective flow velocity and (bio) chemical reaction rates that are notoriously random. By using functional integral methods, we derive exact evolution equations for the probability density function (PDF) of the state variables of the advection–reaction system in the presence of random transport velocity and random reaction rates with rather arbitrary distributions. These PDF equations are solved analytically for transport with deterministic flow velocity and a linear reaction rate represented mathematically by a heterog eneous and strongly-correlated random field. Our analytical solution is then used to investigate the accuracy and robustness of the recently proposed large-eddy diffusivity (LED) closure approximation [1]. We find that the solution to the LED-based PDF equation, which is exact for uncorrelated reaction rates, is accurate even in the presence of strong correlations and it provides an upper bound of predictive uncertainty.

  16. 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.

  17. 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.

  18. Deterministic proton transport solving a one dimensional Fokker-Planck equation

    SciTech Connect

    Marr, D.; Prael, R.; Adams, K.; Alcouffe, R.

    1997-10-01

    The transport of protons through matter is characterized by many interactions which cause small deflections and slight energy losses. The few which are catastrophic or cause large angle scattering can be viewed as extinction for many applications. The transport of protons at this level of approximation can be described by a Fokker Planck Equation. This equation is solved using a deterministic multigroup differencing scheme with a highly resolved set of discrete ordinates centered around the beam direction which is adequate to properly account for deflections and energy losses due to multiple Coulomb scattering. Comparisons with LAHET for a large variety of problems ranging from 800 MeV protons on a copper step wedge to 10 GeV protons on a sandwich of material are presented. The good agreement with the Monte Carlo code shows that the solution method is robust and useful for approximate solutions of selected proton transport problems.

  19. 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.

  20. Self-Adjoint Angular Flux Equation for Coupled Electron-Photon Transport

    SciTech Connect

    Liscum-Powell, J.L.; Lorence, L.J. Jr.; Morel, J.E.; Prinja, A.K.

    1999-07-08

    Recently, Morel and McGhee described an alternate second-order form of the transport equation called the self adjoint angular flux (SAAF) equation that has the angular flux as its unknown. The SAAF formulation has all the advantages of the traditional even- and odd-parity self-adjoint equations, with the added advantages that it yields the full angular flux when it is numerically solved, it is significantly easier to implement reflective and reflective-like boundary conditions, and in the appropriate form it can be solved in void regions. The SAAF equation has the disadvantage that the angular domain is the full unit sphere and, like the even- and odd- parity form, S{sub n} source iteration cannot be implemented using the standard sweeping algorithm. Also, problems arise in pure scattering media. Morel and McGhee demonstrated the efficacy of the SAAF formulation for neutral particle transport. Here we apply the SAAF formulation to coupled electron-photon transport problems using multigroup cross-sections from the CEPXS code and S{sub n} discretization.

  1. Multi-term approximation to the Boltzmann transport equation for electron energy distribution functions in nitrogen

    NASA Astrophysics Data System (ADS)

    Feng, Yue

    Plasma is currently a hot topic and it has many significant applications due to its composition of both positively and negatively charged particles. The energy distribution function is important in plasma science since it characterizes the ability of the plasma to affect chemical reactions, affect physical outcomes, and drive various applications. The Boltzmann Transport Equation is an important kinetic equation that provides an accurate basis for characterizing the distribution function---both in energy and space. This dissertation research proposes a multi-term approximation to solve the Boltzmann Transport Equation by treating the relaxation process using an expansion of the electron distribution function in Legendre polynomials. The elastic and 29 inelastic cross sections for electron collisions with nitrogen molecules (N2) and singly ionized nitrogen molecules ( N+2 ) have been used in this application of the Boltzmann Transport Equation. Different numerical methods have been considered to compare the results. The numerical methods discussed in this thesis are the implicit time-independent method, the time-dependent Euler method, the time-dependent Runge-Kutta method, and finally the implicit time-dependent relaxation method by generating the 4-way grid with a matrix solver. The results show that the implicit time-dependent relaxation method is the most accurate and stable method for obtaining reliable results. The results were observed to match with the published experimental data rather well.

  2. Pseudospectral Methods of Solution of the Linear and Linearized Boltzmann Equations; Transport and Relaxation

    NASA Astrophysics Data System (ADS)

    Shizgal, Bernie D.

    2011-05-01

    The study of the solution of the linearized Boltzmann equation has a very long history arising from the classic work by Chapman and Cowling. For small departures from a Maxwellian, the nonlinear Boltzmann equation can be linearized and the transport coefficients calculated with the Chapman-Enskog approach. This procedure leads to a set of linear integral equations which are generally solved with the expansion of the departure from Maxwellian in Sonine polynomials. The method has been used successfully for many decades to compare experimental transport data in atomic gases with theory generally carried out for realistic atom-atom differential cross sections. There are alternate pseudospectral methods which involve the discretization of the distribution function on a discrete grid. This paper considers a pseudospectral method of solution of the linearized hard sphere Boltzmann equation for the viscosity in a simple gas. The relaxation of a small departure from a Maxwellian is also considered for the linear test particle problem with unit mass ratio which is compared with the relaxation for the linearized one component Boltzmann equation.

  3. Benchmark solutions for the galactic ion transport equations with spatial and energy coupling

    NASA Technical Reports Server (NTRS)

    Ganapol, Barry D.

    1988-01-01

    In order to anticipate future space shielding requirements, NASA has initiated an effort to formulate computational methods to simulate radiation effects in space. As part of the program, numerical transport algorithms have been developed for the deterministic Boltzman equation describing galactic cosmic ray (GCR) interactions with matter. It thus becomes necessary to assess the accuracy of proposed deterministic algorithms. For this reason, analytical benchmark solutions to mathematically tractable galactic cosmic ray equations have recently been obtained. Even though these problems involve simplifying assumptions of the associated physics, they still contain the essential features of the basic transport processes. The solutions obtained are features of the basic transport processes. The solutions obtained are compared to results from numerical algorithms in order to ensure proper coding and to provide a measure of the accuracy of the numerical methods used in the algorithm. For the first time, mathematical methods have been applied to the galactic ion transport (GIT) equations in the straight ahead approximation with constant nuclear properties. The approach utilizes a Laplace transforms inversion yielding a closed form benchmark solution which is also computationally efficient.

  4. Solutions to bi-Maxwellian transport equations for the polar wind

    NASA Technical Reports Server (NTRS)

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

    1989-01-01

    In this study, polar wind solutions are obtained for a broad range of O(+) density, H(+) drift velocity, electron temperature and H(+) temperature boundary conditions. The bi-Maxwellian-based 16-moment set of transport equations is used, since this set is expected to be superior to Maxwellian-based equations in describing large temperature anisotropies and heat flows. The present solutions corroborate earlier results when similar boundary conditions are used. Also, for previously unexplored combinations of boundary conditions, the present solutions are often qualitatively different from any obtained before.

  5. Petrov-galerkin finite element method for solving the neutron transport equation

    SciTech Connect

    Greenbaum, A.; Ferguson, J.M.

    1986-05-01

    A finite element using different trial and test spaces in introduced for solving the neutron transport equation in spherical geometry. It is shown that the widely used discrete ordinates method can also be thought of as such a finite element technique, in which integrals appearing in the difference equations are replaced by one-point Gauss quadrature formulas (midpoint rule). Comparison of accuracy between the new method and the discrete ordinates method is discussed, and numerical examples are given to illustrate the greater accuracy of the new technique.

  6. 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.

  7. Analytical solution of the advection-diffusion transport equation using a change-of-variable and integral transform technique

    Technology Transfer Automated Retrieval System (TEKTRAN)

    This paper presents a formal exact solution of the linear advection-diffusion transport equation with constant coefficients for both transient and steady-state regimes. A classical mathematical substitution transforms the original advection-diffusion equation into an exclusively diffusive equation. ...

  8. 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.

  9. 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)

  10. Exponentially-convergent Monte Carlo for the 1-D transport equation

    SciTech Connect

    Peterson, J. R.; Morel, J. E.; Ragusa, J. C.

    2013-07-01

    We define a new exponentially-convergent Monte Carlo method for solving the one-speed 1-D slab-geometry transport equation. This method is based upon the use of a linear discontinuous finite-element trial space in space and direction to represent the transport solution. A space-direction h-adaptive algorithm is employed to restore exponential convergence after stagnation occurs due to inadequate trial-space resolution. This methods uses jumps in the solution at cell interfaces as an error indicator. Computational results are presented demonstrating the efficacy of the new approach. (authors)

  11. 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.

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

    DOE PAGESBeta

    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

  13. Improved master equation approach to quantum transport: From Born to self-consistent Born approximation

    SciTech Connect

    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.

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

    SciTech Connect

    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.

  15. 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.

  16. 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.

  17. Kinetic equations for hopping transport and spin relaxation in a random magnetic field

    NASA Astrophysics Data System (ADS)

    Shumilin, A. V.; Kabanov, V. V.

    2015-07-01

    We derive the kinetic equations for a hopping transport that take into account an electron spin and the possibility of double occupation. In the Ohmic regime, the equations are reduced to the generalized Miller-Abrahams resistor network. We apply these equations to the problem of the magnetic moment relaxation due to the interaction with the random hyperfine fields. It is shown that in a wide range of parameters the relaxation rate is governed by the hops with the similar rates as spin precession frequency. It is demonstrated that at the large time scale spin relaxation is nonexponential. We argue that the nonexponential relaxation of the magnetic moment is related to the spin of electrons in the slow-relaxing traps. Interestingly, the traps can significantly influence the spin relaxation in the infinite conducting cluster at large times.

  18. 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

  19. 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).

  20. 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.

  1. Derivation of the macroscopic solute transport equation for homogeneous, saturated, porous media

    SciTech Connect

    Chu, S.Y.; Sposito, G.

    1980-06-01

    The macroscopic transport equation for a conservative solute in a homogeneous, water-saturated porous medium is derived on the basis of a rigorous cumulant expansion applied to the equation of mass balance. The essential physical conept underlying the derivation is that of a local volume-averaged solute velocity which fluctuates on a time scale that is orders of magnitude smaller than its autocorrelation time scale, which, in turn, is much smaller than the time scale of interest in a typical solute transport experiment. This clear separation of the scales is illustrated with representative data on solute transport in homogeneous, water-saturated soils and is employed to justify the truncation of an exact cumulant expansion of the divergence of the volume-averaged solute mass flux density. With the cumulant expansion terminated at first order in the ratio of the solute velocity autocorrelation time to the macroscopic solute transport time interval, an expression for the macroscopic solute mass flux density is produced which is the same as Fick's law extended to porous media. 26 references.

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

    NASA Astrophysics Data System (ADS)

    Mantel, T.

    1993-12-01

    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

  3. 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

  4. 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.

  5. 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.

  6. Chiral transport equation from the quantum Dirac Hamiltonian and the on-shell effective field theory

    NASA Astrophysics Data System (ADS)

    Manuel, Cristina; Torres-Rincon, Juan M.

    2014-10-01

    We derive the relativistic chiral transport equation for massless fermions and antifermions by performing a semiclassical Foldy-Wouthuysen diagonalization of the quantum Dirac Hamiltonian. The Berry connection naturally emerges in the diagonalization process to modify the classical equations of motion of a fermion in an electromagnetic field. We also see that the fermion and antifermion dispersion relations are corrected at first order in the Planck constant by the Berry curvature, as previously derived by Son and Yamamoto for the particular case of vanishing temperature. Our approach does not require knowledge of the state of the system, and thus it can also be applied at high temperature. We provide support for our result by an alternative computation using an effective field theory for fermions and antifermions: the on-shell effective field theory. In this formalism, the off-shell fermionic modes are integrated out to generate an effective Lagrangian for the quasi-on-shell fermions/antifermions. The dispersion relation at leading order exactly matches the result from the semiclassical diagonalization. From the transport equation, we explicitly show how the axial and gauge anomalies are not modified at finite temperature and density despite the incorporation of the new dispersion relation into the distribution function.

  7. 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.

  8. Analytical solution of equations describing slow axonal transport based on the stop-and-go hypothesis

    NASA Astrophysics Data System (ADS)

    Kuznetsov, Andrey

    2011-06-01

    This paper presents an analytical solution for slow axonal transport in an axon. The governing equations for slow axonal transport are based on the stop-and-go hypothesis which assumes that organelles alternate between short periods of rapid movement on microtubules (MTs), short on-track pauses, and prolonged off-track pauses, when they temporarily disengage from MTs. The model includes six kinetic states for organelles: two for off-track organelles (anterograde and retrograde), two for running organelles, and two for pausing organelles. An analytical solution is obtained for a steady-state situation. To obtain the analytical solution, the governing equations are uncoupled by using a perturbation method. The solution is validated by comparing it with a high-accuracy numerical solution. Results are presented for neurofilaments (NFs), which are characterized by small diffusivity, and for tubulin oligomers, which are characterized by large diffusivity. The difference in transport modes between these two types of organelles in a short axon is discussed. A comparison between zero-order and first-order approximations makes it possible to obtain a physical insight into the effects of organelle reversals (when organelles change the type of a molecular motor they are attached to, an anterograde versus retrograde motor).

  9. Spatial correlations, additivity, and fluctuations in conserved-mass transport processes

    NASA Astrophysics Data System (ADS)

    Das, Arghya; Chatterjee, Sayani; Pradhan, Punyabrata

    2016-06-01

    We exactly calculate two-point spatial correlation functions in steady state in a broad class of conserved-mass transport processes, which are governed by chipping, diffusion, and coalescence of masses. We find that the spatial correlations are in general short-ranged and, consequently, on a large scale, these transport processes possess a remarkable thermodynamic structure in the steady state. That is, the processes have an equilibrium-like additivity property and, consequently, a fluctuation-response relation, which help us to obtain subsystem mass distributions in the limit of subsystem size large.

  10. Analytic structure of two 1D-transport equations with nonlocal fluxes

    NASA Astrophysics Data System (ADS)

    Baker, Gregory R.; Li, Xiao; Morlet, Anne C.

    We replace the flux term in Burger's equation by two simple alternates that contain contributions depending globally on the solution. In one case, the term is in the form of a hyperbolic equation where the characteristic speed is nonlocal, and in the other the term is in conservation form. In both cases, the nonanalytic is due to the presence of the Hilbert transform. The equations have a loose analogy to the motion of vortex sheets. In particular, they both form singularities in finite time in the absence of viscous effects. Our motivation then is to study the influence of viscosity. In one case, viscosity does not prevent singularity formation. In the other, we can prove solutions exist for all time, and determine the likely weak solution as viscosity vanishes. An interesting aspect of our work is that singularity formation can be viewed as the motion of singularities in the complex physical plane that reach the real axis in finite time. In one case, the singularity is a pole and causes the solution to blow up when it reaches the real axis. In the other, numerical solutions and an asymptotic analysis suggest that the weak solution contains a square root singularity that reaches the real axis in finite time, and then propagates along it. We hope our results will spur further interest in the role of singularities in the complex spatial plane in solutions to transport equations.

  11. 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)

  12. Two-dimensional phase unwrapping using the transport of intensity equation.

    PubMed

    Pandey, Neeraj; Ghosh, Amitava; Khare, Kedar

    2016-03-20

    We report a method for two-dimensional phase unwrapping based on the transport of intensity equation (TIE). Given a wrapped phase profile, we generate an auxiliary complex field and propagate it to small distances to simulate two intensity images on closely spaced planes. Using the longitudinal intensity derivative of the auxiliary field as an input, the TIE is solved by employing the regularized Fourier-transform-based approach. The resultant phase profile is automatically in the unwrapped form, as it has been obtained as a solution of a partial differential equation rather than as an argument of a complex-valued function. Our simulations and experimental results suggest that this approach is fast and accurate and provides a simple and practical solution for routine phase unwrapping tasks in interferometry and digital holography. PMID:27140583

  13. Modeling Heat Conduction and Radiation Transport with the Diffusion Equation in NIF ALE-AMR

    SciTech Connect

    Fisher, A C; Bailey, D S; Kaiser, T B; Gunney, B N; Masters, N D; Koniges, A E; Eder, D C; Anderson, R W

    2009-10-06

    The ALE-AMR code developed for NIF is a multi-material hydro-code that models target assembly fragmentation in the aftermath of a shot. The combination of ALE (Arbitrary Lagrangian Eulerian) hydro with AMR (Adaptive Mesh Refinement) allows the code to model a wide range of physical conditions and spatial scales. The large range of temperatures encountered in the NIF target chamber can lead to significant fluxes of energy due to thermal conduction and radiative transport. These physical effects can be modeled approximately with the aid of the diffusion equation. We present a novel method for the solution of the diffusion equation on a composite mesh in order to capture these physical effects.

  14. Separation of electrostatic and magnetic phase shifts using a modified transport-of-intensity equation.

    PubMed

    Humphrey, E; Phatak, C; Petford-Long, A K; De Graef, M

    2014-04-01

    We introduce a new approach for the separation of the electrostatic and magnetic components of the electron wave phase shift, based on the transport-of-intensity equation (TIE) formalism. We derive two separate TIE-like equations, one for each of the phase shift components. We use experimental results on FeCoB and Permalloy patterned islands to illustrate how the magnetic and electrostatic longitudinal derivatives can be computed. The main advantage of this new approach is the fact that the differences in the power spectra of the two phase components (electrostatic phase shifts often have significant power in the higher frequencies) can be accommodated by the selection of two different Tikhonov regularization parameters for the two phase reconstructions. The extra computational demands of the method are more than compensated by the improved phase reconstruction results. PMID:24513573

  15. A coupling model of the radiative transport equation for calculating photon migration in biological tissue

    NASA Astrophysics Data System (ADS)

    Fujii, Hiroyuki; Okawa, Shinpei; Yamada, Yukio; Hoshi, Yoko; Watanabe, Masao

    2015-12-01

    Development of a physically accurate and computationally efficient photon migration model for turbid media is crucial for optical computed tomography such as diffuse optical tomography. For the development, this paper constructs a space-time coupling model of the radiative transport equation with the photon diffusion equation. In the coupling model, a space-time regime of the photon migration is divided into the ballistic and diffusive regimes with the interaction between the both regimes to improve the accuracy of the results and the efficiency of computation. The coupling model provides an accurate description of the photon migration in various turbid media in a wide range of the optical properties, and reduces computational loads when compared with those of full calculation of the RTE.

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

    NASA Astrophysics Data System (ADS)

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

    2015-12-01

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

  17. Phase retrieval by using the transport-of-intensity equation with Hilbert transform.

    PubMed

    Li, Wei-Shuo; Chen, Chun-Wei; Lin, Kuo-Feng; Chen, Hou-Ren; Tsai, Chih-Ya; Chen, Chyong-Hua; Hsieh, Wen-Feng

    2016-04-01

    Phase recovery by solving the transport-of-intensity equation (TIE) is a non-iterative and non-interferometric phase retrieval technique. From solving the TIE with conventional, one partial derivative and Hilbert transform methods for both the periodic and aperiodic samples, we demonstrate that the Hilbert transform method can provide the smoother phase images with edge enhancement and fine structures. Furthermore, compared with the images measured by optical and atomic force microscopy, the Hilbert transform method has the ability to quantitatively map out the phase images for both the periodic and aperiodic structures. PMID:27192301

  18. 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.

  19. Variational Determination of the Neutron Integral Transport Equation Eigenvalues Using Space Asymptotic Trial Functions

    NASA Astrophysics Data System (ADS)

    Colombo, V.; Ravetto, P.; Sumini, M.

    1988-08-01

    An approximate determination of the critical eigenvalue of the neutron transport equation in integral form, within both the one speed and energy multigroup models, for a homogeneous medium, is achieved by means of a variational technique. The space asymptotic solutions for both the direct and adjoint problems are used as trial functions. A variational procedure is also developed and numerically exploited within the Fourier transformed domain, where noticeable theoretical features can be demonstrated. It is evidenced that excellent results can be obtained with little computational effort, and a set of critical calculations in plane geometry is presented and discussed.

  20. Variational determination of the neutron integral transport equation eigenvalues using space asymptotic trial functions

    SciTech Connect

    Colombo, V.; Ravetto, P.; Sumini, M.

    1988-08-01

    An approximate determination of the critical eigenvalue of the neutron transport equation in integral form, within both the one speed and energy multigroup models, for a homogeneous medium, is achieved by means of a variational technique. The space asymptotic solutions for both the direct and adjoint problems are used as trial functions. A variational procedure is also developed and numerically exploited within the Fourier transformed domain, where noticeable theoretical features can be demonstrated. It is evidenced that excellent results can be obtained with little computational effort, and a set of critical calculations in plane geometry is presented and discussed. copyright 1988 Academic Press, Inc.

  1. Application of the transport of intensity equation to EUV multilayer defect analysis

    NASA Astrophysics Data System (ADS)

    Xu, Dongbo; Evanschitzky, Peter; Erdmann, Andreas

    2015-03-01

    This paper proposes a new method for the characterization of multilayer defects of EUV masks. The method uses measured or simulated EUV projection images at different focus positions. The Transport of Intensity Equation (TIE) is applied to retrieve the phase distribution of the reflected light in the vicinity of the defect. An Artificial Neural Network (ANN) is applied to correlate the optical properties of the intensity and recovered phase of the defect with the defect geometry parameters and to reconstruct the defect geometry parameters from though-focus-images of unknown defects.

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

    DOE PAGESBeta

    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.

  3. Error analysis and correction in wavefront reconstruction from the transport-of-intensity equation

    PubMed Central

    Barbero, Sergio; Thibos, Larry N.

    2007-01-01

    Wavefront reconstruction from the transport-of-intensity equation (TIE) is a well-posed inverse problem given smooth signals and appropriate boundary conditions. However, in practice experimental errors lead to an ill-condition problem. A quantitative analysis of the effects of experimental errors is presented in simulations and experimental tests. The relative importance of numerical, misalignment, quantization, and photodetection errors are shown. It is proved that reduction of photodetection noise by wavelet filtering significantly improves the accuracy of wavefront reconstruction from simulated and experimental data. PMID:20052302

  4. Gluon transport equation with effective mass and dynamical onset of Bose-Einstein condensation

    NASA Astrophysics Data System (ADS)

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

    2016-05-01

    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. 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.

  5. Variance-reduced particle simulation of the Boltzmann transport equation in the relaxation-time approximation.

    PubMed

    Radtke, Gregg A; Hadjiconstantinou, Nicolas G

    2009-05-01

    We present an efficient variance-reduced particle simulation technique for solving the linearized Boltzmann transport equation in the relaxation-time approximation used for phonon, electron, and radiative transport, as well as for kinetic gas flows. The variance reduction is achieved by simulating only the deviation from equilibrium. We show that in the limit of small deviation from equilibrium of interest here, the proposed formulation achieves low relative statistical uncertainty that is also independent of the magnitude of the deviation from equilibrium, in stark contrast to standard particle simulation methods. Our results demonstrate that a space-dependent equilibrium distribution improves the variance reduction achieved, especially in the collision-dominated regime where local equilibrium conditions prevail. We also show that by exploiting the physics of relaxation to equilibrium inherent in the relaxation-time approximation, a very simple collision algorithm with a clear physical interpretation can be formulated. PMID:19518597

  6. 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.

  7. 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

  8. 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.

  9. Fokker-Planck equations for charged-particle transport with a discussion of some higher-order effects

    NASA Technical Reports Server (NTRS)

    Jokipii, J. R.

    1973-01-01

    A derivation of the Fokker-Planck equation, based on the central limit theorem, is presented which clearly illustrates the conditions for its validity. It is reiterated that previous use of the Fokker-Planck equation in cosmic-ray transport is correct. Higher-order effects associated with magnetic mirroring and field line random walk at low energies are discussed heuristically.

  10. An iterative KP1 method for solving the transport equation in 3D domains on unstructured grids

    NASA Astrophysics Data System (ADS)

    Kokonkov, N. I.; Nikolaeva, O. V.

    2015-10-01

    A two-step iterative KP1 method for solving systems of grid equations that approximate the integro-differential transport equation in 3D domains on unstructured grids using nodal SN methods is described. Results of testing the efficiency of the proposed method in solving benchmark problems of reactor protection on tetrahedral grids are presented.

  11. A Synchronous and Iterative Flux-Correction Formalism for Coupled Transport Equations

    NASA Astrophysics Data System (ADS)

    Schär, Christoph; Smolarkiewicz, Piotr K.

    1996-10-01

    Many problems of fluid dynamics involve the coupled transport of several, density-like, dependent variables (for instance, densities of mass and momenta in elastic flows). In this paper, a conservative and synchronous flux-corrected transport (FCT) formalism is developed which aims at a consistent transport of such variables. The technique differs from traditional FCT algorithms in two respects. First, the limiting of transportive fluxes of the primary variables (e.g., mass and momentum) does not derive from smooth estimates of the variables, but it derives from analytic constraints implied by the Lagrangian form of the governing continuity equations, which are imposed on the specific mixing ratios of the variables (e.g., velocity components). Second, the traditional FCT limiting based on sufficiency conditions is augmented by an iterative procedure which approaches the necessity requirements. This procedure can also be used in the framework of traditional FCT schemes, and a demonstration is provided that it can significantly reduce some of the pathological behaviors of FCT algorithms. Although the approach derived is applicable to the transport of arbitrary conserved quantities, it is particularly useful for the synchronous transport of mass and momenta in elastic flows, where it assures intrinsic stability of the algorithm regardless of the magnitude of the mass-density variable. This latter property becomes especially important in fluids with large density variations, or in models with a material "vertical" coordinate (e.g., geophysical hydrostatic stratified flows in isopycnic/isentropic coordinates), where material surfaces can collapse to zero-mass layers admitting, therefore, arbitrarily large local Courant numbers.

  12. Versatile Role of Solvent Additive for Tailoring Morphology in Polymer Solar Cells for Efficient Charge Transport.

    PubMed

    Khatiwada, Devendra; Venkatesan, Swaminathan; Ngo, Evan C; Qiao, Qiquan

    2015-09-01

    In this work role of solvent additive namely 1,8 diiodoctane (DIO) on the nanoscale morphology and its relation with the charge transport of poly(diketopyrrolopyrrole-terthiophene) (PDPP3T):PCBM solar cells has been investigated. Addition of DIO led to enhanced structural ordering as observed from optical measurements. Photovoltaic devices processed with DIO additive showed improved efficiencies due to significant enhancement in short circuit current density. Atomic force microscopy (AFM) and Kelvin probe force microscopy (KPFM) images showed that DIO led to finer phase segregation that gave rise to better photovoltaic performance in additive processed active layers. Photoinduced current extraction by linearly increasing voltage (P-CELIV) measurements on PDPP3T:PCBM solar cells revealed higher mobility and extracted charge carrier density for DIO processed devices. PMID:26716280

  13. 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

  14. Gradient flipping algorithm: introducing non-convex constraints in wavefront reconstructions with the transport of intensity equation.

    PubMed

    Parvizi, A; Van den Broek, W; Koch, C T

    2016-04-18

    The transport of intensity equation (TIE) is widely applied for recovering wave fronts from an intensity measurement and a measurement of its variation along the direction of propagation. In order to get around the problem of non-uniqueness and ill-conditionedness of the solution of the TIE in the very common case of unspecified boundary conditions or noisy data, additional constraints to the solution are necessary. Although from a numerical optimization point of view, convex constraint as imposed to by total variation minimization is preferable, we will show that in many cases non-convex constraints are necessary to overcome the low-frequency artifacts so typical for convex constraints. We will provide simulated and experimental examples that demonstrate the superiority of solutions to the TIE obtained by our recently introduced gradient flipping algorithm over a total variation constrained solution. PMID:27137272

  15. Exact solutions to the interfacial surfactant transport equation on a droplet in a Stokes flow regime

    NASA Astrophysics Data System (ADS)

    Kallendorf, Christina; Fath, Anja; Oberlack, Martin; Wang, Yongqi

    2015-08-01

    In the research literature there exist very rare analytical solutions of the surfactant transport equation on an interface. In the present article, we derive sets of exact solutions to interfacial convection-diffusion equations which describe the interfacial transport of insoluble surfactants in a two-phase flow. The investigated model is based on a Stokes flow setting where a spherical shaped inner phase is dispersed in an outer phase. Under the assumption of the small capillary number, the deformation of the spherical phase interface is not taken into account. Neglecting the dependence of the surface tension on the interfacial surfactant concentration, hence neglecting the Marangoni effect, general exact solutions to the surfactant conservation law on the spherical surface with both convective and diffusive terms are provided by means of Heun's confluent function. For the steady case, it is shown that these solutions collapse to a simple exponential form. Furthermore, for the purely diffusive problem, exact solutions are constructed using Legendre polynomials. Such analytical solutions are very valuable as benchmark problems in numerical investigations.

  16. Application of the multigrid amplitude function method for time-dependent transport equation using MOC

    SciTech Connect

    Tsujita, K.; Endo, T.; Yamamoto, A.

    2013-07-01

    An efficient numerical method for time-dependent transport equation, the mutigrid amplitude function (MAF) method, is proposed. The method of characteristics (MOC) is being widely used for reactor analysis thanks to the advances of numerical algorithms and computer hardware. However, efficient kinetic calculation method for MOC is still desirable since it requires significant computation time. Various efficient numerical methods for solving the space-dependent kinetic equation, e.g., the improved quasi-static (IQS) and the frequency transform methods, have been developed so far mainly for diffusion calculation. These calculation methods are known as effective numerical methods and they offer a way for faster computation. However, they have not been applied to the kinetic calculation method using MOC as the authors' knowledge. Thus, the MAF method is applied to the kinetic calculation using MOC aiming to reduce computation time. The MAF method is a unified numerical framework of conventional kinetic calculation methods, e.g., the IQS, the frequency transform, and the theta methods. Although the MAF method is originally developed for the space-dependent kinetic calculation based on the diffusion theory, it is extended to transport theory in the present study. The accuracy and computational time are evaluated though the TWIGL benchmark problem. The calculation results show the effectiveness of the MAF method. (authors)

  17. 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.

  18. CALIBRATION OF RICHARDS' AND CONVECTION--DISPERSION EQUATIONS TO FIELD-SCALE WATER FLOW AND SOLUTE TRANSPORT UNDER RAINFALL CONDITIONS

    Technology Transfer Automated Retrieval System (TEKTRAN)

    Identification of flow and transport processes under natural boundary conditions in field soils is a complex task since most model parameters are not measurable at that scale. However, combining a numerical solution method of the governing flow and transport equations with an inverse optimization al...

  19. 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...

  20. An unstaggered constrained transport method for the 3D ideal magnetohydrodynamic equations

    NASA Astrophysics Data System (ADS)

    Helzel, Christiane; Rossmanith, James A.; Taetz, Bertram

    2011-05-01

    Numerical methods for solving the ideal magnetohydrodynamic (MHD) equations in more than one space dimension must either confront the challenge of controlling errors in the discrete divergence of the magnetic field, or else be faced with nonlinear numerical instabilities. One approach for controlling the discrete divergence is through a so-called constrained transport method, which is based on first predicting a magnetic field through a standard finite volume solver, and then correcting this field through the appropriate use of a magnetic vector potential. In this work we develop a constrained transport method for the 3D ideal MHD equations that is based on a high-resolution wave propagation scheme. Our proposed scheme is the 3D extension of the 2D scheme developed by Rossmanith [J.A. Rossmanith, An unstaggered, high-resolution constrained transport method for magnetohydrodynamic flows, SIAM J. Sci. Comput. 28 (2006) 1766], and is based on the high-resolution wave propagation method of Langseth and LeVeque [J.O. Langseth, R.J. LeVeque, A wave propagation method for threedimensional hyperbolic conservation laws, J. Comput. Phys. 165 (2000) 126]. In particular, in our extension we take great care to maintain the three most important properties of the 2D scheme: (1) all quantities, including all components of the magnetic field and magnetic potential, are treated as cell-centered; (2) we develop a high-resolution wave propagation scheme for evolving the magnetic potential; and (3) we develop a wave limiting approach that is applied during the vector potential evolution, which controls unphysical oscillations in the magnetic field. One of the key numerical difficulties that is novel to 3D is that the transport equation that must be solved for the magnetic vector potential is only weakly hyperbolic. In presenting our numerical algorithm we describe how to numerically handle this problem of weak hyperbolicity, as well as how to choose an appropriate gauge condition. The

  1. 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

  2. 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

  3. 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)

  4. Nonlinear acceleration of a continuous finite element discretization of the self-adjoint angular flux form of the transport equation

    SciTech Connect

    Sanchez, R.

    2012-07-01

    Nonlinear acceleration of a continuous finite element (CFE) discretization of the transport equation requires a modification of the transport solution in order to achieve local conservation, a condition used in nonlinear acceleration to define the stopping criterion. In this work we implement a coarse-mesh finite difference acceleration for a CFE discretization of the second-order self adjoint angular flux (SAAF) form of the transport equation and use a post processing to enforce local conservation. Numerical results are given for one-group source calculations of one-dimensional slabs. We also give a formal derivation of the boundary conditions for the SAAF. (authors)

  5. Nonlinear Acceleration of a Continuous Finite Element Discretization of the Self-Adjoint Angular Flux Form of the Transport Equation

    SciTech Connect

    Richard Sanchez; Cristian Rabiti; Yaqi Wang

    2013-11-01

    Nonlinear acceleration of a continuous finite element (CFE) discretization of the transport equation requires a modification of the transport solution in order to achieve local conservation, a condition used in nonlinear acceleration to define the stopping criterion. In this work we implement a coarse-mesh finite difference acceleration for a CFE discretization of the second-order self-adjoint angular flux (SAAF) form of the transport equation and use a postprocessing to enforce local conservation. Numerical results are given for one-group source calculations of one-dimensional slabs. We also give a novel formal derivation of the boundary conditions for the SAAF.

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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)

  11. 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.

  12. Effect of imposed boundary conditions on the accuracy of transport of intensity equation based solvers

    NASA Astrophysics Data System (ADS)

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

    2013-05-01

    The transport of intensity equation (TIE) describes the relation between the object phase and the intensity distribution in the Fresnel region and can be used as a non-interferometric technique to estimate the phase distribution of an object. A number of techniques have been developed to solve the TIE. In this work we focus on one popular class of Poisson solvers that are based on Fourier and the Multigrid techniques. The aim of this paper is to present an analysis of these types of TIE solvers taking into account the effect of the boundary condition, i.e. the Neumann Boundary Condition (NBC), the Dirichlet Boundary Condition (DBC), and the Periodic Boundary Condition (PBC). This analysis, which depends on the location of an object wave-front in the detector plane, aims to identify the advantages and disadvantage of these kinds of solvers and to provide the rules for choice of the best fitted boundary condition.

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

    NASA Astrophysics Data System (ADS)

    Hu, Jingwei; Wang, Li

    2015-01-01

    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.

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

    PubMed

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

    2015-04-01

    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. PMID:25968722

  15. Excited nuclear matter at Fermi energies: From transport properties to the equation of state

    NASA Astrophysics Data System (ADS)

    Lopez, O.; Durand, D.; Lehaut, G.

    2016-05-01

    Properties of excited nuclear matter are one of the main subject of investigation in Nuclear Physics. Indeed, the response of nuclear matter under extreme conditions encountered in heavy-ion induced reactions (large compression, thermal and collective excitations, isopin diffusion) around the Fermi energy is strongly needed when studying the nuclear equation of state and the underlying in-medium properties concerning the nuclear interaction. In this contribution, we will present some experimental results concerning the transport properties of nuclear matter, focusing specifically on the determination of in-medium quantities such as mean free pathes and nucleon-nucleon cross sections around the Fermi energy. We will see that, in this specific energy range, energy and isospin dissipations exhibit very peculiar features, such as the crossover between 1-body to 2-body dissipation regimes corresponding to the transition between the nuclear response from Mean-Field to the nucleonic response through the appearance of nucleon-nucleon collisions.

  16. Iterative feedback algorithm for phase retrieval based on transport of intensity equation

    NASA Astrophysics Data System (ADS)

    Liu, Kaifeng; Cheng, Hong; Zhang, Cheng; Shen, Chuan; Zhang, Fen; Wei, Sui

    2015-12-01

    In this paper, a novel phase retrieval algorithm is presented which combines the advantages of the Transport of Intensity Equation (TIE) method and the iteration method. TIE method is fast, but its precision is not high. Though the convergence rate of iteration method is slow, its result is more accurate. This algorithm consists of Iterative Angular Spectrum (IAS) method to utilize the physical constraints between the object and the spectral domain, and the relationship between the intensity and phase among the wave propagation. Firstly, the phase at the object plane is calculated from two intensity images by TIE. Then this result is treated as the initial phase of the IAS. Finally, the phase information at the object plane is acquired according the reversibility of the optical path. During the iteration process, the feedback mechanism is imposed on it that improve the convergence rate and the precision of phase retrieval and the simulation results are given.

  17. 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.

  18. Silicon wafer microstructure imaging using InfraRed Transport of Intensity Equation

    NASA Astrophysics Data System (ADS)

    Li, Hongru; Feng, Guoying; Bourgade, Thomas; Zuo, Chao; Du, Yongzhao; Zhou, Shouhuan; Asundi, Anand

    2015-03-01

    A novel quantitative 3D imaging system of silicon microstructures using InfraRed Transport of Intensity Equation (IRTIE) is proposed in this paper. By recording the intensity at multiple planes and using FFT or DCT based TIE solver, fast and accurate phase retrieval for both uniform and non-uniform intensity distributions is proposed. Numerical simulation and experiments confirm the accuracy and reliability of the proposed method. The application of IR-TIE for inspection of micro-patterns in visibly opaque media using 1310 nm light source is demonstrated. For comparison, micro-patterns are also inspected by the contact scanning mode Taylor Hobson system. Quantitative agreement suggests the possibility of using IR-TIE for phase imaging of silicon wafers.

  19. Master equation approach to charge injection and transport in organic insulators

    NASA Astrophysics Data System (ADS)

    Freire, José A.; Voss, Grasiela

    2005-03-01

    We develop a master equation model of a disordered organic insulator sandwiched between metallic electrodes by treating as rate processes both the injection and the internal transport. We show how the master equation model allows for the inclusion of crucial correlation effects in the charge transport, particularly of the Pauli exclusion principle and of space-charge effects, besides, being dependent on just the microscopic form of the transfer rate between the localized electronic states, it allows for the investigation of different microscopic scenarios in the organic, such as polaronic hopping, correlated energy levels, interaction with image charge, etc. The model allows for a separate analysis of the injection and the recombination currents. We find that the disorder, besides increasing the injection current, eliminates the possibility of observation of a Fowler-Nordheim injection current at zero temperature, and that it does not alter the Schottky barrier size of the zero-field thermionic injection current from the value based on the energy difference between the electrode Fermi level and the highest occupied molecular orbital/lowest unoccupied molecular orbital levels in the organic, but it makes the Arrhenius temperature dependence appear at larger temperatures. We investigate how the I(V ) characteristics of a device is affected by the presence of correlations in the site energy distribution and by the form of the internal hopping rate, specifically the Miller-Abrahams rate and the Marcus or small-polaron rate. We show that the disorder does not modify significantly the eβ√E field dependence of the net current due to the Schottky barrier lowering caused by the attraction between the charge and its image in the electrode.

  20. A discrete ordinates approximation to the neutron transport equation applied to generalized geometries

    SciTech Connect

    DeHart, M.D.

    1992-12-01

    A method for applying the discrete ordinates method for solution of the neutron transport equation in arbitary two-dimensional meshes has been developed. The finite difference approach normally used to approximate spatial derivatives in extrapolating angular fluxes across a cell is replaced by direct solution of the characteristic form of the transport equation for each discrete direction. Thus, computational cells are not restricted to the traditional shape of a mesh element within a given coordinate system. However, in terms of the treatment of energy and angular dependencies, this method resembles traditional discrete ordinates techniques. Using the method developed here, a general two-dimensional space can be approximated by an irregular mesh comprised of arbitrary polygons. The present work makes no assumptions about the orientations or the number of sides in a given cell, and computes all geometric relationships between each set of sides in each cell for each discrete direction. A set of non-reentrant polygons can therefore be used to represent any given two dimensional space. Results for a number of test problems have been compared to solutions obtained from traditional methods, with good agreement. Comparisons include benchmarks against analytical results for problems with simple geometry, as well numerical results obtained from traditional discrete ordinates methods by applying the ANISN and TWOTRAN computer programs. Numerical results were obtained for problems ranging from simple one-dimensional geometry to complicated multidimensional configurations. These results have demonstrated the ability of the developed method to closely approximate complex geometrical configurations and to obtain accurate results for problems that are extremely difficult to model using traditional methods.

  1. Master equation approach to charge injection and transport in organic insulators.

    PubMed

    Freire, José A; Voss, Grasiela

    2005-03-22

    We develop a master equation model of a disordered organic insulator sandwiched between metallic electrodes by treating as rate processes both the injection and the internal transport. We show how the master equation model allows for the inclusion of crucial correlation effects in the charge transport, particularly of the Pauli exclusion principle and of space-charge effects, besides, being dependent on just the microscopic form of the transfer rate between the localized electronic states, it allows for the investigation of different microscopic scenarios in the organic, such as polaronic hopping, correlated energy levels, interaction with image charge, etc. The model allows for a separate analysis of the injection and the recombination currents. We find that the disorder, besides increasing the injection current, eliminates the possibility of observation of a Fowler-Nordheim injection current at zero temperature, and that it does not alter the Schottky barrier size of the zero-field thermionic injection current from the value based on the energy difference between the electrode Fermi level and the highest occupied molecular orbital/lowest unoccupied molecular orbital levels in the organic, but it makes the Arrhenius temperature dependence appear at larger temperatures. We investigate how the I(V) characteristics of a device is affected by the presence of correlations in the site energy distribution and by the form of the internal hopping rate, specifically the Miller-Abrahams rate and the Marcus or small-polaron rate. We show that the disorder does not modify significantly the ebeta square root E field dependence of the net current due to the Schottky barrier lowering caused by the attraction between the charge and its image in the electrode. PMID:15836407

  2. 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.

  3. 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.

  4. First-principles calculation method for electron transport based on the grid Lippmann-Schwinger equation.

    PubMed

    Egami, Yoshiyuki; Iwase, Shigeru; Tsukamoto, Shigeru; Ono, Tomoya; Hirose, Kikuji

    2015-09-01

    We develop a first-principles electron-transport simulator based on the Lippmann-Schwinger (LS) equation within the framework of the real-space finite-difference scheme. In our fully real-space-based LS (grid LS) method, the ratio expression technique for the scattering wave functions and the Green's function elements of the reference system is employed to avoid numerical collapse. Furthermore, we present analytical expressions and/or prominent calculation procedures for the retarded Green's function, which are utilized in the grid LS approach. In order to demonstrate the performance of the grid LS method, we simulate the electron-transport properties of the semiconductor-oxide interfaces sandwiched between semi-infinite jellium electrodes. The results confirm that the leakage current through the (001)Si-SiO_{2} model becomes much larger when the dangling-bond state is induced by a defect in the oxygen layer, while that through the (001)Ge-GeO_{2} model is insensitive to the dangling bond state. PMID:26465580

  5. First-principles calculation method for electron transport based on the grid Lippmann-Schwinger equation

    NASA Astrophysics Data System (ADS)

    Egami, Yoshiyuki; Iwase, Shigeru; Tsukamoto, Shigeru; Ono, Tomoya; Hirose, Kikuji

    2015-09-01

    We develop a first-principles electron-transport simulator based on the Lippmann-Schwinger (LS) equation within the framework of the real-space finite-difference scheme. In our fully real-space-based LS (grid LS) method, the ratio expression technique for the scattering wave functions and the Green's function elements of the reference system is employed to avoid numerical collapse. Furthermore, we present analytical expressions and/or prominent calculation procedures for the retarded Green's function, which are utilized in the grid LS approach. In order to demonstrate the performance of the grid LS method, we simulate the electron-transport properties of the semiconductor-oxide interfaces sandwiched between semi-infinite jellium electrodes. The results confirm that the leakage current through the (001 )Si -SiO2 model becomes much larger when the dangling-bond state is induced by a defect in the oxygen layer, while that through the (001 )Ge -GeO2 model is insensitive to the dangling bond state.

  6. Real-time quantitative phase imaging based on transport of intensity equation with dual simultaneously recorded field of view.

    PubMed

    Tian, Xiaolin; Yu, Wei; Meng, Xin; Sun, Aihui; Xue, Liang; Liu, Cheng; Wang, Shouyu

    2016-04-01

    Since quantitative phase distribution reflects both cellular shapes and conditions from another view, compared to traditional intensity observation, different quantitative phase microscopic methods are proposed for cellular detections. However, the transport of intensity equation-based approach not only presents phase, but also intensity, which attracts much attention. While classical transport of intensity equation needs multi-focal images which often cannot realize simultaneous phase measurement, in this Letter, to break through the limitation, a real-time quantitative phase imaging method using transport of intensity equation is proposed. Two identical CCD cameras are set at the binocular tubes to capture the same field of view but at different focal planes. With a double-frame algorithm assuming that the on-focal image is the average of over- and under-focal information, the proposed method is capable of calculating quantitative phase distributions of samples accurately and simultaneously indicating its potentialities in cellular real-time monitoring. PMID:27192253

  7. Second order time evolution of the multigroup diffusion and P{sub 1} equations for radiation transport

    SciTech Connect

    Olson, Gordon L.

    2011-08-20

    Highlights: {yields} An existing multigroup transport algorithm is extended to be second-order in time. {yields} A new algorithm is presented that does not require a grey acceleration solution. {yields} The two algorithms are tested with 2D, multi-material problems. {yields} The two algorithms have comparable computational requirements. - Abstract: An existing solution method for solving the multigroup radiation equations, linear multifrequency-grey acceleration, is here extended to be second order in time. This method works for simple diffusion and for flux-limited diffusion, with or without material conduction. A new method is developed that does not require the solution of an averaged grey transport equation. It is effective solving both the diffusion and P{sub 1} forms of the transport equation. Two dimensional, multi-material test problems are used to compare the solution methods.

  8. 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

  9. 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.

  10. On the forward-backward-in-time approach for Monte Carlo solution of Parker's transport equation: One-dimensional case

    NASA Astrophysics Data System (ADS)

    Bobik, P.; Boschini, M. J.; Della Torre, S.; Gervasi, M.; Grandi, D.; La Vacca, G.; Pensotti, S.; Putis, M.; Rancoita, P. G.; Rozza, D.; Tacconi, M.; Zannoni, M.

    2016-05-01

    The cosmic rays propagation inside the heliosphere is well described by a transport equation introduced by Parker in 1965. To solve this equation, several approaches were followed in the past. Recently, a Monte Carlo approach became widely used in force of its advantages with respect to other numerical methods. In this approach the transport equation is associated to a fully equivalent set of stochastic differential equations (SDE). This set is used to describe the stochastic path of quasi-particle from a source, e.g., the interstellar space, to a specific target, e.g., a detector at Earth. We present a comparison of forward-in-time and backward-in-time methods to solve the cosmic rays transport equation in the heliosphere. The Parker equation and the related set of SDE in the several formulations are treated in this paper. For the sake of clarity, this work is focused on the one-dimensional solutions. Results were compared with an alternative numerical solution, namely, Crank-Nicolson method, specifically developed for the case under study. The methods presented are fully consistent each others for energy greater than 400 MeV. The comparison between stochastic integrations and Crank-Nicolson allows us to estimate the systematic uncertainties of Monte Carlo methods. The forward-in-time stochastic integrations method showed a systematic uncertainty <5%, while backward-in-time stochastic integrations method showed a systematic uncertainty <1% in the studied energy range.

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

    NASA Astrophysics Data System (ADS)

    Milovanov, Alexander 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 112 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.

  12. 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. PMID:11308983

  13. The piecewise linear discontinuous finite element method applied to the RZ and XYZ transport equations

    NASA Astrophysics Data System (ADS)

    Bailey, Teresa S.

    In this dissertation we discuss the development, implementation, analysis and testing of the Piecewise Linear Discontinuous Finite Element Method (PWLD) applied to the particle transport equation in two-dimensional cylindrical (RZ) and three-dimensional Cartesian (XYZ) geometries. We have designed this method to be applicable to radiative-transfer problems in radiation-hydrodynamics systems for arbitrary polygonal and polyhedral meshes. For RZ geometry, we have implemented this method in the Capsaicin radiative-transfer code being developed at Los Alamos National Laboratory. In XYZ geometry, we have implemented the method in the Parallel Deterministic Transport code being developed at Texas A&M University. We discuss the importance of the thick diffusion limit for radiative-transfer problems, and perform a thick diffusion-limit analysis on our discretized system for both geometries. This analysis predicts that the PWLD method will perform well in this limit for many problems of physical interest with arbitrary polygonal and polyhedral cells. Finally, we run a series of test problems to determine some useful properties of the method and verify the results of our thick diffusion limit analysis. Finally, we test our method on a variety of test problems and show that it compares favorably to existing methods. With these test problems, we also show that our method performs well in the thick diffusion limit as predicted by our analysis. Based on PWLD's solid finite-element foundation, the desirable properties it shows under analysis, and the excellent performance it demonstrates on test problems even with highly distorted spatial grids, we conclude that it is an excellent candidate for radiative-transfer problems that need a robust method that performs well in thick diffusive problems or on distorted grids.

  14. 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.

  15. Improved Hybrid Monte Carlo/n-Moment Transport Equations Model for the Polar Wind

    NASA Astrophysics Data System (ADS)

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

    2013-12-01

    In many space plasma problems (e.g. terrestrial polar wind, solar wind, etc.), the plasma gradually evolves from dense collision-dominated into rarified collisionless conditions. For decades, numerous attempts were made in order to address this type of problem using simulations based on one of two approaches. These approaches are: (1) the (fluid-like) Generalized Transport Equations, GTE, and (2) the particle-based Monte Carlo (MC) techniques. In contrast to the computationally intensive MC, the GTE approach can be considerably more efficient but its validity is questionable outside the collision-dominated region depending on the number of transport parameters considered. There have been several attempts to develop hybrid models that combine the strengths of both approaches. In particular, low-order GTE formulations were applied within the collision-dominated region, while an MC simulation was applied within the collisionless region and in the collisional-to-collisionless transition region. However, attention must be paid to assuring the consistency of the two approaches in the region where they are matched. Contrary to all previous studies, our model pays special attention to the ';matching' issue, and hence eliminates the discontinuities/inaccuracies associated with mismatching. As an example, we applied our technique to the Coulomb-Milne problem because of its relevance to the problem of space plasma flow from high- to low-density regions. We will compare the velocity distribution function and its moments (density, flow velocity, temperature, etc.) from the following models: (1) the pure MC model, (2) our hybrid model, and (3) previously published hybrid models. We will also consider a wide range of the test-to-background mass ratio.

  16. Phase-coherent quantum transport in silicon nanowires based on Wigner transport equation: Comparison with the nonequilibrium-Green-function formalism

    NASA Astrophysics Data System (ADS)

    Barraud, Sylvain

    2009-09-01

    Various theoretical formulations are proposed for investigating the carrier transport in nanoscale electronic devices. In this paper, a discrete formulation of the Wigner transport equation (WTE) for the self-consistent simulation of phase-coherent quantum transport in silicon nanowire metal-oxide-semiconductor field-effect transistor (MOSFET) devices is presented. The device is simulated using an effective-mass Hamiltonian within the mode-space approximation. The numerical scheme proposed in this work solves self-consistently three dimensional Poisson's equation, two dimensional Schrödinger's equation in each cross-sectional plane of the nanowire, and the steady-state one dimensional WTE for each conduction mode to handle the quantum transport along the channel. Details on numerical implementation of the Wigner function method are given, and the results are compared with those of the nonequilibrium Green's function (NEGF) method in the ballistic limit. The calculations of current-voltage electrical characteristics of surround-gated silicon nanowires are performed using both NEGF and WTE formulations. The good agreement observed between these approaches means that a direct solution of the WTE is an accurate simulation method for modeling the ballistic quantum transport in silicon nanowire MOSFETs.

  17. The advective-dispersive equation with spatial fractional derivatives as a model for tracer transport in structured soil

    Technology Transfer Automated Retrieval System (TEKTRAN)

    The classical model to describe solute transport in soil is based on the advective-dispersive equation where Fick’s law is used to explain dispersion. From the microscopic point of view this is equivalent to consider that the motion of the particles of solute may be simulated by the Brownian motion....

  18. COMPARING THE FRACTIONAL AND THE CLASSICAL SOLUTE TRANSPORT EQUATIONS WITH DATA ON SOLUTE BREAKTHROUGH IN SOIL COLUMNS

    Technology Transfer Automated Retrieval System (TEKTRAN)

    Solute transport in soils and sediments is commonly simulated with the parabolic advective-dispersive equation, or ADE. In the last decades, it has been reported that this model cannot take in account several important features of solute movement through soil. Recently, a new model base on the assu...

  19. Light transport in biological tissue using three-dimensional frequency-domain simplified spherical harmonics equations

    NASA Astrophysics Data System (ADS)

    Chu, Michael; Vishwanath, Karthik; Klose, Alexander D.; Dehghani, Hamid

    2009-04-01

    The accuracy of the commonly used diffusion approximation as used in diffuse optical tomography is known to be limited in cases involving strong absorption and in these situations a higher ordered approximation is necessary. In this study, a light transport model has been developed based upon the three-dimensional frequency-domain simplified spherical harmonics (SPN) approximation for orders up to N = 7. The SPN data are tested against a semi-infinite multi-layered Monte Carlo model. It has been shown that the SPN approximation for higher orders (N >1) provides an increase in accuracy over the diffusion equation specifically near sources and at boundaries of regions with increased optical absorption. It is demonstrated that the error of fluence calculated near the sources between the diffusion approximation and the SPN model (N = 7) can be as large as 60%, therefore limiting the use of the diffusion approximation for small animal imaging and in situations where optical changes near sources are critical for tomographic reconstructions.

  20. 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. PMID:25402794

  1. Universal limiter for transient interpolation modeling of the advective transport equations: The ULTIMATE conservative difference scheme

    NASA Technical Reports Server (NTRS)

    Leonard, B. P.

    1988-01-01

    A fresh approach is taken to the embarrassingly difficult problem of adequately modeling simple pure advection. An explicit conservative control-volume formation makes use of a universal limiter for transient interpolation modeling of the advective transport equations. This ULTIMATE conservative difference scheme is applied to unsteady, one-dimensional scalar pure advection at constant velocity, using three critical test profiles: an isolated sine-squared wave, a discontinuous step, and a semi-ellipse. The goal, of course, is to devise a single robust scheme which achieves sharp monotonic resolution of the step without corrupting the other profiles. The semi-ellipse is particularly challenging because of its combination of sudden and gradual changes in gradient. The ULTIMATE strategy can be applied to explicit conservation schemes of any order of accuracy. Second-order schemes are unsatisfactory, showing steepening and clipping typical of currently popular so-called high resolution shock-capturing of TVD schemes. The ULTIMATE third-order upwind scheme is highly satisfactory for most flows of practical importance. Higher order methods give predictably better step resolution, although even-order schemes generate a (monotonic) waviness in the difficult semi-ellipse simulation. Little is to be gained above ULTIMATE fifth-order upwinding which gives results close to the ultimate for which one might hope.

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

    NASA Astrophysics Data System (ADS)

    Kópházi, József; Lathouwers, Danny

    2015-09-01

    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.

  3. 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.

  4. Non-Markovian Effects in the Lindblad Master Equation Approach to Electronic Transport

    NASA Astrophysics Data System (ADS)

    Ribeiro, P.; Vieira, V. R.

    Non-equilibrium processes in open quantum systems can be generically described within the framework of the Lindblad master equation i.e. without a memory kernel. This statement holds even for processes where information can flow-back from the environment to the system. This rather contra-intuitive fact lead to define a process as non Markovian if, during the time evolution of two different initial states of the system, their distinguishability increases, reflecting a back-flow of information from the environment to the system. However, for non Markovian dynamics, the set of conditions to ensure the positivity of the density matrix for all times is not known, making difficult the explicit construction of non Markovian Lindblad operators. Using the Keldysh non equilibrium Green's functions, we explicitly solve a generic quadratic model of electrons coupled at t = 0 to a set of wide-band baths characterized by temperature and chemical potential. We identify the equivalent Lindblad operators describing the evolution of the density matrix and show that the resulting dynamical process is generically non Markovian. We further discuss the cases in which Markovian dynamics is recovered. We apply our approach to a simple model for electronic transport thought a one dimensional wire coupled at t = 0 to wide-band metallic leads, and to a XY spin chain attached to two contacts.

  5. Phase retrieval in arbitrarily shaped aperture with the transport-of-intensity equation

    NASA Astrophysics Data System (ADS)

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

    2015-03-01

    Phase is not easy to detect directly as intensity, but sometimes it contains the really desired information. The transport-of-intensity equation (TIE) is a powerful tool to retrieve the phase from the intensity. However, by considering the boundary energy exchange and the whole energy conversation in the field of view, the current popular Fast Fourier transform (FFT) based TIE solver can only retrieve the phase under homogeneous Neumann boundary condition. For many applications, the boundary condition could be more complex and general. A novel TIE phase retrieval method is proposed to deal with an optical field under a general boundary condition. In this method, an arbitrarily-shape hard aperture is added in the optical field. In our method, the TIE is solved by using iterative discrete cosine transforms (DCT) method, which contains a phase compensation mechanism to improve the retrieval results. The proposed method is verified in simulation with an arbitrary phase, an arbitrarily-shaped aperture, and non-uniform intensity distribution. Experiment is also carried out to check its feasibility and the method proposed in this work is very easy and straightforward to use in a practical measurement as a flexible phase retrieval tool.

  6. 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.

  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. 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.

  9. Addition of cement to lime-based mortars: Effect on pore structure and vapor transport

    SciTech Connect

    Mosquera, M.J. . E-mail: mariajesus.mosquera@uca.es; Silva, B.; Prieto, B.; Ruiz-Herrera, E.

    2006-09-15

    The main focus of this work is to determine the effect of cement addition, a common practice in many restorations, on the pore structure of lime-based mortars. A second target is to establish correlations between microstructure and water vapor transport across the mortar, which is a key characteristic of building decay. In order to achieve these objectives, we prepared a set of mortars consisting of air-hardening lime with a progressively increasing cement content, as well as a mortar containing hydraulic lime. Several different techniques, most notably mercury intrusion porosimetry and scanning electron microscopy in the backscatter mode, were used to investigate the pore structure. The results from these procedures led to the conclusion that porosity and pore size are progressively reduced as cement content increases. Moreover, an excellent correlation between pore radius parameter and the vapor diffusion coefficient was established. Hydraulic lime mortar exhibited textural parameters and diffusivity values halfway between those of the different lime/cement mixes studied.

  10. Two-group interfacial area transport equation in large diameter pipes

    NASA Astrophysics Data System (ADS)

    Smith, Todd Ryan

    2002-01-01

    The closure relations for the two-group interfacial area transport equation (LATE) by which the changes of interfacial area concentration can be dynamically modeled are set forth in this thesis for the case of large diameter pipes. In the two-group formulation, the sources and sink terms are established by mechanistic modeling of the intra-group and inter-group transport of the bubbles based on five major bubble interaction mechanisms. These mechanisms are bubble coalescence as a result of random collision, RC, wake entrainment, WE, bubble break-up due to turbulent impact, TI, small bubble shearing-off of large bubbles, SO, and bubble break-up due to surface instability for large bubbles, SI. The models developed are supported by experiments using a four-sensor conductivity probe in large diameter test sections, 10.16 cm and 15.24 cm in diameter. A total of 31 different flow conditions under atmospheric pressure are examined in the bubbly to churn-turbulent flow regimes. The local flow parameters measured by the multi-sensor conductivity probe include the local time-averaged void fraction, interfacial area concentration, bubble Sauter mean diameter, interfacial velocity, and interface frequency for the two groups of bubbles. The model is evaluated against the extensive database and good agreement is obtained between the model predictions and the experimental data. The average error based on the total interfacial area concentration is around 7.0% for interfacial area concentration in both test sections. Recirculation in the large pipes is given special treatment in the measurement analysis. Using upwards and downwards facing probes, information on the missing bubble signals is obtained which is used to correct the local data by either the Effective Bubble Number or Intrusiveness Factor Method. The correction to void fraction is found to be about a 12% increase in the local area averaged value, while interfacial area concentration may increase upwards of 60% in the

  11. 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.

  12. 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.

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

    NASA Astrophysics Data System (ADS)

    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.

  14. Quantum transport simulations of graphene nanoribbon devices using Dirac equation calibrated with tight-binding π-bond model

    PubMed Central

    2012-01-01

    We present an efficient approach to study the carrier transport in graphene nanoribbon (GNR) devices using the non-equilibrium Green's function approach (NEGF) based on the Dirac equation calibrated to the tight-binding π-bond model for graphene. The approach has the advantage of the computational efficiency of the Dirac equation and still captures sufficient quantitative details of the bandstructure from the tight-binding π-bond model for graphene. We demonstrate how the exact self-energies due to the leads can be calculated in the NEGF-Dirac model. We apply our approach to GNR systems of different widths subjecting to different potential profiles to characterize their device physics. Specifically, the validity and accuracy of our approach will be demonstrated by benchmarking the density of states and transmissions characteristics with that of the more expensive transport calculations for the tight-binding π-bond model. PMID:22325480

  15. Quantum transport simulations of graphene nanoribbon devices using Dirac equation calibrated with tight-binding π-bond model.

    PubMed

    Chin, Sai-Kong; Lam, Kai-Tak; Seah, Dawei; Liang, Gengchiau

    2012-01-01

    We present an efficient approach to study the carrier transport in graphene nanoribbon (GNR) devices using the non-equilibrium Green's function approach (NEGF) based on the Dirac equation calibrated to the tight-binding π-bond model for graphene. The approach has the advantage of the computational efficiency of the Dirac equation and still captures sufficient quantitative details of the bandstructure from the tight-binding π-bond model for graphene. We demonstrate how the exact self-energies due to the leads can be calculated in the NEGF-Dirac model. We apply our approach to GNR systems of different widths subjecting to different potential profiles to characterize their device physics. Specifically, the validity and accuracy of our approach will be demonstrated by benchmarking the density of states and transmissions characteristics with that of the more expensive transport calculations for the tight-binding π-bond model. PMID:22325480

  16. 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.

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

    SciTech Connect

    Thompson, K.G.

    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

  18. 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.

  19. 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.

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

    NASA Technical Reports Server (NTRS)

    Baldwin, Barrett S.; Barth, Timothy J.

    1991-01-01

    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.

  1. Additional thyroid dose factor from transportation sources in Russia after the Chernobyl disaster.

    PubMed Central

    Parshkov, E M; Chebotareva, I V; Sokolov, V A; Dallas, C E

    1997-01-01

    Beginning approximately 4 years after the Chernobyl nuclear accident a steady increase in the incidence of thyroid cancer was observed in children and adolescents of the Bryansk Oblast, which received the highest level of radionuclide contaminants in Russia. We examined the spatial relationship between the residence location of patients with identified thyroid cancer (0-18 years old at the time of the accident) and a number of geographic parameters to better account for the etiology of thyroid cancer spatial distribution. Geographic parameters analyzed included spatial distribution of 137Cs and 131I in soil, population demographics, measurements and reconstructions. of absorbed thyroid 131I doses in the population, and maps of major transportation arteries. An interesting finding is the lack of a consistent correlation between the spatial distribution of radionuclides in the soil and thyroid cancer incidence. Instead, most of the thyroid cancer cases were diagnosed in settlements situated on major railways and roads. Correlating population with thyroid cancer cases and transportation arteries reveals a much higher cancer rate on or near major roads and railways than at a distance from them, again independent of radionuclide soil concentration. There are other important factors, of course, that must be considered in future evaluations of this phenomenon. These include the influence of iodine endemic zones, genetic predisposition to thyroid cancer, and duration of residence time in contaminated areas. The feasibility of radionuclide transport on railways and roads is discussed, together with the vectors for transfer of the contaminants to the human population. Developing a model to reconstruct the radiation dose to the thyroid over time in this geographic region is proposed in light of the impact of transportation arteries. Specific studies are outlined to provide the data necessary to develop this model as well as to better characterize the feasibility and

  2. Parameter scaling to produce different charged-particle beam-transport systems having identical equations of motion

    SciTech Connect

    Wadlinger, E.A.

    1988-04-01

    Designs are freuently required for charged-particle optics channels to transport space-charge (Coulomb) force-dominated beams for use with accelerators under design or construction. It is often desirable to experimentally test a design using an existing accelerator having different parameters from the one under consideration. This paper shows how to scale a charged-particle transport design to make a model experiment for testing the design with an existing accelerator. Sometimes, with the proper choice of accelerator, the model experimetn can be much less expensive than the target device. By scaling variables (beam current and emittance, magnetic fields, etc.) in a way that produces certain invariant quantities, we obtain identical equations of motion for different charged-particle beam channels transporting different beams. The scaling relations take a transport channel design for one application having a given time structure (for instance, the time structure determiend by the radio frequency of a beam bunching cavity), beam energy, current, etc., and determine an equivalent transport channel design for another device with different parameters. Therefore, we can predict particle and beam behavior in one situation by knowing it in another. Even growth in emittance will be modeled correctly in spite of the fact that the devices transport beams with different time structure, energy, and currents. 2 refs., 1 fig., 1 tab.

  3. 41 CFR 102-5.25 - What additional guidance concerning home-to-work transportation should Federal agencies issue?

    Code of Federal Regulations, 2010 CFR

    2010-07-01

    ... 41 Public Contracts and Property Management 3 2010-07-01 2010-07-01 false What additional guidance concerning home-to-work transportation should Federal agencies issue? 102-5.25 Section 102-5.25 Public Contracts and Property Management Federal Property Management Regulations System (Continued) FEDERAL MANAGEMENT REGULATION GENERAL...

  4. On a two-dimensional Schrödinger equation with a magnetic field with an additional quadratic integral of motion

    NASA Astrophysics Data System (ADS)

    Marikhin, V. G.

    2011-10-01

    The problem of commuting quadratic quantum operators with a magnetic field has been considered. It has been shown that any such pair can be reduced to the canonical form, which makes it possible to construct an almost complete classification of the solutions of equations that are necessary and sufficient for a pair of operators to commute with each other. The transformation to the canonical form is performed through the change of variables to the Kovalevskaya-type variables; this change is similar to that in the theory of integrable tops. As an example, this procedure has been considered for the two-dimensional Schrödinger equation with the magnetic field; this equation has an additional quantum integral of motion.

  5. 49 CFR 172.820 - Additional planning requirements for transportation by rail.

    Code of Federal Regulations, 2011 CFR

    2011-10-01

    ... transportation route analysis. For each calendar year, a rail carrier must analyze the safety and security risks... (b) of this section. The route analysis must be in writing and include the factors contained in... siding, or consignee's facility. (2) In performing the analysis required by this paragraph, the...

  6. 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...

  7. 49 CFR 172.820 - Additional planning requirements for transportation by rail.

    Code of Federal Regulations, 2010 CFR

    2010-10-01

    ...) Rail transportation route analysis. For each calendar year, a rail carrier must analyze the safety and... paragraph (b) of this section. The route analysis must be in writing and include the factors contained in... siding, or consignee's facility. (2) In performing the analysis required by this paragraph, the...

  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. 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.

  10. 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.

  11. 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.

  12. Role of non-ideality for the ion transport in porous media: Derivation of the macroscopic equations using upscaling

    NASA Astrophysics Data System (ADS)

    Allaire, Grégoire; Brizzi, Robert; Dufrêche, Jean-François; Mikelić, Andro; Piatnitski, Andrey

    2014-07-01

    This paper is devoted to the homogenization (or upscaling) of a system of partial differential equations describing the non-ideal transport of a N-component electrolyte in a dilute Newtonian solvent through a rigid porous medium. Realistic non-ideal effects are taken into account by an approach based on the mean spherical approximation (MSA) model which takes into account finite size ions and screening effects. We first consider equilibrium solutions in the absence of external forces. In such a case, the velocity and diffusive fluxes vanish and the equilibrium electrostatic potential is the solution of a variant of the Poisson-Boltzmann equation coupled with algebraic equations. Contrary to the ideal case, this nonlinear equation has no monotone structure. However, based on invariant region estimates for the Poisson-Boltzmann equation and for small characteristic value of the solute packing fraction, we prove existence of at least one solution. To our knowledge this existence result is new at this level of generality. When the motion is governed by a small static electric field and a small hydrodynamic force, we generalize O'Brien's argument to deduce a linearized model. Our second main result is the rigorous homogenization of these linearized equations and the proof that the effective tensor satisfies Onsager properties, namely is symmetric positive definite. We eventually make numerical comparisons with the ideal case. Our numerical results show that the MSA model confirms qualitatively the conclusions obtained using the ideal model but there are quantitative differences arising that can be important at high charge or high concentrations.

  13. Fokker-Planck equations for charged-particle transport in random fields.

    NASA Technical Reports Server (NTRS)

    Jokipii, J. R.

    1972-01-01

    The Fokker-Planck equations for charged-particle dynamics are rederived, extending somewhat the elegant discussion of Hasselmann and Wibberenz. It is shown that the usual results are obtae and the conclusions in many cases are correct over a very broad range in energy. In particular, the rate for pitch-angle scattering may be accurately given down to energies much lower than previously thought. Recent claims that these Fokker-Planck equations are in general incorrect are thus shown to be in error.

  14. The nature and role of advection in advection-diffusion equations used for modelling bed load transport

    NASA Astrophysics Data System (ADS)

    Ancey, Christophe; Bohorquez, Patricio; Heyman, Joris

    2016-04-01

    The advection-diffusion equation arises quite often in the context of sediment transport, e.g., for describing time and space variations in the particle activity (the solid volume of particles in motion per unit streambed area). Stochastic models can also be used to derive this equation, with the significant advantage that they provide information on the statistical properties of particle activity. Stochastic models are quite useful when sediment transport exhibits large fluctuations (typically at low transport rates), making the measurement of mean values difficult. We develop an approach based on birth-death Markov processes, which involves monitoring the evolution of the number of particles moving within an array of cells of finite length. While the topic has been explored in detail for diffusion-reaction systems, the treatment of advection has received little attention. We show that particle advection produces nonlocal effects, which are more or less significant depending on the cell size and particle velocity. Albeit nonlocal, these effects look like (local) diffusion and add to the intrinsic particle diffusion (dispersal due to velocity fluctuations), with the important consequence that local measurements depend on both the intrinsic properties of particle displacement and the dimensions of the measurement system.

  15. Is Onsager symmetry relevant in the transport equations for magnetically confined plasmas

    SciTech Connect

    Balescu, R. )

    1991-03-01

    A global, algebraic view of the transport processes in a magnetically confined plasma is developed. Both the neoclassical (banana) and the anomalous transport matrices are represented in a factorized form, thus separating the roles of the dynamics and of the geometric constraints. The self-adjointness of the collision operator (the sole condition for classical Onsager symmetry) is shown to be a necessary, but not sufficient condition for this symmetry in confined plasmas. The latter results for the banana transport matrix from a delicate relationship between dynamic and geometric components. This structure is not present in the anomalous transport matrix, and the Onsager symmetry is broken in this case. It is stressed that the symmetry breaking does not violate any general principles.

  16. Higher-order approximation of contaminant transport equation for turbulent channel flows based on centre manifolds and its numerical solution

    NASA Astrophysics Data System (ADS)

    Ngo-Cong, D.; Mohammed, F. J.; Strunin, D. V.; Skvortsov, A. T.; Mai-Duy, N.; Tran-Cong, T.

    2015-06-01

    The contaminant transport process governed by the advection-diffusion equation plays an important role in modelling industrial and environmental flows. In this article, our aim is to accurately reduce the 2-D advection-diffusion equation governing the dispersion of a contaminant in a turbulent open channel flow to its 1-D approximation. The 1-D model helps to quickly estimate the horizontal size of contaminant clouds based on the values of the model coefficients. We derive these coefficients analytically and investigate numerically the model convergence. The derivation is based on the centre manifold theory to obtain successively more accurate approximations in a consistent manner. Two types of the average velocity profile are considered: the classical logarithmic profile and the power profile. We further develop the one-dimensional integrated radial basis function network method as a numerical approach to obtain the numerical solutions to both the original 2-D equation and the approximate 1-D equations. We compare the solutions of the original models with their centre-manifold approximations at very large Reynolds numbers. The numerical results obtained from the approximate 1-D models are in good agreement with those of the original 2-D model for both the logarithmic and power velocity profiles.

  17. Alternative(s) to fractional-diffusion equations in bedload-transport models

    NASA Astrophysics Data System (ADS)

    Ancey, Christophe; Mettra, François; Mettraux, Valentin

    2010-05-01

    The idea of stochastic sediment transport models emerged in the 1930s, notably with the doctoral work of Hans A. Einstein (1936). Einstein's seminal work gave impulse to several stochastic models, which usually led to thin-tailed or bounded distributions for the particle-transport rate. Experimental observations together with field surveys suggest that particle-transport rate exhibits frequent and large fluctuations, in particular at low flow rates (i.e., when the bottom shear just exceeds the threshold of incipient motion), which cannot be described using classic distributions used so far for modelling bedload transport (e.g., Hamamori's distribution). The existence of these large and frequent fluctuations could offer a wide field of applications to fractional-derivative theory. Alternative approaches exist as well: in this talk, we explore the potentialities of a birth-death Markov model to model sediment transport within a fixed volume of control. Under steady-uniform-flow conditions, the model predicts that the number of moving particles inside the control volume follows a negative binomial distribution. Although this probability distribution does not enter the family of heavy-tailed distributions, it may give rise to large and frequent fluctuations. We investigate the consequences of these fluctuations on bed dynamics, more especially on the features (growth rate and probability distribution) of nascent bedforms that develop on initially planar beds as a result of intermittent bedload transport.

  18. Chemical transport to the seafloor of the equatorial Pacific Ocean across a latitudinal transect at 135°W: Tracking sedimentary major, trace, and rare earth element fluxes at the Equator and the Intertropical Convergence Zone

    NASA Astrophysics Data System (ADS)

    Murray, Richard W.; Leinen, Margaret

    1993-09-01

    accumulation beneath the ITCZ than at the Equator. Thus, adsorptive scavenging by terrigenous paniculate matter, or phases intimately associated with them, appears to be an extremely important process regulating elemental transport to the equatorial Pacific seafloor. These findings emphasize the role of vertical transport to the sediment, and provide additional constraints on the paleochemical use of trace elements to track biogenic and terrigenous fluxes.

  19. 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.

  20. 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.

  1. 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.

  2. Generalized linear Boltzmann equation, describing non-classical particle transport, and related asymptotic solutions for small mean free paths

    NASA Astrophysics Data System (ADS)

    Rukolaine, Sergey A.

    2016-05-01

    In classical kinetic models a particle free path distribution is exponential, but this is more likely to be an exception than a rule. In this paper we derive a generalized linear Boltzmann equation (GLBE) for a general free path distribution in the framework of Alt's model. In the case that the free path distribution has at least first and second finite moments we construct an asymptotic solution to the initial value problem for the GLBE for small mean free paths. In the special case of the one-speed transport problem the asymptotic solution results in a diffusion approximation to the GLBE.

  3. 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.

  4. 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.

  5. Numerical modeling of photon migration in the cerebral cortex of the living rat using the radiative transport equation

    NASA Astrophysics Data System (ADS)

    Fujii, Hiroyuki; Okawa, Shinpei; Nadamoto, Ken; Okada, Eiji; Yamada, Yukio; Hoshi, Yoko; Watanabe, Masao

    2015-03-01

    Accurate modeling and efficient calculation of photon migration in biological tissues is requested for determination of the optical properties of living tissues by in vivo experiments. This study develops a calculation scheme of photon migration for determination of the optical properties of the rat cerebral cortex (ca 0.2 cm thick) based on the three-dimensional time-dependent radiative transport equation assuming a homogeneous object. It is shown that the time-resolved profiles calculated by the developed scheme agree with the profiles measured by in vivo experiments using near infrared light. Also, an efficient calculation method is tested using the delta-Eddington approximation of the scattering phase function.

  6. Transport equation in the problem of the distribution function of nanoparticles in a colloidal solution exposed to laser pulses

    NASA Astrophysics Data System (ADS)

    Kirichenko, N. A.; Shcherbina, M. E.; Serkov, A. A.; Rakov, I. I.

    2015-12-01

    The behaviour of a colloidal solution of gold nanoparticles irradiated by a repetitively pulsed laser with a pulse duration of a few nanoseconds is investigated theoretically and experimentally. A mathematical model is constructed, which allows the behaviour of the nanoparticle distribution function to be described. The model is based on the transport equation in the 'space' of particle sizes. The proposed model allows for a relatively simple study and makes it possible to establish some common patterns in the behaviour of an ensemble of nanoparticles under various conditions. The results obtained are in satisfactory agreement with the available experimental data.

  7. Effects of transportation stress and addition of salt to transport water on the skin mucosal homeostasis of rainbow trout (Oncorhynchus mykiss)

    PubMed Central

    Tacchi, Luca; Lowrey, Liam; Musharrafieh, Rami; Crossey, Kyle; Larragoite, Erin T.; Salinas, Irene

    2015-01-01

    Transportation of live fish is a common practice among aquaculture facilities. Many studies have previously reported how transport elicits physiological stress responses and increases disease susceptibility in farmed fish. The aim of this work is to investigate the changes that the skin of rainbow trout (Oncorhynchus mykiss) experiences due to stress. Since NaCl is commonly added to transport water as a stress mitigator, the effects of salt addition on the skin mucosa and skin-associated bacteria were also examined. Three experimental groups (Control, post-transport no salt (PTNS) and post-transport with salt (PTS)) were analyzed in a 5-hour transport acute stress model. Results indicate that the skin mucosa and the skin-associated bacteria are affected by transport stress. Total numbers of culturable skin-associated bacteria increased by ~10-fold and ~50-fold in the PTS and PTNS groups, respectively. Compared to controls, MUC2 expression was increased by 5-fold and 2-fold in the PTNS and PTS groups, respectively. Claudin-7, 8d and 12 expression levels were higher in both PTNS and PTS groups whereas antimicrobial peptide gene expression was lower than controls. Expression of the anti-inflammatory cytokine TGF-β but not IL-1β, IL-6 and TNF-α was up-regulated 2-3 fold in both the PTS and PTNS groups. The addition of salt diminished some of the physiological responses measured including the numbers of skin-associated bacteria. The responses recorded here appeared to be efficient at controlling bacterial translocation since stress did not lead to significant presence of bacteria in the liver or spleen of rainbow trout. When examining the ability of skin mucus to inhibit or promote growth of the bacterial pathogen Vibrio anguillarum, the skin mucus of PTS trout was more efficient at inhibiting V. anguillarum growth (20% inhibition) compared to control or PTNS mucus (11-12% inhibition). Our data clearly indicate the skin and skin microbiota of rainbow trout undergo

  8. 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.

  9. 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.

  10. 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.

  11. 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.

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

    NASA Astrophysics Data System (ADS)

    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. Effective ionization coefficients and transport parameters in binary and ultradilute SF6-Ar mixtures using Boltzmann equation analysis

    NASA Astrophysics Data System (ADS)

    Cekmen, Z. C.; Dincer, M. S.

    2009-07-01

    The effective ionization coefficients and transport parameters such as electron mean energy drift velocity and transverse diffusion coefficient in binary and ultradilute SF6-Ar gas mixtures have been calculated for density reduced electric field strength E/N values from 10 to 400 Td. These calculations have been performed by using the two-term spherical harmonic expansion to obtain the numerical solution of the Boltzmann transport equation based on the finite element method under steady-state Townsend condition. In order to confirm the model and code developed in this study, the Reid ramp model has been used as a benchmark test and then effective ionization coefficients and transport parameters have been evaluated for SF6 contents of 1%, 10%, 25%, 50%, 70% and 100% in the binary mixture. Finally SF6 contents in the ultradilute mixtures of 0.1%, 0.3%, 0.5% and 0.7% are taken into account with the evaluated effective ionizations and transport parameters of electron mean energy, drift velocity and transverse diffusion coefficients.

  14. Steady state and modulated heat conduction in layered systems predicted by the analytical solution of the phonon Boltzmann transport equation

    NASA Astrophysics Data System (ADS)

    Ordonez-Miranda, Jose; Yang, Ronggui; Volz, Sebastian; Alvarado-Gil, J. J.

    2015-08-01

    Based on the phonon Boltzmann transport equation under the relaxation time approximation, analytical expressions for the temperature profiles of both the steady state and modulated heat conduction inside a thin film deposited on a substrate are derived and analyzed. It is shown that these components of the temperature depend strongly on the ratio between the film thickness and the average phonon mean free path (MFP), and they exhibit the diffusive behavior as predicted by the Fourier's law of heat conduction when this ratio is much larger than unity. In contrast, in the ballistic regime when this ratio is comparable to or smaller than unity, the steady-state temperature tends to be independent of position, while the amplitude and the phase of the modulated temperature appear to be lower than those determined by the Fourier's law. Furthermore, we derive an invariant of heat conduction and a simple formula for the cross-plane thermal conductivity of dielectric thin films, which could be a useful guide for understanding and optimizing the thermal performance of the layered systems. This work represents the Boltzmann transport equation-based extension of the Rosencwaig and Gersho work [J. Appl. Phys. 47, 64 (1976)], which is based on the Fourier's law and has widely been used as the theoretical framework for the development of photoacoustic and photothermal techniques. This work might shed some light on developing a theoretical basis for the determination of the phonon MFP and relaxation time using ultrafast laser-based transient heating techniques.

  15. 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.

  16. Evolution of the ultra high energy cosmic ray spectrum by transport equation

    SciTech Connect

    Hill, C.T.; Schramm, D.N.

    1983-04-01

    Ultra-high energy proton primaries interacting with the 3/sup 0/K photon background are treated as a transport phenomenon. Baryon number is explicitly conserved and the evolved spectrum develops a bump at a scale of order 5x10/sup 19/ eV, below the cutoff, due to the pile-up of energy degraded protons. This may correspond in part to the observed ankle structure in the CR spectrum.

  17. 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

  18. Stochastic modeling in sediment dynamics: Exner equation for planar bed incipient bed load transport conditions

    NASA Astrophysics Data System (ADS)

    Ancey, Christophe

    2010-06-01

    Even under flow equilibrium conditions, river bed topography continuously evolves with time, producing trains of irregular bed forms. The idea has recently emerged that the variability in the bed form geometry results from some randomness in sediment flux. In this paper, we address this issue by using the Exner equation and a population exchange model derived in an earlier paper. In this model, particle entrainment and deposition are idealized as population exchanges between the stream and the bed, which makes it possible to use birth-death Markov process theory to track the number of moving grains. The paper focuses on nascent bed forms on initially planar beds, a situation in which the coupling between the stream and bed is weak. In a steady state, the number of moving particles follows a negative binomial distribution. Although this probability distribution does not enter the family of heavy-tailed distributions, it may give rise to large and frequent fluctuations because the standard deviation can be much larger than the mean, a feature that is not accounted for with classic probability laws (e.g., Hamamori's law) used so far for describing bed load fluctuations. In the large-system limit, the master equation of the birth-death Markov process can be transformed into a Fokker-Planck equation. This transformation is used here to show that the number of moving particles can be described as an Ornstein-Uhlenbeck process. An important consequence is that in the long term, the number of moving particles follows a Gaussian distribution. Laboratory experiments show that this approximation is correct when the mean number per unit length of stream, ?/L, is sufficiently large (typically two particles per centimeter in our experiments). The particle number fluctuations give rise to bed elevation fluctuations, whose spectrum falls off like ω-2 in the high-frequency regime (with ω the angular frequency) and variance grows linearly with time. These features are in agreement

  19. Influence of alumina coating on transport and recombination in DSSCs with 1-methylbenzidazole as electrolyte additives

    NASA Astrophysics Data System (ADS)

    Xu, Xueqing; Barea, Eva Maria; Fabregat-Santiago, Francisco; Bisquert, Juan; Xu, Gang

    2009-08-01

    Nanocrystalline TiO2 electrodes have been coated with alumina by being immersed into the solutions of aluminum isopropoxide and aluminum acetylacetonate respectively. The current-voltage characteristics of the TiO2 and TiO2/Al2O3 electrodes with 1-methylbenzimidazole (MBI) as additives in the electrolytes have been detected. It is found that the TiO2/Al2O3 electrodes immersed in the solutions of aluminum isopropoxide (acetylacetone as coordinate ligands) for 1 hour have obtained great increase of Jsc, and owned the improved cells efficiency by 17%. To discover the origins of this improved photovoltaic performance and investigate the electron properties of the cells, the electrochemical impedance spectroscopy (EIS) has been used both in the dark and under illumination at different applied potentials. It is proposed that with the coating of Al2O3, the adsorption of MBI cations at the surface of TiO2 electrodes decreased with the decrease of the applied potentials, which resulted in the downwards shift of the conduction band position of the TiO2/Al2O3 electrodes at the lower potentials. As a result, the charge transfer resistance Rct decreased, and chemical capacitance Cfilms increased. Under illumination, the decrease of Rct became smaller and the conductivities became larger, which was attributed to the recombination inhibition effect of Al2O3 coating to the photoinjected electrons. As a consequence, the electron lifetime and the effective diffusion length for the TiO2/Al2O3 electrodes increased, leading to the great increase of Jsc. It is indicated that with the coating of Al2O3, the decrease of Jsc could be overcome when MBI is used as the additives of the electrolyte.

  20. High speed transport cruise drag. [scaling laws using Navier-Stokes equations

    NASA Technical Reports Server (NTRS)

    Roberts, Leonard

    1992-01-01

    This report provides scaling laws for the cruise aerodynamics of high speed transport wings based on the results of Navier-Stokes computations. Expressions for the various drag components are found, together with the corresponding values (L/D)(sub m) for various values of the geometric parameter s/l which allow for simple optimization of the wing configurations with respect to the span. It is found that linear theory expressions can be used for this purpose provided the coefficients of these experiments for C(sub D) and (L/D)(sub m) are available using Navier-Stokes results.

  1. 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/. PMID:23085905

  2. Lentiviral hepatitis B pseudotype entry requires sodium taurocholate co-transporting polypeptide and additional hepatocyte-specific factors.

    PubMed

    Meredith, L W; Hu, K; Cheng, X; Howard, C R; Baumert, T F; Balfe, P; van de Graaf, K F; Protzer, U; McKeating, J A

    2016-01-01

    Hepatitis B virus (HBV) is one of the world's major unconquered infections, resulting in progressive liver disease, and current treatments rarely cure infection. A limitation to discovering new therapies is our limited knowledge of HBV entry and dissemination pathways that hinders the development of in vitro culture systems. To address this gap in our understanding we optimized the genesis of infectious lentiviral pseudoparticles (HBVpps). The recent discovery that the bile salt transporter sodium taurocholate co-transporting polypeptide (NTCP) acts as a receptor for HBV enabled us to assess the receptor dependency of HBVpp infection. HBVpps preferentially infect hepatoma cells expressing NTCP, whereas other non-liver cells engineered to express NTCP do not support infection, suggesting that additional hepatocyte-specific factors are required for HBVpp internalization. These results highlight the value of the HBVpp system to dissect the pathways of HBV entry and dissemination. PMID:26474824

  3. Orbit-averaged drift kinetic equation for the study of alpha-particle transport in tokamaks

    SciTech Connect

    Sager, G.T.; Miley, G.H. . Fusion Studies Lab.); Burrell, K.H. )

    1990-11-01

    Neoclassical transport of minority suprathermal alpha particles is investigated. This paper departs from previous investigations in that (a) the banana-width ordering parameter {rho}{sub {theta}}/L is not formally restricted to be a small parameter and (b) a linearized collision operator that retains the effects of pitch-angle scattering, electron and ion drag, and speed diffusion is used. A step model approximation for the large-aspect-ratio, circular-cross-section tokamak magnetic field is adopted to simplify the orbit-averaging procedure. Assuming that the suprathermal alphas are in the banana regime, an asymptotic expansion in {tau}{sub B}/{tau}{sub S} {much lt} l is carried out.

  4. 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. PMID:21929130

  5. 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.

  6. 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.

  7. 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.

  8. 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. PMID:26836869

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

    DOE PAGESBeta

    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 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

  10. 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.

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

    NASA Astrophysics Data System (ADS)

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

    2015-05-01

    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.

  12. Minimising the error in eigenvalue calculations involving the Boltzmann transport equation using goal-based adaptivity on unstructured meshes

    SciTech Connect

    Goffin, Mark A.; Baker, Christopher M.J.; Buchan, Andrew G.; Pain, Christopher C.; Eaton, Matthew D.; Smith, Paul N.

    2013-06-01

    This article presents a method for goal-based anisotropic adaptive methods for the finite element method applied to the Boltzmann transport equation. The neutron multiplication factor, k{sub eff}, is used as the goal of the adaptive procedure. The anisotropic adaptive algorithm requires error measures for k{sub eff} with directional dependence. General error estimators are derived for any given functional of the flux and applied to k{sub eff} to acquire the driving force for the adaptive procedure. The error estimators require the solution of an appropriately formed dual equation. Forward and dual error indicators are calculated by weighting the Hessian of each solution with the dual and forward residual respectively. The Hessian is used as an approximation of the interpolation error in the solution which gives rise to the directional dependence. The two indicators are combined to form a single error metric that is used to adapt the finite element mesh. The residual is approximated using a novel technique arising from the sub-grid scale finite element discretisation. Two adaptive routes are demonstrated: (i) a single mesh is used to solve all energy groups, and (ii) a different mesh is used to solve each energy group. The second method aims to capture the benefit from representing the flux from each energy group on a specifically optimised mesh. The k{sub eff} goal-based adaptive method was applied to three examples which illustrate the superior accuracy in criticality problems that can be obtained.

  13. Boundary-artifact-free phase retrieval with the transport of intensity equation: fast solution with use of discrete cosine transform.

    PubMed

    Zuo, Chao; Chen, Qian; Asundi, Anand

    2014-04-21

    The transport of intensity equation (TIE) is a two-dimensional second order elliptic partial differential equation that must be solved under appropriate boundary conditions. However, the boundary conditions are difficult to obtain in practice. The fast Fourier transform (FFT) based TIE solutions are widely adopted for its speed and simplicity. However, it implies periodic boundary conditions, which lead to significant boundary artifacts when the imposed assumption is violated. In this work, TIE phase retrieval is considered as an inhomogeneous Neumann boundary value problem with the boundary values experimentally measurable around a hard-edged aperture, without any assumption or prior knowledge about the test object and the setup. The analytic integral solution via Green's function is given, as well as a fast numerical implementation for a rectangular region using the discrete cosine transform. This approach is applicable for the case of non-uniform intensity distribution with no extra effort to extract the boundary values from the intensity derivative signals. Its efficiency and robustness have been verified by several numerical simulations even when the objects are complex and the intensity measurements are noisy. This method promises to be an effective fast TIE solver for quantitative phase imaging applications. PMID:24787811

  14. 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

  15. 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. PMID:19138514

  16. Addition of oxytocin to semen extender improves both sperm transport to the oviduct and conception rates in pigs following AI.

    PubMed

    Okazaki, Tetsuji; Ikoma, Erena; Tinen, Tukasa; Akiyoshi, Teiichi; Mori, Manabu; Teshima, Hisanori

    2014-01-01

    Oxytocin (OXT) contained in boar semen is known to produce uterine contraction; therefore, we hypothesized that the co-injection of OXT with sperm would improve artificial insemination (AI) using liquid or frozen-thawed boar sperm. We initially examined whether OXT added to semen extender improved sperm transport to the oviduct. Although the addition of OXT did not affect the fresh or frozen-thawed sperm motility or acrosomal integrity, it significantly increased the number of sperm in the oviduct at 6 h after AI injection with OXT, as compared with the control (P < 0.05). Moreover, some sperm were observed in the sperm reservoir of the isthmus in the OXT treatment group, whereas few sperm were observed in the control. When OXT was added to the semen extender immediately prior to AI, the conception rates were significantly higher in both fresh semen and frozen-thawed semen than in the control group (P < 0.05: liquid, 87.5% vs. 70.5%; frozen-thawed, 89.8% vs. 75.0%). From these results, we concluded that the addition of OXT to the semen extender assisted in sperm transportation from the uterus to the oviduct, which resulted in improved reproductive performance. PMID:23829601

  17. 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.

  18. Efficient yet accurate solution of the linear transport equation in the presence of internal sources - The exponential-linear-in-depth approximation

    NASA Technical Reports Server (NTRS)

    Kylling, Arve; Stamnes, Knut

    1992-01-01

    The present solutions to the linear transport equation pertain to monoenergetic particles' interaction with a multiple scattering/absorbing layered medium with a general anisotropic internal source term. Attention is given to a novel exponential-linear approximation to the internal source, as a function of scattering depth, which furnishes an at-once efficient and accurate solution to the linear transport equation through its reduction of the spatial mesh size. The great superiority of the proposed method is demonstrated by the numerical results obtained in the illustrative cases of (1) an embedded thermal source and (2) a rapidly varying beam pseudosource.

  19. 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.

  20. 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.

  1. Extending the range of validity of Fourier's law into the kinetic transport regime via asymptotic solution of the phonon Boltzmann transport equation

    NASA Astrophysics Data System (ADS)

    Péraud, Jean-Philippe M.; Hadjiconstantinou, Nicolas G.

    2016-01-01

    We derive the continuum equations and boundary conditions governing phonon-mediated heat transfer in the limit of a small but finite mean-free path from the asymptotic solution of the linearized Boltzmann equation in the relaxation time approximation. Our approach uses the ratio of the mean-free path to the characteristic system length scale, also known as the Knudsen number, as the expansion parameter to study the effects of boundaries on the breakdown of the Fourier description. We show that, in the bulk, the traditional heat conduction equation using Fourier's law as a constitutive relation is valid at least up to second order in the Knudsen number for steady problems and first order for time-dependent problems. However, this description does not hold within distances on the order of a few mean-free paths from the boundary; this breakdown is a result of kinetic effects that are always present in the boundary vicinity and require solution of a Boltzmann boundary layer problem to be determined. Matching the inner, boundary layer solution to the outer, bulk solution yields boundary conditions for the Fourier description as well as additive corrections in the form of universal kinetic boundary layers; both are found to be proportional to the bulk-solution gradients at the boundary and parametrized by the material model and the phonon-boundary interaction model (Boltzmann boundary condition). Our derivation shows that the traditional no-jump boundary condition for prescribed temperature boundaries and the no-flux boundary condition for diffusely reflecting boundaries are appropriate only to zeroth order in the Knudsen number; at higher order, boundary conditions are of the jump type. We illustrate the utility of the asymptotic solution procedure by demonstrating that it can be used to predict the Kapitza resistance (and temperature jump) associated with an interface between two materials. All results are validated via comparisons with low-variance deviational Monte

  2. 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.

  3. 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.

  4. 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.

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

    PubMed

    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. PMID:26871095

  6. 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

  7. Boundary-artifact-free phase retrieval with the transport of intensity equation II: applications to microlens characterization.

    PubMed

    Zuo, Chao; Chen, Qian; Li, Hongru; Qu, Weijuan; Asundi, Anand

    2014-07-28

    Boundary conditions play a crucial role in the solution of the transport of intensity equation (TIE). If not appropriately handled, they can create significant boundary artifacts across the reconstruction result. In a previous paper [Opt. Express 22, 9220 (2014)], we presented a new boundary-artifact-free TIE phase retrieval method with use of discrete cosine transform (DCT). Here we report its experimental investigations with applications to the micro-optics characterization. The experimental setup is based on a tunable lens based 4f system attached to a non-modified inverted bright-field microscope. We establish inhomogeneous Neumann boundary values by placing a rectangular aperture in the intermediate image plane of the microscope. Then the boundary values are applied to solve the TIE with our DCT-based TIE solver. Experimental results on microlenses highlight the importance of boundary conditions that often overlooked in simplified models, and confirm that our approach effectively avoid the boundary error even when objects are located at the image borders. It is further demonstrated that our technique is non-interferometric, accurate, fast, full-field, and flexible, rendering it a promising metrological tool for the micro-optics inspection. PMID:25089451

  8. An exact solution of the linearized Boltzmann transport equation and its application to mobility calculations in graphene bilayers

    NASA Astrophysics Data System (ADS)

    Paussa, A.; Esseni, D.

    2013-03-01

    This paper revisits the problem of the linearized Boltzmann transport equation (BTE), or, equivalently, of the momentum relaxation time, momentum relaxation time (MRT), for the calculation of low field mobility, which in previous works has been almost universally solved in approximated forms. We propose an energy driven discretization method that allows an exact determination of the relaxation time by solving a linear, algebraic problem, where multiple scattering mechanisms are naturally accounted for by adding the corresponding scattering rates before the calculation of the MRT, and without resorting to the semi-empirical Matthiessen's rule for the relaxation times. The application of our rigorous solution of the linearized BTE to a graphene bilayer reveals that, for a non monotonic energy relation, the relaxation time can legitimately take negative values with no unphysical implications. We finally compare the mobility calculations provided by an exact solution of the MRT problem with the results obtained with some of the approximations most frequently employed in the literature and so discuss their accuracy.

  9. Coupling between the Liouville equation and a classical Monte Carlo solver for the simulation of electron transport in resonant tunneling diodes

    NASA Astrophysics Data System (ADS)

    Martín, F.; García-García, J.; Oriols, X.; Suñé, J.

    1999-02-01

    A coupling model between a classical Monte Carlo simulator and a Liouville equation solver has been proposed with application to the simulation of vertical transport quantum devices in which extensive regions of the simulation domain behave classically. These devices can be partitioned in regions in which either a classical (Monte Carlo) or a quantum (Wigner formalism) treatment of carrier transport is required making a coupling scheme between adjacent regions necessary. According to this aim, the boundary conditions inferred from the Monte Carlo solver for the integration of the Liouville equation in the quantum regions, as well as the injecting scheme to the Monte Carlo regions provided by the Wigner distribution function at the boundaries have been earlier established. The results of this work, using a resonant tunneling diode as a reference device, show that the proposed technique is promising for the simulation of electron transport in quantum devices.

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

    NASA Astrophysics Data System (ADS)

    Hua, Chengyun; Minnich, Austin J.

    2015-05-01

    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.

  11. 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.

  12. 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. PMID:27095373

  13. Column studies on transport of deicing additive benzotriazole in a sandy aquifer and a zerovalent iron barrier.

    PubMed

    Jia, Yu; Breedveld, Gijs D; Aagaard, Per

    2007-11-01

    Benzotriazole (BTA), a chemical with wide industrial applications, is a typical additive in deicer/anti-icer used at airport. To achieve a better understanding of the transport behaviour and environmental fate of BTA, laboratory column studies have been performed on subsoil samples from Oslo Airport, Gardermoen. To explore possibilities for aquifer remediation, BTA behaviour was also studied in a column of granular zerovalent iron (Fe(0)). The subsoil column study demonstrates a very limited retardation of BTA. Consecutive loadings of BTA of the subsoil column showed no change of the break-through curve (BTC) and complete desorption was observed. The sorption behaviour of BTA to metallic iron (Fe(0)) was rather complex. Considerable retardation was observed in the Fe(0) column and repeated BTA loading resulted in an earlier break-through. Between 20% and 50% of the input concentration was retained permanently in the iron (Fe(0)) column. The BTA sorption to metallic iron was found to be enhanced by chloride which lowered the break-through concentration (i.e the C/C(0) plateau). The fraction of BTA remaining in the iron column was found to vary with the flow rate, indicating a time dependant multilayer sorption mechanism. The steady increase in the amount of adsorbed BTA to the iron column during loading corresponds to a rather strong bonding of 4-15 BTA layers to the iron surface. A very slow desorption of BTA was observed; even after flushing with 753 pore volumes of BTA free water, 7.5% of the BTA remained in the column. A geochemical model was developed based on PHREEQC-2 to simulate the sorption and transport of BTA in the tested materials. The BTA sorption was modelled with Freundlich sorption isotherms, as earlier determined in batch experiments. A slight adjustment of the Freundlich parameters was required to fit the observed column break-through. However, our model was not able to simulate the long-term retainment of BTA in the granular iron columns. The

  14. 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.

  15. In vivo exercise followed by in vitro contraction additively elevates subsequent insulin-stimulated glucose transport by rat skeletal muscle.

    PubMed

    Funai, Katsuhiko; Schweitzer, George G; Castorena, Carlos M; Kanzaki, Makoto; Cartee, Gregory D

    2010-05-01

    The cellular mechanisms whereby prior exercise enhances insulin-stimulated glucose transport (GT) are not well understood. Previous studies suggested that a prolonged increase in phosphorylation of Akt substrate of 160 kDa (AS160) may be important for the postexercise increase in insulin sensitivity. In the current study, the effects of in vivo exercise and in vitro contraction on subsequent insulin-stimulated GT were studied separately and together. Consistent with results from previous studies, prior exercise resulted in an increase in AS160 (642)Thr phosphorylation immediately after exercise in rat epitrochlearis muscles, and this increase remained 3 h postexercise concomitant with enhanced insulin-stimulated GT. For experiments with in vitro contraction, isolated rat epitrochlearis muscles were electrically stimulated to contract in the presence or absence of rat serum. As expected, insulin-stimulated GT measured 3 h after electrical stimulation in serum, but not after electrical stimulation without serum, exceeded resting controls. Immediately after electrical stimulation with or without serum, phosphorylation of both AS160 (detected by phospho-Akt substrate, PAS, antibody, or phospho-(642)Thr antibody) and its paralog TBC1D1 (detected by phospho-(237)Ser antibody) was increased. However, both AS160 and TBC1D1 phosphorylation had reversed to resting values at 3 h poststimulation with or without serum. Increasing the amount of exercise (from 1 to 2 h) or electrical stimulation (from 5 to 10 tetani) did not further elevate insulin-stimulated GT. In contrast, the combination of prior exercise and electrical stimulation had an additive effect on the subsequent increase in insulin-stimulated GT, suggesting that these exercise and electrical stimulation protocols may amplify insulin-stimulated GT through distinct mechanisms, with a persistent increase in AS160 phosphorylation potentially important for increased insulin sensitivity after exercise, but not after in

  16. Equations of state, energy transport and two-temperature hydrodynamic simulations for femtosecond laser irradiated copper and gold

    NASA Astrophysics Data System (ADS)

    Migdal, K. P.; Il'nitsky, D. K.; Petrov, Yu V.; Inogamov, N. A.

    2015-11-01

    In this work, the model of thermodynamic and transport properties of copper and gold at electron-ion non-equilibrium state is presented. Accepted here ranges of electron temperature and pressure are enough to describe the experimentally achievable states. The changes in electron spectra due to electron heating and compression or expansion are taken into account using two-parabolic model. In our previous works, thermal conductivity and electron-ion coupling were considered as dependencies on electron and ion temperatures. Now the dependence on density for these coefficients is taken into account. To include exchange-correlation effects on electron-electron collisions we have found out how this effect can be included in electron screening. In addition, we have renewed our approach for heat conductivity calculation to include thermoelectric phenomena, which are significant at high electron temperatures. The effect of electron heating on sound velocities in aforementioned metals is investigated. The two-temperature hydrodynamics simulation of film expansion was provided with the use of the model presented here.

  17. Application of the Stefan-Maxwell equations to determine limitations of Fick's Law when modeling organic vapor transport in sand columns

    SciTech Connect

    Baehr, A.L. ); Bruell, C.J. )

    1990-06-01

    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., O{sub 2}), 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.

  18. Derivation of new 3D discrete ordinate equations

    SciTech Connect

    Ahrens, C. D.

    2012-07-01

    The Sn equations have been the workhorse of deterministic radiation transport calculations for many years. Here we derive two new angular discretizations of the 3D transport equation. The first set of equations, derived using Lagrange interpolation and collocation, retains the classical Sn structure, with the main difference being how the scattering source is calculated. Because of the formal similarity with the classical S n equations, it should be possible to modify existing computer codes to take advantage of the new formulation. In addition, the new S n-like equations correctly capture delta function scattering. The second set of equations, derived using a Galerkin technique, does not retain the classical Sn structure because the streaming term is not diagonal. However, these equations can be cast into a form similar to existing methods developed to reduce ray effects. Numerical investigation of both sets of equations is under way. (authors)

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

    PubMed

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

    2013-02-01

    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

  20. A zero-equation turbulent electron transport model for cross-field migration and its implementation in a 2-D hybrid plasma Hall thruster simulation

    NASA Astrophysics Data System (ADS)

    Cappelli, Mark; Young, Chris; Cha, Eusnun; Fernandez, Eduardo; Stanford Plasma Physics Laboratory Collaboration; Eckerd College Collaboration

    2015-09-01

    We present a simple, zero-equation turbulence model for electron transport across the magnetic field of a plasma Hall thruster and integrate this model into 2-D hybrid particle-in-cell simulations of a 72 mm diameter laboratory thruster operating at 400 W. The turbulent transport model is based on the assumption that the primary means of electron energy dissipation is the turbulent eddy cascade in the electron fluid to smaller scales. Implementing the model into 2-D hybrid simulations is relatively straightforward and leverages the existing framework for solving the electron fluid equations. We find that the model captures the strong axial variation in the mobility seen in experiments. In particular, it predicts the existence of a strong transport barrier which anchors the region of plasma acceleration. The model also captures the time-averaged experimental discharge current and its fluctuations due to ionization instabilities. We observe quantitative agreement with recent laser induced fluorescence measurements of time-averaged xenon ion and neutral velocities along the channel centerline. This work was supported by the Air Force Office of Scientific Research.

  1. A non-negative moment-preserving spatial discretization scheme for the linearized Boltzmann transport equation in 1-D and 2-D Cartesian geometries

    NASA Astrophysics Data System (ADS)

    Maginot, Peter G.; Morel, Jim E.; Ragusa, Jean C.

    2012-08-01

    We present a new nonlinear spatial finite-element method for the linearized Boltzmann transport equation with Sn angular discretization in 1-D and 2-D Cartesian geometries. This method has two central characteristics. First, it is equivalent to the linear-discontinuous (LD) Galerkin method whenever that method yields a strictly non-negative solution. Second, it always satisfies both the zeroth and first spatial moment equations. Because it yields the LD solution when that solution is non-negative, one might interpret our method as a classical fix-up to the LD scheme. However, fix-up schemes for the LD equations derived in the past have given up solution of the first moment equations when the LD solution is negative in order to satisfy positivity in a simple manner. We present computational results comparing our method in 1-D to the strictly non-negative linear exponential-discontinuous method and to the LD method. We present computational results in 2-D comparing our method to a recently developed LD fix-up scheme and to the LD scheme. It is demonstrated that our method is a valuable alternative to existing methods.

  2. 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.

  3. Mesh adaptation on the sphere using optimal transport and the numerical solution of a Monge-Ampère type equation

    NASA Astrophysics Data System (ADS)

    Weller, Hilary; Browne, Philip; Budd, Chris; Cullen, Mike

    2016-03-01

    An equation of Monge-Ampère type has, for the first time, been solved numerically on the surface of the sphere in order to generate optimally transported (OT) meshes, equidistributed with respect to a monitor function. Optimal transport generates meshes that keep the same connectivity as the original mesh, making them suitable for r-adaptive simulations, in which the equations of motion can be solved in a moving frame of reference in order to avoid mapping the solution between old and new meshes and to avoid load balancing problems on parallel computers. The semi-implicit solution of the Monge-Ampère type equation involves a new linearisation of the Hessian term, and exponential maps are used to map from old to new meshes on the sphere. The determinant of the Hessian is evaluated as the change in volume between old and new mesh cells, rather than using numerical approximations to the gradients. OT meshes are generated to compare with centroidal Voronoi tessellations on the sphere and are found to have advantages and disadvantages; OT equidistribution is more accurate, the number of iterations to convergence is independent of the mesh size, face skewness is reduced and the connectivity does not change. However anisotropy is higher and the OT meshes are non-orthogonal. It is shown that optimal transport on the sphere leads to meshes that do not tangle. However, tangling can be introduced by numerical errors in calculating the gradient of the mesh potential. Methods for alleviating this problem are explored. Finally, OT meshes are generated using observed precipitation as a monitor function, in order to demonstrate the potential power of the technique.

  4. 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.

  5. 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.

  6. Backscattering and absorption coefficients for electrons: Solutions of invariant embedding transport equations using a method of convergence

    SciTech Connect

    Figueroa, C.; Brizuela, H.; Heluani, S. P.

    2014-05-21

    The backscattering coefficient is a magnitude whose measurement is fundamental for the characterization of materials with techniques that make use of particle beams and particularly when performing microanalysis. In this work, we report the results of an analytic method to calculate the backscattering and absorption coefficients of electrons in similar conditions to those of electron probe microanalysis. Starting on a five level states ladder model in 3D, we deduced a set of integro-differential coupled equations of the coefficients with a method know as invariant embedding. By means of a procedure proposed by authors, called method of convergence, two types of approximate solutions for the set of equations, namely complete and simple solutions, can be obtained. Although the simple solutions were initially proposed as auxiliary forms to solve higher rank equations, they turned out to be also useful for the estimation of the aforementioned coefficients. In previous reports, we have presented results obtained with the complete solutions. In this paper, we present results obtained with the simple solutions of the coefficients, which exhibit a good degree of fit with the experimental data. Both the model and the calculation method presented here can be generalized to other techniques that make use of different sorts of particle beams.

  7. Finite Element Flux-Corrected Transport (FEM-FCT) for the Euler and Navier-Stokes equations

    NASA Technical Reports Server (NTRS)

    Loehner, Rainald; Morgan, Ken; Peraire, Jaime; Vahdati, Mehdi

    1987-01-01

    A high resolution finite element method for the solution of problems involving high speed compressible flows is presented. The method uses the concepts of flux-corrected transport and is presented in a form which is suitable for implementation on completely unstructured triangular or tetrahedral meshes. Transient and steady state examples are solved to illustrate the performance of the algorithm.

  8. TESTING THE FRACTIONAL ADVECTIVE-DISPERSIVE EQUATION FOR SOLUTE TRANSPORT IN SOIL WITH DATA FROM MISCIBLE DISPLACEMENT EXPERIMENTS

    Technology Transfer Automated Retrieval System (TEKTRAN)

    Understanding and modeling transport of solutes in porous media is a critical issue in the environmental protection. Contaminants from various industrial and agricultural sources can travel in soil and ground water and eventually affect human and animal health. The parabolic advective-dispersive equ...

  9. 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…

  10. 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.

  11. 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.

  12. 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

  13. 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.

  14. Electron swarm transport coefficients in mixtures of H2O with He and Ar: Experiment and Boltzmann equation calculations

    NASA Astrophysics Data System (ADS)

    de Urquijo, Jaime; Basurto, E.; Juarez, A. M.; Ness, Kevin; Robson, Robert; Brunger, Michael; White, Ron

    2014-10-01

    The drift velocity of electrons in mixtures of gaseous water with helium and argon are measured over the range of reduced electric fields from 0--300 Td using a pulsed-Townsend technique. Small admixtures of water to both helium and argon are found to produce negative differential conductivity (NDC), despite NDC being absent from the pure gases. Comparison of the measured drift velocities with those calculated from a multi-term solution of Boltzmann's equation provides a further discriminative assessment on the accuracy and completeness of electron water vapour cross-sections. Funding acknowledgements: ARC, Mexican govt (PAPIIT IN 111014).

  15. D4Z - a new renumbering for iterative solution of ground-water flow and solute- transport equations

    USGS Publications Warehouse

    Kipp, K.L.; Russell, T.F.; Otto, J.S.

    1992-01-01

    D4 zig-zag (D4Z) is a new renumbering scheme for producing a reduced matrix to be solved by an incomplete LU preconditioned, restarted conjugate-gradient iterative solver. By renumbering alternate diagonals in a zig-zag fashion, a very low sensitivity of convergence rate to renumbering direction is obtained. For two demonstration problems involving groundwater flow and solute transport, iteration counts are related to condition numbers and spectra of the reduced matrices.

  16. Transportation.

    ERIC Educational Resources Information Center

    Crank, Ron

    This instructional unit is one of 10 developed by students on various energy-related areas that deals specifically with transportation and energy use. Its objective is for the student to be able to discuss the implication of energy usage as it applies to the area of transportation. Some topics covered are efficiencies of various transportation…

  17. Implicit solution of Stokes flow equation with material transport: toward thermal convection simulation under the self-gravitating field with free surface

    NASA Astrophysics Data System (ADS)

    Furuichi, M.; Nakagawa, T.; May, D.

    2013-12-01

    Stabilizing a numerical oscillation in free surface treatment is chagrining topic for a geodynamics simulation [e.g. Kaus et al. 2010, Duretz et al., 2011]. It is especially important for the Stokes flow simulation under the self-gravitating field based on 'Spherical Cartesian' method [Gerya et al., 2007], which is useful for simulating a long time scale dynamics of sinking metal rich materials to construct planetary core. The conventional explicit time stepping algorithm, which solves Stokes flow equation for a given material distribution at a previous time step, however has a difficulty for simulating dynamics such as a thermal convection, after the construction of layered structure in the planetary interior because of numerical oscillation. One effective approach for such numerically problematic behavior is an implicit treatment of advection term. In this study, three types of implicit strategy are discussed. First is the full implicit treatment with iterative non-linear solver which uses transported density by maker-in-cell method as nonlinear update. The maker-in-cell method is commonly used as low diffusive advection method, but is computationally expensive with makers to mesh interpolation. Second approach uses semi-Lagrangian method for nonlinear update instead of the maker-in-cell method to reduce computational cost. Third approach is to solve the Stokes flow equation combined with the linearized advection term in central-difference discretization to avoid the nonlinear update by the transport. In the second and third algorithms, physical value at the next time step is still transported by low diffusive maker-in-cell method. These three types of implicit method are examined by numerical experiment.

  18. Asymptotic solutions of neutron transport equation and the limits of correct use of diffusion approximation for rocks.

    PubMed

    Dworak, D; Loskiewicz, J; Janik, M

    2001-05-01

    The diffusion approximation solution for neutron transport has been used in well-logging geophysics for calculating tool responses in boreholes, sometimes with success. The problem of the dimension of different materials to which it can be applied with success is important for the borehole environment. The results obtained show that the diffusion approximation can be used for distances greater than a few millimetre in some rock types. For iron, barium, and other highly absorbing media the use of the diffusion approximation is inappropriate even for large distances. PMID:11258535

  19. An Approach to Quantum Transport Based on Reduced Hierarchy Equations of Motion: Application to a Resonant Tunneling Diode

    NASA Astrophysics Data System (ADS)

    Sakurai, Atsunori; Tanimura, Yoshitaka

    2013-03-01

    The quantum dissipative dynamics of a tunneling process through double barrier structures is investigated on the basis of a rigorous treatment for the first time. We employ a Caldeira--Leggett Hamiltonian with an effective potential calculated self-consistently, accounting for the electron distribution. With this Hamiltonian, we use the reduced hierarchy equations of motion in the Wigner space representation to study the effects of non-Markovian thermal fluctuations and dissipation at finite temperature in a rigorous manner. Hysteresis, double plateau-like behavior, and self-excited current oscillation are observed in a negative differential resistance (NDR) region of the current--voltage curve. We find that while most of the current oscillations decay in time in the NDR region, there is a steady oscillation characterized by a tornado-like rotation in the Wigner space in the upper plateau of the NDR region.

  20. 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.

  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. 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.

  3. Quantum transport equation for systems with rough surfaces and its application to ultracold neutrons in a quantizing gravity field

    NASA Astrophysics Data System (ADS)

    Escobar, M.; Meyerovich, A. E.

    2014-12-01

    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. The effects of superoxide dismutase addition to the transport medium on cumulus-oocyte complex apoptosis and IVF outcome in cats (Felis catus).

    PubMed

    Cocchia, Natascia; Corteggio, Annunziata; Altamura, Gennaro; Tafuri, Simona; Rea, Silviana; Rosapane, Isabella; Sica, Alessandro; Landolfi, Francesco; Ciani, Francesca

    2015-03-01

    The aim of the present study was to examine the effects of superoxide dismutase (SOD) addition to the ovary transport medium (4°C, 3-72 h) on ovarian cell viability and apoptosis and in vitro embryo production (IVEP) in domestic cats. The ovaries collected from 76 mixed-breed domestic queens were randomly assigned to the control or SOD-treated groups and incubated for 3, 24, 48 or 72 h. The ovaries were then subjected to the following: (1) fixed in formalin to assess the incidence of apoptosis (fragmented DNA in situ detection kit), (2) stored at -196°C in liquid nitrogen to evaluate the expression of the pro-apoptotic Bax gene and the anti-apoptotic Bcl-2 gene (RT-PCR), and (3) used to obtain the cumulus-oocyte complexes (COCs) in order to test the cell viability (carboxyfluorescein or trypan blue staining) and IVEP. The incidence of apoptosis appeared to be higher in the control compared with the SOD-treated ovaries. The ovarian expression of Bax was lower and the Bcl-2 expression was higher in the SOD-treated group compared with the control group. The presence of SOD in the transport medium increased the viability of COCs and IVEP compared with the control medium. In summary, the supplementation of the ovary transport medium with SOD reduced cellular apoptosis and enhanced COC survival and IVEP in domestic cats. PMID:25726378

  5. 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.

  6. Transport through an Anderson impurity: Current ringing, nonlinear magnetization, and a direct comparison of continuous-time quantum Monte Carlo and hierarchical quantum master equations

    NASA Astrophysics Data System (ADS)

    Härtle, R.; Cohen, G.; Reichman, D. R.; Millis, A. J.

    2015-08-01

    We give a detailed comparison of the hierarchical quantum master equation (HQME) method to a continuous-time quantum Monte Carlo (CT-QMC) approach, assessing the usability of these numerically exact schemes as impurity solvers in practical nonequilibrium calculations. We review the main characteristics of the methods and discuss the scaling of the associated numerical effort. We substantiate our discussion with explicit numerical results for the nonequilibrium transport properties of a single-site Anderson impurity. The numerical effort of the HQME scheme scales linearly with the simulation time but increases (at worst exponentially) with decreasing temperature. In contrast, CT-QMC is less restricted by temperature at short times, but in general the cost of going to longer times is also exponential. After establishing the numerical exactness of the HQME scheme, we use it to elucidate the influence of different ways to induce transport through the impurity on the initial dynamics, discuss the phenomenon of coherent current oscillations, known as current ringing, and explain the nonmonotonic temperature dependence of the steady-state magnetization as a result of competing broadening effects. We also elucidate the pronounced nonlinear magnetization dynamics, which appears on intermediate time scales in the presence of an asymmetric coupling to the electrodes.

  7. 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.

  8. A sigma-coordinate primitive equation model for studying the circulation in the South Atlantic Part II: Meridional transports and seasonal variability

    NASA Astrophysics Data System (ADS)

    Marchesiello, P.; Barnier, B.; de Miranda, A. P.

    1998-04-01

    The mean and seasonal variability of the circulation and meridional heat transport in the South Atlantic are investigated using a set of numerical experiments. The primitive equation model uses a topography-following (sigma) coordinate. The model domain is limited to the South Atlantic basin. Artificial boundaries at Drake Passage, between Brazil and Angola, and between South Africa and Antarctica are treated as open boundaries. Finally, recent and self-consistent estimates of seasonal fluxes are used to define a model-dependent atmospheric forcing. Quasi-diagnostic simulations forced by constant climatological winds are first conducted to determine the sensitivity of model solutions to bottom topography smoothing, and to diagnose meridional fluxes from a mass field that is relaxed to the annual climatology of Levitus (1982). Model results show good agreement with known climatological circulation features in this basin, especially in the Confluence Region, where coarse resolution models usually give smooth structures. Sensitivity studies show that the more detailed features of the circulation are influenced by the model bathymetry. The model simulates a meridional circulation whose upper branch (the return flow that balances the southward flow of North Atlantic Deep Water) is composed of Intermediate (IW) and Thermocline (TW) Waters. The transport of IW is found to be predominant, and the value of meridional heat transport consequently falls within the low estimates. We notice that the meridional heat balance is sensitive to the position of the Confluence. When this region occurs too far south, the amount of IW contributing to the return flow of the overturning cell is reduced. Prognostic simulations forced by seasonal winds and heat fluxes are studied to quantify the impact of wind forcing on the circulation in the South Atlantic. Particular attention is focused on meridional transports at 30°S. Analysis of the mean annual circulation confirms that the upper

  9. 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.

  10. 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

  11. The serotonin transporter gene polymorphism (5HTTLPR) moderates the effect of adolescent environmental conditions on self-esteem in young adulthood: a structural equation modeling approach.

    PubMed

    Jonassaint, Charles R; Ashley-Koch, Allison; Whitfield, Keith E; Hoyle, Rick H; Richman, Laura Smart; Siegler, Ilene C; Royal, Charmaine D; Williams, Redford

    2012-09-01

    Here we examine the effects of both self-reported and independent observer-reported environmental risk indices, the serotonin transporter gene promoter (5HTTLPR) polymorphism, and their interaction on self-esteem. This trait was assessed during early and mid adolescence (mean age=14 and 16.5, respectively) and young adulthood (mean age=21.8) in a prospective cohort of 1214 unrelated participants in the Longitudinal Study of Adolescent Health (Add Health). Using structural equation modeling we identified a gene-environment (G×E) interaction using observer-report but not self-report measures of environmental stress exposure during adolescence: 5HTTLPR genotype and observer-reports of home and neighborhood quality (HNQ) during adolescence interacted to predict self-esteem levels in young adulthood (p<.004). Carriers of the s allele who lived in poor HNQ conditions during adolescence reported lower self-esteem in young adulthood than those with a good HNQ during adolescence. In contrast, among individuals with the l/l genotype, adolescent HNQ did not predict adulthood self-esteem. Genes may moderate the effect of adolescent environmental conditions on adulthood self-esteem. PMID:22659377

  12. 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.

  13. 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.

  14. Effect of phosphorus additions on the sintering and transport properties of proton conducting BaZr0.85Y0.15O3-δ

    NASA Astrophysics Data System (ADS)

    Soares, H. S.; Zhang, X.; Antunes, I.; Frade, J. R.; Mather, G. C.; Fagg, D. P.

    2012-07-01

    The influence of phosphorous additions on the sintering and electrical transport properties of the proton-conducting perovskite BaZr0.85Y0.15O3-δ (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. P2O5 additions, (1-x)BZY·xP2O5, monotonously promote densification in the intermediate compositional range 0.04≤x≤0.08. Nonetheless, BZY reacts with phosphorous forming the phase Ba3(PO4)2 at temperatures as low as 600 °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.

  15. 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.

  16. Dosimetric impact of an {sup 192}Ir brachytherapy source cable length modeled using a grid-based Boltzmann transport equation solver

    SciTech Connect

    Mikell, Justin K.; Mourtada, Firas

    2010-09-15

    Purpose: To evaluate the dose distributions of an {sup 192}Ir source (model VS2000) in homogeneous water geometry calculated using a deterministic grid-based Boltzmann transport equation solver (GBBS) in the commercial treatment planning system (TPS) (BRACHYVISION-ACUROS v8.8). Methods: Using percent dose differences (%{Delta}D), the GBBS (BV-ACUROS) was compared to the (1) published TG-43 data, (2) MCNPX Monte Carlo (MC) simulations of the {sup 192}Ir source centered in a 15 cm radius water sphere, and (3) TG-43 output from the TPS using vendor supplied (BV-TG43-vendor) and user extended (BV-TG43-extended) 2D anisotropy functions F(r,{theta}). BV-ACUROS assumes 1 mm of NiTi cable, while the TPS TG-43 algorithm uses data based on a 15 cm cable. MC models of various cable lengths were simulated. Results: The MC simulations resulted in >20% dose deviations along the cable for 1, 2, and 3 mm cable lengths relative to 15 cm. BV-ACUROS comparisons with BV-TG43-vendor and BV-TG43-extended yielded magnitude of differences, consistent with those seen in MC simulations. However, differences >20% extended further ({theta}{<=}10 deg.) when using the vendor supplied anisotropy function F{sub ven}(r,{theta}). These differences were also seen in comparisons of F(r,{theta}) derived from the TPS output. Conclusions: The results suggest that %{Delta}D near the cable region is larger than previously estimated. The spatial distribution of the dose deviation is highly dependent on the reference TG-43 data used to compare to GBBS. The differences observed, while important to realize, should not have an impact on clinical dosimetry in homogeneous water.

  17. The Influence of Sn Additions on the Thermoelectric and Transport Properties of FeSb2Te-based Ternary Skutterudites

    NASA Astrophysics Data System (ADS)

    Navrátil, J.; Plecháček, T.; Drašar, Č.; Kucek, V.; Laufek, F.; Černošková, E.; Beneš, L.; Vlček, M.

    2016-06-01

    The influence of Sn additions was studied in a series of samples of a nominal composition FeSb2Te1- x Sn x ( x = 0, 0.05, 0.1, 0.15, 0.2). SnTe compound was primarily identified in the matrix compound of the ternary skutterudite structure in the multiphase composite samples. It was determined that Sn atoms preferentially react with Te atoms which are present in order to form SnTe compound instead of entering the skutterudite structure. A detailed analysis of the composition of the ternary skutterudite matrix compound evoked by the striking similarities of the observed changes between the samples and another two published systems (FeSb2Te1- x Ge x and FeSb2+ x Te1- x ) revealed the crucial role of the Sb/Te ratio as the dominant factor driving the observed changes of the measured properties. The anomalous changes of the measured transport properties values were explained in terms of an effective medium theory for two-phase FeSb2Te-SnTe composites. A maximum value of thermoelectric figure-of-merit, ZT = 0.47 at 673 K, was attained for the sample of a nominal composition FeSb2Te0.85Sn0.15.

  18. Explicit lower bounds for the cost of fast controls for some 1-D parabolic or dispersive equations, and a new lower bound concerning the uniform controllability of the 1-D transport-diffusion equation

    NASA Astrophysics Data System (ADS)

    Lissy, Pierre

    2015-11-01

    In this paper, we prove explicit lower bounds for the cost of fast boundary controls for a class of linear equations of parabolic or dispersive type involving the spectral fractional Laplace operator. We notably deduce the following striking result: in the case of the heat equation controlled on the boundary, Miller's conjecture formulated in Miller (2004) [16] is not verified. Moreover, we also give a new lower bound for the minimal time needed to ensure the uniform controllability of the one-dimensional convection-diffusion equation with negative speed controlled on the left boundary, proving that the conjecture formulated in Coron and Guerrero (2005) [2] concerning this problem is also not verified at least for negative speeds. The proof is based on complex analysis, and more precisely on a representation formula for entire functions of exponential type, and is quite related to the moment method.

  19. Groundwater pollution by organic compounds: a three-dimensional boundary element solution of contaminant transport equations in stratified porous media with multiple non-equilibrium partitioning

    NASA Astrophysics Data System (ADS)

    Elzein, Abbas H.; Booker, John R.

    1999-12-01

    Industrial contaminants and landfill leachates, particularly those with high organic content, may migrate into groundwater streams under conditions of non-equilibrium partitioning. These conditions may either be induced by time-dependent sorption onto the soil skeleton and intra-sorbent diffusion in the soil matrix, or by heterogeneous advective fields within the pore. These processes are known as chemical and physical non-equilibrium processes respectively, and may result in significant deviations from the paths predicted by steady-state partitioning assumptions. In addition, multi-directional soil properties, soil stratification and complex geometries of the pollution source may require a full three-dimensional analysis for accurate contamination prediction.A three-dimensional boundary element solution of the time-dependent diffusive/advective equation in non-homogeneous soils with both physical and chemical non-equilibrium processes is developed. Saturated conditions and rate-limited mass transfer are assumed. The Laplace transform removes the need for time-stepping and the associated numerical complexity, and the use of Green's functions yields accurate solutions of infinite and semi-infinite domains such as soils as well as media with finite dimensions. The solution requires boundary discretization only and can therefore be a valuable tool in bio-remediation and landfill design where different geometries, soil properties and pollutant loads may be analysed at low cost. The proposed technique is validated by comparing its predictions to analytical solutions obtained for different types of soil and contaminant sources. The scope of the method is illustrated by analysing the contamination of multi-layered soils by a neighbouring river and a surface source.

  20. Landscape evolution models: A review of their fundamental equations

    NASA Astrophysics Data System (ADS)

    Chen, Alex; Darbon, Jérôme; Morel, Jean-Michel

    2014-08-01

    This paper reviews the main physical laws proposed in landscape evolution models (LEMs). It discusses first the main partial differential equations involved in these models and their variants. These equations govern water runoff, stream incision, regolith-bedrock interaction, hillslope evolution, and sedimentation. A synthesis of existing LEMs is proposed. It proposes three models with growing complexity and with a growing number of components: two-equation models with only two components, governing water and bedrock evolution; three-equation models with three components where water, bedrock, and sediment interact; and finally models with four equations and four interacting components, namely water, bedrock, suspended sediment, and regolith. This analysis is not a mere compilation of existing LEMs. It attempts at giving the simplest and most general physically consistent set of equations, coping with all requirements stated in LEMs and LEM software. Three issues are in particular addressed and hopefully resolved. The first one is a correct formulation of the water transport equation down slopes. A general formulation for this equation is proposed, coping not only with the simplest form computing the drainage area but also with a sound energy dissipation argument associated with the Saint-Venant shallow water equations. The second issue arises from the coexistence of two competing modes, namely the detachment-limited erosion mode on hillslopes, and the transport-limited sediment transport on river beds. The third issue (linked to the second) is the fact that no conservation law is available for material in these two modes. A simple solution proposed to resolve these issues is the introduction, as suggested by several authors, of an additional variable for suspended sediment load in water. With only three variables and three equations, the above-mentioned contradictions seem to be eliminated. Several numerical experiments on real digital elevation models (DEMs

  1. 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

  2. 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.

  3. Erosion and Optimal Transport

    NASA Astrophysics Data System (ADS)

    Birnir, Bjorn; Rowlett, Julie

    2010-05-01

    We show that the land-surface equation of Birnir, Smith and Merchant, describing erosion of transport limited surfaces have unique weak solutions. The theory of optimal transport is then used to show that these equations constitute an optimal transport of the sediment by the water flow.

  4. Food additives

    MedlinePlus

    Food additives are substances that become part of a food product when they are added during the processing or making of that food. "Direct" food additives are often added during processing to: Add nutrients ...

  5. 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.

  6. 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

  7. 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.

  8. Teaching Equations.

    ERIC Educational Resources Information Center

    Nibbelink, William H.

    1990-01-01

    Proposed is a gradual transition from arithmetic to the idea of an equation with variables in the elementary grades. Vertical and horizontal formats of open sentences, the instructional sequence, vocabulary, and levels of understanding are discussed in this article. (KR)

  9. 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...

  10. 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...

  11. 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...

  12. FAA Smoke Transport Code

    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 codemore » 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.« less

  13. Theory of contributon transport

    SciTech Connect

    Painter, J.W.; Gerstl, S.A.W.; Pomraning, G.C.

    1980-10-01

    A general discussion of the physics of contributon transport is presented. To facilitate this discussion, a Boltzmann-like transport equation for contributons is obtained, and special contributon cross sections are defined. However, the main goal of this study is to identify contributon transport equations and investigate possible deterministic solution techniques. Four approaches to the deterministic solution of the contributon transport problem are investigated. These approaches are an attempt to exploit certain attractive properties of the contributon flux, psi = phi phi/sup +/, where phi and phi/sup +/ are the solutions to the forward and adjoint Boltzmann transport equations.

  14. 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).

  15. Nonequilibrium, steady-state electron transport with N-representable density matrices from the anti-Hermitian contracted Schrödinger equation.

    PubMed

    Rothman, Adam E; Mazziotti, David A

    2010-03-14

    We study molecular conductivity for a one-electron, bath-molecule-bath model Hamiltonian. The primary quantum-mechanical variable is the one-electron reduced density matrix (1-RDM). By identifying similarities between the steady-state Liouville equation and the anti-Hermitian contracted Schrödinger equation (ACSE) [D. A. Mazziotti, Phys. Rev. A 75, 022505 (2007)], we develop a way of enforcing nonequilibrium, steady-state behavior in a time-independent theory. Our results illustrate the relationship between current and voltage in molecular junctions assuming that the total number of electrons under consideration can be fixed across all driving potentials. The impetus for this work is a recent study by Subotnik et al. that also uses the 1-RDM to study molecular conductivity under different assumptions regarding the total number of electrons [J. E. Subotnik et al., J. Chem. Phys. 130, 144105 (2009)]. Unlike calculations in the previous study, our calculations result in 1-RDMs that are fully N-representable. The present work maintains N-representability through a bath-bath mixing that is related to a time-independent relaxation of the baths in the absence of the molecule, as governed by the ACSE. A lack of N-representability can be important since it corresponds to occupying energy states in the molecule or baths with more than one electron or hole (the absence of an electron) in violation of the Pauli principle. For this reason the present work may serve as an important, albeit preliminary, step in designing a 2-RDM/ACSE method for studying steady-state molecular conductivity with an explicit treatment of electron correlation. PMID:20232952

  16. Food additives.

    PubMed

    Berglund, F

    1978-01-01

    The use of additives to food fulfils many purposes, as shown by the index issued by the Codex Committee on Food Additives: Acids, bases and salts; Preservatives, Antioxidants and antioxidant synergists; Anticaking agents; Colours; Emulfifiers; Thickening agents; Flour-treatment agents; Extraction solvents; Carrier solvents; Flavours (synthetic); Flavour enhancers; Non-nutritive sweeteners; Processing aids; Enzyme preparations. Many additives occur naturally in foods, but this does not exclude toxicity at higher levels. Some food additives are nutrients, or even essential nutritents, e.g. NaCl. Examples are known of food additives causing toxicity in man even when used according to regulations, e.g. cobalt in beer. In other instances, poisoning has been due to carry-over, e.g. by nitrate in cheese whey - when used for artificial feed for infants. Poisonings also occur as the result of the permitted substance being added at too high levels, by accident or carelessness, e.g. nitrite in fish. Finally, there are examples of hypersensitivity to food additives, e.g. to tartrazine and other food colours. The toxicological evaluation, based on animal feeding studies, may be complicated by impurities, e.g. orthotoluene-sulfonamide in saccharin; by transformation or disappearance of the additive in food processing in storage, e.g. bisulfite in raisins; by reaction products with food constituents, e.g. formation of ethylurethane from diethyl pyrocarbonate; by metabolic transformation products, e.g. formation in the gut of cyclohexylamine from cyclamate. Metabolic end products may differ in experimental animals and in man: guanylic acid and inosinic acid are metabolized to allantoin in the rat but to uric acid in man. The magnitude of the safety margin in man of the Acceptable Daily Intake (ADI) is not identical to the "safety factor" used when calculating the ADI. The symptoms of Chinese Restaurant Syndrome, although not hazardous, furthermore illustrate that the whole ADI

  17. An enhanced Fourier law derivable from the Boltzmann transport equation and a sample application in determining the mean-free path of nondiffusive phonon modes

    NASA Astrophysics Data System (ADS)

    Ramu, Ashok T.; Ma, Yanbao

    2014-09-01

    An enhanced Fourier law that we term the unified nondiffusive-diffusive (UND) phonon transport model is proposed in order to account for the effect of low-frequency phonon modes of long mean-free path that propagate concomitantly to the dominant high-frequency modes. The theory is based on spherical harmonic expansions of the phonon distribution functions, wherein the high-frequency mode distribution function is truncated at the first order in the expansion, while the low-frequency mode distribution function, which is farther out of thermal equilibrium, is truncated at the second order. As an illustrative application, the predictions of the proposed model are compared with data from a recent experiment that utilized the transient gratings method to investigate the deviation of thermal transport in a silicon membrane from the predictions of the Fourier law. The good fit of the experimental effective thermal conductivity (ETC) with the analytical solution derived in this work yields quantitative information about the mean-free path of the dominant low-frequency heat-transfer mode in silicon.

  18. Addition by subtraction in coupled cluster theory. II. Equation-of-motion coupled cluster method for excited, ionized, and electron-attached states based on the nCC ground state wave function

    NASA Astrophysics Data System (ADS)

    Musiał, Monika; Bartlett, Rodney J.

    2007-07-01

    New iterative double and triple excitation corrections to the equation-of-motion coupled cluster (EOM-CC) based upon the recently developed nCC methods [Bartlett and Musiał, J. Chem. Phys. 125, 204105-1 (2006)] are applied to excitation energies (EEs), ionization potentials (IPs), and electron affinities (EAs). The methods have been tested by the evaluation of the vertical EEs, IPs, and EAs for Ne, BH, CH2, H2O, N2, C2, CH+, CO, and C2H4 compared to full configuration interaction, EOM-CCSD, EOM-CCSDT, and experimental data.

  19. 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.

  20. 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.

  1. Marcus equation

    SciTech Connect

    1998-11-01

    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.

  2. Analysis of the ionosphere-plasmasphere transport of superthermal electrons. I - Transport in the plasmasphere

    NASA Technical Reports Server (NTRS)

    Khazanov, George V.; Gombosi, Tamas I.; Nagy, Andrew F.; Koen, Mikhail A.

    1992-01-01

    Analytical solutions are developed for the kinetic equation which describes the transport of superthermal electrons in the terrestrial plasmasphere, together with a relationship which makes it possible to calculate the transparency of the plasmasphere to these electrons. In addition, analytic expressions are presented for the heating rate of the thermal plasma due to the passage of these superthermal electrons through the plasmasphere.

  3. 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.

  4. Phosphazene additives

    SciTech Connect

    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.

  5. Boltzmann equation and hydrodynamic fluctuations.

    PubMed

    Colangeli, Matteo; Kröger, Martin; Ottinger, Hans Christian

    2009-11-01

    We apply the method of invariant manifolds to derive equations of generalized hydrodynamics from the linearized Boltzmann equation and determine exact transport coefficients, obeying Green-Kubo formulas. Numerical calculations are performed in the special case of Maxwell molecules. We investigate, through the comparison with experimental data and former approaches, the spectrum of density fluctuations and address the regime of finite Knudsen numbers and finite frequencies hydrodynamics. PMID:20364972

  6. 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.

  7. Optimization of Supersonic Transport Trajectories

    NASA Technical Reports Server (NTRS)

    Ardema, Mark D.; Windhorst, Robert; Phillips, James

    1998-01-01

    This paper develops a near-optimal guidance law for generating minimum fuel, time, or cost fixed-range trajectories for supersonic transport aircraft. The approach uses a choice of new state variables along with singular perturbation techniques to time-scale decouple the dynamic equations into multiple equations of single order (second order for the fast dynamics). Application of the maximum principle to each of the decoupled equations, as opposed to application to the original coupled equations, avoids the two point boundary value problem and transforms the problem from one of a functional optimization to one of multiple function optimizations. It is shown that such an approach produces well known aircraft performance results such as minimizing the Brequet factor for minimum fuel consumption and the energy climb path. Furthermore, the new state variables produce a consistent calculation of flight path angle along the trajectory, eliminating one of the deficiencies in the traditional energy state approximation. In addition, jumps in the energy climb path are smoothed out by integration of the original dynamic equations at constant load factor. Numerical results performed for a supersonic transport design show that a pushover dive followed by a pullout at nominal load factors are sufficient maneuvers to smooth the jump.

  8. An upscaled approach for transport in media with extended tailing due to back-diffusion using analytical and numerical solutions of the advection dispersion equation

    NASA Astrophysics Data System (ADS)

    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

  9. 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

  10. 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.

  11. 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.

  12. Elastic constants of B-HMX and tantalum, equations of state of supercritical fluids and fluid mixtures and thermal transport determinations

    SciTech Connect

    Zaug, J M

    1998-08-21

    Ultrasonic sound speed measurements via Impulsive Stimulated Light Scattering (ISLS) were made in single crystals of b-HMX and tantalum over an extended range of temperatures. Elastic constants are consequently determined for b-HMX. Sound speeds are calculated for tantalum, from known elastic constants, and compare favorably with the results presented here. ISLS time-domain fits of tantalum records allowed for thermal diffusion determinations and, correspondingly, thermal conductivity. Measurements of the speed of sound and of the thermal diffusivities of fluid oxygen up to pressures of 13 GPa and at several temperatures are presented. Between 0.1 and 13 GPa the fluid's density increases by a factor of three. Thermal diffusivities rise slowly over this range, and are substantially smaller than those previously measured for the solid b-phase. Additional sound speed measurements were made along the 250 C isotherm in a 1:1 molar ratio mixture of liquid oxygen and nitrogen. These experiments demonstrate the versatility and potential application of a new laboratory within the U. S. DOD and DOE complex. 1

  13. Development and implementation of a finite element solution of the coupled neutron transport and thermoelastic equations governing the behavior of small nuclear assemblies

    NASA Astrophysics Data System (ADS)

    Wilson, Stephen Christian

    Small, highly enriched reactors designed for weapons effects simulations undergo extreme thermal transients during pulsed operations. The primary shutdown mechanism of these reactors---thermal expansion of fuel material---experiences an inertial delay resulting in a different value for the fuel temperature coefficient of reactivity during pulse operation as compared to the value appropriate for steady-state operation. The value appropriate for pulsed operation may further vary as a function of initial reactivity addition. Here we design and implement a finite element numerical method to predict the pulse operation behavior of Sandia Pulsed Reactor (SPR) II, SPR III, and a hypothetical spherical assembly with identical fuel properties without using operationally observed data in our model. These numerical results are compared to available SPR II and SPR III operational data. The numerical methods employed herein may be modified and expanded in functionality to provide both accurate characterization of the behavior of fast burst reactors of any common geometry or isotropic fuel material in the design phase, as well as a computational tool for general coupled thermomechanical-neutronics behavior in the solid state for any reactor type.

  14. Exposure to chemical additives from polyvinyl chloride polymer extrusion processing

    SciTech Connect

    Lamb, C.S.

    1989-12-01

    The report presents a model to predict worker inhalation exposure due to off-gassing of additives during polyvinyl chloride (PVC) extrusion processing. Data on off-gassing of additives were reviewed in the literature, the off-gassing at normal PVC processing temperatures was studied in the laboratory, process variables were estimated from an equipment manufacturer survey, and worker-activities and possible exposure sources were observed in an industrial survey. The purpose of the study was to develop a theoretical model to predict worker inhalation exposure to additives used during PVC extrusion processing. A model to estimate the generation rate of the additive from the polymer extrudate was derived from the mass transport equations governing diffusion. The mass flow rate, initial additive volatile weight fraction, off-gassing time, diffusivity, and slab thickness are required to determine the generation rate from the model.

  15. 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.

  16. Master equation based steady-state cluster perturbation theory

    NASA Astrophysics Data System (ADS)

    Nuss, Martin; Dorn, Gerhard; Dorda, Antonius; von der Linden, Wolfgang; Arrigoni, Enrico

    2015-09-01

    A simple and efficient approximation scheme to study electronic transport characteristics of strongly correlated nanodevices, molecular junctions, or heterostructures out of equilibrium is provided by steady-state cluster perturbation theory. In this work, we improve the starting point of this perturbative, nonequilibrium Green's function based method. Specifically, we employ an improved unperturbed (so-called reference) state ρ̂S, constructed as the steady state of a quantum master equation within the Born-Markov approximation. This resulting hybrid method inherits beneficial aspects of both the quantum master equation as well as the nonequilibrium Green's function technique. We benchmark this scheme on two experimentally relevant systems in the single-electron transistor regime: an electron-electron interaction based quantum diode and a triple quantum dot ring junction, which both feature negative differential conductance. The results of this method improve significantly with respect to the plain quantum master equation treatment at modest additional computational cost.

  17. Additive usage levels.

    PubMed

    Langlais, R

    1996-01-01

    With the adoption of the European Parliament and Council Directives on sweeteners, colours and miscellaneous additives the Commission is now embarking on the project of coordinating the activities of the European Union Member States in the collection of the data that are to make up the report on food additive intake requested by the European Parliament. This presentation looks at the inventory of available sources on additive use levels and concludes that for the time being national legislation is still the best source of information considering that the directives have yet to be transposed into national legislation. Furthermore, this presentation covers the correlation of the food categories as found in the additives directives with those used by national consumption surveys and finds that in a number of instances this correlation still leaves a lot to be desired. The intake of additives via food ingestion and the intake of substances which are chemically identical to additives but which occur naturally in fruits and vegetables is found in a number of cases to be higher than the intake of additives added during the manufacture of foodstuffs. While the difficulties are recognized in contributing to the compilation of food additive intake data, industry as a whole, i.e. the food manufacturing and food additive manufacturing industries, are confident that in a concerted effort, use data on food additives by industry can be made available. Lastly, the paper points out that with the transportation of the additives directives into national legislation and the time by which the food industry will be able to make use of the new food legislative environment several years will still go by; food additives use data by the food industry will thus have to be reviewed at the beginning of the next century. PMID:8792135

  18. Transport critical current density of (Bi1.6Pb0.4)Sr2Ca2Cu3O10/Ag superconductor tapes with addition of nanosized CoFe2O4

    NASA Astrophysics Data System (ADS)

    Hafiz, M.; Abd-Shukor, R.

    2015-09-01

    The effect of nanosized CoFe2O4 (60 nm) addition on the transport critical current density, J c, of (Bi1.6Pb0.4)Sr2Ca2Cu3O10(CoFe2O4) x ( x = 0-0.05 wt%) superconductor prepared by the co-precipitation method was investigated. The optimal J c (measured using the four-point probe method) was observed in the x = 0.01 wt% pellets. Using this optimal wt%, Ag-sheathed (Bi1.6Pb0.4)Sr2Ca2Cu3O10(CoFe2O4)0.01 superconductor tapes were fabricated using the powder-in-tube method. The tapes were sintered for 50 and 100 h at 845 °C. The phase and microstructure of the samples were determined using the powder X-ray diffraction method and scanning electron microscopy, respectively. The temperature dependence of J c for the tapes in various applied magnetic fields was also measured. J c of (Bi1.6Pb0.4)Sr2Ca2Cu3O10(CoFe2O4)0.01/Ag tapes sintered for 100 h was 22,420 A/cm2 at 30 K. The non-added tapes sintered for 100 h showed a much lower J c (8280 A/cm2 at 30 K). This study showed that addition of CoFe2O4 nanoparticles enhanced the transport critical current density in the (Bi1.6Pb0.4)Sr2Ca2Cu3O10 superconductor tapes. This result is consistent with the previous calculations on frozen flux superconductor in a nanomagnet-superconductor hybrid system.

  19. Generalized reduced magnetohydrodynamic equations

    SciTech Connect

    Kruger, S.E.

    1999-02-01

    A new derivation of reduced magnetohydrodynamic (MHD) equations is presented. A multiple-time-scale expansion is employed. It has the advantage of clearly separating the three time scales of the problem associated with (1) MHD equilibrium, (2) fluctuations whose wave vector is aligned perpendicular to the magnetic field, and (3) those aligned parallel to the magnetic field. The derivation is carried out without relying on a large aspect ratio assumption; therefore this model can be applied to any general configuration. By accounting for the MHD equilibrium and constraints to eliminate the fast perpendicular waves, equations are derived to evolve scalar potential quantities on a time scale associated with the parallel wave vector (shear-Alfven wave time scale), which is the time scale of interest for MHD instability studies. Careful attention is given in the derivation to satisfy energy conservation and to have manifestly divergence-free magnetic fields to all orders in the expansion parameter. Additionally, neoclassical closures and equilibrium shear flow effects are easily accounted for in this model. Equations for the inner resistive layer are derived which reproduce the linear ideal and resistive stability criterion of Glasser, Greene, and Johnson. The equations have been programmed into a spectral initial value code and run with shear flow that is consistent with the equilibrium input into the code. Linear results of tearing modes with shear flow are presented which differentiate the effects of shear flow gradients in the layer with the effects of the shear flow decoupling multiple harmonics.

  20. Evolutions equations in computational anatomy.

    PubMed

    Younes, Laurent; Arrate, Felipe; Miller, Michael I

    2009-03-01

    One of the main purposes in computational anatomy is the measurement and statistical study of anatomical variations in organs, notably in the brain or the heart. Over the last decade, our group has progressively developed several approaches for this problem, all related to the Riemannian geometry of groups of diffeomorphisms and the shape spaces on which these groups act. Several important shape evolution equations that are now used routinely in applications have emerged over time. Our goal in this paper is to provide an overview of these equations, placing them in their theoretical context, and giving examples of applications in which they can be used. We introduce the required theoretical background before discussing several classes of equations of increasingly complexity. These equations include energy minimizing evolutions deriving from Riemannian gradient descent, geodesics, parallel transport and Jacobi fields. PMID:19059343

  1. 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.

  2. Extended rate equations

    SciTech Connect

    Shore, B.W.

    1981-01-30

    The equations of motion are discussed which describe time dependent population flows in an N-level system, reviewing the relationship between incoherent (rate) equations, coherent (Schrodinger) equations, and more general partially coherent (Bloch) equations. Approximations are discussed which replace the elaborate Bloch equations by simpler rate equations whose coefficients incorporate long-time consequences of coherence.

  3. 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.

  4. 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. PMID:27176431

  5. 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.

  6. CMFD acceleration of spatial domain-decomposed neutron transport problems

    SciTech Connect

    Kelley, B. W.; Larsen, E. W.

    2012-07-01

    A significant limitation to parallelizing the solution of neutron transport problems is the need for sweeps across the entirety of the problem domain. Angular domain decomposition is common practice, as the equations for each direction are independent aside from their shared scattering/fission source. Accordingly, spatial domain decomposition does not naturally arise in the transport equations and is therefore less frequent in practice. In this paper, we show that a neutron transport domain can be straightforwardly divided into independent, parallelizable sweep regions, globally linked with the standard CMFD method, with an additional update equation. We verify, theoretically (via Fourier analysis) and computationally, that the convergence properties of this method are stable and nominally as rapid as standard CMFD. (authors)

  7. 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.

  8. Novel Parallel Numerical Methods for Radiation& Neutron Transport

    SciTech Connect

    Brown, P N

    2001-03-06

    In many of the multiphysics simulations performed at LLNL, transport calculations can take up 30 to 50% of the total run time. If Monte Carlo methods are used, the percentage can be as high as 80%. Thus, a significant core competence in the formulation, software implementation, and solution of the numerical problems arising in transport modeling is essential to Laboratory and DOE research. In this project, we worked on developing scalable solution methods for the equations that model the transport of photons and neutrons through materials. Our goal was to reduce the transport solve time in these simulations by means of more advanced numerical methods and their parallel implementations. These methods must be scalable, that is, the time to solution must remain constant as the problem size grows and additional computer resources are used. For iterative methods, scalability requires that (1) the number of iterations to reach convergence is independent of problem size, and (2) that the computational cost grows linearly with problem size. We focused on deterministic approaches to transport, building on our earlier work in which we performed a new, detailed analysis of some existing transport methods and developed new approaches. The Boltzmann equation (the underlying equation to be solved) and various solution methods have been developed over many years. Consequently, many laboratory codes are based on these methods, which are in some cases decades old. For the transport of x-rays through partially ionized plasmas in local thermodynamic equilibrium, the transport equation is coupled to nonlinear diffusion equations for the electron and ion temperatures via the highly nonlinear Planck function. We investigated the suitability of traditional-solution approaches to transport on terascale architectures and also designed new scalable algorithms; in some cases, we investigated hybrid approaches that combined both.

  9. Bedload transport in alluvial channels

    USGS Publications Warehouse

    Bravo-Espinosa, M.; Osterkamp, W.R.; Lopes, V.L.

    2003-01-01

    Hydraulic, sediment, land-use, and rock-erosivity data of 22 alluvial streams were used to evaluate conditions of bedload transport and the performance of selected bedload-transport equations. Transport categories of transport-limited (TL), partially transport-limited (PTL), and supply-limited (SL) were identified by a semiquantitative approach that considers hydraulic constraints on sediment movement and the processes that control sediment availability at the basin scale. Equations by Parker et al. in 1982, Schoklitsch in 1962, and Meyer-Peter and Muller in 1948 adequately predicted sediment transport in channels with TL condition, whereas the equations of Bagnold in 1980, and Schoklitsch, in 1962, performed well for PTL and SL conditions. Overall, the equation of Schoklitsch predicted well the measured bedload data for eight of 22 streams, and the Bagnold equation predicted the measured data in seven streams.

  10. A multilevel method for coupling the neutron kinetics and heat transfer equations

    SciTech Connect

    Tamang, A.; Anistratov, D. Y.

    2013-07-01

    We present a computational method for adequate and efficient coupling the neutron transport equation with the precursor and heat transfer equations. It is based on the multilevel nonlinear quasidiffusion (QD) method for solving the multigroup transport equation. The system of equations includes the time-dependent high-order transport equation and time-dependent multigroup and effective one-group low-order QD equations. We also formulate a method applying the {alpha}-approximation for the time-dependent high-order transport equation. This approach enables one to avoid storing the angular flux from the previous time step. Numerical results for a model transient problem are presented. (authors)

  11. 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.

  12. Generalized reduced MHD equations

    SciTech Connect

    Kruger, S.E.; Hegna, C.C.; Callen, J.D.

    1998-07-01

    A new derivation of reduced magnetohydrodynamic (MHD) equations is presented. A multiple-time-scale expansion is employed. It has the advantage of clearly separating the three time scales of the problem associated with (1) MHD equilibrium, (2) fluctuations whose wave vector is aligned perpendicular to the magnetic field, and (3) those aligned parallel to the magnetic field. The derivation is carried out without relying on a large aspect ratio assumption; therefore this model can be applied to any general toroidal configuration. By accounting for the MHD equilibrium and constraints to eliminate the fast perpendicular waves, equations are derived to evolve scalar potential quantities on a time scale associated with the parallel wave vector (shear-alfven wave time scale), which is the time scale of interest for MHD instability studies. Careful attention is given in the derivation to satisfy energy conservation and to have manifestly divergence-free magnetic fields to all orders in the expansion parameter. Additionally, neoclassical closures and equilibrium shear flow effects are easily accounted for in this model. Equations for the inner resistive layer are derived which reproduce the linear ideal and resistive stability criterion of Glasser, Greene, and Johnson.

  13. The Hirota Method for Reaction-Diffusion Equations with Three Distinct Roots

    SciTech Connect

    Tanoglu, Gamze; Pashaev, Oktay

    2004-10-04

    The Hirota Method, with modified background is applied to construct exact analytical solutions of nonlinear reaction-diffusion equations of two types. The first equation has only nonlinear reaction part, while the second one has in addition the nonlinear transport term. For both cases, the reaction part has the form of the third order polynomial with three distinct roots. We found analytic one-soliton solutions and the relationships between three simple roots and the wave speed of the soliton. For the first case, if one of the roots is the mean value of other two roots, the soliton is static. We show that the restriction on three distinct roots to obtain moving soliton is removed in the second case by, adding nonlinear transport term to the first equation.

  14. Lie-transform theory of transport in plasma turbulence

    SciTech Connect

    Wang, Shaojie

    2014-07-15

    From the Vlasov equation, a phase-space transport equation is derived by using the Lie-transform approach, and its connection with the quasilinear transport, nonlinear stochastic transport, and fractional transport equations are discussed. The phase-space transport equation indicates a particle redistribution in the real space induced by the inhomogeneity in the energy space distribution and by the correlation between the change of position and the change of energy.

  15. Spin field equations and Heun's equations

    NASA Astrophysics Data System (ADS)

    Jiang, Min; Wang, Xuejing; Li, Zhongheng

    2015-06-01

    The Kerr-Newman-(anti) de Sitter metric is the most general stationary black hole solution to the Einstein-Maxwell equation with a cosmological constant. We study the separability of the equations of the massless scalar (spin s=0), neutrino ( s=1/2), electromagnetic ( s=1), Rarita-Schwinger ( s=3/2), and gravitational ( s=2) fields propagating on this background. We obtain the angular and radial master equations, and show that the master equations are transformed to Heun's equation. Meanwhile, we give the condition of existence of event horizons for Kerr-Newman-(anti) de Sitter spacetime by using Sturm theorem.

  16. 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.

  17. 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.

  18. Deterministic photon kerma distribution based on the Boltzmann equation for external beam radiation therapy

    SciTech Connect

    Yuan Jiankui; Jette, David; Chen Weimin

    2008-09-15

    A photon transport algorithm for fully three-dimensional radiotherapy treatment planning has been developed based on the discrete ordinates (S{sub N}) solution of the Boltzmann equation. The algorithm is characterized by orthogonal adaptive meshes, which place additional points where large gradients occur and a procedure to evaluate the collided flux using the representation of spherical harmonic expansion instead of the summation of the volume-weighted contribution from discrete angles. The Boltzmann equation was solved in the form of S{sub N} spatial, energy, and angular discretization with mitigation of ray effects by the first-collision source method. Unlike existing S{sub N} codes, which were designed for general purpose for multiparticle transport in areas such as nuclear engineering, our code is optimized for medical radiation transport. To validate the algorithm, several examples were employed to calculate the photon flux distribution. Numerical results show good agreement with the Monte Carlo calculations using EGSnrc.

  19. Bogoliubov equations and functional mechanics

    NASA Astrophysics Data System (ADS)

    Volovich, I. V.

    2010-09-01

    The functional classical mechanics based on the probability approach, where a particle is described not by a trajectory in the phase space but by a probability distribution, was recently proposed for solving the irreversibility problem, i.e., the problem of matching the time reversibility of microscopic dynamics equations and the irreversibility of macrosystem dynamics. In the framework of functional mechanics, we derive Bogoliubov-Boltzmann-type equations for finitely many particles. We show that a closed equation for a one-particle distribution function can be rigorously derived in functional mechanics without any additional assumptions required in the Bogoliubov method. We consider the possibility of using diffusion processes and the Fokker-Planck-Kolmogorov equation to describe isolated particles.

  20. Influence of transport variables on isospin transport ratios

    NASA Astrophysics Data System (ADS)

    Coupland, D. D. S.; Lynch, W. G.; Tsang, M. B.; Danielewicz, P.; Zhang, Yingxun

    2011-11-01

    The symmetry energy in the nuclear equation of state affects many aspects of nuclear astrophysics, nuclear structure, and nuclear reactions. Recent constraints from heavy-ion collisions, including isospin diffusion observables, have started to put constraints on the symmetry energy below nuclear saturation density, but these constraints depend on the employed transport model and input physics other than the symmetry energy. To understand these dependencies, we study the influence of the symmetry energy, isoscalar mean-field compressibility and momentum dependence, in-medium nucleon-nucleon cross sections, and light cluster production on isospin diffusion within the pBUU transport code. In addition to the symmetry energy, several uncertain issues strongly affect isospin diffusion, most notably the cross sections and cluster production. In addition, there is a difference in the calculated isospin transport ratios, depending on whether they are computed using the isospin asymmetry either of the residue or of all forward-moving fragments. Measurements that compare the isospin transport ratios of these two quantities would help place constraints on the input physics, such as the density dependence of the symmetry energy.

  1. Collector Efficiency Equations for Colloid Filtration in Saturated Porous Media (Invited)

    NASA Astrophysics Data System (ADS)

    Ginn, T. R.; Nelson, K. E.

    2010-12-01

    Pore-scale simulation of colloid transport and filtration in models based on the classical idealized Happel cell concept is giving rise to a number of new insights on colloid fate and transport in granular porous media. After a very brief summary of recent approaches and results in the context of colloid filtration theory (CFT), we present a new expression for the collector efficiency of CFT. This equation is developed via nonlinear regression on the numerical results of 3750 Lagrangian simulation suites in Happel’s sphere-in-cell porous media model, conducted over a wide range of input parameters representative of both natural and engineered flow conditions. The new equation accommodates departures from power law dependence of collection rate on the Peclet and gravity numbers, thus extending CFT to both very low groundwater transport velocities and to small (nanoscale) particles. Comparison against the available data for nanoparticles suggests an improvement over prior equations; further data are required for comprehensive testing of these new regions of application. Additionally, we describe incorporation of the effect of horizontal flow direction on collector rate prediction, whereas CFT is based on vertical flow. Finally, we demonstrate the importance of consistency in the conceptualization of particle flux through the single collector model on which most collection rate equations are based, in terms of achieving a mechanistic understanding of the transport and attachment steps of CFT.

  2. 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.

  3. 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. PMID:24628169

  4. 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

  5. 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.

  6. Test Equating Procedures: A Primer on the Logic and Applications of Test Equating.

    ERIC Educational Resources Information Center

    Buras, Avery

    The logic and uses of test equating are discussed, including three methods of test equating. The focus is on the conceptual underpinnings of each test equating method, rather than on the mathematics of the procedures. Additional consideration is given to the assumptions of each method and its respective strengths and weaknesses. A commonly…

  7. 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.

  8. 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)

  9. Equations and closure methods

    NASA Technical Reports Server (NTRS)

    1977-01-01

    Basic differential equations governing compressible turbulent boundary layer flow are reviewed, including conservation of mass and energy, momentum equations derived from Navier-Stokes equations, and equations of state. Closure procedures were broken down into: (1) simple or zeroth-order methods, (2) first-order or mean field closure methods, and (3) second-order or mean turbulence field methods.

  10. The structure of constitutive equations for semiconductor devices

    SciTech Connect

    Buchanan, G.R.; Girrens, S.P.; Bennett, J.G.

    1987-01-01

    The fundamental equations that describe carrier transport in semiconductor materials are developed using the methods of continuum mixture theory and Maxwell's equations for electrodynamics. There are five basic equations that govern the behavior of current flux, electrostatic potential, electrons, and holes. The bahavior of the electrical chemical potentials are introduced and their relation to the current flux is discussed.

  11. The Dirac equation

    SciTech Connect

    Thaller, B.

    1992-01-01

    This monograph treats most of the usual material to be found in texts on the Dirac equation such as the basic formalism of quantum mechanics, representations of Dirac matrices, covariant realization of the Dirac equation, interpretation of negative energies, Foldy-Wouthuysen transformation, Klein's paradox, spherically symmetric interactions and a treatment of the relativistic hydrogen atom, etc., and also provides excellent additional treatments of a variety of other relevant topics. The monograph contains an extensive treatment of the Lorentz and Poincare groups and their representations. The author discusses in depth Lie algebaic and projective representations, covering groups, and Mackey's theory and Wigner's realization of induced representations. A careful classification of external fields with respect to their behavior under Poincare transformations is supplemented by a basic account of self-adjointness and spectral properties of Dirac operators. A state-of-the-art treatment of relativistic scattering theory based on a time-dependent approach originally due to Enss is presented. An excellent introduction to quantum electrodynamics in external fields is provided. Various appendices containing further details, notes on each chapter commenting on the history involved and referring to original research papers and further developments in the literature, and a bibliography covering all relevant monographs and over 500 articles on the subject, complete this text. This book should satisfy the needs of a wide audience, ranging from graduate students in theoretical physics and mathematics to researchers interested in mathematical physics.

  12. Semianalytical Solutions of Radioactive or Reactive Tracer Transport in Layered Fractured Media

    SciTech Connect

    G.J. Moridis; G. S. Bodvarsson

    2001-10-01

    In this paper, semianalytical solutions are developed for the problem of transport of radioactive or reactive tracers (solutes or colloids) through a layered system of heterogeneous fractured media with misaligned fractures. The tracer transport equations in the matrix account for (a) diffusion, (b) surface diffusion (for solutes only), (c) mass transfer between the mobile and immobile water fractions, (d) linear kinetic or equilibrium physical, chemical, or combined solute sorption or colloid filtration, and (e) radioactive decay or first order chemical reactions. Any number of radioactive decay daughter products (or products of a linear, first-order reaction chain) can be tracked. The tracer-transport equations in the fractures account for the same processes, in addition to advection and hydrodynamic dispersion. Additionally, the colloid transport equations account for straining and velocity adjustments related to the colloidal size. The solutions, which are analytical in the Laplace space, are numerically inverted to provide the solution in time and can accommodate any number of fractured and/or porous layers. The solutions are verified using analytical solutions for limiting cases of solute and colloid transport through fractured and porous media. The effect of important parameters on the transport of {sup 3}H, {sup 237}Np and {sup 239}Pu (and its daughters) is investigated in several test problems involving layered geological systems of varying complexity. {sup 239}Pu colloid transport problems in multilayered systems indicate significant colloid accumulations at straining interfaces but much faster transport of the colloid than the corresponding strongly sorbing solute species.

  13. Semianalytical solutions of radioactive or reactive tracer transport in layered fractured media

    SciTech Connect

    Moridis, G.J.; Bodvarsson, G.S.

    2001-10-10

    In this paper, semianalytical solutions are developed for the problem of transport of radioactive or reactive tracers (solutes or colloids) through a layered system of heterogeneous fractured media with misaligned fractures. The tracer transport equations in the matrix account for (a) diffusion, (b) surface diffusion (for solutes only), (c) mass transfer between the mobile and immobile water fractions, (d) linear kinetic or equilibrium physical, chemical, or combined solute sorption or colloid filtration, and (e) radioactive decay or first order chemical reactions. Any number of radioactive decay daughter products (or products of a linear, first-order reaction chain) can be tracked. The tracer-transport equations in the fractures account for the same processes, in addition to advection and hydrodynamic dispersion. Additionally, the colloid transport equations account for straining and velocity adjustments related to the colloidal size. The solutions, which are analytical in the Laplace space, are numerically inverted to provide the solution in time and can accommodate any number of fractured and/or porous layers. The solutions are verified using analytical solutions for limiting cases of solute and colloid transport through fractured and porous media. The effect of important parameters on the transport of {sup 3}H, {sup 237}Np and {sup 239}Pu (and its daughters) is investigated in several test problems involving layered geological systems of varying complexity. {sup 239}Pu colloid transport problems in multilayered systems indicate significant colloid accumulations at straining interfaces but much faster transport of the colloid than the corresponding strongly sorbing solute species.

  14. Elliptic scattering equations

    NASA Astrophysics Data System (ADS)

    Cardona, Carlos; Gomez, Humberto

    2016-06-01

    Recently the CHY approach has been extended to one loop level using elliptic functions and modular forms over a Jacobian variety. Due to the difficulty in manipulating these kind of functions, we propose an alternative prescription that is totally algebraic. This new proposal is based on an elliptic algebraic curve embedded in a mathbb{C}{P}^2 space. We show that for the simplest integrand, namely the n - gon, our proposal indeed reproduces the expected result. By using the recently formulated Λ-algorithm, we found a novel recurrence relation expansion in terms of tree level off-shell amplitudes. Our results connect nicely with recent results on the one-loop formulation of the scattering equations. In addition, this new proposal can be easily stretched out to hyperelliptic curves in order to compute higher genus.

  15. Lattice Boltzmann model for a steady radiative transfer equation.

    PubMed

    Yi, Hong-Liang; Yao, Feng-Ju; Tan, He-Ping

    2016-08-01

    A complete lattice Boltzmann model (LBM) is proposed for the steady radiative transfer equation (RTE). The RTE can be regarded as a pure convection equation with a source term. To derive the expressions for the equilibrium distribution function and the relaxation time, an artificial isotropic diffusion term is introduced to form a convection-diffusion equation. When the dimensionless relaxation time has a value of 0.5, the lattice Boltzmann equation (LBE) is exactly applicable to the original steady RTE. We also perform a multiscale analysis based on the Chapman-Enskog expansion to recover the macroscopic RTE from the mesoscopic LBE. The D2Q9 model is used to solve the LBE, and the numerical results obtained by the LBM are comparable to the results obtained by other methods or analytical solutions, which demonstrates that the proposed model is highly accurate and stable in simulating multidimensional radiative transfer. In addition, we find that the convergence rate of the LBM depends on the transport properties of RTE: for diffusion-dominated RTE with a large optical thickness, the LBM shows a second-order convergence rate in space, while for convection-dominated RTE with a small optical thickness, a lower convergence rate is observed. PMID:27627417

  16. 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.

  17. Direct propagation of probability density functions in hydrological equations

    NASA Astrophysics Data System (ADS)

    Kunstmann, Harald; Kastens, Marko

    2006-06-01

    Sustainable decisions in hydrological risk management require detailed information on the probability density function ( pdf) of the model output. Only then probabilities for the failure of a specific management option or the exceedance of critical thresholds (e.g. of pollutants) can be derived. A new approach of uncertainty propagation in hydrological equations is developed that directly propagates the probability density functions of uncertain model input parameters into the corresponding probability density functions of model output. The basics of the methodology are presented and central applications to different disciplines in hydrology are shown. This work focuses on the following basic hydrological equations: (1) pumping test analysis (Theis-equation, propagation of uncertainties in recharge and transmissivity), (2) 1-dim groundwater contaminant transport equation (Gauss-equation, propagation of uncertainties in decay constant and dispersivity), (3) evapotranspiration estimation (Penman-Monteith-equation, propagation of uncertainty in roughness length). The direct propagation of probability densities is restricted to functions that are monotonically increasing or decreasing or that can be separated in corresponding monotonic branches so that inverse functions can be derived. In case no analytic solutions for inverse functions could be derived, semi-analytical approximations were used. It is shown that the results of direct probability density function propagation are in perfect agreement with results obtained from corresponding Monte Carlo derived frequency distributions. Direct pdf propagation, however, has the advantage that is yields exact solutions for the resulting hydrological pdfs rather than approximating discontinuous frequency distributions. It is additionally shown that the type of the resulting pdf depends on the specific values (order of magnitude, respectively) of the standard deviation of the input pdf. The dependency of skewness and kurtosis

  18. The Einstein Relation for the KPZ Equation

    NASA Astrophysics Data System (ADS)

    Gonçalves, Patrícia; Jara, Milton

    2015-03-01

    We compute the non-universal constants in the KPZ equation in one dimension, in terms of the thermodynamical quantities associated to the underlying microscopic dynamics. In particular, we derive the second-order Einstein relation for the transport coefficient of the KPZ equation, in terms of the conserved quantity , the diffusion coefficient , the strength of the asymmetry and the static compressibility of the system.

  19. Quantum lattice gas algorithm for the telegraph equation

    NASA Astrophysics Data System (ADS)

    Coffey, Mark W.; Colburn, Gabriel G.

    2009-06-01

    The telegraph equation combines features of both the diffusion and wave equations and has many applications to heat propagation, transport in disordered media, and elsewhere. We describe a quantum lattice gas algorithm (QLGA) for this partial differential equation with one spatial dimension. This algorithm generalizes one previously known for the diffusion equation. We present an analysis of the algorithm and accompanying simulation results. The QLGA is suitable for simulation on combined classical-quantum computers.

  20. 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.

  1. CORE-COLLAPSE SUPERNOVA EQUATIONS OF STATE BASED ON NEUTRON STAR OBSERVATIONS

    SciTech Connect

    Steiner, A. W.; Hempel, M.; Fischer, T.

    2013-09-01

    Many of the currently available equations of state for core-collapse supernova simulations give large neutron star radii and do not provide large enough neutron star masses, both of which are inconsistent with some recent neutron star observations. In addition, one of the critical uncertainties in the nucleon-nucleon interaction, the nuclear symmetry energy, is not fully explored by the currently available equations of state. In this article, we construct two new equations of state which match recent neutron star observations and provide more flexibility in studying the dependence on nuclear matter properties. The equations of state are also provided in tabular form, covering a wide range in density, temperature, and asymmetry, suitable for astrophysical simulations. These new equations of state are implemented into our spherically symmetric core-collapse supernova model, which is based on general relativistic radiation hydrodynamics with three-flavor Boltzmann neutrino transport. The results are compared with commonly used equations of state in supernova simulations of 11.2 and 40 M{sub Sun} progenitors. We consider only equations of state which are fitted to nuclear binding energies and other experimental and observational constraints. We find that central densities at bounce are weakly correlated with L and that there is a moderate influence of the symmetry energy on the evolution of the electron fraction. The new models also obey the previously observed correlation between the time to black hole formation and the maximum mass of an s = 4 neutron star.

  2. 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.

  3. Stochastic partial differential equations in turbulence related problems

    NASA Technical Reports Server (NTRS)

    Chow, P.-L.

    1978-01-01

    The theory of stochastic partial differential equations (PDEs) and problems relating to turbulence are discussed by employing the theories of Brownian motion and diffusion in infinite dimensions, functional differential equations, and functional integration. Relevant results in probablistic analysis, especially Gaussian measures in function spaces and the theory of stochastic PDEs of Ito type, are taken into account. Linear stochastic PDEs are analyzed through linearized Navier-Stokes equations with a random forcing. Stochastic equations for waves in random media as well as model equations in turbulent transport theory are considered. Markovian models in fully developed turbulence are discussed from a stochastic equation viewpoint.

  4. Interpretation of Bernoulli's Equation.

    ERIC Educational Resources Information Center

    Bauman, Robert P.; Schwaneberg, Rolf

    1994-01-01

    Discusses Bernoulli's equation with regards to: horizontal flow of incompressible fluids, change of height of incompressible fluids, gases, liquids and gases, and viscous fluids. Provides an interpretation, properties, terminology, and applications of Bernoulli's equation. (MVL)

  5. 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)

  6. 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.

  7. 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…

  8. A Semiconductor Device Noise Model: A Deterministic Approach to Semiconductor Device Current Noise for Semiclassical Transport

    SciTech Connect

    Noaman, B. A.; Korman, C. E.

    2009-04-23

    In this paper, we present a deterministic approach to calculate terminal current noise characteristics in semiconductor devices in the framework of semiclassical transport based on the spherical harmonics of the Boltzmann Transport Equation. The model relies on the solution of the Boltzmann equation in the frequency domain with special initial and boundary conditions. The terminal current fluctuation is directly related to scattering without the additional Langevin noise term added to the calculation. Simulation results are presented for the terminal current spectral density for a 1-D n{sup +}nn{sup +} structure due to elastic-acoustic and intervally scattering.

  9. Regularized 13 moment equations for hard sphere molecules: Linear bulk equations

    NASA Astrophysics Data System (ADS)

    Struchtrup, Henning; Torrilhon, Manuel

    2013-05-01

    The regularized 13 moment equations of rarefied gas dynamics are derived for a monatomic hard sphere gas in the linear regime. The equations are based on an extended Grad-type moment system, which is systematically reduced by means of the Order of Magnitude Method [H. Struchtrup, "Stable transport equations for rarefied gases at high orders in the Knudsen number," Phys. Fluids 16(11), 3921-3934 (2004)], 10.1063/1.1782751. Chapman-Enskog expansion of the final equations yields the linear Burnett and super-Burnett equations. While the Burnett coefficients agree with literature values, this seems to be the first time that super-Burnett coefficients are computed for a hard sphere gas. As a first test of the equations the dispersion and damping of sound waves is considered.

  10. Linear superposition in nonlinear equations.

    PubMed

    Khare, Avinash; Sukhatme, Uday

    2002-06-17

    Several nonlinear systems such as the Korteweg-de Vries (KdV) and modified KdV equations and lambda phi(4) theory possess periodic traveling wave solutions involving Jacobi elliptic functions. We show that suitable linear combinations of these known periodic solutions yield many additional solutions with different periods and velocities. This linear superposition procedure works by virtue of some remarkable new identities involving elliptic functions. PMID:12059300

  11. 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...

  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, 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...

  14. 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.

  15. A computational study of the quantum transport properties of a Cu–CNT composite† †Electronic supplementary information (ESI) available. See DOI: 10.1039/c5cp01470k Click here for additional data file.

    PubMed Central

    Koziol, Krzysztof

    2015-01-01

    The quantum transport properties of a Cu–CNT composite are studied using a non-equilibrium Green's function approach combined with the self-consistent-charge density-functional tight-binding method. The results show that the electrical conductance of the composite depends strongly on CNT density and alignment but more weakly on chirality. Alignment with the applied bias is preferred and the conductance of the composite increases as its mass density increases. PMID:26120607

  16. Methods for diffusive relaxation in the Pn equation

    SciTech Connect

    Hauck, Cory D; Mcclarren, Ryan G; Lowrie, Robert B

    2008-01-01

    We present recent progress in the development of two substantially different approaches for simulating the so-called of P{sub N} equations. These are linear hyperbolic systems of PDEs that are used to model particle transport in a material medium, that in highly collisional regimes, are accurately approximated by a simple diffusion equation. This limit is based on a balance between function values and gradients of certain variables in the P{sub N} system. Conventional reconstruction methods based on upwinding approximate such gradients with an error that is dependent on the size of the computational mesh. Thus in order to capture the diffusion limit, a given mesh must resolve the dynamics of the continuum equation at the level of the mean-free-path, which tends to zero in the diffusion limit. The two methods analyzed here produce accurate solutions in both collisional and non-collisional regimes; in particular, they do not require resolution of the mean-free-path in order to properly capture the diffusion limit. The first method is a straight-forward application of the discrete Galerkin (DG) methodology, which uses additional variables in each computational cell to capture the balance between function values and gradients, which are computed locally. The second method uses a temporal splitting of the fast and slow dynamics in the P{sub N} system to derive so-called regularized equations for which the diffusion limit is built-in. We focus specifically on the P{sub N} equations for one-dimensional, slab geometries. Preliminary results for several benchmark problems are presented which highlight the advantages and disadvantages of each method. Further improvements and extensions are also discussed.

  17. 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.

  18. The generalized diffusion-convection equation

    NASA Technical Reports Server (NTRS)

    Jones, Frank C.

    1990-01-01

    Starting from the Boltzmann equation, a transport equation is derived for energetic particles in a moving magnetized plasma in which the scattering centers that keep the particles quasi-isotropic are moving with a velocity that is not necessarily the same as that of the plasma. The scattering is characterized by three very loose constraints: (1) there is a rest frame for each scatterer in which the particles scatter elastically; (2) in this frame the scattering will not disturb an isotropic distribution; and (3) the momentum transfer in an average collision may be described by a tensor operating on the particles original momentum. Since the strength of the scattering is not specified, the derivation should be as valid for plasma microturbulence as for hard-sphere scattering. The results show clearly which phenomena are responsible for tying the particles to the plasma in the transport equation.

  19. Putting Phase Equilibria into Geodynamic Models: An Equation of State Approach (Invited)

    NASA Astrophysics Data System (ADS)

    Connolly, J.

    2009-12-01

    The use of free energy minimization codes to calculate the proportions and properties of minerals and consequently bulk rock properties is now commonplace in geophysical modeling. In effect such applications imply the existence of an equation of state, which is the optimized free energy as a function of its independent variables, for the rocks of interest. The essential feature of the equation of state is that all thermodynamic properties can be derived from it, a feature that requires that its derivatives are continuous. The equation of state may be calculated dynamically within the larger framework of a geodynamic code or it may be implemented statically via tables that are calculated prior to the solution of the geodynamic application. The virtues of static implementation is its extreme simplicity, computational efficiency, and that the finite resolution of the table assures that the equation of state is numerically differentiable for any choice of independent state variables. However, the memory required to store the requisite multidimensional tables may necessitate dynamic implementations for problems involving multi-component mass transfer, e.g., as in reactive melt transport. Paradoxically, the unlimited accuracy of dynamic solutions creates a potential numerical instability, the Stefan problem, for geodynamic governing equations formulated in terms of pressure and temperature. This instability arises because the derivatives of an equation of state for a polyphase aggregate as a function of pressure and temperature are singular at the conditions of a low order phase transformation. An equation of state as a function of specific entropy, specific volume and chemical composition eliminates this difficulty and, additionally, leads to a robust formulation of the energy and mass conservation equations. In this formulation, energy and mass conservation furnish evolution equations for entropy and volume and the equation of state serves as an update rule for

  20. 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.