350 research outputs found
LNCS
We define the model-measuring problem: given a model M and specification Ï, what is the maximal distance Ï such that all models MâČ within distance Ï from M satisfy (or violate) Ï. The model measuring problem presupposes a distance function on models. We concentrate on automatic distance functions, which are defined by weighted automata. The model-measuring problem subsumes several generalizations of the classical model-checking problem, in particular, quantitative model-checking problems that measure the degree of satisfaction of a specification, and robustness problems that measure how much a model can be perturbed without violating the specification. We show that for automatic distance functions, and Ï-regular linear-time and branching-time specifications, the model-measuring problem can be solved. We use automata-theoretic model-checking methods for model measuring, replacing the emptiness question for standard word and tree automata by the optimal-weight question for the weighted versions of these automata. We consider weighted automata that accumulate weights by maximizing, summing, discounting, and limit averaging. We give several examples of using the model-measuring problem to compute various notions of robustness and quantitative satisfaction for temporal specifications
Field theory of directed percolation with long-range spreading
It is well established that the phase transition between survival and
extinction in spreading models with short-range interactions is generically
associated with the directed percolation (DP) universality class. In many
realistic spreading processes, however, interactions are long ranged and well
described by L\'{e}vy-flights, i.e., by a probability distribution that decays
in dimensions with distance as . We employ the powerful
methods of renormalized field theory to study DP with such long range,
L\'{e}vy-flight spreading in some depth. Our results unambiguously corroborate
earlier findings that there are four renormalization group fixed points
corresponding to, respectively, short-range Gaussian, L\'{e}vy Gaussian,
short-range DP and L\'{e}vy DP, and that there are four lines in the plane which separate the stability regions of these fixed points. When the
stability line between short-range DP and L\'{e}vy DP is crossed, all critical
exponents change continuously. We calculate the exponents describing L\'{e}vy
DP to second order in -expansion, and we compare our analytical
results to the results of existing numerical simulations. Furthermore, we
calculate the leading logarithmic corrections for several dynamical
observables.Comment: 12 pages, 3 figure
Multifractal properties of resistor diode percolation
Focusing on multifractal properties we investigate electric transport on
random resistor diode networks at the phase transition between the
non-percolating and the directed percolating phase. Building on first
principles such as symmetries and relevance we derive a field theoretic
Hamiltonian. Based on this Hamiltonian we determine the multifractal moments of
the current distribution that are governed by a family of critical exponents
. We calculate the family to two-loop order in a
diagrammatic perturbation calculation augmented by renormalization group
methods.Comment: 21 pages, 5 figures, to appear in Phys. Rev.
Nonequilibrium wetting
When a nonequilibrium growing interface in the presence of a wall is
considered a nonequilibrium wetting transition may take place. This transition
can be studied trough Langevin equations or discrete growth models. In the
first case, the Kardar-Parisi-Zhang equation, which defines a very robust
universality class for nonequilibrium moving interfaces, with a soft-wall
potential is considered. While in the second, microscopic models, in the
corresponding universality class, with evaporation and deposition of particles
in the presence of hard-wall are studied. Equilibrium wetting is related to a
particular case of the problem, it corresponds to the Edwards-Wilkinson
equation with a potential in the continuum approach or to the fulfillment of
detailed balance in the microscopic models. In this review we present the
analytical and numerical methods used to investigate the problem and the very
rich behavior that is observed with them.Comment: Review, 36 pages, 16 figure
The non-equilibrium phase transition of the pair-contact process with diffusion
The pair-contact process 2A->3A, 2A->0 with diffusion of individual particles
is a simple branching-annihilation processes which exhibits a phase transition
from an active into an absorbing phase with an unusual type of critical
behaviour which had not been seen before. Although the model has attracted
considerable interest during the past few years it is not yet clear how its
critical behaviour can be characterized and to what extent the diffusive
pair-contact process represents an independent universality class. Recent
research is reviewed and some standing open questions are outlined.Comment: Latexe2e, 53 pp, with IOP macros, some details adde
Non equilibrium steady states: fluctuations and large deviations of the density and of the current
These lecture notes give a short review of methods such as the matrix ansatz,
the additivity principle or the macroscopic fluctuation theory, developed
recently in the theory of non-equilibrium phenomena. They show how these
methods allow to calculate the fluctuations and large deviations of the density
and of the current in non-equilibrium steady states of systems like exclusion
processes. The properties of these fluctuations and large deviation functions
in non-equilibrium steady states (for example non-Gaussian fluctuations of
density or non-convexity of the large deviation function which generalizes the
notion of free energy) are compared with those of systems at equilibrium.Comment: 35 pages, 9 figure
Ballistic Annihilation
Ballistic annihilation with continuous initial velocity distributions is
investigated in the framework of Boltzmann equation. The particle density and
the rms velocity decay as and , with the
exponents depending on the initial velocity distribution and the spatial
dimension. For instance, in one dimension for the uniform initial velocity
distribution we find . We also solve the Boltzmann equation
for Maxwell particles and very hard particles in arbitrary spatial dimension.
These solvable cases provide bounds for the decay exponents of the hard sphere
gas.Comment: 4 RevTeX pages and 1 Eps figure; submitted to Phys. Rev. Let
Jacobson generators, Fock representations and statistics of sl(n+1)
The properties of A-statistics, related to the class of simple Lie algebras
sl(n+1) (Palev, T.D.: Preprint JINR E17-10550 (1977); hep-th/9705032), are
further investigated. The description of each sl(n+1) is carried out via
generators and their relations, first introduced by Jacobson. The related Fock
spaces W_p (p=1,2,...) are finite-dimensional irreducible sl(n+1)-modules. The
Pauli principle of the underlying statistics is formulated. In addition the
paper contains the following new results: (a) The A-statistics are interpreted
as exclusion statistics; (b) Within each W_p operators B(p)_1^\pm, ...,
B(p)_n^\pm, proportional to the Jacobson generators, are introduced. It is
proved that in an appropriate topology the limit of B(p)_i^\pm for p going to
infinity is equal to B_i^\pm, where B_i^\pm are Bose creation and annihilation
operators; (c) It is shown that the local statistics of the degenerated
hard-core Bose models and of the related Heisenberg spin models is p=1
A-statistics.Comment: LaTeX-file, 33 page
Quasi-stationary regime of a branching random walk in presence of an absorbing wall
A branching random walk in presence of an absorbing wall moving at a constant
velocity undergoes a phase transition as the velocity of the wall
varies. Below the critical velocity , the population has a non-zero
survival probability and when the population survives its size grows
exponentially. We investigate the histories of the population conditioned on
having a single survivor at some final time . We study the quasi-stationary
regime for when is large. To do so, one can construct a modified
stochastic process which is equivalent to the original process conditioned on
having a single survivor at final time . We then use this construction to
show that the properties of the quasi-stationary regime are universal when
. We also solve exactly a simple version of the problem, the
exponential model, for which the study of the quasi-stationary regime can be
reduced to the analysis of a single one-dimensional map.Comment: 2 figures, minor corrections, one reference adde
Nonequilibrium Steady States of Matrix Product Form: A Solver's Guide
We consider the general problem of determining the steady state of stochastic
nonequilibrium systems such as those that have been used to model (among other
things) biological transport and traffic flow. We begin with a broad overview
of this class of driven diffusive systems - which includes exclusion processes
- focusing on interesting physical properties, such as shocks and phase
transitions. We then turn our attention specifically to those models for which
the exact distribution of microstates in the steady state can be expressed in a
matrix product form. In addition to a gentle introduction to this matrix
product approach, how it works and how it relates to similar constructions that
arise in other physical contexts, we present a unified, pedagogical account of
the various means by which the statistical mechanical calculations of
macroscopic physical quantities are actually performed. We also review a number
of more advanced topics, including nonequilibrium free energy functionals, the
classification of exclusion processes involving multiple particle species,
existence proofs of a matrix product state for a given model and more
complicated variants of the matrix product state that allow various types of
parallel dynamics to be handled. We conclude with a brief discussion of open
problems for future research.Comment: 127 pages, 31 figures, invited topical review for J. Phys. A (uses
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