A New 2D-Transport, 1D-Diffusion Approximation of the Boltzmann Transport equation
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.
2D/1D approximations to the 3D neutron transport equation. II: Numerical comparisons
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)
2D/1D approximations to the 3D neutron transport equation. I: Theory
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)
Discontinuous Galerkin finite element method applied to the 1-D spherical neutron transport equation
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.
Exponentially-convergent Monte Carlo for the 1-D transport equation
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)
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.
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.
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.
Quadratic Finite Element Method for 1D Deterministic Transport
Tolar, Jr., D R; Ferguson, J M
2004-01-06
In the discrete ordinates, or SN, numerical solution of the transport equation, both the spatial ({und r}) and angular ({und {Omega}}) dependences on the angular flux {psi}{und r},{und {Omega}}are modeled discretely. While significant effort has been devoted toward improving the spatial discretization of the angular flux, we focus on improving the angular discretization of {psi}{und r},{und {Omega}}. Specifically, we employ a Petrov-Galerkin quadratic finite element approximation for the differencing of the angular variable ({mu}) in developing the one-dimensional (1D) spherical geometry S{sub N} equations. We develop an algorithm that shows faster convergence with angular resolution than conventional S{sub N} algorithms.
Mass conservation: 1-D open channel flow equations
DeLong, Lewis L.
1989-01-01
Unsteady flow simulation in natural rivers is often complicated by meandering channels of compound section. Hydraulic properties and the length of the wetted channel may vary significantly as a meandering river inundates its adjacent floodplain. The one-dimensional, unsteady, open-channel flow equations can be extended to simulate floods in channels of compound section. It will be shown that equations derived from the addition of differential equations individually describing flow in main and overbank channels do not in general conserve mass when overbank and main channels are of different lengths.
Popovic, Marta; Zaja, Roko; Fent, Karl; Smital, Tvrtko
2014-10-01
Polyspecific transporters from the organic anion transporting polypeptide (OATP/Oatp) superfamily mediate the uptake of a wide range of compounds. In zebrafish, Oatp1d1 transports conjugated steroid hormones and cortisol. It is predominantly expressed in the liver, brain and testes. In this study we have characterized the transport of xenobiotics by the zebrafish Oatp1d1 transporter. We developed a novel assay for assessing Oatp1d1 interactors using the fluorescent probe Lucifer yellow and transient transfection in HEK293 cells. Our data showed that numerous environmental contaminants interact with zebrafish Oatp1d1. Oatp1d1 mediated the transport of diclofenac with very high affinity, followed by high affinity towards perfluorooctanesulfonic acid (PFOS), nonylphenol, gemfibrozil and 17α-ethinylestradiol; moderate affinity towards carbaryl, diazinon and caffeine; and low affinity towards metolachlor. Importantly, many environmental chemicals acted as strong inhibitors of Oatp1d1. A strong inhibition of Oatp1d1 transport activity was found by perfluorooctanoic acid (PFOA), chlorpyrifos-methyl, estrone (E1) and 17β-estradiol (E2), followed by moderate to low inhibition by diethyl phthalate, bisphenol A, 7-acetyl-1,1,3,4,4,6-hexamethyl-1,2,3,4 tetrahydronapthalene and clofibrate. In this study we identified Oatp1d1 as a first Solute Carrier (SLC) transporter involved in the transport of a wide range of xenobiotics in fish. Considering that Oatps in zebrafish have not been characterized before, our work on zebrafish Oatp1d1 offers important new insights on the understanding of uptake processes of environmental contaminants, and contributes to the better characterization of zebrafish as a model species. - Highlights: • We optimized a novel assay for determination of Oatp1d1 interactors • Oatp1d1 is the first SLC characterized fish xenobiotic transporter • PFOS, nonylphenol, diclofenac, EE2, caffeine are high affinity Oatp1d1substrates • PFOA, chlorpyrifos
Popovic, Marta; Zaja, Roko; Fent, Karl; Smital, Tvrtko
2014-10-01
Polyspecific transporters from the organic anion transporting polypeptide (OATP/Oatp) superfamily mediate the uptake of a wide range of compounds. In zebrafish, Oatp1d1 transports conjugated steroid hormones and cortisol. It is predominantly expressed in the liver, brain and testes. In this study we have characterized the transport of xenobiotics by the zebrafish Oatp1d1 transporter. We developed a novel assay for assessing Oatp1d1 interactors using the fluorescent probe Lucifer yellow and transient transfection in HEK293 cells. Our data showed that numerous environmental contaminants interact with zebrafish Oatp1d1. Oatp1d1 mediated the transport of diclofenac with very high affinity, followed by high affinity towards perfluorooctanesulfonic acid (PFOS), nonylphenol, gemfibrozil and 17α-ethinylestradiol; moderate affinity towards carbaryl, diazinon and caffeine; and low affinity towards metolachlor. Importantly, many environmental chemicals acted as strong inhibitors of Oatp1d1. A strong inhibition of Oatp1d1 transport activity was found by perfluorooctanoic acid (PFOA), chlorpyrifos-methyl, estrone (E1) and 17β-estradiol (E2), followed by moderate to low inhibition by diethyl phthalate, bisphenol A, 7-acetyl-1,1,3,4,4,6-hexamethyl-1,2,3,4 tetrahydronapthalene and clofibrate. In this study we identified Oatp1d1 as a first Solute Carrier (SLC) transporter involved in the transport of a wide range of xenobiotics in fish. Considering that Oatps in zebrafish have not been characterized before, our work on zebrafish Oatp1d1 offers important new insights on the understanding of uptake processes of environmental contaminants, and contributes to the better characterization of zebrafish as a model species. PMID:25088042
Benchmarks and models for 1-D radiation transport in stochastic participating media
Miller, D S
2000-08-21
Benchmark calculations for radiation transport coupled to a material temperature equation in a 1-D slab and 1-D spherical geometry binary random media are presented. The mixing statistics are taken to be homogeneous Markov statistics in the 1-D slab but only approximately Markov statistics in the 1-D sphere. The material chunk sizes are described by Poisson distribution functions. The material opacities are first taken to be constant and then allowed to vary as a strong function of material temperature. Benchmark values and variances for time evolution of the ensemble average of material temperature energy density and radiation transmission are computed via a Monte Carlo type method. These benchmarks are used as a basis for comparison with three other approximate methods of solution. One of these approximate methods is simple atomic mix. The second approximate model is an adaptation of what is commonly called the Levermore-Pomraning model and which is referred to here as the standard model. It is shown that recasting the temperature coupling as a type of effective scattering can be useful in formulating the third approximate model, an adaptation of a model due to Su and Pomraning which attempts to account for the effects of scattering in a stochastic context. This last adaptation shows consistent improvement over both the atomic mix and standard models when used in the 1-D slab geometry but shows limited improvement in the 1-D spherical geometry. Benchmark values are also computed for radiation transmission from the 1-D sphere without material heating present. This is to evaluate the performance of the standard model on this geometry--something which has never been done before. All of the various tests demonstrate the importance of stochastic structure on the solution. Also demonstrated are the range of usefulness and limitations of a simple atomic mix formulation.
Transport equations in tokamak plasmas
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
Validation of 1-D transport and sawtooth models for ITER
Connor, J.W.; Turner, M.F.; Attenberger, S.E.; Houlberg, W.A.
1996-12-31
In this paper the authors describe progress on validating a number of local transport models by comparing their predictions with relevant experimental data from a range of tokamaks in the ITER profile database. This database, the testing procedure and results are discussed. In addition a model for sawtooth oscillations is used to investigate their effect in an ITER plasma with alpha-particles.
von Neumann Stability Analysis of Numerical Solution Schemes for 1D and 2D Euler Equations
NASA Astrophysics Data System (ADS)
Konangi, Santosh; Palakurthi, Nikhil Kumar; Ghia, Urmila
2014-11-01
A von Neumann stability analysis is conducted for numerical schemes for the full system of coupled, density-based 1D and 2D Euler equations, closed by an isentropic equation of state. The governing equations are discretized on a staggered grid, which permits equivalence to finite-volume discretization. Presently, first-order accurate spatial and temporal finite-difference techniques are analyzed. The momentum convection term is treated as explicit, semi-implicit or implicit. Density upwind bias is included in the spatial operator of the continuity equation. By combining the discretization techniques, ten solution schemes are formulated. For each scheme, unstable and stable regimes are identified through the stability analysis, and the maximum allowable CFL number is predicted. The predictions are verified for selected schemes, using the Riemann problem at incompressible and compressible Mach numbers. Very good agreement is obtained between the analytically predicted and ``experimentally'' observed CFL values for all cases, thereby validating the analysis. The demonstrated analysis provides an accurate indication of stability conditions for the Euler equations, in contrast to the simplistic conditions arising from model equations, such as the wave equation.
NASA Astrophysics Data System (ADS)
Lauer, J. Wesley; Viparelli, Enrica; Piégay, Hervé
2016-07-01
Bed material transported in geomorphically active gravel bed rivers often has a local source at nearby eroding banks and ends up sequestered in bars not far downstream. However, most 1-D numerical models for gravel transport assume that gravel originates from and deposits on the channel bed. In this paper, we present a 1-D framework for simulating morphodynamic evolution of bed elevation and size distribution in a gravel-bed river that actively exchanges sediment with its floodplain, which is represented as an off-channel sediment reservoir. The model is based on the idea that sediment enters the channel at eroding banks whose elevation depends on total floodplain sediment storage and on the average elevation of the floodplain relative to the channel bed. Lateral erosion of these banks occurs at a specified rate that can represent either net channel migration or channel widening. Transfer of material out of the channel depends on a typical bar thickness and a specified lateral exchange rate due either to net channel migration or narrowing. The model is implemented using an object oriented framework that allows users to explore relationships between bank supply, bed structure, and lateral change rates. It is applied to a ∼50-km reach of the Ain River, France, that experienced significant reduction in sediment supply due to dam construction during the 20th century. Results are strongly sensitive to lateral exchange rates, showing that in this reach, the supply of sand and gravel at eroding banks and the sequestration of gravel in point bars can have strong influence on overall reach-scale sediment budgets.
Staggered grid leap-frog scheme for the (2+1)D Dirac equation
NASA Astrophysics Data System (ADS)
Hammer, René; Pötz, Walter
2014-01-01
A numerical scheme utilizing a grid which is staggered in both space and time is proposed for the numerical solution of the (2+1)D Dirac equation in the presence of an external electromagnetic potential. It preserves the linear dispersion relation of the free Weyl equation for wave vectors aligned with the grid and facilitates the implementation of open (absorbing) boundary conditions via an imaginary potential term. This explicit scheme has second order accuracy in space and time. A functional for the norm is derived and shown to be conserved. Stability conditions are derived. Several numerical examples, ranging from generic to specific to textured topological insulator surfaces, demonstrate the properties of the scheme which can handle general electromagnetic potential landscapes.
A mass-conservative finite volume predictor-corrector solution of the 1D Richards' equation
NASA Astrophysics Data System (ADS)
Lai, Wencong; Ogden, Fred L.
2015-04-01
Numerical solution of the Richards' equation (RE) in variably saturated soils continues to be a challenge due to its highly non-linear behavior. This is particularly true as soils approach saturation and the behavior of the fundamental partial differential equation changes from elliptic to parabolic. In this paper, a finite volume predictor-corrector method with adaptive time-stepping was developed to solve the 1D vertical RE. The numerical method was mass-conservative and non-iterative. In the predictor step, the pressure head-based form of the RE was solved using the cell-centered finite volume method and the pressure head was updated. In the corrector step, the soil water content was calculated by solving the mixed form RE. Five different schemes to evaluate the inter-cell hydraulic conductivity were investigated. The robustness and accuracy of the numerical model were demonstrated through simulation of experimental tests, including free drainage, field infiltration into wet and dry soils, and laboratory infiltration with falling water table. Numerical results were compared against laboratory measurements, simulation results from the Hydrus-1D program, or analytical solution when available. Results showed that the developed scheme is robust and accurate in simulating variably saturated flows with various boundary conditions. The arithmetic mean and Szymkiewicz's mean of inter-cell hydraulic conductivity performed better than other methods especially in the case of infiltration into very dry soil.
NASA Astrophysics Data System (ADS)
Chew, J. V. L.; Sulaiman, J.
2016-06-01
This paper considers Newton-MSOR iterative method for solving 1D nonlinear porous medium equation (PME). The basic concept of proposed iterative method is derived from a combination of one step nonlinear iterative method which known as Newton method with Modified Successive Over Relaxation (MSOR) method. The reliability of Newton-MSOR to obtain approximate solution for several PME problems is compared with Newton-Gauss-Seidel (Newton-GS) and Newton-Successive Over Relaxation (Newton-SOR). In this paper, the formulation and implementation of these three iterative methods have also been presented. From four examples of PME problems, numerical results showed that Newton-MSOR method requires lesser number of iterations and computational time as compared with Newton-GS and Newton-SOR methods.
Schmidts, Miriam; Hou, Yuqing; Cortés, Claudio R; Mans, Dorus A; Huber, Celine; Boldt, Karsten; Patel, Mitali; van Reeuwijk, Jeroen; Plaza, Jean-Marc; van Beersum, Sylvia E C; Yap, Zhi Min; Letteboer, Stef J F; Taylor, S Paige; Herridge, Warren; Johnson, Colin A; Scambler, Peter J; Ueffing, Marius; Kayserili, Hulya; Krakow, Deborah; King, Stephen M; Beales, Philip L; Al-Gazali, Lihadh; Wicking, Carol; Cormier-Daire, Valerie; Roepman, Ronald; Mitchison, Hannah M; Witman, George B
2015-01-01
The analysis of individuals with ciliary chondrodysplasias can shed light on sensitive mechanisms controlling ciliogenesis and cell signalling that are essential to embryonic development and survival. Here we identify TCTEX1D2 mutations causing Jeune asphyxiating thoracic dystrophy with partially penetrant inheritance. Loss of TCTEX1D2 impairs retrograde intraflagellar transport (IFT) in humans and the protist Chlamydomonas, accompanied by destabilization of the retrograde IFT dynein motor. We thus define TCTEX1D2 as an integral component of the evolutionarily conserved retrograde IFT machinery. In complex with several IFT dynein light chains, it is required for correct vertebrate skeletal formation but may be functionally redundant under certain conditions. PMID:26044572
Schmidts, Miriam; Hou, Yuqing; Cortés, Claudio R.; Mans, Dorus A.; Huber, Celine; Boldt, Karsten; Patel, Mitali; van Reeuwijk, Jeroen; Plaza, Jean-Marc; van Beersum, Sylvia E. C.; Yap, Zhi Min; Letteboer, Stef J. F.; Taylor, S. Paige; Herridge, Warren; Johnson, Colin A.; Scambler, Peter J.; Ueffing, Marius; Kayserili, Hulya; Krakow, Deborah; King, Stephen M.; Beales, Philip L.; Al-Gazali, Lihadh; Wicking, Carol; Cormier-Daire, Valerie; Roepman, Ronald; Mitchison, Hannah M.; Witman, George B.; Al-Turki, Saeed; Anderson, Carl; Anney, Richard; Antony, Dinu; Asimit, Jennifer; Ayub, Mohammad; Barrett, Jeff; Barroso, Inês; Bentham, Jamie; Bhattacharya, Shoumo; Blackwood, Douglas; Bobrow, Martin; Bochukova, Elena; Bolton, Patrick; Boustred, Chris; Breen, Gerome; Brion, Marie-Jo; Brown, Andrew; Calissano, Mattia; Carss, Keren; Chatterjee, Krishna; Chen, Lu; Cirak, Sebhattin; Clapham, Peter; Clement, Gail; Coates, Guy; Collier, David; Cosgrove, Catherine; Cox, Tony; Craddock, Nick; Crooks, Lucy; Curran, Sarah; Daly, Allan; Danecek, Petr; Smith, George Davey; Day-Williams, Aaron; Day, Ian; Durbin, Richard; Edkins, Sarah; Ellis, Peter; Evans, David; Farooqi, I. Sadaf; Fatemifar, Ghazaleh; Fitzpatrick, David; Flicek, Paul; Floyd, Jamie; Foley, A. Reghan; Franklin, Chris; Futema, Marta; Gallagher, Louise; Gaunt, Tom; Geschwind, Daniel; Greenwood, Celia; Grozeva, Detelina; Guo, Xiaosen; Gurling, Hugh; Hart, Deborah; Hendricks, Audrey; Holmans, Peter; Huang, Jie; Humphries, Steve E.; Hurles, Matt; Hysi, Pirro; Jackson, David; Jamshidi, Yalda; Jewell, David; Chris, Joyce; Kaye, Jane; Keane, Thomas; Kemp, John; Kennedy, Karen; Kent, Alastair; Kolb-Kokocinski, Anja; Lachance, Genevieve; Langford, Cordelia; Lee, Irene; Li, Rui; Li, Yingrui; Ryan, Liu; Lönnqvist, Jouko; Lopes, Margarida; MacArthur, Daniel G.; Massimo, Mangino; Marchini, Jonathan; Maslen, John; McCarthy, Shane; McGuffin, Peter; McIntosh, Andrew; McKechanie, Andrew; McQuillin, Andrew; Memari, Yasin; Metrustry, Sarah; Min, Josine; Moayyeri, Alireza; Morris, James; Muddyman, Dawn; Muntoni, Francesco; Northstone, Kate; O'Donovan, Michael; O'Rahilly, Stephen; Onoufriadis, Alexandros; Oualkacha, Karim; Owen, Michael; Palotie, Aarno; Panoutsopoulou, Kalliope; Parker, Victoria; Parr, Jeremy; Paternoster, Lavinia; Paunio, Tiina; Payne, Felicity; Perry, John; Pietilainen, Olli; Plagnol, Vincent; Quail, Michael A.; Quaye, Lydia; Raymond, Lucy; Rehnström, Karola; Brent Richards, J.; Ring, Sue; Ritchie, Graham R S; Savage, David B.; Schoenmakers, Nadia; Semple, Robert K.; Serra, Eva; Shihab, Hashem; Shin, So-Youn; Skuse, David; Small, Kerrin; Smee, Carol; Soler, Artigas María; Soranzo, Nicole; Southam, Lorraine; Spector, Tim; St Pourcain, Beate; St. Clair, David; Stalker, Jim; Surdulescu, Gabriela; Suvisaari, Jaana; Tachmazidou, Ioanna; Tian, Jing; Timpson, Nic; Tobin, Martin; Valdes, Ana; van Kogelenberg, Margriet; Vijayarangakannan, Parthiban; Wain, Louise; Walter, Klaudia; Wang, Jun; Ward, Kirsten; Wheeler, Ellie; Whittall, Ros; Williams, Hywel; Williamson, Kathy; Wilson, Scott G.; Wong, Kim; Whyte, Tamieka; ChangJiang, Xu; Zeggini, Eleftheria; Zhang, Feng; Zheng, Hou-Feng
2015-01-01
The analysis of individuals with ciliary chondrodysplasias can shed light on sensitive mechanisms controlling ciliogenesis and cell signalling that are essential to embryonic development and survival. Here we identify TCTEX1D2 mutations causing Jeune asphyxiating thoracic dystrophy with partially penetrant inheritance. Loss of TCTEX1D2 impairs retrograde intraflagellar transport (IFT) in humans and the protist Chlamydomonas, accompanied by destabilization of the retrograde IFT dynein motor. We thus define TCTEX1D2 as an integral component of the evolutionarily conserved retrograde IFT machinery. In complex with several IFT dynein light chains, it is required for correct vertebrate skeletal formation but may be functionally redundant under certain conditions. PMID:26044572
Epitaxial 1D electron transport layers for high-performance perovskite solar cells.
Han, Gill Sang; Chung, Hyun Suk; Kim, Dong Hoe; Kim, Byeong Jo; Lee, Jin-Wook; Park, Nam-Gyu; Cho, In Sun; Lee, Jung-Kun; Lee, Sangwook; Jung, Hyun Suk
2015-10-01
We demonstrate high-performance perovskite solar cells with excellent electron transport properties using a one-dimensional (1D) electron transport layer (ETL). The 1D array-based ETL is comprised of 1D SnO2 nanowires (NWs) array grown on a F:SnO2 transparent conducting oxide substrate and rutile TiO2 nanoshells epitaxially grown on the surface of the 1D SnO2 NWs. The optimized devices show more than 95% internal quantum yield at 750 nm, and a power conversion efficiency (PCE) of 14.2%. The high quantum yield is attributed to dramatically enhanced electron transport in the epitaxial TiO2 layer, compared to that in conventional nanoparticle-based mesoporous TiO2 (mp-TiO2) layers. In addition, the open space in the 1D array-based ETL increases the prevalence of uniform TiO2/perovskite junctions, leading to reproducible device performance with a high fill factor. This work offers a method to achieve reproducible, high-efficiency perovskite solar cells with high-speed electron transport. PMID:26324759
A Least-Squares Transport Equation Compatible with Voids
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 S_{n} formulation represents an excellent alternative to existing second-order S_{n} transport formulations
NASA Astrophysics Data System (ADS)
Hassan, Kazi; Allen, Deonie; Haynes, Heather
2016-04-01
This paper considers 1D hydraulic model data on the effect of high flow clusters and sequencing on sediment transport. Using observed flow gauge data from the River Caldew, England, a novel stochastic modelling approach was developed in order to create alternative 50 year flow sequences. Whilst the observed probability density of gauge data was preserved in all sequences, the order in which those flows occurred was varied using the output from a Hidden Markov Model (HMM) with generalised Pareto distribution (GP). In total, one hundred 50 year synthetic flow series were generated and used as the inflow boundary conditions for individual flow series model runs using the 1D sediment transport model HEC-RAS. The model routed graded sediment through the case study river reach to define the long-term morphological changes. Comparison of individual simulations provided a detailed understanding of the sensitivity of channel capacity to flow sequence. Specifically, each 50 year synthetic flow sequence was analysed using a 3-month, 6-month or 12-month rolling window approach and classified for clusters in peak discharge. As a cluster is described as a temporal grouping of flow events above a specified threshold, the threshold condition used herein is considered as a morphologically active channel forming discharge event. Thus, clusters were identified for peak discharges in excess of 10%, 20%, 50%, 100% and 150% of the 1 year Return Period (RP) event. The window of above-peak flows also required cluster definition and was tested for timeframes 1, 2, 10 and 30 days. Subsequently, clusters could be described in terms of the number of events, maximum peak flow discharge, cumulative flow discharge and skewness (i.e. a description of the flow sequence). The model output for each cluster was analysed for the cumulative flow volume and cumulative sediment transport (mass). This was then compared to the total sediment transport of a single flow event of equivalent flow volume
Efficient 3D/1D self-consistent integral-equation analysis of ICRH antennae
NASA Astrophysics Data System (ADS)
Maggiora, R.; Vecchi, G.; Lancellotti, V.; Kyrytsya, V.
2004-08-01
This work presents a comprehensive account of the theory and implementation of a method for the self-consistent numerical analysis of plasma-facing ion-cyclotron resonance heating (ICRH) antenna arrays. The method is based on the integral-equation formulation of the boundary-value problem, solved via a weighted-residual scheme. The antenna geometry (including Faraday shield bars and a recess box) is fairly general and three-dimensional (3D), and the plasma is in the one-dimensional (1D) 'slab' approximation; finite-Larmor radius effects, as well as plasma density and temperature gradients, are considered. Feeding via the voltages in the access coaxial lines is self-consistently accounted throughout and the impedance or scattering matrix of the antenna array obtained therefrom. The problem is formulated in both the dual space (physical) and spectral (wavenumber) domains, which allows the extraction and simple handling of the terms that slow the convergence in the spectral domain usually employed. This paper includes validation tests of the developed code against measured data, both in vacuo and in the presence of plasma. An example of application to a complex geometry is also given.
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)
Epitaxial 1D electron transport layers for high-performance perovskite solar cells
NASA Astrophysics Data System (ADS)
Han, Gill Sang; Chung, Hyun Suk; Kim, Dong Hoe; Kim, Byeong Jo; Lee, Jin-Wook; Park, Nam-Gyu; Cho, In Sun; Lee, Jung-Kun; Lee, Sangwook; Jung, Hyun Suk
2015-09-01
We demonstrate high-performance perovskite solar cells with excellent electron transport properties using a one-dimensional (1D) electron transport layer (ETL). The 1D array-based ETL is comprised of 1D SnO2 nanowires (NWs) array grown on a F:SnO2 transparent conducting oxide substrate and rutile TiO2 nanoshells epitaxially grown on the surface of the 1D SnO2 NWs. The optimized devices show more than 95% internal quantum yield at 750 nm, and a power conversion efficiency (PCE) of 14.2%. The high quantum yield is attributed to dramatically enhanced electron transport in the epitaxial TiO2 layer, compared to that in conventional nanoparticle-based mesoporous TiO2 (mp-TiO2) layers. In addition, the open space in the 1D array-based ETL increases the prevalence of uniform TiO2/perovskite junctions, leading to reproducible device performance with a high fill factor. This work offers a method to achieve reproducible, high-efficiency perovskite solar cells with high-speed electron transport.We demonstrate high-performance perovskite solar cells with excellent electron transport properties using a one-dimensional (1D) electron transport layer (ETL). The 1D array-based ETL is comprised of 1D SnO2 nanowires (NWs) array grown on a F:SnO2 transparent conducting oxide substrate and rutile TiO2 nanoshells epitaxially grown on the surface of the 1D SnO2 NWs. The optimized devices show more than 95% internal quantum yield at 750 nm, and a power conversion efficiency (PCE) of 14.2%. The high quantum yield is attributed to dramatically enhanced electron transport in the epitaxial TiO2 layer, compared to that in conventional nanoparticle-based mesoporous TiO2 (mp-TiO2) layers. In addition, the open space in the 1D array-based ETL increases the prevalence of uniform TiO2/perovskite junctions, leading to reproducible device performance with a high fill factor. This work offers a method to achieve reproducible, high-efficiency perovskite solar cells with high-speed electron transport
Assessment of an efficient numerical solution of the 1D Richards' equation on bare soil
NASA Astrophysics Data System (ADS)
Varado, N.; Braud, I.; Ross, P. J.; Haverkamp, R.
2006-05-01
A new numerical scheme has been proposed by Ross [Ross, P.J., 2003. Modeling soil water and solute transport—fast, simplified numerical solutions. Agronomy Journal 95, 1352-1361] to solve the 1D Richards' equation [Richards, L.A., 1931. Capillary conduction of liquids through porous medium. Physics 1, 318-333]. This non-iterative solution uses the description of soil properties proposed by Brooks and Corey [Brooks, R.H., Corey, A.T., 1964. Hydraulic properties of porous media. Colorado State University, Fort Collins]. It allows the derivation of an analytical expression for the Kirchhoff potential used in the calculation of water fluxes. The degree of saturation is used as the dependent variable when the soil is unsaturated and the Kirchhoff potential is used in case of saturation. A space and time discretisation scheme leads to a tridiagonal set of linear equations that is solved non-iteratively. We propose in this paper an extensive test of this numerical method, evaluated only on a single case by Ross. The tests are conducted in two steps. First, the solution is assessed against two analytical solutions. The first one [Basha, H.A., 1999. Multidimensional linearized nonsteady infiltration with prescribed boundary conditions at the soil surface. Water Resources Research 35(1), 75-93] provides the water content profile when simplified soil characteristics such as the exponential law of Gardner [Gardner, W.R., 1958. Some steady-state solutions of the unsaturated moisture flow equations with application to evaporation from a water table. Soil Science 85, 228-232] are used. The Ross solution is compared to this solution on eight different soils that were fitted to this law. Analytical solution with the Brooks and Corey models is not available at the moment for the moisture profile but some exist for cumulative infiltration. Therefore, the second analytical solution, used in this study, is the one developed by Parlange et al. [Parlange, J.-Y., Haverkamp, R., Touma, J
Langevin equation approach to reactor noise analysis: stochastic transport equation
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.
Faltermann, Susanne; Prétôt, René; Pernthaler, Jakob; Fent, Karl
2016-02-01
Microcystin-LR (MC-LR) and nodularin are hepatotoxins produced by several cyanobacterial species. Their toxicity is based on active cellular uptake and subsequent inhibition of protein phosphatases PP1/2A, leading to hyperphosphorylation and cell death. To date, uptake of MC-LR and nodularin in fish is poorly understood. Here, we investigated the role of the organic anion transporting polypeptide Oatp1d1 in zebrafish (drOatp1d1, Slco1d1) in cellular uptake in zebrafish. We stably transfected CHO and HEK293 cell lines expressing drOatp1d1. In both transfectants, uptake of MC-LR and nodularin was demonstrated by competitive inhibition of uptake with fluorescent substrate lucifer yellow. Direct uptake of MC-LR was demonstrated by immunostaining, and indirectly by the high cytotoxicity in stable transfectants. By means of a synthesized fluorescent labeled MC-LR derivative, direct uptake was further confirmed in HEK293 cells expressing drOatp1d1. Additionally, uptake and toxicity was investigated in the permanent zebrafish liver cell line ZFL. These cells had only a low relative abundance of drOatp1d1, drOatp2b1 and drOatp1f transcripts, which correlated with the lack of MC-LR induced cytotoxicity and transcriptional changes of genes indicative of endoplasmic reticulum stress, a known effect of this toxin. Our study demonstrates that drOatp1d1 functions as an uptake transporter for both MC-LR and nodularin in zebrafish. PMID:26769064
Electronic and Transport Properties of Quasi-1D Wires of Biological Molecules
NASA Astrophysics Data System (ADS)
Oetzel, Björn; Matthes, Lars; Tandetzky, Falk; Ortmann, Frank; Bechstedt, Friedhelm; Hannewald, Karsten
2010-03-01
In the search for organic materials with good charge-transport properties, artificial stacks of biological molecules are considered attractive candidates [1,2]. In this spirit, we present ab-initio DFT calculations of the structural, electronic, and quantum-transport properties of quasi-1D wires based on guanine and eumelanin molecules [3]. Hereby, a special focus is put on the results for the electronic bandwidths and the consequences for potential applications. [4pt] [1] R. di Felice et al., Phys. Rev. B 65, 045104 (2001) [0pt] [2] P. Meredith et al., Pigment Cell Res. 19, 572 (2006) [0pt] [3] B. Oetzel et al. (unpublished)
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.
High-Order Central WENO Schemes for 1D Hamilton-Jacobi Equations
NASA Technical Reports Server (NTRS)
Bryson, Steve; Levy, Doron; Biegel, Bryan A. (Technical Monitor)
2002-01-01
In this paper we derive fully-discrete Central WENO (CWENO) schemes for approximating solutions of one dimensional Hamilton-Jacobi (HJ) equations, which combine our previous works. We introduce third and fifth-order accurate schemes, which are the first central schemes for the HJ equations of order higher than two. The core ingredient is the derivation of our schemes is a high-order CWENO reconstructions in space.
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.
Zhao Dun; Zhang Yujuan; Lou Weiwei; Luo Honggang
2011-04-15
By constructing nonisospectral Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy, we investigate the nonautonomous nonlinear Schroedinger (NLS) equations which have been used to describe the Feshbach resonance management in matter-wave solitons in Bose-Einstein condensate and the dispersion and nonlinearity managements for optical solitons. It is found that these equations are some special cases of a new integrable model of nonlocal nonautonomous NLS equations. Based on the Lax pairs, the Darboux transformation and conservation laws are explored. It is shown that the local external potentials would break down the classical infinite number of conservation laws. The result indicates that the integrability of the nonautonomous NLS systems may be nontrivial in comparison to the conventional concept of integrability in the canonical case.
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.
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
Stochastic Heat Equation Limit of a (2 + 1)d Growth Model
NASA Astrophysics Data System (ADS)
Borodin, Alexei; Corwin, Ivan; Toninelli, Fabio Lucio
2016-07-01
We determine a {q to 1} limit of the two-dimensional q-Whittaker driven particle system on the torus studied previously in Corwin and Toninelli (Electron. Commun. Probab. 21(44):1-12, 2016). This has an interpretation as a (2 + 1)-dimensional stochastic interface growth model, which is believed to belong to the so-called anisotropic Kardar-Parisi-Zhang (KPZ) class. This limit falls into a general class of two-dimensional systems of driven linear SDEs which have stationary measures on gradients. Taking the number of particles to infinity we demonstrate Gaussian free field type fluctuations for the stationary measure. Considering the temporal evolution of the stationary measure, we determine that along characteristics, correlations are asymptotically given by those of the (2 + 1)-dimensional additive stochastic heat equation. This confirms (for this model) the prediction that the non-linearity for the anisotropic KPZ equation in (2 + 1)-dimension is irrelevant.
Shock capturing data assimilation algorithm for 1D shallow water equations
NASA Astrophysics Data System (ADS)
Tirupathi, Seshu; T. Tchrakian, Tigran; Zhuk, Sergiy; McKenna, Sean
2016-02-01
We propose a new data assimilation algorithm for shallow water equations in one dimension. The algorithm is based upon Discontinuous Galerkin spatial discretization of shallow water equations (DG-SW model) and the continuous formulation of the minimax filter. The latter allows for construction of a robust estimation of the state of the DG-SW model and computes worst-case bounds for the estimation error, provided the uncertain parameters belong to a given bounding set. Numerical studies show that, given sparse observations from numerical or physical experiments, the proposed algorithm quickly reconstructs the true solution even in the presence of shocks, rarefaction waves and unknown values of model parameters. The minimax filter is compared against the ensemble Kalman filter (EnKF) for a benchmark dam-break problem and the results show that the minimax filter converges faster to the true solution for sparse observations.
Comprehensive 1D Modelling of Reactive Chemical Transport in Unsaturated Soil
NASA Astrophysics Data System (ADS)
Wissmeier, L.; Barry, D. A.
2007-12-01
Computer models for simulating environmental processes of water flow, solute transport and geochemical reactions have greatly advanced during recent years. However, there is still demand for the development of programs that a capable of simulating the numerous interactions between physical transport processes and biogeochemical reactions in natural soils. We present a new tool for simulating transient vadose zone flow and solute transport according to the moisture- based form of Richards' equation within the widely used geochemical software PHREEQC. The direct implementation into the geochemical framework provides access to comprehensive geochemical models, giving capabilities beyond existing software for coupled unsaturated flow and reaction. Possible reactions include complex aqueous speciation, cation exchange, equilibrium phase dissolution and precipitation, formation of solid solutions, redox reactions, gas phase exchange, surface adsorption considering electrostatics and kinetic reactions with user-defined rate equations, among others. As a result of the close coupling procedure, the influence of geochemical reactions on water content, e.g., through dissolution or precipitation of water-containing phases, can be investigated. For the solution of the partial differential equations of flow and transport, an explicit finite-difference formulation with a second-order space discretization and first-order time discretization was employed. The use of integrated diffusivities transforms Richards' equation into a simple advection-diffusion equation. Changes in water content and solute concentration were conceptualized as local kinetic reactions of individual elements where changes in moisture content result from fluxes of oxygen and hydrogen across cell boundaries. Reactions and chemical element transport are coupled via sequential two-step operator splitting. The scheme was implemented into PHREEQC without any source code modification such that it can be applied by
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.
Zeng, Y; Albertus, P; Klein, R; Chaturvedi, N; Kojic, A; Bazant, MZ; Christensen, J
2013-06-07
Mathematical models of batteries which make use of the intercalation of a species into a solid phase need to solve the corresponding mass transfer problem. Because solving this equation can significantly add to the computational cost of a model, various methods have been devised to reduce the computational time. In this paper we focus on a comparison of the formulation, accuracy, and order of the accuracy for two numerical methods of solving the spherical diffusion problem with a constant or non-constant diffusion coefficient: the finite volume method and the control volume method. Both methods provide perfect mass conservation and second order accuracy in mesh spacing, but the control volume method provides the surface concentration directly, has a higher accuracy for a given numbers of mesh points and can also be easily extended to variable mesh spacing. Variable mesh spacing can significantly reduce the number of points that are required to achieve a given degree of accuracy in the surface concentration (which is typically coupled to the other battery equations) by locating more points where the concentration gradients are highest. (C) 2013 The Electrochemical Society. All rights reserved.
Periodic solutions for a 1D-model with nonlocal velocity via mass transport
NASA Astrophysics Data System (ADS)
Ferreira, Lucas C. F.; Valencia-Guevara, Julio C.
2016-05-01
This paper concerns periodic solutions for a 1D-model with nonlocal velocity given by the periodic Hilbert transform. There is a rich literature showing, via numerics and rigorous analysis, that this model presents singular behavior of solutions. For instance, they can blow up by forming mass-concentration. We develop a global well-posedness theory for periodic measure initial data that allows, in particular, to analyze how the model evolves from those singularities. Our results are based on periodic mass transport theory and the abstract gradient flow theory in metric spaces developed by Ambrosio et al. (2005). A viscous version of the model is also analyzed and inviscid limit properties are obtained.
NASA Astrophysics Data System (ADS)
Hooshyar, M.; Hagen, S. C.; Wang, D.
2014-12-01
Hydrodynamic models are widely applied to coastal areas in order to predict water levels and flood inundation and typically involve solving a form of the Shallow Water Equations (SWE). The SWE are routinely discretized by applying numerical methods, such as the finite element method. Like other numerical models, hydrodynamic models include uncertainty. Uncertainties are generated due to errors in the discrete approximation of coastal geometry, bathymetry, bottom friction and forcing functions such as tides and wind fields. Methods to counteract these uncertainties should always begin with improvements to physical characterization of: the geometric description through increased resolution, parameters that describe land cover variations in the natural and urban environment, parameters that enhance transfer of surface forcings to the water surface, open boundary forcings, and the wetting/drying brought upon by flood and ebb cycles. When the best possible physical representation is achieved, we are left with calibration and data assimilation to reduce model uncertainty. Data assimilation has been applied to coastal hydrodynamic models to better estimate system states and/or system parameters by incorporating observed data into the model. Kalman Filter is one of the most studied data assimilation methods that minimizes the mean square errors between model state estimations and the observed data in linear systems (Kalman , 1960). For nonlinear systems, as with hydrodynamic models, a variation of Kalman filter called Ensemble Kalman Filter (EnKF), is applied to update the system state according to error statistics in the context of Monte Carlo simulations (Evensen , 2003) & (Hitoshi et. al, 2014). In this research, Kalman Filter is incorporated to simultaneously estimate an influential parameter used in the shallow water equations, bottom roughness, and to adjust the physical feature of bathymetry. Starting from an initial estimate of bottom roughness and bathymetry, and
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.
Resolution of the 1D regularized Burgers equation using a spatial wavelet approximation
NASA Technical Reports Server (NTRS)
Liandrat, J.; Tchamitchian, PH.
1990-01-01
The Burgers equation with a small viscosity term, initial and periodic boundary conditions is resolved using a spatial approximation constructed from an orthonormal basis of wavelets. The algorithm is directly derived from the notions of multiresolution analysis and tree algorithms. Before the numerical algorithm is described these notions are first recalled. The method uses extensively the localization properties of the wavelets in the physical and Fourier spaces. Moreover, the authors take advantage of the fact that the involved linear operators have constant coefficients. Finally, the algorithm can be considered as a time marching version of the tree algorithm. The most important point is that an adaptive version of the algorithm exists: it allows one to reduce in a significant way the number of degrees of freedom required for a good computation of the solution. Numerical results and description of the different elements of the algorithm are provided in combination with different mathematical comments on the method and some comparison with more classical numerical algorithms.
Transport of an interacting Bose gas in 1D disordered lattices
D'Errico, C.; Chaudhuri, S.; Gori, L.; Kumar, A.; Lucioni, E.; Tanzi, L.; Inguscio, M.; Modugno, G.
2014-08-20
We use ultracold atoms in a quasiperiodic lattice to study two outstanding problems in the physics of disordered systems: a) the anomalous diffusion of a wavepacket in the presence of disorder, interactions and noise; b) the transport of a disordered superfluid. a) Our results show that the subdiffusion, observed when interaction alone is present, can be modelled with a nonlinear diffusion equation and the peculiar shape of the expanding density profiles can be connected to the microscopic nonlinear diffusion coefficients. Also when noise alone is present we can describe the observed normal diffusion dynamics by existing microscopic models. In the unexplored regime in which noise and interaction are combined, instead, we observe an anomalous diffusion, that we model with a generalized diffusion equation, where noise- and interaction-induced contributions add each other. b) We find that an instability appearing at relatively large momenta can be employed to locate the fluid-insulator crossover driven by disorder. By investigating the momentum-dependent transport, we observe a sharp crossover from a weakly dissipative regime to a strongly unstable one at a disorder-dependent critical momentum. The set of critical disorder and interaction strengths for which such critical momentum vanishes, can be identified with the separation between a fluid regime and an insulating one and can be related to the predicted zero-temperature superfluid-Bose glass transition.
Alternative formulation of the monokinetic transport equation
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.
Reactive Transport Modeling of Microbially-Mediated Chromate Reduction in 1-D Soil Columns
NASA Astrophysics Data System (ADS)
Qiu, H.; Viamajala, S.; Alam, M. M.; Peyton, B. M.; Petersen, J. N.; Yonge, D. R.
2002-12-01
Cr(VI) reduction tests were performed with the well known metal reducing bacterium Shewanella oneidensis MR-1 in liquid phase batch reactors and continuous flow soil columns under anaerobic conditions. In the batch tests, the cultures were grown with fumarate as the terminal electron acceptor and lactate as the electron donor in a simulated groundwater medium to determine yield coefficients and specific growth rates. The bench-scale soil column experiments were carried out with MR-1 to test the hypothesis that the kinetic parameters obtained in batch studies, combined with microbial attachment /detachment processes, will accurately predict reactive transport of Cr(VI) during bacterial Cr(VI) reduction in a soil matrix. Cr(VI)-free simulated groundwater media containing fumarate as the limiting substrate and lactate was supplied to a 2.1cm (ID) x 15 cm soil column inoculated with MR-1 for a duration of 9 residence times to allow for biomass to build-up in the column. Thereafter the column was supplied with both Cr(VI) and substrate. The concentrations of effluent substrate, biomass and Cr(VI) were monitored on a periodic basis and attached biomass in the column was measured in the termination of each column test. A reactive transport model was developed in which 6 governing equations deal with Cr(VI) bioreaction, fumarate (as electron donor) consumption, aqueous biomass growth and transport, solid biomass detachment and attachment kinetics, aqueous and solid phase enzyme reaction and transport, respectively. The model incorporating the enzyme reaction kinetics for Cr(VI) reduction, Monod kinetic expressions for substrate depletion, nonlinear attachment and detachment kinetics for aqueous and solid phase microorganism concentration, was solved by a fully implicit, finite-difference procedure using RT3D (A Modular Computer Code for Reactive Multi-species Transport in 3-Dimensional Groundwater Systems) platform in one dimension. Cr(VI)-free column data was used to
Box model and 1D longitudinal model of flow and transport in Bosten Lake, China
NASA Astrophysics Data System (ADS)
Li, Ning; Kinzelbach, Wolfgang; Li, WenPeng; Dong, XinGuang
2015-05-01
Bosten Lake in the southeast of Yanqi Catchment, China, supports the downstream agricultural and natural environments. Over the last few decades the intensive agricultural activities in Yanqi Catchment resulted in decreased lake levels and deteriorated lake water quality. A two-box model is constructed to understand the evolution of lake level and salinity between 1958 and 2008. The two-box model of the lake indicates that the evaporation does have the same trend as the observed lake area and the annual average evaporation agrees with the value obtained from the Penman-Monteith approach. To achieve a correct salt balance, the ratio of outflow concentration and average lake concentration has to be around 0.7. This is due to the incomplete mixing of the lake caused by short-circuiting between tributary inflow and the main outflow via the pump stations abstracting water from the lake. This short-circuiting is investigated in more detail by a 1D numerical flow and transport model of the lake calibrated with observations of lake level and lake concentrations. The distributed model reproduces the correct time-varying outflow concentration. It is used for the assessment of two basic management options: increasing river discharge (by water saving irrigation, reduction of phreatic evaporation or reduction of agricultural area) and diverting saline drainage water to the desert. Increasing river discharge to the lake by 20% reduces the east basin salt concentration by 0.55 kg/m3, while capturing all the drainage water and discharging it to depressions instead of the lake reduces the east basin salt concentration by 0.63 kg/m3. A combination of increasing river inflow and decreasing drainage salt flux is sufficient to bring future lake TDS below the required 1 kg/m3, to keep a lake level that sustains the lake ecosystem, and to supply more water for downstream development and ecosystem rehabilitation.
Column Testing and 1D Reactive Transport Modeling to Evaluate Uranium Plume Persistence Processes
NASA Astrophysics Data System (ADS)
Johnson, R. H.; Morrison, S.; Morris, S.; Tigar, A.; Dam, W. L.; Dayvault, J.
2015-12-01
At many U.S. Department of Energy Office of Legacy Management sites, 100 year natural flushing was selected as a remedial option for groundwater uranium plumes. However, current data indicate that natural flushing is not occurring as quickly as expected and solid-phase and aqueous uranium concentrations are persistent. At the Grand Junction, Colorado office site, column testing was completed on core collected below an area where uranium mill tailings have been removed. The total uranium concentration in this core was 13.2 mg/kg and the column was flushed with laboratory-created water with no uranium and chemistry similar to the nearby Gunnison River. The core was flushed for a total of 91 pore volumes producing a maximum effluent uranium concentration of 6,110 μg/L at 2.1 pore volumes and a minimum uranium concentration of 36.2 μg/L at the final pore volume. These results indicate complex geochemical reactions at small pore volumes and a long tailing affect at greater pore volumes. Stop flow data indicate the occurrence of non-equilibrium processes that create uranium concentration rebound. These data confirm the potential for plume persistence, which is occurring at the field scale. 1D reactive transport modeling was completed using PHREEQC (geochemical model) and calibrated to the column test data manually and using PEST (inverse modeling calibration routine). Processes of sorption, dual porosity with diffusion, mineral dissolution, dispersion, and cation exchange were evaluated separately and in combination. The calibration results indicate that sorption and dual porosity are major processes in explaining the column test data. These processes are also supported by fission track photographs that show solid-phase uranium residing in less mobile pore spaces. These procedures provide valuable information on plume persistence and secondary source processes that may be used to better inform and evaluate remedial strategies, including natural flushing.
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.
Dispersion in tidally averaged transport equation
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
A marching in space and time (MAST) solver of the shallow water equations. Part I: The 1D model
NASA Astrophysics Data System (ADS)
Aricò, C.; Tucciarelli, T.
2007-05-01
A new approach is presented for the numerical solution of the complete 1D Saint-Venant equations. At each time step, the governing system of partial differential equations (PDEs) is split, using a fractional time step methodology, into a convective prediction system and a diffusive correction system. Convective prediction system is further split into a convective prediction and a convective correction system, according to a specified approximated potential. If a scalar exact potential of the flow field exists, correction vanishes and the solution of the convective correction system is the same solution of the prediction system. Both convective prediction and correction systems are shown to have at each x - t point a single characteristic line, and a corresponding eigenvalue equal to the local velocity. A marching in space and time (MAST) technique is used for the solution of the two systems. MAST solves a system of two ordinary differential equations (ODEs) in each computational cell, using for the time discretization a self-adjusting fraction of the original time step. The computational cells are ordered and solved according to the decreasing value of the potential in the convective prediction step and to the increasing value of the same potential in the convective correction step. The diffusive correction system is solved using an implicit scheme, that leads to the solution of a large linear system, with the same order of the cell number, but sparse, symmetric and well conditioned. The numerical model shows unconditional stability with regard of the Courant-Friedrichs-Levi (CFL) number, requires no special treatment of the source terms and a computational effort almost proportional to the cell number. Several tests have been carried out and results of the proposed scheme are in good agreement with analytical solutions, as well as with experimental data.
Quantum and semi-classical transport in RTDs using NEMO 1-D
NASA Technical Reports Server (NTRS)
Klimeck, G.; Stout, P.; Bowen, R. C.
2003-01-01
NEMO 1-D has been developed primarily for the simulation of resonant tunneling diodes, and quantitative and predictive agreements with experimental high performance, high current density devices have been achieved in the past.
GIS-based channel flow and sediment transport simulation using CCHE1D coupled with AnnAGNPS
Technology Transfer Automated Retrieval System (TEKTRAN)
CCHE1D (Center for Computational Hydroscience and Engineering 1-Dimensional model) simulates unsteady free-surface flows with nonequilibrium, nonuniform sediment transport in dendritic channel networks. Since early 1990’s, the model and its software packages have been developed and continuously main...
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.
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.
NASA Astrophysics Data System (ADS)
Düben, Peter D.; Dolaptchiev, Stamen I.
2015-08-01
Inexact hardware can reduce computational cost, due to a reduced energy demand and an increase in performance, and can therefore allow higher-resolution simulations of the atmosphere within the same budget for computation. We investigate the use of emulated inexact hardware for a model of the randomly forced 1D Burgers equation with stochastic sub-grid-scale parametrisation. Results show that numerical precision can be reduced to only 12 bits in the significand of floating-point numbers—instead of 52 bits for double precision—with no serious degradation in results for all diagnostics considered. Simulations that use inexact hardware on a grid with higher spatial resolution show results that are significantly better compared to simulations in double precision on a coarser grid at similar estimated computing cost. In the second half of the paper, we compare the forcing due to rounding errors to the stochastic forcing of the stochastic parametrisation scheme that is used to represent sub-grid-scale variability in the standard model setup. We argue that stochastic forcings of stochastic parametrisation schemes can provide a first guess for the upper limit of the magnitude of rounding errors of inexact hardware that can be tolerated by model simulations and suggest that rounding errors can be hidden in the distribution of the stochastic forcing. We present an idealised model setup that replaces the expensive stochastic forcing of the stochastic parametrisation scheme with an engineered rounding error forcing and provides results of similar quality. The engineered rounding error forcing can be used to create a forecast ensemble of similar spread compared to an ensemble based on the stochastic forcing. We conclude that rounding errors are not necessarily degrading the quality of model simulations. Instead, they can be beneficial for the representation of sub-grid-scale variability.
This technical report describes the new one-dimensional (1D) hydrodynamic and sediment transport model EFDC1D. This model that can be applied to stream networks. The model code and two sample data sets are included on the distribution CD. EFDC1D can simulate bi-directional unstea...
Complementing Graphenes: 1D Interplanar Charge Transport in Polymeric Graphitic Carbon Nitrides.
Merschjann, Christoph; Tschierlei, Stefanie; Tyborski, Tobias; Kailasam, Kamalakannan; Orthmann, Steven; Hollmann, Dirk; Schedel-Niedrig, Thomas; Thomas, Arne; Lochbrunner, Stefan
2015-12-22
Charge transport in polymeric graphitic carbon nitrides is shown to proceed via diffusive hopping of electron and hole polarons with reasonably high mobilities >10(-5) cm(2) V(-1) s(-1). The power-law behavior of the ultrafast luminescence decay exhibits that the predominant transport direction is perpendicular to the graphitic polymer sheets, thus complementing 2D materials like graphene. PMID:26543003
MULTICOMPONENT GEOCHEMICAL TRANSPORT MODELING USING HYDRUS-1D AND HP1
Technology Transfer Automated Retrieval System (TEKTRAN)
The transport of reactive contaminants in the subsurface is generally affected by a large number of nonlinear and often interactive physical, chemical, and biological processes. Simulating these processes requires a comprehensive reactive transport code that couples the physical processes of water f...
MULTICOMPONENT GEOCHEMICAL TRANSPORT MODELING USING THE HYDRUS-1D COMPUTER SOFTWARE PACKAGE
Technology Transfer Automated Retrieval System (TEKTRAN)
ABSTRACT: The transport of reactive contaminants in the subsurface is generally affected by a large number of nonlinear and often interactive physical, chemical and biological processes. Simulating these processes requires a coupled reactive transport code that couples the physical processes of wate...
Detection and characterization of uranium-humic complexes during 1D transport studies
Lesher, Emily K.; Honeyman, Bruce D.; Ranville, James F.
2013-05-01
The speciation and transport of uranium (VI) through porous media is highly dependent on solution conditions, the presence of complexing ligands, and the nature of the porous media. The dependency on many variables makes prediction of U transport in bench-scale experiments and in the field difficult. In particular, the identification of colloidal U phases poses a technical challenge. Transport of U in the presence and absence of natural organic matter (Suwannee River humic acid, SRHA) through silica sand and hematite coated silica sand was tested at pH 4 and 5 using static columns, where flow is controlled by gravity and residence time between advective pore volume exchanges can be strictly controlled. The column effluents were characterized by traditional techniques including ICPMS quantification of total [U] and [Fe], TOC analysis of [DOC], and pH analysis, and also by non-traditional techniques: flow field flow fractionation with online ICPMS detection (FlFFF-ICPMS) and specific UV absorbance (SUVA) characterization of effluent fractions. Key results include that the transport of U through the columns was enhanced by pre-equilibration with SRHA, and previously deposited U was remobilized by the addition of SRHA. The advanced techniques yielded important insights on the mechanisms of transport: FlFFF-ICPMS identified a U-SRHA complex as the mobile U species and directly quantified relative amounts of the complex, while specific UV absorbance (SUVA) measurements indicated a composition-based fractionation onto the porous media.
Linear transport of domain walls confined to propagating 1-D potential wells
NASA Astrophysics Data System (ADS)
Negotia, M.; Hodges, M. P. P.; Bryan, M. T.; Fry, P. W.; Im, M.-Y.; Fischer, P.; Allwood, D. A.; Hayward, T. J.
2013-10-01
We present a method of controllably propagating domain walls (DWs) in magnetic nanowires over extended linear distances by confining them to geometrically defined energy minima. Using simple models, magnetic transmission soft x-ray microscopy and magneto-optic Kerr effect measurements, we show that the technique allows DWs to be moved at arbitrary, user-defined velocities and be positioned with micrometer precision. Our approach is expected to be of utility in applications where the precise transport and positioning of DWs take precedent over the absolute speed of propagation, for example, where the fields produced by DWs are used to trap and transport magnetized particles.
1D momentum-conserving systems: the conundrum of anomalous versus normal heat transport
NASA Astrophysics Data System (ADS)
Li, Yunyun; Liu, Sha; Li, Nianbei; Hänggi, Peter; Li, Baowen
2015-04-01
Transport and the spread of heat in Hamiltonian one dimensional momentum conserving nonlinear systems is commonly thought to proceed anomalously. Notable exceptions, however, do exist of which the coupled rotator model is a prominent case. Therefore, the quest arises to identify the origin of manifest anomalous energy and momentum transport in those low dimensional systems. We develop the theory for both, the statistical densities for momentum- and energy-spread and particularly its momentum-/heat-diffusion behavior, as well as its corresponding momentum/heat transport features. We demonstrate that the second temporal derivative of the mean squared deviation of the momentum spread is proportional to the equilibrium correlation of the total momentum flux. Subtracting the part which corresponds to a ballistic momentum spread relates (via this integrated, subleading momentum flux correlation) to an effective viscosity, or equivalently, to the underlying momentum diffusivity. We next put forward the intriguing hypothesis: normal spread of this so adjusted excess momentum density causes normal energy spread and alike normal heat transport (Fourier Law). Its corollary being that an anomalous, superdiffusive broadening of this adjusted excess momentum density in turn implies an anomalous energy spread and correspondingly anomalous, superdiffusive heat transport. This hypothesis is successfully corroborated within extensive molecular dynamics simulations over large extended time scales. Our numerical validation of the hypothesis involves four distinct archetype classes of nonlinear pair-interaction potentials: (i) a globally bounded pair interaction (the noted coupled rotator model), (ii) unbounded interactions acting at large distances (the coupled rotator model amended with harmonic pair interactions), (iii) the case of a hard point gas with unbounded square-well interactions and (iv) a pair interaction potential being unbounded at short distances while displaying an
NASA Astrophysics Data System (ADS)
Li, Yeping
2016-06-01
In this paper, we consider the one-dimensional (1D) compressible bipolar Navier-Stokes-Poisson equations. We know that when the viscosity coefficient and Debye length are zero in the compressible bipolar Navier-Stokes-Poisson equations, we have the compressible Euler equations. Under the case that the compressible Euler equations have a rarefaction wave with one-side vacuum state, we can construct a sequence of the approximation solution to the one-dimensional bipolar Navier-Stokes-Poisson equations with well-prepared initial data, which converges to the above rarefaction wave with vacuum as the viscosity and the Debye length tend to zero. Moreover, we also obtain the uniform convergence rate. The results are proved by a scaling argument and elaborate energy estimate.
On diagonalization of coupled hydrologic transport and geochemical reaction equations
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.
NASA Astrophysics Data System (ADS)
Volders, Kim
2010-09-01
This paper deals with stability in the numerical solution of general one-dimensional partial differential equations with variable coefficients. We will generalize stability results for central finite difference schemes on non-uniform grids that were obtained by In't Hout & Volders (2009) for the Black-Scholes equation. Subsequently we will apply our stability results to the CEV model.
Development of a 3D to 1D Particle Transport Model to Predict Deposition in the Lungs
NASA Astrophysics Data System (ADS)
Oakes, Jessica M.; Grandmont, Celine; Shadden, Shawn C.; Vignon-Clementel, Irene E.
2014-11-01
Aerosolized particles are commonly used for therapeutic drug delivery as they can be delivered to the body systemically or be used to treat lung diseases. Recent advances in computational resources have allowed for sophisticated pulmonary simulations, however it is currently impossible to solve for airflow and particle transport for all length and time scales of the lung. Instead, multi-scale methods must be used. In our recent work, where computational methods were employed to solve for airflow and particle transport in the rat airways (Oakes et al. (2014), Annals of Biomedical Engineering 42, 899), the number of particles to exit downstream of the 3D domain was determined. In this current work, the time-dependent Lagrangian description of particles was used to numerically solve a 1D convection-diffusion model (trumpet model, Taulbee and Yu (1975), Journal of Applied Physiology, 38, 77) parameterized specifically for the lung. The expansion of the airway dimensions was determined based on data collected from our aerosol exposure experiments (Oakes et al. (2014), Journal of Applied Physiology, 116, 1561). This 3D-1D framework enables us to predict the fate of particles in the whole lung. This work was supported by the Whitaker Foundation at the IIE, a INRIA Associated Team Postdoc Grant, and a UC Presidential Fellowship.
Stable Difference Schemes for the Neutron Transport Equation
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.
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.
NASA Astrophysics Data System (ADS)
Moustafa, Salli; Févotte, François; Lathuilière, Bruno; Plagne, Laurent
2014-06-01
The past few years have been marked by a noticeable increase in the interest in 3D whole-core heterogeneous deterministic neutron transport solvers for reference calculations. Due to the extremely large problem sizes tackled by such solvers, they need to use adapted numerical methods and need to be efficiently implemented to take advantage of the full computing power of modern systems. As for numerical methods, one possible approach consists in iterating over resolutions of 2D and 1D MOC problems by taking advantage of prismatic geometries. The MICADO solver, developed at EDF R&D, is a parallel implementation of such a method in distributed and shared memory systems. However it is currently unable to use SIMD vectorization to leverage the full computing power of modern CPUs. In this paper, we describe our first effort to support vectorization in MICADO, typically targeting Intel© SSE CPUs. Both the 2D and 1D algorithms are vectorized, allowing for high expected speedups for the whole spatial solver. We present benchmark computations, which show nearly optimal speedups for our vectorized implementation on the TAKEDA case.
NASA Astrophysics Data System (ADS)
Gloesener, Elodie; Karatekin, Özgür; Dehant, Véronique
2016-04-01
MSL Rover Environmental Monitoring Station (REMS) performed high-resolution measurements of temperature and relative humidity during more than one Martian year. In this work, a 1D subsurface model is used to study water vapor exchange between the atmosphere and the subsurface at Gale crater using REMS data. The thermal model used includes several layers of varying thickness with depth and properties that can be changed to correspond to those of Martian rocks at locations studied. It also includes the transport of water vapor through porous Martian regolith and the different phases considered are vapor, ice and adsorbed H2O. The total mass flux is given by the sum of diffusive and advective transport. The role of an adsorbing regolith on water transfer as well as the range of parameters with significant effect on water transport in Martian conditions are investigated. In addition, kinetics of the adsorption process is considered to examine its influence on the water vapor exchange between the subsurface and the atmosphere.
NASA Astrophysics Data System (ADS)
Lauer, Wesley; Viparelli, Enrica; Piegay, Herve
2014-05-01
Sedimentary deposits adjacent to rivers can represent important sources and sinks for bed material sediment, particularly on decadal and longer timescales. The Morphodynamics and Sediment Tracers in 1-D model (MAST-1D) is a size-specific sediment transport model that allows for active exchange between channel and floodplain sediment on river reaches of tens to hundreds of kilometers in length. The model is intended to provide a mechanism for performing a first-order assessment of the likely importance of off-channel sediment exchange in controlling decadal-scale geomorphic trends, thereby helping plan and/or prioritize field data collection and higher resolution modeling work. The model develops a sediment budget for short segments of an alluvial valley. Each segment encompasses several active river bends. In each segment, a sediment transport capacity computation is performed to determine the downstream flux of bed material sediment, following the approach of most other 1-D sediment transport models. However, the model differs from most other bed evolution models in that sediment can be exchanged with the floodplain in each segment, and mass conservation is applied to both the active layer and floodplain sediment storage reservoirs. The potential for net imbalances in overall exchange as well as the size specific nature of the computations allows the model to simulate reach-scale aggradation/degradation and/or changes in bed texture. The inclusion of fine sediment in the model allows it to track geochemical tracer material and also provides a mechanism to simulate, to first order, the effects of changes in the supply of silt and clay on overall channel hydraulic capacity. The model is applied to a ~40 km reach of the Ain River, a tributary of the Rhône River in eastern France that has experienced a significant sediment deficit as a result of the construction of several dams between 1920 and 1970. MAST-1D simulations result in both incision and the formation of a
Adhikari, K; Pal, S; Chakraborty, B; Mukherjee, S N; Gangopadhyay, A
2014-10-01
The movement of contaminants through soil imparts a variety of geo-environmental problem inclusive of lithospheric pollution. Near-surface aquifers are often vulnerable to contamination from surface source if overlying soil possesses poor resilience or contaminant attenuation capacity. The prediction of contaminant transport through soil is urged to protect groundwater from sources of pollutants. Using field simulation through column experiments and mathematical modeling like HYDRUS-1D, assessment of soil resilience and movement of contaminants through the subsurface to reach aquifers can be predicted. An outfall site of effluents of a coke oven plant comprising of alarming concentration of phenol (4-12.2 mg/L) have been considered for studying groundwater condition and quality, in situ soil characterization, and effluent characterization. Hydrogeological feature suggests the presence of near-surface aquifers at the effluent discharge site. Analysis of groundwater of nearby locality reveals the phenol concentration (0.11-0.75 mg/L) exceeded the prescribed limit of WHO specification (0.002 mg/L). The in situ soil, used in column experiment, possess higher saturated hydraulic conductivity (KS = 5.25 × 10(-4) cm/s). The soil containing 47 % silt, 11 % clay, and 1.54% organic carbon content was found to be a poor absorber of phenol (24 mg/kg). The linear phenol adsorption isotherm model showed the best fit (R(2) = 0.977, RMSE = 1.057) to the test results. Column experiments revealed that the phenol removal percent and the length of the mass transfer zone increased with increasing bed heights. The overall phenol adsorption efficiency was found to be 42-49%. Breakthrough curves (BTCs) predicted by HYDRUS-1D model appears to be close fitting with the BTCs derived from the column experiments. The phenol BTC predicted by the HYDRUS-1D model for 1.2 m depth subsurface soil, i.e., up to the depth of groundwater in the study area, showed that the exhaustion
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.
NASA Astrophysics Data System (ADS)
Olson, Gordon L.
2012-04-01
When using polynomial expansions for the angular variables in the radiation transport equation, the usual procedure is to truncate the series by setting all higher order terms to zero. At low order, such simple closures may not give the optimum solution. This work tests alternate closures that scale either the time- or spatial-derivatives in the highest order equation. These scale factors can be chosen such that waves propagate at exactly the speed of light in optically thin media. Alternatively, they may be chosen to significantly improve the accuracy of low-order solutions with no additional computational cost. The same scaling procedure and scale factors work in one- and multi-dimensions. In multidimensions, reducing the order of a solution can save significant amounts of computer time.
New method for computation of band structures in 1D photonic crystals based on the Fresnel equations
NASA Astrophysics Data System (ADS)
Roshan Entezar, S.
2013-02-01
In this paper, we present a new method for calculation of band structure in one-dimensional bilayer photonic crystals, based on the Fresnel equations. We derive a new relation to obtain the band structure without using the Floquet theorem. It is shown that this relation can be simplified under the assumption that the single-path phase-shift acquired through the individual layers of the photonic crystal be equal to ? . The results obtained by our method are compared with the ones obtained from the transfer matrix method to show that they are exactly identical.
A 2D/1D coupling neutron transport method based on the matrix MOC and NEM methods
Zhang, H.; Zheng, Y.; Wu, H.; Cao, L.
2013-07-01
A new 2D/1D coupling method based on the matrix MOC method (MMOC) and nodal expansion method (NEM) is proposed for solving the three-dimensional heterogeneous neutron transport problem. The MMOC method, used for radial two-dimensional calculation, constructs a response matrix between source and flux with only one sweep and then solves the linear system by using the restarted GMRES algorithm instead of the traditional trajectory sweeping process during within-group iteration for angular flux update. Long characteristics are generated by using the customization of commercial software AutoCAD. A one-dimensional diffusion calculation is carried out in the axial direction by employing the NEM method. The 2D and ID solutions are coupled through the transverse leakage items. The 3D CMFD method is used to ensure the global neutron balance and adjust the different convergence properties of the radial and axial solvers. A computational code is developed based on these theories. Two benchmarks are calculated to verify the coupling method and the code. It is observed that the corresponding numerical results agree well with references, which indicates that the new method is capable of solving the 3D heterogeneous neutron transport problem directly. (authors)
NASA Astrophysics Data System (ADS)
Epperlein, J.; Do, A. L.; Gross, T.; Siegmund, S.
2013-10-01
A linear system ẋ=Ax, A∈R, x∈Rn, with rkA=n-1, has a one-dimensional center manifold Ec={v∈Rn:Av=0}. If a differential equation ẋ=f(x) has a one-dimensional center manifold Wc at an equilibrium x∗ then Ec is tangential to Wc with A=Df(x∗) and for stability of Wc it is necessary that A has no spectrum in C+, i.e. if A is symmetric, it has to be negative semi-definite. We establish a graph theoretical approach to characterize semi-definiteness. Using spanning trees for the graph corresponding to A, we formulate meso-scale conditions with certain principal minors of A which are necessary for semi-definiteness. We illustrate these results by the example of the Kuramoto model of coupled oscillators.
A new least-squares transport equation compatible with voids
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)
Relativistic transport equations for electromagnetic scalar, and pseudoscalar potentials
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.
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.
Central role of the observable electric potential in transport equations.
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
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.
Volume transport and generalized hydrodynamic equations for monatomic fluids.
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
Transport equations for the inflationary trispectrum
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.
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.
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.
NASA Astrophysics Data System (ADS)
Hammer, René; Pötz, Walter; Arnold, Anton
2014-01-01
A finite difference scheme is presented for the Dirac equation in (1+1)D. It can handle space- and time-dependent mass and potential terms and utilizes exact discrete transparent boundary conditions (DTBCs). Based on a space- and time-staggered leap-frog scheme it avoids fermion doubling and preserves the dispersion relation of the continuum problem for mass zero (Weyl equation) exactly. Considering boundary regions, each with a constant mass and potential term, the associated DTBCs are derived by first applying this finite difference scheme and then using the Z-transform in the discrete time variable. The resulting constant coefficient difference equation in space can be solved exactly on each of the two semi-infinite exterior domains. Admitting only solutions in l2 which vanish at infinity is equivalent to imposing outgoing boundary conditions. An inverse Z-transformation leads to exact DTBCs in form of a convolution in discrete time which suppress spurious reflections at the boundaries and enforce stability of the whole space-time scheme. An exactly preserved functional for the norm of the Dirac spinor on the staggered grid is presented. Simulations of Gaussian wave packets, leaving the computational domain without reflection, demonstrate the quality of the DTBCs numerically, as well as the importance of a faithful representation of the energy-momentum dispersion relation on a grid.
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.
Optical Testing Using the Transport-of-Intensity Equation
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.
Sun, Jianjun; Xu, Jinbin; Cairns, Nigel J.; Perlmutter, Joel S.; Mach, Robert H.
2012-01-01
The dopamine D1, D2, D3 receptors, vesicular monoamine transporter type-2 (VMAT2), and dopamine transporter (DAT) densities were measured in 11 aged human brains (aged 77–107.8, mean: 91 years) by quantitative autoradiography. The density of D1 receptors, VMAT2, and DAT was measured using [3H]SCH23390, [3H]dihydrotetrabenazine, and [3H]WIN35428, respectively. The density of D2 and D3 receptors was calculated using the D3-preferring radioligand, [3H]WC-10 and the D2-preferring radioligand [3H]raclopride using a mathematical model developed previously by our group. Dopamine D1, D2, and D3 receptors are extensively distributed throughout striatum; the highest density of D3 receptors occurred in the nucleus accumbens (NAc). The density of the DAT is 10–20-fold lower than that of VMAT2 in striatal regions. Dopamine D3 receptor density exceeded D2 receptor densities in extrastriatal regions, and thalamus contained a high level of D3 receptors with negligible D2 receptors. The density of dopamine D1 linearly correlated with D3 receptor density in the thalamus. The density of the DAT was negligible in the extrastriatal regions whereas the VMAT2 was expressed in moderate density. D3 receptor and VMAT2 densities were in similar level between the aged human and aged rhesus brain samples, whereas aged human brain samples had lower range of densities of D1 and D2 receptors and DAT compared with the aged rhesus monkey brain. The differential density of D3 and D2 receptors in human brain will be useful in the interpretation of PET imaging studies in human subjects with existing radiotracers, and assist in the validation of newer PET radiotracers having a higher selectivity for dopamine D2 or D3 receptors. PMID:23185343
Quantum Non-Markovian Langevin Equations and Transport Coefficients
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.
A rain splash transport equation assimilating field and laboratory measurements
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.
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.
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.
Singular perturbation analysis of the neutron transport equation
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.
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.
Pastura, F C H; Guimarães, C P; Zamberlan, M C P; Cid, G L; Santos, V S; Streit, P; Paranhos, A G; Cobbe, R T; Cobbe, K T; Batista, D S
2012-01-01
The goal of this paper is to present 1D and 3D anthropometric data applied to two distinct design situations: one related to the interior layout of a public transport vehicle and another one related to oil and gas laboratories work environment design. On this study, the 1D anthropometric data were extracted from the Brazilian anthropometric database developed by INT and the 3D anthropometric data were obtained using a Cyberware 3D whole body scanner. A second purpose of this paper is to present the 3D human scanning data as a tool that can help designers on decision making. PMID:22317431
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.
NASA Astrophysics Data System (ADS)
Mello, Pier A.; Shi, Zhou; Genack, Azriel Z.
2015-11-01
We study the average energy - or particle - density of waves inside disordered 1D multiply-scattering media. We extend the transfer-matrix technique that was used in the past for the calculation of the intensity beyond the sample to study the intensity in the interior of the sample by considering the transfer matrices of the two segments that form the entire waveguide. The statistical properties of the two disordered segments are found using a maximum-entropy ansatz subject to appropriate constraints. The theoretical expressions are shown to be in excellent agreement with 1D transfer-matrix simulations.
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.
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.
Moment transport equations for the primordial curvature perturbation
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}.
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.
NASA Astrophysics Data System (ADS)
Brown, A.; Dahlke, H. E.
2015-12-01
The ability of soil to infiltrate large volumes of water is fundamental to managed aquifer recharge (MAR) when using infiltration basins or agricultural fields. In order to investigate the feasibility of using agricultural fields for MAR we conducted a field experiment designed to not only assess the resilience of alfalfa (Medicago sativa) to large ( 300 mm ), short duration (1.5 hour), repeated irrigation events during the winter but also how crop resilience was influenced by soil water movement. We hypothesized that large irrigation amounts designed for groundwater recharge could cause prolonged saturated conditions in the root-zone and yield loss. Tensiometers were installed at two depths (60 and 150 cm) in a loam soil to monitor the changes in soil matric potential within and below the root-zone following irrigation events in each of five experimental plots (8 x 16 m2). To simulate the individual infiltration events we employed the HYDRUS-1D computational module (Simunek et al., 2005) and compared the finite-water content vadose zone flow method (Ogden et al. 2015) with numerical solutions to the Richards' equation. For both models we assumed a homogenous and isotropic root zone that is initially unsaturated with no water flow. Here we assess the ability of these two models to account for the control volume applied to the plots and to capture sharp changes in matric potential that were observed in the early time after an irrigation pulse. The goodness-of-fit of the models was evaluated using the root mean square error (RMSE) for observed and predicted values of cumulative infiltration over time, wetting front depth over time and water content at observation nodes. For the finite-water content method, the RMSE values and output for observation nodes were similar to that from the HYDRUS-1D solution. This indicates that the finite-water content method may be useful for predicting the fate of large volumes of water applied for MAR. Moreover, both models suggest a
NASA Astrophysics Data System (ADS)
Brown, A.; Dahlke, H. E.
2015-12-01
The ability of soil to infiltrate large volumes of water is fundamental to managed aquifer recharge (MAR) when using infiltration basins or agricultural fields. In order to investigate the feasibility of using agricultural fields for MAR we conducted a field experiment designed to not only assess the resilience of alfalfa (Medicago sativa) to large (300 mm), short duration (1.5 hour), repeated irrigation events during the winter but also how crop resilience was influenced by soil water movement. We hypothesized that large irrigation amounts designed for groundwater recharge could cause prolonged saturated conditions in the root-zone and yield loss. Tensiometers were installed at two depths (60 and 150 cm) in a loam soil to monitor the changes in soil matric potential within and below the root-zone following irrigation events in each of five experimental plots (8 x 16 m2). To simulate the individual infiltration events we employed the HYDRUS-1D computational module (Simunek et al., 2005) and compared the finite-water content vadose zone flow method (Ogden et al. 2015) with numerical solutions to the Richards' equation. For both models we assumed a homogenous and isotropic root zone that is initially unsaturated with no water flow. Here we assess the ability of these two models to account for the control volume applied to the plots and to capture sharp changes in matric potential that were observed in the early time after an irrigation pulse. The goodness-of-fit of the models was evaluated using the root mean square error (RMSE) for observed and predicted values of cumulative infiltration over time, wetting front depth over time and water content at observation nodes. For the finite-water content method, the RMSE values and output for observation nodes were similar to that from the HYDRUS-1D solution. This indicates that the finite-water content method may be useful for predicting the fate of large volumes of water applied for MAR. Moreover, both models suggest a
NASA Astrophysics Data System (ADS)
Carmelo, J. M. P.; Gu, Shi-Jian; Sampaio, M. J.
2014-06-01
Finite-temperature T > 0 transport properties of integrable and nonintegrable one-dimensional (1D) many-particle quantum systems are rather different, showing ballistic and diffusive behavior, respectively. The repulsive 1D Hubbard model is a prominent example of an integrable correlated system. For electronic densities n ≠ 1 (and spin densities m ≠ 0) it is an ideal charge (and spin) conductor, with ballistic charge (and spin) transport for T ⩾ 0. In spite of the fact that it is solvable by the Bethe ansatz, at n = 1 (and m = 0) its T > 0 charge (and spin) transport properties are an issue that remains poorly understood. Here we combine this solution with symmetry and the explicit calculation of current-operator matrix elements between energy eigenstates to show that for on-site repulsion U > 0 and at n = 1 the charge stiffness Dη(T) vanishes for T > 0 in the thermodynamic limit. A similar behavior is found by such methods for the spin stiffness Ds(T) for U > 0 and T > 0, which vanishes at m = 0. This absence of finite temperature n = 1 ballistic charge transport and m = 0 ballistic spin transport are exact results that clarify long-standing open problems.
NASA Astrophysics Data System (ADS)
Saha, Srilekha; Maiti, Santanu K.; Karmakar, S. N.
2016-09-01
Electronic behavior of a 1D Aubry chain with Hubbard interaction is critically analyzed in presence of electric field. Multiple energy bands are generated as a result of Hubbard correlation and Aubry potential, and, within these bands localized states are developed under the application of electric field. Within a tight-binding framework we compute electronic transmission probability and average density of states using Green's function approach where the interaction parameter is treated under Hartree-Fock mean field scheme. From our analysis we find that selective transmission can be obtained by tuning injecting electron energy, and thus, the present model can be utilized as a controlled switching device.
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.
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.
NASA Astrophysics Data System (ADS)
Maher Abourabia, Aly; Hassan, Kawsar Mohammad; Abo-Elghar, Eman Mohammad
2015-02-01
We investigate a bio-system composed of a shape memory alloy (SMA) immersed and subjected to heat convection in a blood vessel, affected by heart beats that create a wave motion of long wavelength. The tackled model in (2+1)-D is based on the continuity and momentum equations for the fluid phase, besides; the state of the SMA are described via previous works in the form of statistical distributions of energy for both Martensite and Austenite phases. The solution based on the reductive perturbation technique gives a thermal diffusion-like equation as a key for expressing the temperature and velocity components of the blood. In terms of two cases concerning the difference between the wave numbers in the perpendicular directions, it is found that the system's temperature increases nonlinearly from a minimum initial temperature 293 K (20 °C) up to a maximum value about 316.68 K (43.68 °C), then tends to decrease along the blood flow (anisotropy of K and L) direction. In both cases it is observed that the SMA acquires most of this temperature raising not the blood because of its conventional biological limits (37-40 °C). The range of the heart beats wave numbers characteristic for each person plays an important role in realizing phase changes in the anisotropic case leading to the formation of the hysteresis loops Martensite-Austenite-Martensite or vice versa, according to the energy variation. The entropy generation σ is investigated for the system (Blood + SMA), it predicts that along the flow direction the system gains energy convectively up to a maximum value, then reverses his tendency to gradually loosing energy passing by the equilibrium state, then the system looses energy to the surroundings by the same amount which was gained beforehand. The loss diminishes but stops before arriving to equilibrium again. For certain differences in wave numbers the system starts to store energy again after it passes by the state of equilibrium for the second time. In the
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.
Grant, K.E.; Taylor, K.E.; Ellis, J.S.; Wuebbles, D.J.
1987-07-01
The authors have implemented a series of state of the art radiation transport submodels in previously developed one dimensional and two dimensional chemical transport models of the troposphere and stratosphere. These submodels provide the capability of calculating accurate solar and infrared heating rates. They are a firm basis for further radiation submodel development as well as for studying interactions between radiation and model dynamics under varying conditions of clear sky, clouds, and aerosols. 37 refs., 3 figs.
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
Implicitly causality enforced solution of multidimensional transient photon transport equation.
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
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.
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.
Vorticity Preserving Flux Corrected Transport Scheme for the Acoustic Equations
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.
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.
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.
Advanced Nodal P_{3}/SP_{3} Axial Transport Solvers for the MPACT 2D/1D Scheme
Stimpson, Shane G; Collins, Benjamin S
2015-01-01
As part of its initiative to provide multiphysics simulations of nuclear reactor cores, the Consortium for Advanced Simulation of Light Water Reactors (CASL) is developing the Virtual Environment for Reactor Applications Core Simulator (VERA-CS). The MPACT code, which is the primary neutron transport solver of VERA-CS, employs the two-dimensional/one-dimensional (2D/1D) method to solve 3-dimensional neutron transport problems and provide sub-pin-level resolution of the power distribution. While 2D method of characteristics is used to solve for the transport effects within each plane, 1D-nodal methods are used axially. There have been extensive studies of the 2D/1D method with a variety nodal methods, and the P_{3}/SP_{3} solver has proved to be an effective method of providing higher-fidelity solutions while maintaining a low computational burden.The current implementation in MPACT wraps a one-node nodal expansion method (NEM) kernel for each moment, iterating between them and performing multiple sweeps to resolve flux distributions. However, it has been observed that this approach is more sensitive to convergence problems. This paper documents the theory and application two new nodal P_{3}/SP_{3} approaches to be used within the 2D/1D method in MPACT. These two approaches aim to provide enhanced stability compared with the pre-existing one-node approach. Results from the HY-NEM-SP_{3} solver show that the accuracy is consistent with the one-node formulations and provides improved convergence for some problems; but the solver has issues with cases in thin planes. Although the 2N-SENM-SP_{3} solver is still under development, it is intended to resolve the issues with HY-NEM-SP_{3} but it will incur some additional computational burden by necessitating an additional 1D-CMFD-P_{3} solver to generate the second moment cell-averaged scalar flux.
Technology Transfer Automated Retrieval System (TEKTRAN)
Watershed modeling is a key component of watershed management that involves the simulation of hydrological and fluvial processes for predicting flow and sediment transport within a watershed. For practical purposes, most numerical models have been developed to simulate either runoff and soil erosion...
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.
Transport equations of electrodiffusion processes in the laboratory reference frame.
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
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.
Marin-Valencia, Isaac; Good, Levi B; Ma, Qian; Malloy, Craig R; Pascual, Juan M
2013-01-01
It has been postulated that triheptanoin can ameliorate seizures by supplying the tricarboxylic acid cycle with both acetyl-CoA for energy production and propionyl-CoA to replenish cycle intermediates. These potential effects may also be important in other disorders associated with impaired glucose metabolism because glucose supplies, in addition to acetyl-CoA, pyruvate, which fulfills biosynthetic demands via carboxylation. In patients with glucose transporter type I deficiency (G1D), ketogenic diet fat (a source only of acetyl-CoA) reduces seizures, but other symptoms persist, providing the motivation for studying heptanoate metabolism. In this work, metabolism of infused [5,6,7-13C3]heptanoate was examined in the normal mouse brain and in G1D by 13C-nuclear magnetic resonance spectroscopy, gas chromatography-mass spectrometry (GC-MS), and liquid chromatography-mass spectrometry (LC-MS). In both groups, plasma glucose was enriched in 13C, confirming gluconeogenesis from heptanoate. Acetyl-CoA and glutamine levels became significantly higher in the brain of G1D mice relative to normal mice. In addition, brain glutamine concentration and 13C enrichment were also greater when compared with glutamate in both animal groups, suggesting that heptanoate and/or C5 ketones are primarily metabolized by glia. These results enlighten the mechanism of heptanoate metabolism in the normal and glucose-deficient brain and encourage further studies to elucidate its potential antiepileptic effects in disorders of energy metabolism. PMID:23072752
Marin-Valencia, Isaac; Good, Levi B; Ma, Qian; Malloy, Craig R; Pascual, Juan M
2013-02-01
It has been postulated that triheptanoin can ameliorate seizures by supplying the tricarboxylic acid cycle with both acetyl-CoA for energy production and propionyl-CoA to replenish cycle intermediates. These potential effects may also be important in other disorders associated with impaired glucose metabolism because glucose supplies, in addition to acetyl-CoA, pyruvate, which fulfills biosynthetic demands via carboxylation. In patients with glucose transporter type I deficiency (G1D), ketogenic diet fat (a source only of acetyl-CoA) reduces seizures, but other symptoms persist, providing the motivation for studying heptanoate metabolism. In this work, metabolism of infused [5,6,7-(13)C(3)]heptanoate was examined in the normal mouse brain and in G1D by (13)C-nuclear magnetic resonance spectroscopy, gas chromatography-mass spectrometry (GC-MS), and liquid chromatography-mass spectrometry (LC-MS). In both groups, plasma glucose was enriched in (13)C, confirming gluconeogenesis from heptanoate. Acetyl-CoA and glutamine levels became significantly higher in the brain of G1D mice relative to normal mice. In addition, brain glutamine concentration and (13)C enrichment were also greater when compared with glutamate in both animal groups, suggesting that heptanoate and/or C5 ketones are primarily metabolized by glia. These results enlighten the mechanism of heptanoate metabolism in the normal and glucose-deficient brain and encourage further studies to elucidate its potential antiepileptic effects in disorders of energy metabolism. PMID:23072752
NASA Technical Reports Server (NTRS)
Egan, Michael P.; Leung, Chun Ming; Spagna, George F., Jr.
1988-01-01
The program solves the radiation transport problem in a dusty medium with one-dimensional planar, spherical or cylindrical geometry. It determines self-consistently the effects of multiple scattering, absorption, and re-emission of photons on the temperature of dust grains and the characteristics of the internal radiation field. The program can treat radiation field anisotropy, linear anisotropic scattering, and multi-grain components. The program output consists of the dust-temperature distribution, flux spectrum, surface brightness at each frequency and the observed intensities (involving a convolution with a telescope beam pattern).
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.
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.
NASA Astrophysics Data System (ADS)
Chen, Xuwen; Holmer, Justin
2016-08-01
We consider the dynamics of N bosons in 1D. We assume that the pair interaction is attractive and given by {N^{β-1}V(N^{β}.) where } where {int V ≤slant 0}. We develop new techniques in treating the N-body Hamiltonian so that we overcome the difficulties generated by the attractive interaction and establish new energy estimates. We also prove the optimal 1D collapsing estimate which reduces the regularity requirement in the uniqueness argument by half a derivative. We derive rigorously the 1D focusing cubic NLS with a quadratic trap as the {N → ∞} limit of the N-body dynamic and hence justify the mean-field limit and prove the propagation of chaos for the focusing quantum many-body system.
Transport of Energetic Electrons Produced from Two-Plasmon Decay in the 1-D Hydrodynamic Code LILAC
NASA Astrophysics Data System (ADS)
Delettrez, J. A.; Goncharov, V. N.; Radha, P. B.; Stoeckl, C.; Maximov, A. V.; Sangster, T. C.; Frenje, J. A.; Shvarts, D.
2007-11-01
The effect of two-plasmon-decay electrons on the implosion of cryogenic targets has been the subject of intense scrutiny at the Laboratory for Laser Energetics. Preheat of the fuel caused by these electrons can reduce the maximum areal density attainable at stagnation. The electrons are created at the quarter-critical surface when a threshold depending on laser intensity and local thermal electron scale length is attained. The fraction of laser energy absorbed is a parameter that depends exponentially on the threshold condition and saturates at laser intensities of 10^15 W/cm^2. The source distribution is Maxwellian with a temperature scaling inferred from the measurement of hard x rays. The electrons are transported with a multigroup diffusion model in which the free-streaming electrons are treated by a modified P2 model. Simulation results from warm plastic and cryogenic implosions are compared with the following experimental diagnostics: the hard-x-ray temporal and time-integrated emission, the fast-ion spectrum, and the neutron-averaged areal density at stagnation. This work was supported by the U.S. Department of Energy Office of Inertial Confinement Fusion under Cooperative Agreement DE-FC52-92SF19460.
Transport of Energetic Electrons Produced from Two-Plasmon Decay in the 1-D Hydrodynamic Code LILAC
NASA Astrophysics Data System (ADS)
Delettrez, J. A.; Gocharov, V. N.; Radha, P. B.; Stoeckl, C.; Maximov, A. V.; Sangster, T. C.; Frenje, J. A.; Shvarts, D.
2008-11-01
The effect of two-plasmon-decay electrons on direct-drive cryogenic implosions on the OMEGA laser is modeled. The electrons are created at the quarter-critical surface when a threshold depending on laser intensity and local thermal-electron conditions is attained. The fraction of the absorbed laser energy is a parameter that depends exponentially on the threshold condition and saturates at laser intensities of 10^15 W/cm^2. The source distribution is a Maxwellian with a temperature scaling inferred from hard x-ray measurements. The electrons are transported with a multi-group diffusion model for the low energy electrons and a straight-line model for the high-energy electrons. Simulation results from warm plastic and cryogenic implosions are compared with the following diagnostics: the hard x-ray emission, the fast-ion spectrum, and the neutron-averaged areal density at stagnation. This work was supported by the U.S. Department of Energy Office of Inertial Confinement Fusion under Cooperative Agreement No. DE-FC52-08NA28302.
Variational Phase Imaging Using the Transport-of-Intensity Equation.
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
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.
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.
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.
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.
A simple Boltzmann transport equation for ballistic to diffusive transient heat transport
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.
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.
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.
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.
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
Transport in the spatially tempered, fractional Fokker-Planck equation
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
NASA Astrophysics Data System (ADS)
Delettrez, J. A.; Myatt, J. F.; Yaakobi, B.
2015-11-01
The modeling of the fast-electron transport in the 1-D hydrodynamic code LILAC was modified because of the addition of cross-beam-energy-transfer (CBET) in implosion simulations. Using the old fast-electron with source model CBET results in a shift of the peak of the hard x-ray (HXR) production from the end of the laser pulse, as observed in experiments, to earlier in the pulse. This is caused by a drop in the laser intensity of the quarter-critical surface from CBET interaction at lower densities. Data from simulations with the laser plasma simulation environment (LPSE) code will be used to modify the source algorithm in LILAC. In addition, the transport model in LILAC has been modified to include deviations from the straight-line algorithm and non-specular reflection at the sheath to take into account the scattering from collisions and magnetic fields in the corona. Simulation results will be compared with HXR emissions from both room-temperature plastic and cryogenic target experiments. This material is based upon work supported by the Department of Energy National Nuclear Security Administration under Award Number DE-NA0001944.
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
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.
Karabacak, Yasemin; Sase, Sunetra; Aher, Yogesh D; Sase, Ajinkya; Saroja, Sivaprakasam R; Cicvaric, Ana; Höger, Harald; Berger, Michael; Bakulev, Vasiliy; Sitte, Harald H; Leban, Johann; Monje, Francisco J; Lubec, Gert
2015-01-01
A series of drugs have been reported to increase memory performance modulating the dopaminergic system and herein modafinil was tested for its working memory (WM) enhancing properties. Reuptake inhibition of dopamine, serotonin (SERT) and norepinephrine (NET) by modafinil was tested. Sixty male Sprague-Dawley rats were divided into six groups (modafinil-treated 1-5-10 mg/kg body weight, trained and untrained and vehicle treated trained and untrained rats; daily injected intraperitoneally for a period of 10 days) and tested in a radial arm maze (RAM), a paradigm for testing spatial WM. Hippocampi were taken 6 h following the last day of training and complexes containing the unphosphorylated or phosphorylated dopamine transporter (DAT-CC and pDAT-CC) and complexes containing the D1-3 dopamine receptor subunits (D1-D3-CC) were determined. Modafinil was binding to the DAT but insignificantly to SERT or NET and dopamine reuptake was blocked specifically (IC50 = 11.11 μM; SERT 1547 μM; NET 182 μM). From day 8 (day 9 for 1 mg/kg body weight) modafinil was decreasing WM errors (WMEs) in the RAM significantly and remarkably at all doses tested as compared to the vehicle controls. WMEs were linked to the D2R-CC and the pDAT-CC. pDAT and D1-D3-CC levels were modulated significantly and modafinil was shown to enhance spatial WM in the rat in a well-documented paradigm at all the three doses and dopamine reuptake inhibition with subsequent modulation of D1-3-CC is proposed as a possible mechanism of action. PMID:26347626
A Photon Free Method to Solve Radiation Transport Equations
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.
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.
Moment-based effective transport equations for energy straggling.
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.
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.
Jiang, Shuang; Pang, Liping; Buchan, Graeme D; Simůnek, Jirí; Noonan, Mike J; Close, Murray E
2010-02-01
HYDRUS-1D was used to simulate water flow and leaching of fecal coliforms and bromide (Br) through six undisturbed soil lysimeters (70 cm depth by 50 cm diameter) under field conditions. Dairy shed effluent (DSE) spiked with Br was applied to the lysimeters, which contained fine sandy loam layers. This application was followed by fortnightly spray or flood water irrigation. Soil water contents were measured at four soil depths over 171 days, and leachate was collected from the bottom. The post-DSE period simulations yielded a generally decreased saturated water content compared to the pre-DSE period, and an increased saturated hydraulic conductivity and air-entry index, suggesting that changes in soil hydraulic properties (e.g. via changes in structure) can be induced by irrigation and seasonal effects. The single-porosity flow model was successful in simulating water flow under natural climatic conditions and spray irrigation. However, for lysimeters under flood irrigation, when the effect of preferential flow paths becomes more significant, the good agreement between predicted and observed water contents could only be achieved by using a dual-porosity flow model. Results derived from a mobile-immobile transport model suggest that compared to Br, bacteria were transported through a narrower pore-network with less mass exchange between mobile and immobile water zones. Our study suggests that soils with higher topsoil clay content and soils under flood irrigation are at a high risk of bacteria leaching through preferential flow paths. Irrigation management strategies must minimize the effect of preferential flow to reduce bacterial leaching from land applications of effluent. PMID:19775719
Fevotte, F.; Lathuiliere, B.
2013-07-01
The large increase in computing power over the past few years now makes it possible to consider developing 3D full-core heterogeneous deterministic neutron transport solvers for reference calculations. Among all approaches presented in the literature, the method first introduced in [1] seems very promising. It consists in iterating over resolutions of 2D and ID MOC problems by taking advantage of prismatic geometries without introducing approximations of a low order operator such as diffusion. However, before developing a solver with all industrial options at EDF, several points needed to be clarified. In this work, we first prove the convergence of this iterative process, under some assumptions. We then present our high-performance, parallel implementation of this algorithm in the MICADO solver. Benchmarking the solver against the Takeda case shows that the 2D-1D coupling algorithm does not seem to affect the spatial convergence order of the MOC solver. As for performance issues, our study shows that even though the data distribution is suited to the 2D solver part, the efficiency of the ID part is sufficient to ensure a good parallel efficiency of the global algorithm. After this study, the main remaining difficulty implementation-wise is about the memory requirement of a vector used for initialization. An efficient acceleration operator will also need to be developed. (authors)
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.
NASA Astrophysics Data System (ADS)
Khosravi, M.; Baron, P.; Urban, J.; Froidevaux, L.; Jonsson, A. I.; Kasai, Y.; Kuribayashi, K.; Mitsuda, C.; Murtagh, D. P.; Sagawa, H.; Santee, M. L.; Sato, T. O.; Shiotani, M.; Suzuki, M.; von Clarmann, T.; Walker, K. A.; Wang, S.
2012-08-01
The diurnal variation of HOCl and the related species ClO, HO2 and HCl measured by satellites has been compared with the results of a one-dimensional photochemical model. The study compares the data from various limb-viewing instruments with model simulations from the middle stratosphere to the lower mesosphere. Data from three sub-millimeter instruments and two infrared spectrometers are used, namely from the Sub-Millimeter Radiometer (SMR) on board Odin, the Microwave Limb Sounder (MLS) on board Aura, the Superconducting Submillimeter-wave Limb-Emission Sounder (SMILES) on the International Space Station, the Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) on board ENVISAT, and the Atmospheric Chemistry Experiment Fourier Transform Spectrometer (ACE-FTS) on board SCISAT. Inter-comparison of the measurements from instruments on sun-synchronous satellites (SMR, MLS, MIPAS) and measurements from solar occultation instruments (ACE-FTS) is challenging since the measurements correspond to different solar zenith angles (or local times). However, using a model which covers all solar zenith angles and the new SMILES instrument which measures at all local times over a period of several months provides the possibility to indirectly compare the diurnally variable species. The satellite data were averaged for latitudes of 20° S to 20° N for the SMILES observation period from November 2009 to April 2010 and were compared at three altitudes: 35, 45 and 55 km. This study presents the first evaluation of HO2 Odin/SMR data and also the first comparison of the new SMILES data and the latest version of MLS (version 3.3) with other satellite observations. The MISU-1D model has been run for conditions and locations of the observations. The diurnal cycle features for the species investigated here are generally well reproduced by the model. The satellite observations and the model generally agree well in terms of absolute mixing ratios as well as differences between
Studies of Kink-AntiKink Collisions in 1+1 D in φ^4 and Double Sine Gordon Nonlinear Wave Equations
NASA Astrophysics Data System (ADS)
Fasano, Christopher G.
1996-11-01
The manner in which kink and antikink solutions interact in nonlinear systems is strongly dependent upon the velocities in the collision. In certain velocity regions, the kink and antikink annihilate, while in other regions they bounce off of one another. We present studies of multiple bounce solutions for the collision of kinks and antikinks in a 1 + 1 dimensional φ^4 and Double Sine-Gordon systems. We confirm the existence of a repeated level structure for velocities at which 3, 4, 5, and 6 bounce solutions occur φ^4 as presented by previous authors ( Michael Peyrard and David K. Campbell, Physica 9D) (1983) 33, Peter Anninos, Samuel Oliveira, and Richard A. Matzner, Phys. Rev. D44 (1991) 1147 and we characterize the onset of each multiple bounce solution. The positions of these levels may be described by a simple extension of previous works, and imply that the system follows a specific ``route'' to ``chaotic'' annihilation. An analysis of kink-antinkink collisions in the Double-Sine Gordon equation will also be presented. This analysis reveals both interesting similarities and differences when compared to φ^4
NASA Astrophysics Data System (ADS)
Khosravi, M.; Baron, P.; Urban, J.; Froidevaux, L.; Jonsson, A. I.; Kasai, Y.; Kuribayashi, K.; Mitsuda, C.; Murtagh, D. P.; Sagawa, H.; Santee, M. L.; Sato, T. O.; Shiotani, M.; Suzuki, M.; von Clarmann, T.; Walker, K. A.; Wang, S.
2013-08-01
The diurnal variation of HOCl and the related species ClO, HO2 and HCl measured by satellites has been compared with the results of a one-dimensional photochemical model. The study compares the data from various limb-viewing instruments with model simulations from the middle stratosphere to the lower mesosphere. Data from three sub-millimetre instruments and two infrared spectrometers are used, namely from the Sub-Millimetre Radiometer (SMR) on board Odin, the Microwave Limb Sounder (MLS) on board Aura, the Superconducting Submillimeter-wave Limb-Emission Sounder (SMILES) on the International Space Station, the Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) on board ENVISAT, and the Atmospheric Chemistry Experiment Fourier Transform Spectrometer (ACE-FTS) on board SCISAT. Inter-comparison of the measurements from instruments on sun-synchronous satellites (SMR, MLS, MIPAS) and measurements from solar occultation instruments (ACE-FTS) is challenging since the measurements correspond to different solar zenith angles (or local times). However, using a model which covers all solar zenith angles and data from the SMILES instrument which measured at all local times over a period of several months provides the possibility to verify the model and to indirectly compare the diurnally variable species. The satellite data were averaged for latitudes of 20° S to 20° N for the SMILES observation period from November 2009 to April 2010 and were compared at three altitudes: 35, 45 and 55 km. Besides presenting the SMILES data, the study also shows a first comparison of the latest MLS data (version 3.3) of HOCl, ClO, and HO2 with other satellite observations, as well as a first evaluation of HO2 observations made by Odin/SMR. The MISU-1D model has been carefully initialised and run for conditions and locations of the observations. The diurnal cycle features for the species investigated here are generally well reproduced by the model. The satellite observations
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.
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.
NASA Astrophysics Data System (ADS)
Mogensen, Ditte; Aaltonen, Hermanni; Aalto, Juho; Bäck, Jaana; Kieloaho, Antti-Jussi; Gierens, Rosa; Smolander, Sampo; Kulmala, Markku; Boy, Michael
2015-04-01
Volatile organic compounds (VOCs) are emitted from the biosphere and can work as precursor gases for aerosol particles that can affect the climate (e.g. Makkonen et al., ACP, 2012). VOC emissions from needles and leaves have gained the most attention, however other parts of the ecosystem also have the ability to emit a vast amount of VOCs. This, often neglected, source can be important e.g. at periods where leaves are absent. Both sources and drivers related to forest floor emission of VOCs are currently limited. It is thought that the sources are mainly due to degradation of organic matter (Isidorov and Jdanova, Chemosphere, 2002), living roots (Asensio et al., Soil Biol. Biochem., 2008) and ground vegetation. The drivers are biotic (e.g. microbes) and abiotic (e.g. temperature and moisture). However, the relative importance of the sources and the drivers individually are currently poorly understood. Further, the relative importance of these factors is highly dependent on the tree species occupying the area of interest. The emission of isoprene and monoterpenes where measured from the boreal forest floor at the SMEAR II station in Southern Finland (Hari and Kulmala, Boreal Env. Res., 2005) during the snow-free period in 2010-2012. We used a dynamic method with 3 automated chambers analyzed by Proton Transfer Reaction - Mass Spectrometer (Aaltonen et al., Plant Soil, 2013). Using this data, we have developed empirical parameterizations for the emission of isoprene and monoterpenes from the forest floor. These parameterizations depends on abiotic factors, however, since the parameterizations are based on field measurements, biotic features are captured. Further, we have used the 1D chemistry-transport model SOSAA (Boy et al., ACP, 2011) to test the seasonal relative importance of inclusion of these parameterizations of the forest floor compared to the canopy crown emissions, on the atmospheric reactivity throughout the canopy.
NASA Astrophysics Data System (ADS)
Irvine, Dylan J.; Cartwright, Ian; Post, Vincent E. A.; Simmons, Craig T.; Banks, Eddie W.
2016-02-01
Steady state 1-D analytical solutions to estimate groundwater fluxes from temperature profiles are an attractive option because they are simple to apply, with no complex boundary or initial conditions. Steady state solutions have been applied to estimate both aquifer scale fluxes as well as to estimate groundwater discharge to streams. This study explores the sources of uncertainty in flux estimates from regional scale aquifers caused by sensor precision, aquifer heterogeneity, multidimensional flow and variations in surface temperature due to climate change. Synthetic temperature profiles were generated using 2-D groundwater flow and heat transport models with homogeneous and heterogeneous hydraulic and thermal properties. Temperature profiles were analyzed assuming temperature can be determined with a precision between 0.1°C and 0.001°C. Analysis of synthetic temperature profiles show that the Bredehoeft and Papadopulos (1965) method can provide good estimates of the mean vertical Darcy flux over the length of the temperature profile. Reliable flux estimates were obtained when the ratio of vertical to horizontal flux was as low as 0.1, and in heterogeneous media, providing that temperature at the upper boundary was constant in time. However, temporal increases in surface temperature led to over-estimation of fluxes. Overestimates increased with time since the onset of, and with the rate of surface warming. Overall, the Bredehoeft and Papadopulos (1965) method may be more robust for the conditions with constant temperature distributions than previously thought, but that transient methods that account for surface warming should be used to determine fluxes in shallow aquifers.
NASA Astrophysics Data System (ADS)
Driba, D. L.; De Lucia, M.; Peiffer, S.
2014-12-01
Fluid-rock interactions in geothermal reservoirs are driven by the state of disequilibrium that persists among solid and solutes due to changing temperature and pressure. During operation of enhanced geothermal systems, injection of cooled water back into the reservoir disturbs the initial thermodynamic equilibrium between the reservoir and its geothermal fluid, which may induce modifications in permeability through changes in porosity and pore space geometry, consequently bringing about several impairments to the overall system.Modeling of fluid-rock interactions induced by injection of cold brine into Groß Schönebeck geothermal reservoir system situated in the Rotliegend sandstone at 4200m depth have been done by coupling geochemical modeling Code Phreeqc with OpenGeoSys. Through batch modeling the re-evaluation of the measured hydrochemical composition of the brine has been done using Quintessa databases, the results from the calculation indicate that a mineral phases comprising of K-feldspar, hematite, Barite, Calcite and Dolomite was found to match the hypothesis of equilibrium with the formation fluid, Reducing conditions are presumed in the model (pe = -3.5) in order to match the amount of observed dissolved Fe and thus considered as initial state for the reactive transport modeling. based on a measured composition of formation fluids and the predominant mineralogical assemblage of the host rock, a preliminary 1D Reactive transport modeling (RTM) was run with total time set to 30 years; results obtained for the initial simulation revealed that during this period, no significant change is evident for K-feldspar. Furthermore, the precipitation of calcite along the flow path in the brine results in a drop of pH from 6.2 to a value of 5.2 noticed over the simulated period. The circulation of cooled fluid in the reservoir is predicted to affect the temperature of the reservoir within the first 100 -150m from the injection well. Examination of porosity change in
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.
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.
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.
Pascual, Juan M.; Liu, Peiying; Mao, Deng; Kelly, Dorothy; Hernandez, Ana; Sheng, Min; Good, Levi B.; Ma, Qian; Marin-Valencia, Isaac; Zhang, Xuchen; Park, Jason Y.; Hynan, Linda S.; Stavinoha, Peter; Roe, Charles R.; Lu, Hanzhang
2015-01-01
Objective G1D is commonly associated with electrographic spike-wave and - less-noticeably – with absence seizures. The G1D syndrome has long been attributed to energy (i.e., ATP-synthetic) failure, as have experimental, toxic-rodent epilepsies to impaired brain metabolism and tricarboxylic acid (TCA) cycle intermediate depletion. Indeed, a (seldom-acknowledged) function of glucose and other substrates is the generation of brain TCAs via carbon-donor reactions collectively named anaplerosis. However, TCAs are preserved in murine G1D. This renders inferences about energy failure premature and suggests a different hypothesis, also grounded on our findings, that consumption of alternate TCA precursors is stimulated, potentially detracting from other functions. Second, common ketogenic diets can ameliorate G1D seizures, but lead to a therapeutically-counterintuitive reduction in blood glucose available to the brain, and they can prove ineffective in 1/3 of cases. While developing G1D treatments, all of this motivated us to: a) uphold (rather than attenuate) the residual brain glucose flux that all G1D patients possess; and b) stimulate the TCA cycle, including anaplerosis. Therefore, we tested the medium-chain triglyceride triheptanoin, a widely-used medical food supplement that can fulfill both of these metabolic roles. The rationale is that ketone bodies derived from ketogenic diets are not anaplerotic, in contrast with triheptanoin metabolites, as we have shown in the G1D mouse brain. Design We supplemented the regular diet of a case series of G1D patients with food-grade triheptanoin. First we confirmed that, despite their frequent electroencephalographic (EEG) presence as spike-waves, most seizures are rarely visible, such that perceptions by patients or others are inadequate for treatment evaluation. Thus, we used EEG, quantitative neuropsychological, blood analytical, and MRI cerebral metabolic rate measurements as main outcomes. Setting Academic and
Solving parallel transport equations in the higher-dimensional Kerr-NUT-(A)dS spacetimes
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.
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.
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.
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...
PC-1D installation manual and user's guide
Basore, P.A.
1991-05-01
PC-1D is a software package for personal computers that uses finite-element analysis to solve the fully-coupled two-carrier semiconductor transport equations in one dimension. This program is particularly useful for analyzing the performance of optoelectronic devices such as solar cells, but can be applied to any bipolar device whose carrier flows are primarily one-dimensional. This User's Guide provides the information necessary to install PC-1D, define a problem for solution, solve the problem, and examine the results. Example problems are presented which illustrate these steps. The physical models and numerical methods utilized are presented in detail. This document supports version 3.1 of PC-1D, which incorporates faster numerical algorithms with better convergence properties than previous versions of the program. 51 refs., 17 figs., 5 tabs.
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.
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).
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.
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)
A two-equation integral model for particle transport in renewal statistical media
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.
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.
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...
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...
Conservative differencing of the electron Fokker-Planck transport equation
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.
NASA Astrophysics Data System (ADS)
Mello, Pier A.; Shi, Zhou; Genack, Azriel Z.
2016-08-01
We study the average energy - or particle - density of waves inside disordered 1D multiply-scattering media. We extend the transfer-matrix technique that was used in the past for the calculation of the intensity beyond the sample to study the intensity in the interior of the sample by considering the transfer matrices of the two segments that form the entire waveguide. The statistical properties of the two disordered segments are found using a maximum-entropy ansatz subject to appropriate constraints. The theoretical expressions are shown to be in excellent agreement with 1D transfer-matrix simulations.
A massively parallel semi-Lagrangian algorithm for solving the transport equation
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.
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.
Least-squares finite element discretizations of neutron transport equations in 3 dimensions
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.
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.
Explicit solutions of the radiative transport equation in the P{sub 3} approximation
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.
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.
Generalized parallel heat transport equations in collisional to weakly collisional plasmas
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.
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
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.
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.
Solution and Study of the Two-Dimensional Nodal Neutron Transport Equation
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)
One-dimensional transport equation models for sound energy propagation in long spaces: theory.
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
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.
A grain scale non-equilibrium sediment transport model for unsteady flow
Technology Transfer Automated Retrieval System (TEKTRAN)
A one dimensional (1-D) finite-volume model was developed for simulating non-equilibrium sediment transport in unsteady flow. The governing equations are the 1-D St. Venant equations for sediment-laden flow and the Exner equation including both bed load and suspended-load transport. The Rouse profil...
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.
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
Variance estimates for transport in stochastic media by means of the master equation
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)
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.
Solving the transport equation with quadratic finite elements: Theory and applications
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.
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.
Equations of state and transport properties of mixtures in the warm dense regime
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.
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.
Un-collided-flux preconditioning for the first order transport equation
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)
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.
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.
Exactly averaged stochastic equations for flow and transport in random media
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
Development of a hybrid deterministic/stochastic method for 1D nuclear reactor kinetics
NASA Astrophysics Data System (ADS)
Terlizzi, Stefano; Rahnema, Farzad; Zhang, Dingkang; Dulla, Sandra; Ravetto, Piero
2015-12-01
A new method has been implemented for solving the time-dependent neutron transport equation efficiently and accurately. This is accomplished by coupling the hybrid stochastic-deterministic steady-state coarse-mesh radiation transport (COMET) method [1,2] with the new predictor-corrector quasi-static method (PCQM) developed at Politecnico di Torino [3]. In this paper, the coupled method is implemented and tested in 1D slab geometry.
Development of a hybrid deterministic/stochastic method for 1D nuclear reactor kinetics
Terlizzi, Stefano; Dulla, Sandra; Ravetto, Piero; Rahnema, Farzad; Zhang, Dingkang
2015-12-31
A new method has been implemented for solving the time-dependent neutron transport equation efficiently and accurately. This is accomplished by coupling the hybrid stochastic-deterministic steady-state coarse-mesh radiation transport (COMET) method [1,2] with the new predictor-corrector quasi-static method (PCQM) developed at Politecnico di Torino [3]. In this paper, the coupled method is implemented and tested in 1D slab geometry.
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...
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...
Parallel algorithms for 2-D cylindrical transport equations of Eigenvalue problem
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)
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.
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...
Coupling lattice Boltzmann and continuum equations for flow and reactive transport in porous media.
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.
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.
Exact PDF equations and closure approximations for advective-reactive transport
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.
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.
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.
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.
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⊥L^{2}_{∥}/X1L^{2}_{⊥} → 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.
Deterministic proton transport solving a one dimensional Fokker-Planck equation
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.
Self-Adjoint Angular Flux Equation for Coupled Electron-Photon Transport
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.
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.
Averaging of Stochastic Equations for Flow and Transport in PorousMedia
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.
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.
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.
Saroja, Sivaprakasam R; Aher, Yogesh D; Kalaba, Predrag; Aher, Nilima Y; Zehl, Martin; Korz, Volker; Subramaniyan, Saraswathi; Miklosi, Andras G; Zanon, Lisa; Neuhaus, Winfried; Höger, Harald; Langer, Thierry; Urban, Ernst; Leban, Johann; Lubec, Gert
2016-10-01
A series of compounds targeting the dopamine transporter (DAT) haS been shown to improve memory performance most probably by re-uptake inhibition. Although specific DAT inhibitors are available, there is limited information about specificity, mechanism and in particular the effect on dopamine receptors. It was therefore the aim of the study to test the DAT inhibitor 4-(diphenyl-methanesulfinylmethyl)-2-methyl-thiazole (code: CE-111), synthetized in our laboratory for the specificity to target DAT, for the effects upon spatial memory and for induced dopamine receptor modulation. Re-uptake inhibition was tested for DAT (IC50=3.2μM), serotonin transporter, SERT (IC50=272291μM) and noradrenaline transporter, NET (IC50=174μM). Spatial memory was studied in the radial arm maze (RAM) in male Sprague-Dawley rats that were intraperitoneally injected with CE-111 (1 or 10mg/kg body weight). Performance in the RAM was improved using 1 and 10mg/kg body weight of CE-111. Training and treatment effects on presynaptic, postsynaptic and extrasynaptic D1 and D2- receptors and dopamine receptor containing complexes as well as on activated DAT were observed. CE-111 was crossing the blood-brain barrier comparable to modafinil and was identified as effective to improve memory performance in the RAM. Dopamine re-uptake inhibition along with modulations in dopamine receptors are proposed as potential underlying mechanisms. PMID:27288589
Boeuf, J. P.; Chaudhury, B.; Garrigues, L.
2012-11-15
Magnetic filters are used in negative ion sources for neutral beam injection in fusion devices to reduce the electron temperature in the extraction region in order to limit negative ion destruction by fast electrons. The drop in electron temperature through the filter is due to the enhanced residence time and collisional energy losses of electrons trapped in the magnetic field. The mechanisms controlling particle and energy transport through the magnetic filter in negative ion sources of the ITER type are still not clear and the aim of this paper is to clarify and quantify these mechanisms. A particle-in-cell Monte Carlo simulation is used to revisit and analyze the role and operation of the magnetic filter in an 'ideal' one-dimensional configuration and to study the stability of the one-dimensional solution in a two-dimensional configuration with periodic boundary conditions. The roles of collisions and instabilities on electron transport through the filter are discussed. The influence of a more realistic geometry on electron transport through the filter is analyzed in the companion paper [Boeuf et al., Phys. Plasmas 19, 113510 (2012)].
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.
Petrov-galerkin finite element method for solving the neutron transport equation
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.
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. ...
Yu, Shi; Pratelli, Réjane; Denbow, Cynthia; Pilot, Guillaume
2015-01-01
Intracellular amino acid transport across plant membranes is critical for metabolic pathways which are often split between different organelles. In addition, transport of amino acids across the plasma membrane enables the distribution of organic nitrogen through the saps between leaves and developing organs. Amino acid importers have been studied for more than two decades, and their role in this process is well-documented. While equally important, amino acid exporters are not well-characterized. The over-expression of GDU1, encoding a small membrane protein with one transmembrane domain, leads to enhancement of amino acid export by Arabidopsis cells, glutamine secretion at the leaf margin, early senescence and size reduction of the plant, possibly caused by the stimulation of amino acid exporter(s). Previous work reported the identification of suppressor mutations of the GDU1 over-expression phenotype, which affected the GDU1 and LOG2 genes, the latter encoding a membrane-bound ubiquitin ligase interacting with GDU1. The present study focuses on the characterization of three additional suppressor mutations affecting GDU1. Size, phenotype, glutamine transport and amino acid tolerance were recorded for recapitulation plants and over-expressors of mutagenized GDU1 proteins. Unexpectedly, the over-expression of most mutated GDU1 led to plants with enhanced amino acid export, but failing to display secretion of glutamine and size reduction. The results show that the various effects triggered by GDU1 over-expression can be dissociated from one another by mutagenizing specific residues. The fact that these residues are not necessarily conserved suggests that the diverse biochemical properties of the GDU1 protein are not only born by the characterized transmembrane and VIMAG domains. These data provide a better understanding of the structure/function relationships of GDU1 and may enable modifying amino acid export in plants without detrimental effects on plant fitness
Sase, Ajinkya; Aher, Yogesh D; Saroja, Sivaprakasam R; Ganesan, Minu Karthika; Sase, Sunetra; Holy, Marion; Höger, Harald; Bakulev, Vasiliy; Ecker, Gerhard F; Langer, Thierry; Sitte, Harald H; Leban, Johann; Lubec, Gert
2016-03-01
A series of compounds have been reported to enhance memory via the DA system and herein a heterocyclic compound was tested for working memory (WM) enhancement. 2-((benzhydrylsulfinyl)methyl)thiazole (CE-103) was synthesized in a six-step synthesis. Binding of CE-103 to the dopamine (DAT), serotonin (SERT) and norepinephrine (NET) transporters and dopamine reuptake inhibition was tested as well as blood brain permeation and a screen for GPCR targets. 60 male Sprague Dawley rats were divided into six groups: CE-103 treated 1-10 mg/kg body weight, trained (TDI) and yoked (YDI) and vehicle treated, trained (TVI) and yoked (YVI) rats. Daily single intraperitoneal injections for a period of 10 days were administered and rats were tested in a radial arm maze (RAM). Hippocampi were taken 6 h following the last day of training and complexes containing the unphosphorylated or phosphorylated dopamine transporter (DAT) and complexes containing the D1-3 dopamine receptor subunits were determined. CE-103 was binding to the DAT but insignificantly to SERT or NET and dopamine reuptake was blocked specifically (IC50 = 14.73 μM). From day eight the compound was decreasing WM errors in the RAM significantly at both doses tested as compared to the vehicle controls. In the trained CE-103-treated group levels of the complex containing the phosphorylated dopamine transporter (pDAT) as well as D1R were decreased while levels of complexes containing D2R and D3R were significantly increased. CE-103 was shown to enhance spatial WM and DA reuptake inhibition with subsequent modulation of D1-3 receptors is proposed as a possible mechanism of action. PMID:26407764
Electron and ion transport equations in computational weakly-ionized plasmadynamics
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.
TRANSPORT EQUATION FOR MHD TURBULENCE: APPLICATION TO PARTICLE ACCELERATION AT INTERPLANETARY SHOCKS
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)
NASA Astrophysics Data System (ADS)
Mkhitaryan, Vagharsh; Dobrovitski, Viatcheslav; 0 Team
2015-03-01
The hyperfine coupling of a carrier spin to a nuclear spin bath is a predominant channel for the carrier spin relaxation in organic semiconductors. We investigate the hyperfine-induced spin relaxation of a carrier performing a random walk on a d-dimensional regular lattice theoretically, in a transport regime typical for organic semiconductors. We show that in d = 1 and d = 2 the time dependence of spin polarization, P (t) , is dominated by a superexponential decay, crossing over to an exponential tail at long times. The faster decay is attributed to multiple self-intersections (returns) of the random walk trajectories, which occur more often in lower dimensions. We also show, analytically and numerically, that the returns lead to sensitivity of P (t) to external electric and magnetic fields, and this sensitivity strongly depends on dimensionality of the system (d = 1 vs. d = 3). Furthermore, we consider the coordinate dependence of spin polarization, σ (r) , in a hypothetic lateral or vertical organic spin-valve device. We demonstrate that, while σ (r) is essentially exponential, the effect of multiple self-intersections can be identified in transport measurements from the specific field-dependence of spin relaxation length. This work was supported by the Department of Energy-Basic Energy Sciences under Contract No. DE-AC02-07CH11358.
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.
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.
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.
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.
Transport in simple networks described by an integrable discrete nonlinear Schrödinger equation.
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
Derivation of the macroscopic solute transport equation for homogeneous, saturated, porous media
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.
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
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