In an earlier paper, we studied the approximation of solutions V (t) to a class of SPDEs by the empirical measure V n(t) of a system of n interacting diffusions. In the present paper, we consider a central limit type problem, showing that √ n(V n − V ) converges weakly, in the dual of a nuclear space, to the unique solution of a stochastic evolution equation. Analogous results in which the diff...

We revisit functional central limit theorems for additive functionals of ergodic Markov diffusion processes. Translated in the language of partial differential equations of evolution, they appear as diffusion limits in the asymptotic analysis of FokkerPlanck type equations. We focus on the square integrable framework, and we provide tractable conditions on the infinitesimal generator, including...

Recently, large datasets stored on the Internet have enabled the analysis of processes, such as large-scale diffusions of information, at new levels of detail. In a recent study, Liben-Nowell and Kleinberg [(2008) Proc Natl Acad Sci USA 105:4633-4638] observed that the flow of information on the Internet exhibits surprising patterns whereby a chain letter reaches its typical recipient through l...

A one-component bistable reaction-diffusion system with asymmetric nonlocal coupling is derived as a limiting case of a two-component activator-inhibitor reaction-diffusion model with differential advection. The effects of asymmetric nonlocal couplings in such a bistable reaction-diffusion system are then compared to the previously studied case of a system with symmetric nonlocal coupling. We c...

We present an algorithm for extracting high quality temporally coherent alpha mattes of objects from a video. Our approach extends the conventional image matting approach, i.e. closed-form matting, to video by using multi-frame nonlocal matting Laplacian. Our multi-frame nonlocal matting Laplacian is defined over a nonlocal neighborhood in spatial temporal domain, and it solves the alpha mattes...

In this paper, the stability characteristics of single-walled carbon nanotubes (SWCNTs) under the action of axial load are investigated. To this end, a nonlocal Flügge shell model is developed to accommodate the small length scale effects. The analytical Rayleigh-Ritz method with beam functions is applied to the variational statement derived from the Flügge-type buckling equations. Molecular dy...

this paper presents the thermal vibration analysis of double-layer graphene sheet embedded in polymer elastic medium, using the plate theory and nonlocal continuum mechanics for small scale effects. the graphene is modeled based on continuum plate theory and the axial stress caused by the thermal effects is also considered. nonlocal governing equations of motion for this double-layer graphene s...

In this paper, the stability characteristics of single-walled carbon nanotubes (SWCNTs) under the action of axial load are investigated. To this end, a nonlocal Flügge shell model is developed to accommodate the small length scale effects. The analytical Rayleigh-Ritz method with beam functions is applied to the variational statement derived from the Flügge-type buckling equations. Molecular dy...

In this paper, the bond-based peridynamic system is analyzed as a nonlocal boundary value problem with volume constraint. The study extends earlier works in the literature on nonlocal diffusion and nonlocal peridynamic models to include non-positive definite kernels. We prove the well-posedness of both linear and nonlinear variational problems with volume constraints. The analysis is based on s...