A random process can be represented as a series expansion involving a complete set of deterministic functions with corresponding random coe<cients. Karhunen–Loeve (K–L) series expansion is based on the eigen-decomposition of the covariance function. Its applicability as a simulation tool for both stationary and non-stationary Gaussian random processes is examined numerically in this paper. The ...

The series representation consisting of eigenfunctions as the orthogonal basis is called the Karhunen–Loeve expansion. This paper demonstrates that the determination of eigensolutions using a wavelet-Galerkin scheme for Karhunen–Loeve expansion is computationally equivalent to using wavelet directly for stochastic expansion and simulating the correlated random coefficients using eigen decomposi...

The present study investigates the peristaltic flow of couple stress fluid in a non-uniform rectangular duct with compliant walls. Mathematical modeling is based upon the laws of mass and linear momentum. Analytic solutions are carried out by the eigen function expansion method under long-wavelength and low-Reynolds number approximations. The features of the flow characteristics are analyzed by...

Modified group projector technique for induced representations is a powerful tool for calculation and symmetry quantum numbers assignation of a tight binding Hamiltonian energy bands of crystals. Namely, the induced type structure of such a Hamiltonian enables efficient application of the procedure: only the interior representations of the orbit stabilizers are to be considered. Then the genera...

This paper derives the multi-layer heat conduction Green’s function, by integrating the eigen-expansion technique and the classic transmission line theories, and presents a logarithmic full-chip thermal analysis algorithm, which is verified by comparisons with a computational fluid dynamics tool (FLUENT). The paper considers Dirichlet’s and general heat convection boundary conditions at chip su...

Cylindrically symmetric inhomogeneous string cosmological model of the universe in presence of electromagnetic field is investigated. We have assumed that F12 is the only non-vanishing component of electromagnetic field tensor Fij . The Maxwell’s equations show that F12 is the function of x alone whereas the magnetic permeability is the function of x and t both. To get the deterministic solutio...

Cylindrically symmetric inhomogeneous string cosmological models in presence of electromagnetic field is investigated. We have assumed that F12 is the only non-vanishing component of Fij . The Maxwell’s equations show that F12 is the function of x alone whereas the magnetic permeability is the function of x and t both. To get the deterministic solution, it has been assumed that the expansion (θ...