ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik
Copyright © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Recently Published Articles
- Numerical solution of stochastic partial differential equations using a collocation method
Article first published online: 23 FEB 2015 | DOI: 10.1002/zamm.201400080
In this article we apply spectral collocation method to find a numerical solution of stochastic partial differential equations (SPDEs). Spectral collocation method is known to be impressively efficient for PDEs. We investigate this method for numerical solution of SPDEs and we obtain its rate of convergence. At first, the results are expressed for equations with globally Lipschitz coefficient, then we extend it to cases with locally Lipschitz coefficient. The analysis is supported by numerical results for some important SPDEs such as stochastic Kuramoto-Sivashinksy equation.
- Stability analysis of some fully developed mixed convection flows in a vertical channel
Article first published online: 23 FEB 2015 | DOI: 10.1002/zamm.201400248
Stability of fully developed mixed convection flows, with significant viscous dissipation, in a vertical channel bounded by isothermal plane walls having the same temperature and subject to pressure gradient is investigated. It is shown that one of the dual solutions is always unstable and that both are unstable when the total flow rate is big enough. The completely passive natural convection flow is shown to be unstable.
- On the inverse problem of the two-velocity tree-like graph
Sergei Avdonin, Choque Rivero Abdon, Günter Leugering and Victor Mikhaylov
Article first published online: 23 FEB 2015 | DOI: 10.1002/zamm.201400126
In this article the authors continue the discussion in about inverse problems for second order elliptic and hyperbolic equations on metric trees from boundary measurements. In the present paper we prove the identifiability of varying densities of a planar tree-like network of strings along with the complete information on the graph, i.e. the lengths of the edges, the edge degrees and the angles between neighbouring edges. The results are achieved using the Titchmarch-Weyl function for the spectral problem and the Steklov-Poincaré operator for the dynamic wave equation on the tree. The general result is obtained by a peeling argument which reduces the inverse problem layer-by-layer from the leaves to the clamped root of the tree.
- A representation theorem for the circular inclusion problem
Article first published online: 23 FEB 2015 | DOI: 10.1002/zamm.201300147
A representation theorem is obtained for an arbitrarily loaded elastic bimaterial solid consisting of an infinite plane containing a circular inhomogeneity. The elastic image method is used for the analysis. The theorem expresses the Airy stress functions that generate the elastic fields for the composite solid explicitly in terms of the Airy stress function for the corresponding homogeneous infinite solid. It shows that if the solution for the homogeneous infinite solid is available, then the solutions for the corresponding bimaterial solid can be deduced by the process of differentiation and integration. The result could provide the important advantage of economy of effort in the determination of the elastic fields for composite planes with circular interfaces.
- A strain-softening bar revisited
Serge N. Gavrilov and Ekaterina V. Shishkina
Article first published online: 23 FEB 2015 | DOI: 10.1002/zamm.201400155
We revisit, from the standpoint of the modern theory of phase transitions, the classical problem on stretching of a strain-softening bar, considered earlier by Bažant, Belytschko et al. The known solution is singular and predicts localization of deformations at a single point (an interval with zero length) of the bar. We use the model of a phase transforming bar with trilinear stress-strain relation and analytically consider the particular limiting case where the stiffness of a new phase inclusion in the phase-transforming bar is much less than the stiffness of the initial phase. This allows us to construct a regular solution, which converges to the known singular solution in the limiting case of zero new phase stiffness.