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  • 1
    Electronic Resource
    Electronic Resource
    Mathematical models of magnetic insulation (1998)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 5 (1998), S. 1522-1534 
    Details
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The problem of magnetic insulation in a plane diode is discussed. Starting from the Child–Langmuir asymptotics of the stationary Vlasov–Maxwell system, various limit problems are exhibited and solved. Explicit formulas for the magnetic field at the cathode and for the electron sheath width are provided. The analysis allows one to recover and to complete the various known results related to magnetic insulation. In addition, an ensemble of intermediate models ranging from the quasilaminar to the laminar model, and involving the formation of virtual cathodes, is exhibited. A stability analysis is then performed to determine which of these models are stable. The virtual cathode models are shown to be unstable under dissipation effects, and most of them are shown to be unstable under geometry effects (i.e., when replacing the planar geometry by the cylindrical one). The stability argument shows that in some situations, the laminar model is unstable while in other situations the quasilaminar one is unstable. This gives some indication for the choice of the appropriate magnetic insulation model. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.872810
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  • 2
    Electronic Resource
    Electronic Resource
    Existence of Solutions of a Kinetic Equation Modeling Cometary Flows (1999)
    Springer
    Journal of statistical physics 96 (1999), S. 361-376 
    Details
    ISSN: 1572-9613
    Keywords: kinetic equation ; wave–particle collision operator ; cometary flows ; cosmic rays ; quasilinear plasma theory ; approximate solution ; dispersive lemma
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A global existence theorem is presented for a kinetic problem of the form ∂ t f+v·∇ x f=Q(f), f(t=0)=f 0, where Q(f) is a simplified model wave–particle collision operator extracted from quasilinear plasma physics. Evaluation of Q(f) requires the computation of the mean velocity of the distribution f. Therefore, the assumptions on the data are such that vacuum regions, where the mean velocity is not well defined, are excluded. Also the initial data are assumed to have bounded total energy. As additional results conservation laws for mass, momentum, and energy are derived, as well as an entropy dissipation law and the propagation of higher order moments.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004584719071
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  • 3
    Electronic Resource
    Electronic Resource
    An entropy scheme for the Fokker-Planck collision operator of plasma kinetic theory (1994)
    Springer
    Numerische Mathematik 68 (1994), S. 239-262 
    Details
    ISSN: 0945-3245
    Keywords: Mathematics Subject Classification (1991): 65M06, 82C40, 82C80, 82D10
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary. We propose a finite difference scheme to approximate the Fokker-Planck collision operator in 3 velocity dimensions. The principal feature of this scheme is to provide a decay of the numerical entropy. As a consequence, it preserves the collisional invariants and its stationary solutions are the discrete Maxwellians. We consider both the whole velocity-space problem and the bounded velocity problem. In the latter case, we provide artificial boundary conditions which preserve the decay of the entropy.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002110050059
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  • 4
    Electronic Resource
    Electronic Resource
    A mathematical analysis of quantum transport in three-dimensional crystals (1991)
    Springer
    Annali di matematica pura ed applicata 160 (1991), S. 171-191 
    Details
    ISSN: 1618-1891
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We present an existence and uniqueness result for a quantum transport model in three dimensional crystals. The model consists of a quantum transport (Wigner) equation posed on the phase space consisting of a discrete position variable and a «continuous» wave vector, which is restricted to a bounded domain inR 3 (first Brillouin zone of the crystal). The potential is modeled self-consistently by a discrete Poisson equation (Coulomb interaction). Also we investigate the limits of solutions of this model as the grid spacing tends to zero and show that they converge to the solution of a quantum transport model posed on the «fully continuous» phase space. The transport model derived by this limiting procedure treats the band diagram of the crystal in a semi-classical way and the potential energy term quantum mechanically.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01764126
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  • 5
    Electronic Resource
    Electronic Resource
    A steady state potential flow model for semiconductors (1993)
    Springer
    Annali di matematica pura ed applicata 165 (1993), S. 87-98 
    Details
    ISSN: 1618-1891
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We present a three-dimensional steady state irrotational flow model for semiconductors which is based on the hydrodynamic equations. We prove existence and local uniqueness of smooth solutions under a smallness assumptions on the data. This assumption implies subsonic flow of electrons in the semiconductors device.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01765842
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  • 6
    Electronic Resource
    Electronic Resource
    On a mathematical model for hot carrier injection in semiconductors (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 1193-1212 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study a collisionless transport model for electrons in a semiconductor, and we perform an asymptotic analysis for low temperatures or large applied biases. We derive analytic relations for the built-in potential and for the current which flows through the structure.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670171503
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  • 7
    Electronic Resource
    Electronic Resource
    A steady-state system in non-equilibrium thermodynamics including thermal and electrical effects (1998)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 1399-1413 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The steady-state equations for a charged gas or fluid consisting of several components, exposed to an electric field, are considered. These equations form a system of strongly coupled, quasilinear elliptic equations which in some situations can be derived from the Boltzmann equation. The model uses the duality between the thermodynamic fluxes and the thermodynamic forces. Physically motivated mixed Dirichlet-Neumann boundary conditions are prescribed. The existence of generalized solutions is proven. The key of the proof is a transformation of the problem by using the entropic variables, or electro-chemical potentials, which symmetrize the equations. The uniqueness of weak solutions is shown under the assumption that the boundary data are not far from the thermal equilibrium. A general uniqueness result cannot be expected for physical reasons. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
    Type of Medium: Electronic Resource
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