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  • 1
    Electronic Resource
    Electronic Resource
    Erratum: "The Riemann–Hilbert problem for nonsymmetric systems'' [J. Math. Phys. 32, 3540 (1991)] (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1566-1566 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529982
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  • 2
    Electronic Resource
    Electronic Resource
    The Riemann–Hilbert problem for nonsymmetric systems (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 3540-3545 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A comparison of the Riemann–Hilbert problem and the Wiener–Hopf factorization problem arising in the solution of half-space singular integral equations is presented. Emphasis is on the factorization of functions lacking the reflection symmetry usual in transport theory.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529415
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  • 3
    Electronic Resource
    Electronic Resource
    Reply to the comments of Bertrand et al. (1991)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 3 (1991), S. 501-501 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.859898
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  • 4
    Electronic Resource
    Electronic Resource
    Numerical simulations of perturbed Vlasov equilibria (1990)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 2 (1990), S. 1252-1255 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: In this work, the long-time behavior of the solutions of the Vlasov–Poisson system when starting near a spatially homogeneous equilibrium is analyzed numerically. It is found that the asymptotic state toward which the system evolves is not a Bernstein–Green–Kruskal (BGK) equilibrium, but can rather be described by a superposition of BGK modes. Also, it is shown that the small oscillations at the plasma frequency after saturation in the one-sided bump-on-tail instability are due to beating between the unstable mode and the least stable mode.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.859265
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  • 5
    Electronic Resource
    Electronic Resource
    Single-mode saturation of a linearly unstable plasma (1985)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 28 (1985), S. 110-115 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The nonlinear oscillations of an electron plasma described by the collisionless Vlasov equation are studied using a perturbation technique previously applied by Simon and Rosenbluth [Phys. Fluids 19, 1567 (1976)]. It is proved by a characteristic argument that the plasma is globally stable, so that Bogoliuboff's method of "secular regularization'' is applicable. Assuming the plasma is confined in a box, and that only the lowest mode is unstable, it is shown that the "eigenmode dominance'' approximation of Simon and Rosenbluth fails to conserve energy, but that energy and momentum conservation can be regained by considering interaction between the discrete and continuum modes. A formula is derived for the amplitude and phase of the saturated nonlinear oscillations. In a subsidiary result, it is shown that nonlinear effects damp the steady-state oscillations predicted by linearized theory for some stable plasmas.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.865190
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  • 6
    Electronic Resource
    Electronic Resource
    Time-dependent dissipation in nonlinear Schrödinger systems (1995)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 36 (1995), S. 1274-1283 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A coupled nonlinear Schrödinger–Poisson equation is considered which contains a time-dependent dissipation function as a specific model of dissipation effects in nonlinear quantum transport theory and other areas. The Wigner–Poisson equation associated with this system is derived. Using conservation and quasiconservation laws and certain growth assumptions for the nonlinearities and the dissipation function, global existence of solutions to the Cauchy problem of the time-dependent Schrödinger–Poisson system is shown both for small (attractive case) or arbitrary data (repulsive case). © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.531120
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  • 7
    Electronic Resource
    Electronic Resource
    Dissipation in Wigner–Poisson systems (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1513-1521 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The Wigner–Poisson (WP) system (or quantum Vlasov–Poisson system) is modified to include dissipative terms in the Hamiltonian. By utilizing the equivalence of the WP system to the Schrödinger–Poisson system, global existence and uniqueness are proved and regularity properties are deduced. The proof differs somewhat from that for the nondissipative case treated previously by Brezzi–Markowich and Illner et al.; in particular the Hille–Yosida Theorem is used since the linear evolution is not unitary, and a Liapunov function is introduced to replace the energy, which is not conserved.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530887
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  • 8
    Electronic Resource
    Electronic Resource
    A Fokker-Planck equation for growing cell populations (1987)
    Springer
    Journal of mathematical biology 25 (1987), S. 61-72 
    Details
    ISSN: 1432-1416
    Keywords: Fokker-Planck ; Cell population ; Reproduction rules
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Closed form solutions are obtained for a Fokker-Planck model for cell growth as a function of maturation velocity and degree of maturation. For reproduction rules where daughter cells inherit their parent's maturation velocity the complete solution is derived in terms of Airy functions. For more complicated reproduction rules partial results are obtained. Emphasis is given to the relationship of these problems to time dependent linear transport theory.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00275888
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  • 9
    Electronic Resource
    Electronic Resource
    Generalized kinetic equations (1984)
    Springer
    Integral equations and operator theory 7 (1984), S. 60-95 
    Details
    ISSN: 1420-8989
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We study the abstract differential equation $$T\frac{{\partial f}}{{\partial x}} + Af = 0$$ on a Hilbert space H, which represents a variety of different kinetic equations. T is assumed bounded and self-adjoint on H, and A (unbounded) positive self-adjoint and Fredholm. For partial range boundary conditions and 0≤x〈∞, we prove existence and (non-) uniqueness theorems and give representations of the solution. Various examples from neutron transport, radiative transfer of polarized and unpolarized light, and electron transport are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01204914
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  • 10
    Electronic Resource
    Electronic Resource
    A note on the spectral theorem (1986)
    Springer
    Integral equations and operator theory 9 (1986), S. 305-324 
    Details
    ISSN: 1420-8989
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We give necessary and sufficient conditions to prove a spectral theorem and a functional calculus for certain nonselfadjoint operators, H. Our method is non-perturbative: the conditions are given in terms of the resolvent (z-H)−1. We give an example of an operator satisfying these conditions. This operator is not a spectral operator of scalar type. Its spectral projections are unbounded operators defined on a common dense domainD.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01199348
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