Extended thermodynamics tested beyond the linear regime: The case of electron transport in silicon semiconductors

Anile, A. M.; Muscato, Orazio

doi:10.1007/bf01181851

Cited by 25 publications

(23 citation statements)

References 16 publications

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“…Hypotheses in the unbounded case. H-1) The cross section is in W 2;1 (IR 2d ), symmetric (k; k 0 ) = (k 0 ; k) and 0 (k; k 0 ) 1 (2) for some positive constants 0 and 1 . Under these hypotheses, it is known 11] and 12] that there exists a unique classical solution f " of (1) on any time interval 0; T] and which satis es…”

Section: Hypotheses and Formal Resultsmentioning

confidence: 99%

The High Field Asymptotics for Degenerate Semiconductors

Abdallah

Chaker

2001

Math. Models Methods Appl. Sci.

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Section: Hypotheses and Formal Resultsmentioning

confidence: 99%

The High Field Asymptotics for Degenerate Semiconductors

Abdallah

Chaker

2001

Math. Models Methods Appl. Sci.

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“…It follows that f satisfies ot Interacting particles: case of a smooth potential (3) To treat the case of interacting particles , we now need to distinguish between smooth potentials and discontinuous potentials. We first treat the case of smooth potentials.…”

Section: Non-interacting Particlesmentioning

confidence: 99%

“…(4) The term Fmf(x, t) is called the mean-field force and n(x , t) is the local particle density at point x , i.e., n(x, t) dx is the number of particles contained in the volume dx of position space. Then, one can use F mf as if it werean externalforce in the free-transport equation (3). This leads to the so-calledVlasov mean-field equation…”

Section: Non-interacting Particlesmentioning

confidence: 99%

“…It contains third-order derivatives (which lead to dispersive type terms) and, for that reason, the model is generally ill posed. The model with 0(e 3 ) terms is called the super-Burnett model. Like the Burnett model it is ill posed.…”

Section: (Nta(u)u + (5j2)nt'v X T)mentioning

confidence: 99%

“…It has been used in practice in several physical contexts (e.g., in semiconductor modelling [2), [3) and for radiative transfer problems [59]). However, it also requires us to solve a number of difficult questions raised in particular by M. Junk [89].…”

Section: Pdegondmentioning

confidence: 99%

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Macroscopic limits of the Boltzmann equation: a review

Degond

2004

Modeling and Simulation in Science, Engineering and Technology

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This document is concerned with the modeling of particle systems via kinetic equations . First , the hierarchy of available models for particle systems is reviewed, from particle dynamics to fluid models through kinetic equations. In particular the derivation of the gas dynamics Boltzmann equation is recalled and a few companion models are discussed. Then, the basic propert ies of kinetic models and particularly of the Boltzmann colli sion operator are reviewed. The core of this work is the derivation of macroscopic models (as e.g. , the Euler or Navier-Stokes equations) from the Boltzmann equation by means of the Hilbert and Chapman-Enskog methods . This matter is first discussed in the context of the BGK equation, which is a simpler model than the full Boltzmann equat ion. The extens ion to the Boltzmann equation is summarized at the end of this discussion . Finally, a certain number of current research directions are reviewed. Our goal is to give a synthetic descript ion of this subject , so as to allow the reader to acquire a rapid knowledge of the basic aspects of kinetic theory. The reader is referred to the bibliography for more details on the various items which are reviewed here . P. Degond et al. (eds.), Modeling and Computational Methods for Kinetic Equations © Springer Science+Business Media New York 2004 r S r 'This is a model for the interaction force between molecules in a usual gas. Sometimes, one considers a more realistic interaction force in the form of a combination of power laws (e.g., a Lennard-Jones potential, [80], Appendix IV).One important feature of Newton's equations of motion for N-particle dynamics is their time reversibility : Consider the evolution of the system from t = 0 to t = T.This takes the initial datum (Xi(O), Vi(0» to (xi(T) , vi(T». Suppose that at time T, one reverses the velocities: Vi(T) -7 -Vi (T). Then one evolves the system again according to Newton's equations of motion up to t = 2T. The state of the system at time t = 2T is given by (Xi(O), -Vi(O», i.e., the system is back to its original state, but for a reversal of the velocities .

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An extended hydrodynamic model for silicon semiconductor devices

Muscato¹

1997

Progress in Industrial Mathematics at ECMI 96

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Extended thermodynamics tested beyond the linear regime: The case of electron transport in silicon semiconductors

Cited by 25 publications

References 16 publications

The High Field Asymptotics for Degenerate Semiconductors

The High Field Asymptotics for Degenerate Semiconductors

Macroscopic limits of the Boltzmann equation: a review

An extended hydrodynamic model for silicon semiconductor devices

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