Random Field Description Research Articles

Structural Description of Geophysical Random Fields with Non-Gaussian Statistics

The article considers an approach to the description of random fields as a set of intense structures with random parameters. Such structures are observed both in optical fields propagating in inhomogeneous media and in fields of hydrodynamic origin and are formed because of focusing of radiation or deformation of flows. The article discusses the filtration methods and the evolution of such structures. Different modes of structures, modes of periodic and stochastic oscillations, are described.

Description of random fields by systems of conditional distributions

In this paper, we consider the direct and inverse problems of the description of lattice positive random fields by various systems of finite-dimensional (as well as one-point) probability distributions parameterized by boundary conditions. In the majority of cases, we provide necessary and sufficient conditions for the system to be a conditional distribution of a (unique) random field. The exception is Dobrushin-type systems for which only sufficient conditions are known. Also, we discuss possible applications of the considered systems.

On the structural description of random fields

The article considers an approach to the description of random fields as a set of intense structures with random parameters. Such structures are observed both in optical fields propagating in inhomogeneous media and fields of hydrodynamic origin and are formed because of focusing on radiation or deformation of flows. The article discusses the filtration methods and the evolution of such structures. Different modes of structures, modes of periodic and stochastic oscillations, are described.

Combinatorial Approach to the Description of Random Fields

Combinatorial Approach to the Description of Random Fields

A random field approach to the Lagrangian modeling of turbulent transport in vegetated canopies

We present an application of a Lagrangian Stochastic Model (LSM) to turbulent dispersion over complex terrain, where turbulent coherent structures are known to play a crucial role. We investigate the case of a vegetated canopy by using semi-empirical parameterizations of turbulence profiles in the region inside and above a canopy layer. The LSM is based on a 4-dimensional Fokker-Planck (4DFP) equation, which extends the standard Thomson87 Lagrangian approach. The 4DFP model is derived by means of a Random Field description of the turbulent velocity field. The main advantage of this approach is that not only the experimental Eulerian one-point statistics, but also the Eulerian two-point two-time covariance structure can be included explicitly in the LSM. At variance with the standard Thomson87 approach, the 4DFP model allows to consider explicit parameterizations of the turbulent coherent structures as it explicitly includes both spatial and temporal correlation functions. In order to investigate the effect of the turbulent geometrical structure on a scalar concentration profile, we performed numerical simulations with two different covariance parameterizations, the first one isotropic and the second anisotropic. We show that the accumulation of scalars near the ground is due to the anisotropic geometrical properties of the turbulent boundary layer.

Effects of material uncertainty in the structural response of metal foam core sandwich beams

The present study is concerned with a numerical analysis of the uncertainties in the response of foam core sandwich structures caused by the uncertain microstructure of the core material. In the sense of an integrated computational materials engineering type approach, a three-step procedure is proposed. In the first step, the effective material properties of the core material are computed. For this purpose, a probabilistic homogenization procedure is adopted for the prediction of all elastic constants together with their probability distributions as well as all spatial correlations and interrelations between the individual parameters. In the second step, a random field model for the core material is derived, based on the homogenization results obtained in the first step. The random fields are found to reproduce all stochastic features of the uncertain core material in a proper manner. Using the random field description as an input for a Monte-Carlo-type structural analysis, the uncertainties in the stiffness and strength of sandwich structures are computed in the third step. The capabilities of the proposed procedure are demonstrated using the example of a single edge clamped sandwich beam under transverse loads.

Uncertainty quantification for metal foam structures by means of image analysis

A metal foam may consist of a very heterogeneous structure, such that the size of the representative volume element is rather large. Therefore, macroscopic properties of components made of metal foams might show a large scatter.To predict the scatter of eigenfrequencies for bending beam structures, a consistent formulation from image analysis to the distribution of macroscopic properties is developed. With the help of computed tomography, statistical characteristics of the cell geometry of open cell foams are estimated. This information allows to fit a random tessellation model to the material, which reproduces the statistical properties of the cell geometry. To compute the linear elastic properties as well as the mass density of metal foams, three dimensional volume elements from random model realizations are analyzed and distributions of apparent properties are computed. The covariance function is estimated by considering volume elements at different locations of the macrostructure. Having a description of random fields for the apparent properties at hand, Monte Carlo simulations are applied to predict the eigenfrequencies, their scatter and the associated eigenforms of beams made of metal foams. The procedure is validated by experiments.

Description of random fields by means of one-point finite-conditional distributions

The aim of this note is to investigate the relationship between strictly positive random fields on a lattice ℤν and the conditional probability measures at one point given the values on a finite subset of the lattice ℤν. We exhibit necessary and sufficient conditions for a one-point finite-conditional system to correspond to a unique strictly positive probability measure. It is noteworthy that the construction of the aforementioned probability measure is done explicitly by some simple procedure. Finally, we introduce a condition on the one-point finite conditional system that is sufficient for ensuring the mixing of the underlying random field.

Junction-aware extraction and regularization of urban road networks in high-resolution SAR images

A general processing framework for urban road network extraction in high-resolution synthetic aperture radar images is proposed. It is based on novel multiscale detection of street candidates, followed by optimization using a Markov random field description of the road network. The latter step, in the path of recent technical literature, is enriched by the inclusion of a priori knowledge about road junctions and the automatic choice of most of the involved parameters. Advantages over existing and previous extraction and optimization procedures are proved by comparison using data from different sensors and locations

A random field description for stochastic boundary elements

Stochastic boundary element techniques which account for the spatial variability of mechanical properties of the body under investigation generally mix the boundary equations which solve the deterministic mechanical problem with field integrals over sub-domains (cells). This paper approaches a linear elasto-dynamic problem and introduces a description of the stochastic fields which allows one to reduce all the field integrals to boundary integrals. A perturbation technique then leads to an analytical characterization of the response in a probabilistic sense.

Gaussian random field description of fluctuating fluid vesicles.

Gaussian random processes on spheres are studied as models of fluctuating fluid vesicles. We derive expressions for the mean volume, surface area, curvature, and square curvature of vesicles with arbitrarily strong Gaussian fluctuations. A Feynman-Hellman approximation allows, by variational minimization, a consistent derivation of structure factor and free energy of vesicles. As an example, we investigate a fluctuating vesicle with fixed mean surface area and volume for a wide range of values of the bending modulus. \textcopyright{} 1996 The American Physical Society.

Theory of electron scattering in substitutionally disordered solid solutions

A unified approach is proposed for the description of random fields caused by doping in substitutionally disordered solid solutions. On the basis of the microscopic theory, which only takes into account the difference in atomic pseudopotentials of the solvent and the solute substance, it is shown that the treatment of the random field of elastic deformations can be reduced to the renormalization of the atomic pseudopotential of the solvent.

The Description of a Random Field by Means of Conditional Probabilities and Conditions of Its Regularity

The Description of a Random Field by Means of Conditional Probabilities and Conditions of Its Regularity