Abstract. In this paper a direct correspondence is made between the effective stochastic dynamics of elastic structures of an Immersed Boundary Method incorporating thermal fluctuations and Stokesian-Brownian Dynamics. The correspondence is made in the limit of small Reynolds number, in which the fluid relaxes rapidly on the time scale of the motion of the immersed structures, by performing an ...

in this paper the substantiation of the method of full averaging for fuzzy differential inclusions is considered. these results generalize the results of [17, 20] for differential inclusions with hukuhara derivative and of [18] for fuzzy differential equations.

Abstract. In this paper, we present a new stochastic algorithm, namely the stochastic block mirror descent (SBMD) method for solving large-scale nonsmooth and stochastic optimization problems. The basic idea of this algorithm is to incorporate the block-coordinate decomposition and an incremental block averaging scheme into the classic (stochastic) mirror-descent method, in order to significant...

The macroscopic behavior of dissipative stochastic partial differential equations usually can be described by a finite dimensional system. This article proves that a macroscopic reduced model may be constructed for stochastic reaction-diffusion equations with cubic nonlinearity by artificial separating the system into two distinct slow-fast time parts. An averaging method and a deviation estima...

In this paper, we present a new stochastic algorithm, namely the stochastic block mirror descent (SBMD) method for solving large-scale nonsmooth and stochastic optimization problems. The basic idea of this algorithm is to incorporate the block-coordinate decomposition and an incremental block averaging scheme into the classic (stochastic) mirror-descent method, in order to significantly reduce ...

We present discrete-time stochastic extremum seeking algorithms and prove their convergence using stochastic averaging theory that we recently developed. First, we provide a discrete stochastic extremum seeking algorithm for a static map, in which measurement noise is considered and an ergodic discrete-time stochastic process is used as the excitation signal. Second, for discrete-time nonlinear...

The method of characteristics (the averaging over the characteristic formula) and the weak-sense numerical integration of ordinary stochastic differential equations together with the Monte Carlo technique are used to propose numerical methods for linear stochastic partial differential equations (SPDEs). Their orders of convergence in the mean-square sense and in the sense of almost sure converg...

We consider the formation of large scale structures (zonal jets and vortices), in geostrophic turbulence forced by random forces, within the barotropic quasi-geostrophic model. We study the limit of a time scale separation between inertial dynamics on one hand, and the effect of forces and dissipation on the other hand. We prove that stochastic averaging can be performed explicitly in this prob...

We formulate the Kohn-Sham density functional theory (KS-DFT) as a statistical theory in which the electron density is determined from an average of correlated stochastic densities in a trace formula. The key idea is that it is sufficient to converge the total energy per electron to within a predefined statistical error in order to obtain reliable estimates of the electronic band structure, the...

We discuss model reduction of multiscale networks of biochemical reactions used in systems biology as models for cell physiology and pathology. For linear kinetic models, which appear as ”pseudo-monomolecular” subsystems of the nonlinear reaction networks, we obtain a general reduction algorithm based on cycle averaging and surgery. The same algorithm, when applied to stochastic networks, allow...