assessment of the correlation between rock brittleness and rock fracture toughness has been the subject of extensive research works in the recent years. unfortunately, the brittleness measurement methods have not yet been standardized, and rock fracture toughness cannot be estimated satisfactorily by the proposed indices. in the present study, statistical analyses are performed on some data col...

one of the main distinctions between geomaterials and other engineering materials is the spatial variation of their properties in different directions. this characteristic of geomaterials -so called heterogeneity- is studied herewith. several spatial distributions are introduced to describe probabilistic variation of geotechnical properties of soils. among all, the absolute normal distribution ...

the purpose of this study is to compare the results of different probabilistic methods such as the perturbation method, stochastic finite element method (sfem) and monte carlo method. these methods were used to study the convergence of direct approach for slope stability analysis and are developed for a linear soil behavior. in this study, two dimensional random fields are used and both the fir...

We solve the large deviations of Kardar-Parisi-Zhang (KPZ) equation in one dimension at short time by introducing an approach which combines field theoretical, probabilistic and integrable techniques. expand program weak noise theory, maps onto a non-linear hydrodynamic problem, unveil its complete solvability through connection to integrability Zakharov-Shabat system. Exact solutions, dependin...

We consider the problem of numerically approximating the solution of the coupling of the flow equation in a porous medium, with the advection-diffusion equation in the presence of uncertainty on the permeability of the medium. Random coefficients are classically used in the flow equation to modelize uncertainty. More precisely, we propose the numerical analysis of a method developed to compute ...

Motivated by applications in systems biology, a probabilistic framework based on Markov processes is proposed to represent intracellular processes. The formal relationships between different stochastic models referred to in the systems biology literature are reviewed. As part of this review, a novel derivation of the differential Chapman-Kolmogorov equation for a general multidimensional Markov...

Given a positive energy solution of the Klein-Gordon equation, the motion of the free, spinless, relativistic particle is described in a fixed Lorentz frame by a Markov diffusion process with non-constant diffusion coefficient. Proper time is an increasing stochastic process and we derive a probabilistic generalization of the equation (dτ)2 = − 1 c dXνdXν . A random time-change transformation p...

Efficient numerical algorithms are proposed for a class of forward-backward stochastic differential equations (FBSDEs) connected with semilinear parabolic partial differential equations. As in [J. Douglas, Jr., J. Ma, and P. Protter, Ann. Appl. Probab., 6 (1996), pp. 940–968], the algorithms are based on the known four-step scheme for solving FBSDEs. The corresponding semilinear parabolic equat...

A new method is described for constructing a generalized solution for stochastic differential equations. The method is based on the Cameron-Martin version of the Wiener Chaos expansion and provides a unified framework for the study of ordinary and partial differential equations driven by finiteor infinite-dimensional noise with either adapted or anticipating input. Existence, uniqueness, regula...