Related papers: Local Stability of Dynamical Processes in Random M…
The universal fractality of river networks is very well known, however understanding of the underlying mechanisms for them is still lacking in terms of stochastic processes. By introducing probability changing dynamically, we have described…
The aim of the present paper is to provide necessary and sufficient conditions to maintain a stochastic coupled system, with porous media components and gradient-type noise in a prescribed set of constraints by using internal controls. This…
In this work, we deal with the stochastic counterpart of the nonlocal Cahn-Hilliard equation with regular potential in a smooth bounded one-, two- or three-dimensional domain. The problem is endowed with homogeneous Neumann boundary…
The emergence of localised radial patterns from a Turing instability has been well studied in two and three dimensional settings and predicted for higher spatial dimensions. We prove the existence of localised $(n+1)$-dimensional radial…
We consider the problem of adaptive stabilization for discrete-time, multi-dimensional linear systems with bounded control input constraints and unbounded stochastic disturbances, where the parameters of the true system are unknown. To…
We present a new diffuse interface model for the dynamics of inextensible vesicles in a viscous fluid. A new feature of this work is the implementation of the local inextensibility condition in the diffuse interface context. Local…
We introduce the notion of a quasistatic dynamical system, which generalizes that of an ordinary dynamical system. Quasistatic dynamical systems are inspired by the namesake processes in thermodynamics, which are idealized processes where…
A calculational approach in fluid turbulence is presented. Use is made of the attracting nature of the fluid-dynamic dynamical system. An approach is offered that effectively propagates the statistics in time. Loss of sensitivity to an…
A formalism is introduced to describe a number of physical processes that may break down the coherence of a matter wave over a characteristic length scale l. In a second-quantized description, an appropriate master equation for a set of…
The influence of small random perturbations on a deterministic dynamical system with a locally stable equilibrium is considered. The perturbed system is described by the It\^{o} stochastic differential equation. It is assumed that the noise…
An ensemble of classical subsystems interacting with surrounding particles has been considered. In general case, a phase volume of the subsystems ensemble was shown to be a function of time. The evolutional equations of the ensemble are…
Stochastic hydrodynamics provides a dynamical framework for the evolution of fluctuations in heavy-ion collisions, but poses significant challenges in numerical simulations. We present an algorithm for the simulation of non-relativistic…
We develop a rigorous treatment of discontinuous stochastic unitary evolution for a system of quantum particles that interacts singularly with quantum "bubbles" at random instants of time. This model of a "cloud chamber" allows to watch and…
We develop here the method for obtaining approximate stability boundaries in the space of parameters for systems with parametric excitation. The monodromy (Floquet) matrix of linearized system is found by averaging method. For system with 2…
This thesis consists of two separate parts: in each we study the stability under small perturbations of certain probability models in different contexts. In the first, we study small random perturbations of a deterministic dynamical system…
The predictability of turbulent flows remains a challenging problem for mathematicians, physicists, and meteorologists. In this context, we consider the 3D incompressible Navier-Stokes equations with small-scale random forcing on…
At the macroscopic scale, many important models of collective motion fall into the class of kinematic flows for which both velocity and diffusion terms depend only on particle density. When total particle numbers are fixed and finite,…
Stability of dynamical systems is a central topic with applications in widespread areas such as economy, biology, physics and mechanical engineering. The dynamics of nonlinear systems may completely change due to perturbations forcing the…
Randomly-assembled dynamical systems are theoretically predicted to be unstable upon crossing a critical threshold of complexity, as first shown by May. Yet, empirical complex systems exhibit remarkable stability, indicating the presence of…
The effect of focusing and defocusing nonlinearities on Anderson localization in highly nonlocal media is theoretically and numerically investigated. A perturbative approach is developed to solve the nonlocal nonlinear Schroedinger equation…