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  • Articles  (79)
  • 2015-2019  (79)
  • 2015  (79)
  • ZAMP - Zeitschrift für Angewandte Mathematik und Physik  (79)
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  • Articles  (79)
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  • 2015-2019  (79)
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  • 1
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    Influence of nonlinear effects on the efficiency of a thermoelectric generator (2015)
    Springer
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    Publication Date: 2015-11-18
    Description: We propose a nonlinear model for thermoelectric coupling which is based on the thermomass theory for heat conduction. We show that in this model, the second Kelvin relation and the classical Onsager relations are no longer satisfied simultaneously, namely, if one holds, then the other one breaks down, and viceversa. As a function of the different breaking, we evaluate the efficiency of a thermoelectric generator. The influence of the electric-charge gradient on the efficiency of thermoelectric coupling is investigated as well.
    Print ISSN: 0044-2275
    Electronic ISSN: 1420-9039
    Topics: Mathematics , Physics
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  • 2
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    Isometric immersions via compensated compactness for slowly decaying negative Gauss curvature and rough data (2015)
    Springer
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    Publication Date: 2015-10-21
    Description: In this paper, the method of compensated compactness is applied to the problem of isometric immersion of a two-dimensional Riemannian manifold with negative Gauss curvature into three-dimensional Euclidean space. Previous applications of the method to this problem have required decay of order t −4 in the Gauss curvature. Here, we show that the decay of Hong (Commun Anal Geom 1:487−514, 1993 ) t −2− δ /2 where δ ∈ (0, 4) suffices.
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    Electronic ISSN: 1420-9039
    Topics: Mathematics , Physics
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  • 3
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    Nonlinear perturbations of a periodic Schrödinger equation with supercritical growth (2015)
    Springer
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    Publication Date: 2015-10-19
    Description: In this paper, we establish the existence of positive solutions for a class of quasilinear Schrödinger equations involving supercritical growth. By using a change of variables, the quasilinear equation is reduced to a semilinear equation. Then, variational method is used together with a truncation argument used in Del Pino and Felmer (Calc var Partial Differ Equ 4:121–137, 1996 ) and concentration compactness principle given in Zelati and Rabinowtiz (Commun Pure Appl Math 45:1217–1269, 1992 .
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    Topics: Mathematics , Physics
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  • 4
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    TEM wave propagation in a microstrip line on a substrate of circular segment cross section (2015)
    Springer
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    Publication Date: 2015-10-16
    Description: TEM mode wave propagation in a microstrip transmission line on a dielectric substrate of circular segment cross section is of concern. A suggested design of a microstrip is convenient for manufacturing and allows to miniaturize microstrips since there is no lateral fringing effect of the substrate in the transmitted fundamental TEM mode. By using the bipolar orthogonal coordinates, the plane potential problem is reformulated in the form of trigonometric dual integral equations. The discontinuous integrals containing Legendre functions of complex degree and the Abel integral equation are employed to reduce the dual equations to a Fredholm equation of the second kind. The structure of the Fredholm integral equation allows to obtain a simple approximate solution. Basing on this solution, rigorous approximate formulas for the characteristic impedance are derived. The characteristic impedance of a microstrip transmission line on a silicon substrate is computed and plotted as an example.
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    Electronic ISSN: 1420-9039
    Topics: Mathematics , Physics
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  • 5
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    A generalized nonlocal vector calculus (2015)
    Springer
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    Publication Date: 2015-10-16
    Description: A nonlocal vector calculus was introduced in Du et al. (Math Model Meth Appl Sci 23:493–540, 2013 ) that has proved useful for the analysis of the peridynamics model of nonlocal mechanics and nonlocal diffusion models. A formulation is developed that provides a more general setting for the nonlocal vector calculus that is independent of particular nonlocal models. It is shown that general nonlocal calculus operators are integral operators with specific integral kernels. General nonlocal calculus properties are developed, including nonlocal integration by parts formula and Green’s identities. The nonlocal vector calculus introduced in Du et al. (Math Model Meth Appl Sci 23:493–540, 2013 ) is shown to be recoverable from the general formulation as a special example. This special nonlocal vector calculus is used to reformulate the peridynamics equation of motion in terms of the nonlocal gradient operator and its adjoint. A new example of nonlocal vector calculus operators is introduced, which shows the potential use of the general formulation for general nonlocal models.
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    Topics: Mathematics , Physics
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  • 6
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    Periodic solutions to nonlinear wave equations with spatially dependent coefficients (2015)
    Springer
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    Publication Date: 2015-10-16
    Description: This paper investigates the existence and uniqueness of weak solutions to a periodic boundary value problem for a system of nonlinear wave equations with spatially dependent coefficients. Priori estimates of weak solutions are also established for the periodic boundary value problem. The arguments rely on spectral properties of the corresponding wave operator and a global inverse function theorem. The results presented in this paper extend the ones known in the literature in that eigenvalues of nonlinear perturbing terms appeared in the system of nonlinear wave equations can be chosen from the spectrum of the underlying wave operator.
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    Electronic ISSN: 1420-9039
    Topics: Mathematics , Physics
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  • 7
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    On uniqueness and stability of Sobolev’s solution in scattering by wedges (2015)
    Springer
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    Publication Date: 2015-10-16
    Description: We prove that the solution of the scattering problem of pulses, constructed by Sobolev (Proc Seismol Inst Acad Sci URSS 41:1–15, 1934 ), coincides with the solution obtained by our method of complex characteristics. The coincidence holds for the DD- and NN-boundary conditions. The method of complex characteristics has been developed by Komech and Merzon in 2002–2007. Its main advantage is that it provides (a) the existence and uniqueness of the solutions in suitable functional classes and (b) the limiting amplitude principle. The uniqueness in the Sobolev approach was not considered. Our result means that Sobolev’s solution belongs to our functional classes and agrees with the limiting amplitude principle.
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  • 8
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    Blow-up analysis for a semilinear parabolic equation with time-dependent coefficients under nonlinear boundary flux (2015)
    Springer
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    Publication Date: 2015-10-16
    Description: A blow-up analysis for a nonlinear divergence form of parabolic equation with time-dependent coefficients is given under nonlinear boundary flux in a bounded star-shaped region. We establish some conditions on time-dependent coefficients and nonlinearities to guarantee existence of global solution or blow-up solution at some finite time t *. Moreover, an upper bound for t * is derived. Under somewhat more restrictive conditions, a lower bound for t * can be obtained. Finally, some application examples to verify the bounds of t * are presented.
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    Topics: Mathematics , Physics
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  • 9
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    Blow-up phenomena for compressible Euler equations with non-vacuum initial data (2015)
    Springer
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    Publication Date: 2015-10-16
    Description: In this article, we study the blow-up phenomena of compressible Euler equations with non-vacuum initial data. Our new results, which cover a general class of testing functions, present new initial value blow-up conditions. The corresponding blow-up results of the 1-dimensional case in non-radial symmetry are also included.
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    Topics: Mathematics , Physics
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  • 10
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    A nanosized circular inhomogeneity in finite plane elastostatics (2015)
    Springer
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    Publication Date: 2015-10-16
    Description: We consider the deformation of a nanocomposite by incorporating the effect of surface elasticity on the finite plane deformations of a circular inhomogeneity embedded in a particular class of compressible hyperelastic materials of harmonic type subjected to uniform remote Piola stresses. We incorporate the surface mechanics by using a version of the continuum-based surface/interface model of Gurtin and Murdoch. A complete solution is derived by reducing the original boundary value problem to two coupled first-order differential equations which can be solved analytically. The solution clearly demonstrates that the stress fields in the composite are size dependent and that the stress field inside a circular inhomogeneity is, in general, non-uniform. Two special cases which admit an internal uniform, yet size-dependent stress field, are discussed.
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    Topics: Mathematics , Physics
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