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We present a stochastic turbulence generator based on a vorticity formulation where the generated turbulent field implicitly fulfills the kinematic constraints of an incompressible flow. The generator allows direct access to the turbulent…
A sequence of large invertible matrices given by a small random perturbation around a fixed diagonal and positive matrix induces a random dynamics on a high-dimensional sphere. For a certain class of rotationally invariant random…
We study the cosmological dynamics of non-minimally coupled matter models using the Brown's variational approach to relativistic fluids in General Relativity. After decomposing the Ricci scalar into a bulk and a boundary term, we construct…
We study the traffic flow on a highway with ramps through numerical simulations of a hydrodynamic traffic flow model. It is found that the presence of the external vehicle flux through ramps generates a new state of recurring humps (RH).…
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…
The method of distributions is developed for systems that are governed by hyperbolic conservation laws with stochastic forcing. The method yields a deterministic equation for the cumulative density distribution (CDF) of a system state,…
We discuss some important issues arising from computational efforts in dynamical systems and fluid dynamics. Various individuals have misunderstood these issues since the onset of these problem areas; indeed, they have been routinely…
Most literature on quantum collision models (CMs) usually considers periodic weak collisions featuring a fixed waiting time between two next collisions. Some works have yet addressed CMs with random waiting time and strong collisions…
We construct classes of stochastic differential equations with fluctuating friction forces that generate a dynamics correctly described by Tsallis statistics and nonextensive statistical mechanics. These systems generalize the way in which…
We consider a statistical limit of solutions to the compressible Navier--Stokes system in the high Reynolds number regime in a domain exterior to a rigid body. We investigate to what extent this highly turbulent regime can be modeled by an…
Some topological properties of stochastic flow $\varphi_t(x)$ generated by stochastic differential equation in a ${\mathbb R}^d_+$ with normal reflection at the boundary are investigated. Sobolev differentiability in initial condition is…
We show by means of experiments, theory and simulations, that the slow dynamics of coarsening systems displays dynamic heterogeneity similar to that observed in glass-forming systems. We measure dynamic heterogeneity via novel multi-point…
A stochastic differential equation with coefficients defined in a scale of Hilbert spaces is considered. The existence and uniqueness of finite time solutions is proved by an extension of the Ovsyannikov method. This result is applied to a…
The inclusion of stochastic terms in equations of motion for fluid problems enables a statistical representation of processes which are left unresolved by numerical computation. Here, we derive stochastic equations for the behaviour of…
Stochastic HYPE is a novel process algebra that models stochastic, instantaneous and continuous behaviour. It develops the flow-based approach of the hybrid process algebra HYPE by replacing non-urgent events with events with…
A new vehicular traffic flow model based on a stochastic jump process in vehicle acceleration and braking is introduced. It is based on a master equation for the single car probability density in space, velocity and acceleration with an…
Some properties of random Conley index are obtained and then a sufficient condition for the existence of abstract bifurcation points for both discrete-time and continuous-time random dynamical systems is presented. This stochastic…
The stochastic thermodynamics provides a framework for the description of systems that are out of thermodynamic equilibrium. It is based on the assumption that the elementary constituents are acted by random forces that generate a…
We search for steady states in a class of fluctuating and driven physical systems that exhibit sustained currents. We find that the physical concept of a steady state, well known for systems at equilibrium, must be generalised to describe…
A fluid motion through the flow element is presented in the kind of an autooscillating system with the distributed parameters: mass, elasticity, viscosity. The system contains a self-excited oscillator and possesses a self-regulation on…