Related papers: On a stationary random knot
The topological analysis of chaos based on a knot-theoretic characterization of unstable periodic orbits has proved a powerful method, however knot theory can only be applied to three-dimensional systems. Still, the core principles upon…
We numerically study the evolution of a small turbulent region of quantised vorticity in superfluid helium, a regime which can be realised in the laboratory. We show that the turbulence achieves a fluctuating steady-state in terms of…
We construct two knot invariants. The first knot invariant is a sum constructed using linking numbers. The second is an invariant of flat knots and is a formal sum of flat knots obtained by smoothing pairs of crossings. This invariant can…
We study the motion of elastic networks driven over a random substrate. Our model which includes local friction forces leads to complex dynamical behavior. We find a transition to a sliding state which belongs to a new universality class.…
This paper is centered on the random graph generated by a Doeblin-type coupling of discrete time processes on a countable state space whereby when two paths meet, they merge. This random graph is studied through a novel subgraph, called a…
We explore topological edge states in periodically driven nonlinear systems. Based on a self-consistency method adjusted to periodically driven systems, we obtain stationary states associated with topological phases unique to Floquet…
I review few conceptual steps in analytic description of topological interactions, which constitute the basis of a new interdisciplinary branch in mathematical physics, "Statistical Topology", emerged at the edge of topology and statistical…
We propose a new mechanism for pattern formation based on the global alternation of two dynamics neither of which exhibits patterns. When driven by either one of the separate dynamics, the system goes to a spatially homogeneous state…
In many interesting physical settings, such as the vulcanization of rubber, the introduction of permanent random constraints between the constituents of a homogeneous fluid can cause a phase transition to a random solid state. In this…
The properties of motion close to the transition of a stable family of periodic orbits to complex instability is investigated with two symplectic 4D mappings, natural extensions of the standard mapping. As for the other types of…
This paper deals a continuous-time state-dependent jump linear system, a particular kind of stochastic switching system. In particular, we consider a situation when the transition rate of the random jump process depends on the state…
We examine theoretically the effects of random topographical substrates on the motion of two-dimensional droplets via appropriate statistical approaches. Different random substrate families are represented as stationary random functions.…
Time-delayed control in a balancing problem may be a nonsmooth function for a variety of reasons. In this paper we study a simple model of the control of an inverted pendulum by either a connected movable cart or an applied torque for which…
It is shown that a random binary process with impulse-like autocorrelation can be generated by randomizing the length of symbols occurring in a random Bernoulli process. Such randomization is achieved by random (or judiciously designed…
A two dimensional flow model is introduced with deterministic behavior consisting of bursts which become successively larger, with longer interburst time intervals between them. The system is symmetric in one variable x and there are bursts…
We address the dynamics of interacting particles on a disordered lattice formed by a random comb. The dynamics comprises that of the asymmetric simple exclusion process, whereby motion to nearest-neighour sites that are empty is more likely…
A switching random walk, commonly known under the misnomer `oscillating random walk', is a real-valued Markov chain whose distribution of increments is determined by the sign of the current position. We explicitly identify an invariant…
We study the structure of stationary non equilibrium states for interacting particle systems from a microscopic viewpoint. In particular we discuss two different discrete geometric constructions. We apply both of them to determine non…
This work is concerned with the stability properties of linear stochastic differential equations with random (drift and diffusion) coefficient matrices, and the stability of a corresponding random transition matrix (or exponential…
Localized noncommutative structures for manifolds with connection are constructed based on the use of vertical star products. The model's main feature is that two points that are far away from each other will not be subject to a deviation…