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  • Engineering  (6,285)
  • 2000-2004  (3)
  • 1995-1999  (2,961)
  • 1990-1994  (3,321)
  • 11
    Electronic Resource
    Electronic Resource
    Scattering Frequencies and a Class of Perturbed Systems of Elastic Waves (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 699-716 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider the system of elastic waves in three dimensions under the presence of an impurity of the medium which we represent by a real-valued function q(x) (or q(x,t)). The medium is assumed to be isotropic and occupies the whole space Ω = ∝3. We study the location of the scattering frequencies associated with such phenomenon. We conclude that there is a large region on the complex plane which is free of scattering frequencies. In the remaining region they are discrete provided that q satisfies suitable assumptions concerning its behaviour at infinity.
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  • 12
    Electronic Resource
    Electronic Resource
    The Validity of Generalized Ginzburg-Landau Equations (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 717-736 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider parabolic systems defined on cylindrical domains close to the threshold of instability, in which the Fourier modes with positive growth rates are concentrated at a non-zero critical wave number. In particular, we consider systems for which a so-called Ginzburg-Landau equation can be derived. Due to the presence of continuous spectrum, classical bifurcation theory is not available to describe bifurcating solutions. Thus, we consider a modified system with artificial spectral gap, which possesses an infinite-dimensional centre manifold. The amplitude equation on this manifold is called a generalized Ginzburg-Landau equation. From previous work [18] it is known that the Fourier modes are exponentially concentrated at integer multiples of the critical wave number. Hence, the error made by this modification is exponentially small in powers of the bifurcation parameter. The approximations obtained via the generalized Ginzburg-Landau equation are valid on a much longer time scale than those obtained by using the classical Ginzburg-Landau equation as an amplitude equation.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
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  • 13
    Electronic Resource
    Electronic Resource
    Exact Solutions of Discrete Kinetic Models and Stationary Problems for the Plane Broadwell Model (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 825-845 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A review of exact solutions of discrete velocity models is given. Different methods of constructing the solutions are discussed. New methods are proposed for the stationary Broadwell model, and new class of solutions is obtained. Two-dimensional flows in channel are studied on the basis of exact solutions and analogy with the Carleman model. Explicit example of non-unique solution to a boundary value problem is given. Exact hydrodynamic equations are derived for the stationary Broadwell model. A role of the Navier-Stokes approximation is discussed in detail by comparison with these exact equations.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
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  • 14
    Electronic Resource
    Electronic Resource
    Relationship Between the Albedo and Scattering Operators for the Boltzmann Equation with Semi-transparent Boundary Conditions (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 1-13 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The albedo and scattering operators are central objects in the time-dependent transport theory. Their mutual relationship has recently been established by Arianfar and Emamirad for the case of transparent boundaries. In this paper, we extend the result to general boundary conditions. To allow for this extension, the scattering theory for a transport-like equation is generalized to include partially reflecting boundary conditions. The existence of the wave and scattering operators is directly inferred from the properties of the evolution operators that are determined, in turn, by the physics of collisions within and at the boundaries of the scattering domain.
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  • 15
    Electronic Resource
    Electronic Resource
    Monodromy Groups and Bilinear Monodromy Invariant Combinations of Generalized Hypergeometric Type Integrals (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 257-285 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The problem of determining bilinear combinations of holomorphic and antiholomorphic generalized hypergeometric type integrals left invariant under the action of the monodromy groups of the integrals is studied. In the special cases of simple Pochhammer type integrals and of twofold hypergeometric type integrals the existence and uniqueness of the bilinear invariants are proved, and the bilinear invariants are explicitly computed. Preparing the tools it is shown how to linearize and iterate representations of the braid group Bn as automorphism groups of certain free subgroups of the braid group Bn+1, and how the resulting iterated linear representations of the braid group in a natural way provide an algorithm to compute the monodromy group of generalized hypergeometric type integrals. Explicit formulae for different types of integration contours are given in the case of simple and twofold integrals.
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  • 16
    Electronic Resource
    Electronic Resource
    Announcement (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 255-255 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670190402
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  • 17
    Electronic Resource
    Electronic Resource
    Periodic Solutions of Non-linear Anisotropic Partial Differential Equations (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 363-374 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Periodic solutions of arbitrary period to semilinear partial differential equations of Zabusky or Boussinesq type are obtained. More generally, for a linear differential operator A(y,∂), the equation A(y,∂)u = (-1)∣γ∣∂γf(y,∂γu), y = (t,x)∊∝k×G is studied, where homogeneous boundary conditions on ∂G and periodicity conditions on t are imposed. The solutions are obtained by variational methods in anisotropic Sobolev spaces.
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  • 18
    Electronic Resource
    Electronic Resource
    Asymptotic Analysis of a Semiconductor Model Based on Fermi-Dirac Statistics (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 401-424 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The quasi-hydrodynamic carrier transport equations for semiconductors extended to Fermi-Dirac statistics are considered. It is shown that in the high injection case, these equations reduce to a drift-diffusion model with non-linear diffusion terms. The limiting procedure is proved rigorously and error estimates are shown. We compute numerically static voltage-current characteristics of a forward biased pn-junction diode and compare the curves with the corresponding characteristics obtained from the standard drift-diffusion model based on Boltzmann statistics. It turns out that there exists a so-called threshold voltage at which the behaviour of the characteristic changes. Under high injection conditions, the dependence of the current on the bias appears to be approximately polynomial. The characteristics are studied analytically for a unipolar device.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
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  • 19
    Electronic Resource
    Electronic Resource
    Generalized linear elasticity in exterior domains. I: Radiation problems (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1469-1500 
    Details
    ISSN: 0170-4214
    Keywords: radiating solutions ; exterior boundary value problem in elasticity ; variable coefficients ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We use Hodge-Helmholtz decompositions of weighted Sobolev spaces to solve time-harmonic exterior-boundary value problems for perturbations of the (aδd+bdδ)-system (δ: the co-differential, a, b〉0). We prove, that a Fredholm alternative holds true, the eigensolutions decay polynomially at infinity, and that the positive eigenvalues do not accumulate. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 20
    Electronic Resource
    Electronic Resource
    The 2-D Neumann problem in an exterior domain bounded by closed and open curves (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1551-1562 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The Neumann problem for the Laplace equation in an exterior connected plane region bounded by closed and open curves is studied. The existence of classical solution is proved by potential theory. The problem is reduced to the Fredholm equation of the second kind, which is uniquely solvable. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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