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The seminal physical model for investigating formulations of nonlinear dynamics is the billiard. Gravitational billiards provide an experimentally accessible arena for their investigation. We present a mathematical model that captures the…
We suggest a simple synthesis model of an eclipsing binary system which includes one component with strong stellar wind. Numerical simulations show that the shape of the light curve (and in particularly the widths of the minima) strongly…
We consider three different schemes for signal routing on a tree. The vertices of the tree represent transceivers that can transmit and receive signals, and are equipped with i.i.d. weights representing the strength of the transceivers. The…
A micro-hydrodynamics model based on elastic collisions of light point solvent particles with a heavy solute particle is investigated in the setting where the light particles have velocity distribution corresponding to a background flow.…
We define a new class of plane billiards - the `pensive billiard' - in which the billiard ball travels along the boundary for some distance depending on the incidence angle before reflecting, while preserving the billiard rule of equality…
The propagation speed of a circumstellar pattern revealed in the plane of the sky is often assumed to represent the expansion speed of the wind matter ejected from a post-main-sequence star at the center. We point out that the often-adopted…
This paper presents a statistical model for stationary ergodic point processes, estimated from a single realization observed in a square window. With existing approaches in stochastic geometry, it is very difficult to model processes with…
The dynamics of a beam held on a horizontal frame by springs and bouncing off a step is described by a separable two degrees of freedom Hamiltonian system with impacts that respect, point wise, the separability symmetry. The energy in each…
In acoustics, ultrasonics and in electromagnetic wave propagation, the crossed medium can be often modelled by a linear invariant filter (LIF) which acts on a wide-sense stationary process. Its complex gain follows the Beer-Lambert law i.e…
The problem of partially hinged and partially free rectangular plate that aims to represent a suspension bridge subject to some external forces (for example the wind) is considered in order to model and simulate the unstable end behavior.…
We consider a dynamical system on a metric graph, that corresponds to a semiclassical solution of a time-dependent Schr\"odinger equation. We omit all details concerning mathematical physics and work with a purely discrete problem. We find…
Active Matter models commonly consider particles with overdamped dynamics subject to a force (speed) with constant modulus and random direction. Some models include also random noise in particle displacement (Wiener process) resulting in a…
We provide a numerical study of the macroscopic model of [3] derived from an agent-based model for a system of particles interacting through a dynamical network of links. Assuming that the network remodelling process is very fast, the…
We investigate particle transport in the honeycomb billiard that consists of connected channels placed on the edges of a honeycomb structure. The spreading of particles is superdiffusive due to the existence of ballistic trajectories which…
Billiard models of single particles moving freely in two-dimensional regions enclosed by hard walls, have long provided ideal toy models for the investigation of dynamical systems and chaos. Recently, billiards with (semi-)permeable walls…
The motion of a particle in a correlated random potential under the influence of a driving force is investigated in mean field theory. The correlations of the disorder are characterized by a short distance cutoff and a power law decay with…
Periodic trees are combinatorial structures which are in bijection with cluster tilting objects in cluster categories of affine type $\tilde{A}_{n-1}$. The internal edges of the tree encode the $c$-vectors corresponding to the cluster…
We study the biased diffusion of particles moving in one direction under the action of a constant force in the presence of a piecewise linear random potential. Using the overdamped equation of motion, we represent the first and second…
What we are going to call in this paper "diffractive phenomena" in billiards is far from being deeply understood. These are sorts of singularities that, for example, some kind of corners introduce in the energy eigenfunctions. In this paper…
We consider a slowly rotating rectangular billiard with moving boundaries and use the canonical perturbation theory to describe the dynamics of a billiard particle. In the process of slow evolution certain resonance conditions can be…