相关论文: Switched flow systems: pseudo billiard dynamics

The design of decision and control strategies for switched systems typically requires complete knowledge of (i) mathematical models of the subsystems and (ii) restrictions on admissible switches between the subsystems. We propose an active…

We define variational properties for dynamical systems with subexponential complexity, and study these properties in certain specific examples. By computing the value of slow entropy directly, we show that some subshifts are not…

Rational polygonal billiards are one of the key models among the larger class of pseudo-integrable billiards. Their billiard flow may be lifted to the geodesic flow on a translation surface. Whereas such classical billiards have been much…

Novel technological applications often involve fluid flows in the Knudsen regime in which the mean free path is comparable to the system size. We use molecular dynamics simulations to study the transition between the dilute gas and the…

We study the dynamics of a bouncing coin whose motion is restricted to the two-dimensional plane. Such coin model is equivalent to the system of two equal masses connected by a rigid rod, making elastic collisions with a flat boundary. We…

We explore some beginning steps in stochastic thermodynamics of billiard-like mechanical systems by introducing extremely simple and explicit random mechanical processes capable of exhibiting steady-state irreversible thermodynamical…

Motivated by the study of billiards in polyhedra, we study linear flows in a family of singular flat $3$-manifolds which we call translation prisms. Using ideas of Furstenberg and Veech, we connect results about weak mixing properties of…

In this paper we study the ergodic properties of mathematical billiards describing the uniform motion of a point in a flat torus from which finitely many, pairwise disjoint, tubular neighborhoods of translated subtori (the so called…

Time-discrete dynamical systems on a finite state space have been used with great success to model natural and engineered systems such as biological networks, social networks, and engineered control systems. They have the advantage of being…

Billiards tables - a minimal model for particles moving in a confined region - are known to present classical (and quantum) different features according to their shape, ranging from strongly chaotic to integrable dynamics. Here we consider…

Many complex systems satisfy a set of constraints on their degrees of freedom, and at the same time, they are able to work and adapt to different conditions. Here, we describe the emergence of this ability in a simplified model in which the…

Slow dynamics in an amorphous quasi-two-dimensional complex plasma, comprised of microparticles of two different sizes, was studied experimentally. The motion of individual particles was observed using video microscopy, and the self-part of…

We examine the linear stability of fluid interfaces subjected to a shear flow. Our main object is to generalize previous work to arbitrary Atwood number, and to allow for surface tension and weak compressibility. The motivation derives from…

We investigate the dynamics of no-slip billiards, a model in which small rotating disks may exchange linear and angular momentum at collisions with the boundary. We give new results on periodicity and boundedness of orbits which suggest…

We analyze the morphological transition of a one-dimensional system described by a scalar field, where a flat state looses its stability. This scalar field may for example account for the position of a crystal growth front, an order…

We call a system bouncing ball billiard if it consists of a particle that is subjected to a constant vertical force and bounces inelastically on a one-dimendional vibrating periodically corrugated floor. Here we choose circular scatterers…

The behavior of complex systems is determined not only by the topological organization of their interconnections but also by the dynamical processes taking place among their constituents. A faithful modeling of the dynamics is essential…

A hard-wall billiard is a mathematical model describing the confinement of a free particle that collides specularly and instantaneously with boundaries and discontinuities. Soft billiards are a generalization that includes a smooth boundary…

Spatial diffusion of particles in periodic potential models has provided a good framework for studying the role of chaos in global properties of classical systems. Here a bidimensional "soft" billiard, classically modeled from an optical…

We introduce a cellular automaton model coupled with a transport equation for flows on graphs. The direction of the flow is described by a switching process where the switching probability dynamically changes according to the value of the…