[PDF] Top 20 Stochastic PDEs with multiscale structure

... to stochastic PDEs, where the forcing term may be a highly irregular Gaussian signal taking values in spaces of rather irregular distributions, see for example [3, 7] for introductory texts on the ...for ... See full document

... hcp structure generally permits for a relatively simple activation of slip on the basal plane, whereas strain accommodation on other planes is not as easy to accom- ...other structure metal [195], favorable ... See full document

... Basically, a RBF network can be considered as a universal approximator. In RBF- based methods, the considered domain is discretised by a set of data points which are distributed regularly or randomly and the unknown ... See full document

... for PDEs. We have proposed a multiscale model reduction method for several standard types of elliptic, parabolic, hyperbolic, and convection-diffusion ...the multiscale coefficient of the governing ... See full document

... a stochastic variational principle, and the up-scaling is taken care of by an application of FLAVOR (Chapters 2 and ...classical structure preserving properties of vari- ational integrators are shown by ... See full document

... analytic structure that allows to formulate the equation and (ii) all the stochastic processes entering the expansion converge (after ...analytic structure, but there are examples, where ... See full document

... An open question in the field of neuroscience is to understand what defines the duration of the Up-states and their oscillation frequencies. The interspike interval (time between two consecutive population spikes) ... See full document

... CIR stochastic pro- cess (along a preset trajectory in space), not only allows plausible ore-body grade simulations to be produced, but also allows the model to be constructed as a single ... See full document

... HOMOGENIZATION PERTURBATION-BASED Consider a unit cell representing an inhomogeneous solid with periodically arranged microstructure and containing various types of random microstructures such as fibers, particles, ... See full document

... Figure 3 shows the MSP montage for a 1/f time series, which represents a complex, fractal structure character- ized by correlations between data points across multiple time scales. The conventional (single-scale) ... See full document

... In this paper, we are to study the stability of a class of delayed Takagi-Sugeno (T-S) fuzzy Markovian jumping p-Laplace partial differential equations (PDEs) which owns a wide range of physics and engineering ... See full document

... These data based on consideration ten successive months have normal distribution and their scaled parameters are presented in Tables 4.2 and 4.3. We want to assess the total performance of these units. We suppose that ¯ ... See full document

... the stochastic implied trinomial tree is fixed throughout, it may not be possible to fit very large local volatilities, which may occur at various nodes and at different times during the simulation, with ... See full document

... K t as the map element M (t). The benefit we get from an immediate matrix lookup as opposed to having to manually construct the matrices can be immense. Using the map M produces identical results to not using M (because ... See full document

... the multiscale factorization among one-parameter exponential fami- lies (Kolaczyk and Nowak, ...the stochastic variations of X when observations are measured ...the multiscale framework and a prior ... See full document

... transversely isotropic properties of shale rocks with the multi-inclusion and ITZ effects. The explicit form solutions for the transversely isotropic properties are obtained by utilizing the Hill polarization tensor ... See full document

... introduce stochastic differential equa- tions along with some basic existence and uniqueness results and some properties of It¯ o ...introduce stochastic representation of solutions to partial differential ... See full document

... We developed a methodology to remove these limits, generalizing the determination of commu- nity structure via quality functions to multislice networks that are defined by coupling multiple adjacency matrices ... See full document

... the Stochastic Galerkin approximation of u; next we state the estimate for the decay of the spectral approximation of u and explain how to build practically the TD-FC polynomial subspaces that stem from ... See full document

... In this chapter, we understand integration of Banach-valued functions against Brownian mo- tion, as an extension of the Itˆ o integral. This will allow us to solve stochastic partial differential equations through ... See full document