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This paper examines the temporal evolution of a two-stage stochastic model for spherical random fields. The model uses a time-fractional stochastic hyperbolic diffusion equation, which describes the evolution of spherical random fields on…
Statistical inference for time series such as curve estimation for time-varying models or testing for existence of change-point have garnered significant attention. However, these works are generally restricted to the assumption of…
This paper investigate the local times and modulus of nondifferentiability of the spherical Gaussian random fields. We extend the methods for studying the local times of Gaussian to the spherical setting. The new main ingredient is the…
We consider a stochastic perturbation of the phase field alpha-Navier-Stokes model with vesicle-fluid interaction. It consists in a system of nonlinear evolution partial differential equations modeling the fluid-structure interaction…
We study suspensions of solid particles in a viscous incompressible fluid in the presence of highly oscillatory velocity-dependent surface forces. The flow at a small Reynolds number is modeled by the Stokes equations coupled with the…
The mobility of an overdamped particle, in a periodic potential tilted by a constant external field and moving in a medium with periodic friction coefficient is examined. When the potential and the friction coefficient have the same…
Modeling a precipitation field is challenging due to its intermittent and highly scale-dependent nature. Motivated by the features of high-frequency precipitation data from a network of rain gauges, we propose a threshold space-time $t$…
This work deals with two real scalar fields in two-dimensional spacetime, with the fields coupled to allow the study of localized configurations. We consider models constructed to engender geometric constrictions, and use them to…
We develop a general theory dealing with stochastic models for dynamical systems that are governed by various nonlinear, ordinary or partial differential, equations. In particular, we address the problem how flows in the random medium…
In a wide range of applications, the stochastic properties of the observed time series change over time. The changes often occur gradually rather than abruptly: the properties are (approximately) constant for some time and then slowly start…
In this paper, the single-spin transition dynamics is used to investigate the kinetic Gaussian model in a periodic external field. We first derive the fundamental dynamic equations, and then treat an isotropic d-dimensional hypercubic…
Numerical simulations of a model of plane Couette flow focusing on its in-plane spatio-temporal properties are used to study the dynamics of turbulent spots.
We introduce a class of isotropic time dependent random fields on the non-homogeneous sphere represented by a time-changed spherical Brownian motion of order \nu \in (0,1] with which some anisotrophies can be captured in Cosmology. This…
The mean-field limit of a Markovian model describing the interaction of several classes of permanent connections in a network is analyzed. Each of the connections has a self-adaptive behavior in that its transmission rate along its route…
A stationary spatial model is an idealization and we expect that the true dependence structures of physical phenomena are spatially varying, but how should we handle this non-stationarity in practice? We study the challenges involved in…
The modeling of risk situations that occur in a space-time framework can be done using max-stable random fields on lattices. Although the summary coefficients for the spatial and temporal behaviour do not characterize the finite-dimensional…
We investigate a stochastic model hierarchy for pedestrian flow. Starting from a microscopic social force model, where the pedestrians switch randomly between the two states stop-or-go, we derive an associated macroscopic model of…
The method of point transformation of the functions and variables for construction of particular solutions of the Equations of Nonstationary Transonic Gas Flows is used.
Traffic flow is a very prominent example of a driven non-equilibrium system. A characteristic phenomenon of traffic dynamics is the spontaneous and abrupt drop of the average velocity on a stretch of road leading to congestion. Such a…
We consider the motion of a particle governed by a weakly random Hamiltonian flow. We identify temporal and spatial scales on which the particle trajectory converges to a spatial Brownian motion. The main technical issue in the proof is to…