325 research outputs found
A new approach to the chap LQ regulator exploiting the geometric properties of the Hamiltonian system
The cheap LQ regulator is reinterpreted as an output nulling problem which is a basic problem of the geometric control theory. In fact, solving the LQ regulator problem is equivalent to keep the output of the related Hamiltonian system identically zero. The solution lies on a controlled invariant subspace whose dimension is characterized in terms of the minimal conditioned invariant of the original system, and the optimal feedback gain is computed as the friend matrix of the resolving subspace. This study yields a new computational framework for the cheap LQ regulator, relying only on the very basic and simple tools of the geometric approach, namely the algorithms for controlled and conditioned invariant subspaces and invariant zeros
Binary Reactive Adsorbate on a Random Catalytic Substrate
We study the equilibrium properties of a model for a binary mixture of
catalytically-reactive monomers adsorbed on a two-dimensional substrate
decorated by randomly placed catalytic bonds. The interacting and
monomer species undergo continuous exchanges with particle reservoirs and react
() as soon as a pair of unlike particles appears on sites
connected by a catalytic bond.
For the case of annealed disorder in the placement of the catalytic bonds
this model can be mapped onto a classical spin model with spin values , with effective couplings dependent on the temperature and on the mean
density of catalytic bonds. This allows us to exploit the mean-field theory
developed for the latter to determine the phase diagram as a function of in
the (symmetric) case in which the chemical potentials of the particle
reservoirs, as well as the and interactions are equal.Comment: 12 pages, 4 figure
Exactly Solvable Model of Monomer-Monomer Reactions on a Two-Dimensional Random Catalytic Substrate
We present an \textit{exactly solvable} model of a monomer-monomer reaction on a 2D inhomogeneous, catalytic substrate and study the
equilibrium properties of the two-species adsorbate. The substrate contains
randomly placed catalytic bonds of mean density which connect neighboring
adsorption sites. The interacting and (monomer) species undergo
continuous exchanges with corresponding adjacent gaseous reservoirs. A reaction
takes place instantaneously if and particles
occupy adsorption sites connected by a catalytic bond. We find that for the
case of \textit{annealed} disorder in the placement of the catalytic bonds the
reaction model under study can be mapped onto the general spin (GS1)
model. Here we concentrate on a particular case in which the model reduces to
an exactly solvable Blume-Emery-Griffiths (BEG) model (T. Horiguchi, Phys.
Lett. A {\bf 113}, 425 (1986); F.Y. Wu, Phys. Lett. A, {\bf 116}, 245 (1986))
and derive an exact expression for the disorder-averaged equilibrium pressure
of the two-species adsorbate. We show that at equal partial vapor pressures of
the and species this system exhibits a second-order phase transition
which reflects a spontaneous symmetry breaking with large fluctuations and
progressive coverage of the entire substrate by either one of the species.Comment: 4 pages, 2 figures, submitted to Phys. Rev. Let
Survival Probabilities of History-Dependent Random Walks
We analyze the dynamics of random walks with long-term memory (binary chains
with long-range correlations) in the presence of an absorbing boundary. An
analytically solvable model is presented, in which a dynamical phase-transition
occurs when the correlation strength parameter \mu reaches a critical value
\mu_c. For strong positive correlations, \mu > \mu_c, the survival probability
is asymptotically finite, whereas for \mu < \mu_c it decays as a power-law in
time (chain length).Comment: 3 pages, 2 figure
Survival probabilities in time-dependent random walks
We analyze the dynamics of random walks in which the jumping probabilities
are periodic {\it time-dependent} functions. In particular, we determine the
survival probability of biased walkers who are drifted towards an absorbing
boundary. The typical life-time of the walkers is found to decrease with an
increment of the oscillation amplitude of the jumping probabilities. We discuss
the applicability of the results in the context of complex adaptive systems.Comment: 4 pages, 3 figure
Population Dynamics in Spatially Heterogeneous Systems with Drift: the generalized contact process
We investigate the time evolution and stationary states of a stochastic,
spatially discrete, population model (contact process) with spatial
heterogeneity and imposed drift (wind) in one- and two-dimensions. We consider
in particular a situation in which space is divided into two regions: an oasis
and a desert (low and high death rates). Carrying out computer simulations we
find that the population in the (quasi) stationary state will be zero,
localized, or delocalized, depending on the values of the drift and other
parameters. The phase diagram is similar to that obtained by Nelson and
coworkers from a deterministic, spatially continuous model of a bacterial
population undergoing convection in a heterogeneous medium.Comment: 8 papes, 12 figure
Steady States of a Nonequilibrium Lattice Gas
We present a Monte Carlo study of a lattice gas driven out of equilibrium by
a local hopping bias. Sites can be empty or occupied by one of two types of
particles, which are distinguished by their response to the hopping bias. All
particles interact via excluded volume and a nearest-neighbor attractive force.
The main result is a phase diagram with three phases: a homogeneous phase, and
two distinct ordered phases. Continuous boundaries separate the homogeneous
phase from the ordered phases, and a first-order line separates the two ordered
phases. The three lines merge in a nonequilibrium bicritical point.Comment: 14 pages, 24 figure
Exactly solvable model of A + A \to 0 reactions on a heterogeneous catalytic chain
We present an exact solution describing equilibrium properties of the
catalytically-activated A + A \to 0 reaction taking place on a one-dimensional
lattice, where some of the sites possess special "catalytic" properties. The A
particles undergo continuous exchanges with the vapor phase; two neighboring
adsorbed As react when at least one of them resides on a catalytic site (CS).
We consider three situations for the CS distribution: regular, annealed random
and quenched random. For all three CS distribution types, we derive exact
results for the disorder-averaged pressure and present exact asymptotic
expressions for the particles' mean density. The model studied here furnishes
another example of a 1D Ising-type system with random multi-site interactions
which admits an exact solution.Comment: 7 pages, 3 Figures, appearing in Europhysics Letter
Phase separation in systems with absorbing states
We study the problem of phase separation in systems with a positive definite
order parameter, and in particular, in systems with absorbing states. Owing to
the presence of a single minimum in the free energy driving the relaxation
kinetics, there are some basic properties differing from standard phase
separation. We study analytically and numerically this class of systems; in
particular we determine the phase diagram, the growth laws in one and two
dimensions and the presence of scale invariance. Some applications are also
discussed.Comment: Submitted to Europhysics Let
Cluster approximations for infection dynamics on random networks
In this paper, we consider a simple stochastic epidemic model on large
regular random graphs and the stochastic process that corresponds to this
dynamics in the standard pair approximation. Using the fact that the nodes of a
pair are unlikely to share neighbors, we derive the master equation for this
process and obtain from the system size expansion the power spectrum of the
fluctuations in the quasi-stationary state. We show that whenever the pair
approximation deterministic equations give an accurate description of the
behavior of the system in the thermodynamic limit, the power spectrum of the
fluctuations measured in long simulations is well approximated by the
analytical power spectrum. If this assumption breaks down, then the cluster
approximation must be carried out beyond the level of pairs. We construct an
uncorrelated triplet approximation that captures the behavior of the system in
a region of parameter space where the pair approximation fails to give a good
quantitative or even qualitative agreement. For these parameter values, the
power spectrum of the fluctuations in finite systems can be computed
analytically from the master equation of the corresponding stochastic process.Comment: the notation has been changed; Ref. [26] and a new paragraph in
Section IV have been adde
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