Related papers: Algebraic approach to directed stochastic avalanch…
A framework for deriving probabilistic data-driven closure models is proposed for coarse-grained numerical simulations of turbulence in statistically stationary state. The approach unites the ideal large-eddy simulation model and data…
I introduce an innovative methodology for deriving numerical models of systems of partial differential equations which exhibit the evolution of spatial patterns. The new approach directly produces a discretisation for the evolution of the…
The adhesive dynamics of a one-dimensional aggregating gas of point particles is rigorously described. The infinite hierarchy of kinetic equations for the distributions of clusters of nearest neighbours is shown to be equivalent to a system…
The current literature on sandpile models mainly deals with the abelian sandpile model (ASM) and its variants. We treat a less known - but equally interesting - model, namely Zhang's sandpile. This model differs in two aspects from the ASM.…
The avalanche polynomial on a graph captures the distribution of avalanches in the abelian sandpile model. Studied on trees, this polynomial could be defined by simply considering the size of the subtrees of the original tree. In this…
We introduce a sandpile model where, at each unstable site, all grains are transferred randomly to downstream neighbors. The model is local and conservative, but not Abelian. This does not appear to change the universality class for the…
Vicsek fractal graphs are an important class of infinite graphs with self similar properties, polynomial growth and treelike features, on which several dynamical processes such as random walks or Abelian sandpiles can be rigorously analyzed…
We describe how to construct the dynamics of relativistic particles following, either timelike or null curves, by means of an auxiliary variables method instead of the standard theory of deformations for curves. There are interesting…
The Abelian Sandpile Model, seen as a deterministic lattice automaton, on two-dimensional periodic graphs generates complex regular patterns displaying (fractal) self-similarity. In particular, on a variety of lattices and initial…
The paper develops one-parametric family of the sand-piles dealing with the grains' local losses on the fixed amount. The family exhibits the crossover between the models with deterministic and stochastic relaxation. The mean height of the…
The diffusion in two dimensions of non-interacting active particles that follow an arbitrary motility pattern is considered for analysis. Accordingly, the transport equation is generalized to take into account an arbitrary distribution of…
The existing estimation of the upper critical dimension of the Abelian Sandpile Model is based on a qualitative consideration of avalanches as self-avoiding branching processes. We find an exact representation of an avalanche as a sequence…
A Bayesian data assimilation scheme is formulated for advection-dominated advective and diffusive evolutionary problems, based upon the Dynamic Likelihood (DLF) approach to filtering. The DLF was developed specifically for hyperbolic…
This paper focuses on natural dualities for varieties of bilattice-based algebras.Such varieties have been widely studied as semantic models in situations where information is incomplete or inconsistent. The most popular tool for studying…
We present a new method for stochastic shape optimisation of engineering structures. The method generalises an existing deterministic scheme, in which the structure is represented and evolved by a level-set method coupled with mathematical…
The supersaturation equation for a vertically moving adiabatic cloud parcel is analysed. The effects of turbulent updrafts are incorporated in the shape of a stochastic Lagrangian model, with spatial and time correlations expressed in terms…
We consider the one-dimensional partially asymmetric exclusion model with open boundaries. The model describes a system of hard-core particles that hop stochastically in both directions with different rates. At both boundaries particles are…
Particle based optimization algorithms have recently been developed as sampling methods that iteratively update a set of particles to approximate a target distribution. In particular Stein variational gradient descent has gained attention…
This paper introduces AdaSDCA: an adaptive variant of stochastic dual coordinate ascent (SDCA) for solving the regularized empirical risk minimization problems. Our modification consists in allowing the method adaptively change the…
Stochastic motion of particles in a highly unstable potential generates a number of diverging trajectories leading to undefined statistical moments of the particle position. This makes experiments challenging and breaks down a standard…