Related papers: Algebraic approach to directed stochastic avalanch…

An infinite dimensional algebra, which is useful for deriving exact solutions of the generalized pairing problem, is introduced. A formalism for diagonalizing the corresponding Hamiltonian is also proposed. The theory is illustrated with…

Stochastic gradient methods have been a popular and powerful choice of optimization methods, aimed at minimizing functions. Their advantage lies in the fact that that one approximates the gradient as opposed to using the full Jacobian…

Extending the `metric spaces' of Lawvere, we study `real metrics', with values in the extended real line. Formally, this ordered set is a symmetric monoidal closed category, and our structures are enriched categories on the latter.…

This paper is devoted to constructing and studying exactly solvable dynamical systems in discrete time obtained from some algebraic operations on matrices, to reductions of such systems leading to classical field theory models in…

Abelian integrals arise in the mathematical description of various physical processes. According to Abel's theorem these integrals are related to motion of a set of points along a plane curve around fixed points, which are relatively little…

We show that tilting a model sandpile that has dynamic disorder leads to bistability and hysteresis at the angle of repose. Also the distribution of {\it local slopes} shows an interesting dependence on the amount of tilt - weakly tilted…

Numerical resolution of high-dimensional nonlinear PDEs remains a huge challenge due to the curse of dimensionality. Starting from the weak formulation of the Lawson-Euler scheme, this paper proposes a stochastic particle method (SPM) by…

The accurate numerical solution of partial differential equations is a central task in numerical analysis allowing to model a wide range of natural phenomena by employing specialized solvers depending on the scenario of application. Here,…

This paper exposes a novel exploratory formalism, which end goal is the numerical simulation of the dynamics of a cloud of particles weakly or strongly coupled with a turbulent fluid. Giventhe large panel of expertise of the list of…

As a general rule, differential equations driven by a multi-dimensional irregular path $\Gamma$ are solved by constructing a rough path over $\Gamma$. The domain of definition ? and also estimates ? of the solutions depend on upper bounds…

We propose a stochastic extension of the primal-dual hybrid gradient algorithm studied by Chambolle and Pock in 2011 to solve saddle point problems that are separable in the dual variable. The analysis is carried out for general…

We present calculations of forces for two dimensional static sandpile models. Using a symbolic calculation software we obtain exact results for several different orientations of the lattice and for different types of supporting surfaces.…

Statistical inference for spatial processes from partially realized or scattered data has seen voluminous developments in diverse areas ranging from environmental sciences to business and economics. Inference on the associated rates of…

We investigate the bulldozing motion of a granular sandpile driven forwards by a vertical plate. The problem is set up in the laboratory by emplacing the pile on a table rotating underneath a stationary plate; the continual circulation of…

Large scale computer simulations are presented to investigate the avalanche statistics of sand piles using molecular dynamics. We could show that different methods of measurement lead to contradicting conclusions, presumably due to…

The dynamics of the avalanche mixing in a slowly rotated 2D upright drum is studied in the situation where the difference $\delta$ between the angle of marginal stability and the angle of repose of the granular material is finite. An…

We study a generalization of the Brownian bridge as a stochastic process that models the position and velocity of inertial particles between the two end-points of a time interval. The particles experience random acceleration and are assumed…

We explore the limit of stochastic differential equations driven by some random processes satisfying singularly perturbed second order stochastic differential equations. The main tool we employ is the universal limit theorem in rough path…

We consider the Bak-Tang-Wiesenfeld sandpile model on square lattices in different dimensions (D>=6). A finite size scaling analysis of the avalanche probability distributions yields the values of the distribution exponents, the dynamical…

We described a method to solve deterministic and stochastic Walras equilibrium models based on associating with the given problem a bifunction whose maxinf-points turn out to be equilibrium points. The numerical procedure relies on an…