2,558 research outputs found
Controllability for chains of dynamical scatterers
In this paper, we consider a class of mechanical models which consists of a
linear chain of identical chaotic cells, each of which has two small lateral
holes and contains a rotating disk at its center. Particles are injected at
characteristic temperatures and rates from stochastic heat baths located at
both ends of the chain. Once in the system, the particles move freely within
the cells and will experience elastic collisions with the outer boundary of the
cells as well as with the disks. They do not interact with each other but can
transfer energy from one to another through collisions with the disks. The
state of the system is defined by the positions and velocities of the particles
and by the angular positions and angular velocities of the disks. We show that
each model in this class is controllable with respect to the baths, i.e. we
prove that the action of the baths can drive the system from any state to any
other state in a finite time. As a consequence, one obtains the existence of at
most one regular invariant measure characterizing its states (out of
equilibrium)
Temperature Profiles in Hamiltonian Heat Conduction
We study heat transport in the context of Hamiltonian and related stochastic
models with nearest-neighbor coupling, and derive a universal law for the
temperature profiles of a large class of such models. This law contains a
parameter , and is linear only when . The value of
depends on energy-exchange mechanisms, including the range of motion of tracer
particles and their times of flight.Comment: Revised text, same results Second revisio
Dual Fronts Propagating into an Unstable State
The interface between an unstable state and a stable state usually develops a
single confined front travelling with constant velocity into the unstable
state. Recently, the splitting of such an interface into {\em two} fronts
propagating with {\em different} velocities was observed numerically in a
magnetic system. The intermediate state is unstable and grows linearly in time.
We first establish rigorously the existence of this phenomenon, called ``dual
front,'' for a class of structurally unstable one-component models. Then we use
this insight to explain dual fronts for a generic two-component
reaction-diffusion system, and for the magnetic system.Comment: 19 pages, Postscript, A
Network dynamics of ongoing social relationships
Many recent large-scale studies of interaction networks have focused on
networks of accumulated contacts. In this paper we explore social networks of
ongoing relationships with an emphasis on dynamical aspects. We find a
distribution of response times (times between consecutive contacts of different
direction between two actors) that has a power-law shape over a large range. We
also argue that the distribution of relationship duration (the time between the
first and last contacts between actors) is exponentially decaying. Methods to
reanalyze the data to compensate for the finite sampling time are proposed. We
find that the degree distribution for networks of ongoing contacts fits better
to a power-law than the degree distribution of the network of accumulated
contacts do. We see that the clustering and assortative mixing coefficients are
of the same order for networks of ongoing and accumulated contacts, and that
the structural fluctuations of the former are rather large.Comment: to appear in Europhys. Let
Properties of Stationary Nonequilibrium States in the Thermostatted Periodic Lorentz Gas II: The many point particles system
We study the stationary nonequilibrium states of N point particles moving
under the influence of an electric field E among fixed obstacles (discs) in a
two dimensional torus. The total kinetic energy of the system is kept constant
through a Gaussian thermostat which produces a velocity dependent mean field
interaction between the particles. The current and the particle distribution
functions are obtained numerically and compared for small E with analytic
solutions of a Boltzmann type equation obtained by treating the collisions with
the obstacles as random independent scatterings. The agreement is surprisingly
good for both small and large N. The latter system in turn agrees with a self
consistent one particle evolution expected to hold in the limit of N going to
infinity.Comment: 14 pages, 9 figure
A numerical study of infinitely renormalizable area-preserving maps
It has been shown in (Gaidashev et al, 2010) and (Gaidashev et al, 2011) that
infinitely renormalizable area-preserving maps admit invariant Cantor sets with
a maximal Lyapunov exponent equal to zero. Furthermore, the dynamics on these
Cantor sets for any two infinitely renormalizable maps is conjugated by a
transformation that extends to a differentiable function whose derivative is
Holder continuous of exponent alpha>0.
In this paper we investigate numerically the specific value of alpha. We also
present numerical evidence that the normalized derivative cocycle with the base
dynamics in the Cantor set is ergodic. Finally, we compute renormalization
eigenvalues to a high accuracy to support a conjecture that the renormalization
spectrum is real
Large deviations of lattice Hamiltonian dynamics coupled to stochastic thermostats
We discuss the Donsker-Varadhan theory of large deviations in the framework
of Hamiltonian systems thermostated by a Gaussian stochastic coupling. We
derive a general formula for the Donsker-Varadhan large deviation functional
for dynamics which satisfy natural properties under time reversal. Next, we
discuss the characterization of the stationary state as the solution of a
variational principle and its relation to the minimum entropy production
principle. Finally, we compute the large deviation functional of the current in
the case of a harmonic chain thermostated by a Gaussian stochastic coupling.Comment: Revised version, published in Journal of Statistical Physic
On Turing dynamical systems and the Atiyah problem
Main theorems of the article concern the problem of M. Atiyah on possible
values of l^2-Betti numbers. It is shown that all non-negative real numbers are
l^2-Betti numbers, and that "many" (for example all non-negative algebraic)
real numbers are l^2-Betti numbers of simply connected manifolds with respect
to a free cocompact action. Also an explicit example is constructed which leads
to a simply connected manifold with a transcendental l^2-Betti number with
respect to an action of the threefold direct product of the lamplighter group
Z/2 wr Z. The main new idea is embedding Turing machines into integral group
rings. The main tool developed generalizes known techniques of spectral
computations for certain random walk operators to arbitrary operators in
groupoid rings of discrete measured groupoids.Comment: 35 pages; essentially identical to the published versio
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