Related papers: Orbits closeness for slowly mixing dynamical syste…

We investigate quantifying the difference between two hybrid dynamical systems under noise and initial-state uncertainty. While the set of traces for these systems is infinite, it is possible to symbolically approximate trace sets using…

We study the flow of fluid in porous media in dimensions $d=2$ and 3. The medium is modeled by bond percolation on a lattice of $L^d$ sites, while the flow front is modeled by tracer particles driven by a pressure difference between two…

We consider a chain of $n$ coupled oscillators placed on a one-dimensional lattice with periodic boundary conditions. The interaction between particles is determined by a weakly anharmonic potential $V_n = r^2/2 + \sigma_nU(r)$, where $U$…

Very weakly bound systems may manifest intriguing "universal" properties, independent of the specific interaction which keeps the system bound. An interesting example is given by relations between the size of the system and the separation…

The stability of the orbital motion of two long cylindrical magnets interacting exclusively with magnetic forces is described. To carry out analytical studies a model of magnetically interacting symmetric tops [1] is used. The model was…

Minimising movements are investigated for an energy which is the superposition of a convex functional and fast small oscillations. Thus a minimising movement scheme involves a temporal parameter $\tau$ and a spatial parameter $\epsilon$,…

This paper provides a brief overview of dynamo scaling relationships for the degree of equipartition between magnetic and kinetic energies. Three basic approaches are adopted to explore these scaling relationships, with a first look at two…

Given a collection of n opaque unit disks in the plane, we want to find a stacking order for them that maximizes their visible perimeter---the total length of all pieces of their boundaries visible from above. We prove that if the centers…

We are interested in a kinetic equation intended to describe the interactions of particles with their environment. We focus on the long time behaviour. We prove that the time derivative of the spatial density goes to 0 and exhibit the omega…

We study the minimum time related to the quantum speed limit that characterizes the evolution of an open quantum system with the help of a simple model in the short and long time limits. We compare in particular the situation corresponding…

We consider a switched system of two subsystems that are activated as the trajectory enters the regions $\{(x,y):x>\bar x\}$ and $\{(x,y):x<-\bar x\}$ respectively, where $\bar x$ is a positive parameter. We prove that a regular…

The effective interaction between two probe particles in a one-dimensional driven system is studied. The analysis is carried out using an asymmetric simple exclusion process with nearest-neighbor interactions. It is found that the driven…

We propose a two-dimensional flow model of a viscous fluid between two close moving surfaces. We show that its asymptotic behavior, when the distance between the two surfaces tends to zero, is the same as that of the the Navier-Stokes…

For a large class of quickly mixing dynamical systems, we prove that the error in the almost sure approximation with a Brownian motion is of order O((log n)^a) with a $\ge$ 2. Specifically, we consider nonuniformly expanding maps with…

We study fundamental reachability problems on pseudo-orbits of linear dynamical systems. Pseudo-orbits can be viewed as a model of computation with limited precision and pseudo-reachability can be thought of as a robust version of classical…

We show that transport in the presence of entropic barriers exhibits peculiar characteristics which makes it distinctly different from that occurring through energy barriers. The constrained dynamics yields a scaling regime for the particle…

Among the several topological properties of complex networks, the shortest path represents a particularly important characteristic because of its potential impact not only on other topological properties, but mainly for its influence on…

Using Newtonian and Brownian dynamics simulations, the structural and transport properties of hard and soft spheres have been studied. The soft spheres were modeled using inverse power potentials ($V\sim r^{-n}$, with $1/n$ the potential…

Periodic orbit theory provides two important functions---the dynamical zeta function and the spectral determinant for the calculation of dynamical averages in a nonlinear system. Their cycle expansions converge rapidly when the system is…

Dust-gas mixtures are the simplest example of a two fluid mixture. We show that when simulating such mixtures with particles or with particles coupled to grids a problem arises due to the need to resolve a very small length scale when the…