Browsing by Author "Sabelfeld, Karl K."

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    Elastostatics of a half-plane under random boundary excitations
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Shalimova, Irina; Sabelfeld, Karl K.
    A stochastic analysis of an elastostatics problem for a half-plane under random white noise excitations of the displacement vector prescribed on the boundary is given. Solutions of the problem are inhomogeneous random fields homogeneous in the longitudinal direction. This is used to model the displacements and represent their correlation tensor via spectral expansion. This approach makes it possible to derive exact representations for other functionals of interest, in particular, the vorticity, the strain tensor, and the elastic energy.
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    Stochastic analysis of an elastic 3D half-space respond to random boundary displacements : exact results and Karhunen-Loéve expansion
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Shalimova, Irina A.; Sabelfeld, Karl K.
    A stochastic response of an elastic 3D half-space to random displacement excitations on the boundary plane is studied. We derive exact results for the case of white noise excitations which are then used to give convolution representations for the case of general finite correlation length fluctuations of displacements prescribed on the boundary. Solutions to this elasticity problem are random fields which appear to be horizontally homogeneous but inhomogeneous in the vertical direction. This enables us to construct explicitly the Karhunen-Loève (K-L) series expansion by solving the eigen-value problem for the correlation operator. Simulation results are presented and compared with the exact representations derived for the displacement correlation tensor. This paper is a complete 3D generalization of the 2D case study we presented in J. Stat. Physics, v.132 (2008), N6, 1071-1095.
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    Stochastic flow simulation and particle transport in a 2D layer of random porous medium
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Kurbanmuradov, Orazgeldi A.; Sabelfeld, Karl K.
    A stochastic numerical method is developed for simulation of flows and particle transport in a 2D layer of porous medium. The hydraulic conductivity is assumed to be a random field of a given statistical structure, the flow is modeled in the layer with prescribed boundary conditions. Numerical experiments are carried out by solving the Darcy equation for each sample of the hydraulic conductivity by a direct solver for sparse matrices, and tracking Lagrangian trajectories in the simulated flow. We present and analyze different Eulerian and Lagrangian statistical characteristics of the flow such as transverse and longitudinal velocity correlation functions, longitudinal dispersion coefficient, and the mean displacement of Lagrangian trajectories. We discuss the effect of long-range correlations of the longitudinal velocities which we have found in our numerical simulations. The related anomalous diffusion is also analyzed.