Solution of the multivalley Boltzmann transport equations in Si and GaAs based on the time scales of hydrodynamic equations

1995 ◽  
Vol 78 (7) ◽  
pp. 4490-4504 ◽  
Author(s):  
Ming‐C. Cheng ◽  
Rambabu Chennupati ◽  
Ying Wen
Keyword(s):  
Time Scales ◽  
Transport Equations ◽  
Hydrodynamic Equations ◽  
Boltzmann Transport

A descriptive model of thermoelectric transport in a resonant system of PbSe doped with Tl

2019 ◽  
Vol 7 (20) ◽  
pp. 12859-12868 ◽  
Author(s):  
Zhenyu Pan ◽  
Heng Wang
Keyword(s):  
Transport Properties ◽  
Transport Equations ◽  
Boltzmann Transport ◽  
Resonant System ◽  
Descriptive Model ◽  
Thermoelectric Transport

Transport properties in resonant system PbSe:Tl are now quantitatively explained with Boltzmann transport equations.

scholarly journals Equations of state for ions in non-LTE plasmas

1992 ◽  
Vol 10 (3) ◽  
pp. 495-504 ◽  
Author(s):  
S. Eliezer ◽  
E. Mínguez
Keyword(s):  
Equations Of State ◽  
Planck Equation ◽  
Transport Equations ◽  
Rate Equations ◽  
Hydrodynamic Equations ◽  
Ion Density ◽  
Stochastic Force ◽  
General Transport ◽  
Explicit Rate ◽  
Fokker Planck

For nonlocal thermodynamic equilibrium (LTE), the equations of state are not well defined and therefore the hydrodynamic equations are not applicable. In this case, the general transport equations (e.g., Boltzmann or Fokker–Planck) should be used. However, the coupling between atomic physics (rate equations) and the transport equations is extremely complicated. This article shows how the information given by the rate equations is translated into an effective potential. This “potential” theory is explicitly shown for two cases: lithium-like iron plasmas and aluminum plasmas. Moreover, it is suggested that the “collision terms,” and all other interactions that are not taken into account by the explicit rate equations, are described by a stochastic force given by a Langevin equation or equivalently by a Fokker-Planck equation in the ion density space.

Modeling Of Turbulent Transport Equations

1996 ◽  
Author(s):  
Charles G. Speziale
Keyword(s):  
Turbulent Flows ◽  
Reynolds Stress ◽  
Time Scales ◽  
Eddy Viscosity ◽  
Ad Hoc ◽  
Stokes Equations ◽  
Transport Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Stress Models

The high-Reynolds-number turbulent flows of technological importance contain such a wide range of excited length and time scales that the application of direct or large-eddy simulations is all but impossible for the foreseeable future. Reynolds stress models remain the only viable means for the solution of these complex turbulent flows. It is widely believed that Reynolds stress models are completely ad hoc, having no formal connection with solutions of the full Navier-Stokes equations for turbulent flows. While this belief is largely warranted for the older eddy viscosity models of turbulence, it constitutes a far too pessimistic assessment of the current generation of Reynolds stress closures. It will be shown how secondorder closure models and two-equation models with an anisotropic eddy viscosity can be systematically derived from the Navier-Stokes equations when one overriding assumption is made: the turbulence is locally homogeneous and in equilibrium. A brief review of zero equation models and one equation models based on the Boussinesq eddy viscosity hypothesis will first be provided in order to gain a perspective on the earlier approaches to Reynolds stress modeling. It will, however, be argued that since turbulent flows contain length and time scales that change dramatically from one flow configuration to the next, two-equation models constitute the minimum level of closure that is physically acceptable. Typically, modeled transport equations are solved for the turbulent kinetic energy and dissipation rate from which the turbulent length and time scales are built up; this obviates the need to specify these scales in an ad hoc fashion. While two-equation models represent the minimum acceptable closure, second-order closure models constitute the most complex level of closure that is currently feasible from a computational standpoint. It will be shown how the former models follow from the latter in the equilibrium limit of homogeneous turbulence. However, the two-equation models that are formally consistent with second-order closures have an anisotropic eddy viscosity with strain-dependent coefficients - a feature that most of the commonly used models do not possess.

scholarly journals On Electro- and Thermomigration and Thermoelectric Transport Coefficients in Metals

1982 ◽  
Vol 37 (12) ◽  
pp. 1327-1332
Author(s):  
H.-J. Bohn ◽  
G. Simon
Keyword(s):  
Effective Charge ◽  
Transport Coefficients ◽  
Cross Coupling ◽  
Transport Equations ◽  
Wave Number ◽  
Boltzmann Transport ◽  
Thermoelectric Transport ◽  
Coupling Terms ◽  
The Cross ◽  
Set Up

AbstractThe system of coupled Boltzmann transport equations for electrons, phonons and impurities in metals is set up and solved with special interest for the effect of the cross-coupling terms. General expressions for the effective charge in electromigration and heat of transport in thermomigration are given. The cross-coupling terms in the transport equations lead to a number of corrections in the thermoelectric transport coefficients. Noteworthy is the result that the resistance by impurities depends now on the temperature. The investigation is restricted to high temperatures, isotropic dependence of the energies of electrons and phonons on wave number vector, and to normal scattering processes of phonons.

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