Constructing a numerically statistical model of a homogeneous random field with the given distribution of the integral over one of the phase coordinates

The problem of constructing a numerically realizable model of a three-dimensional homogeneous random field in a horizontal layer 0 z H with given one-dimensional distribution and correlation function of the integral over vertical coordinate z is solved. An aggregate of n independent elementary horizontal layers of thickness h = H/n, vertically shifted by a random value uniformly distributed in the interval (0, h) is considered as a basic model.

Study on Random Analysis Method and its Application to Structures

The evaluation of the reliability of structural systems is of extreme importance in structural design, mainly when the variables are random. A method is presented to efficiently assess the random response of stochastic structures. The article uses two-level sampling method to partial fiber element. First, the homogeneous random field of concrete and rebar can be created by modified Latin-hypercube sampling. Then section discretization method is adopted to assign fiber random variables of concrete section fiber. The algorithm is then used to analyze the random response of a concrete beam, and the result proves that the method is efficient.

Natural Frequencies and Mode Shapes of Deterministic and Stochastic Non-Homogeneous Rods

In this study the natural frequencies and mode shapes of the kth order of nonhomogeneous (deterministic and stochastic) rods are found. The solution is based on the functional perturbation method (FPM). The natural frequency and mode shape of the kth order is found analytically to any desired degree of accuracy. In the deterministic it is shown that the FPM accuracy range for the frequency ω and the mode shape is less then 1%. The stochastic case demonstrates the power of this method. The material and geometrical properties will be considered as statistically homogeneous random field with exponential two-point correlation. It is shown that the accuracy depends on the stochastic information used, the correlation distance (roughly the “grain size”), and whether we are interested in the properties of ω or ω2.

SELF-INTERSECTION LOCAL TIME FOR ${\mathcal S}' ({\mathbb R}^d)$-WIENER PROCESSES AND RELATED ORNSTEIN–UHLENBECK PROCESSES

Existence and continuity results are obtained for self-intersection local time of [Formula: see text]-valued Ornstein–Uhlenbeck processes [Formula: see text], where X0 is Gaussian, Wt is an [Formula: see text]-Wiener process (independent of X0), and T't is the adjoint of a semigroup Tt on [Formula: see text]. Two types of covariance kernels for X0 and for W are considered: square tempered kernels and homogeneous random field kernels. The case where Tt corresponds to the spherically symmetric α-stable process in ℝd, α∈(0,2], is treated in detail. The method consists in proving first results for self-intersection local times of the ingredient processes: Wt, T't X0 and [Formula: see text], from which the results for Xt are derived. As a by-product, a class of non-finite tempered measures on ℝd whose Fourier transforms are functions is identified. The tools are mostly analytical.