Search results for " statistical mechanics"
showing 10 items of 557 documents
Hunting active Brownian particles: Learning optimal behavior
2021
We numerically study active Brownian particles that can respond to environmental cues through a small set of actions (switching their motility and turning left or right with respect to some direction) which are motivated by recent experiments with colloidal self-propelled Janus particles. We employ reinforcement learning to find optimal mappings between the state of particles and these actions. Specifically, we first consider a predator-prey situation in which prey particles try to avoid a predator. Using as reward the squared distance from the predator, we discuss the merits of three state-action sets and show that turning away from the predator is the most successful strategy. We then rem…
Calculation of local pressure tensors in systems with many-body interactions
2003
Local pressures are important in the calculation of interface tensions and in analyzing micromechanical behavior. The calculation of local pressures in computer simulations has been limited to systems with pairwise interactions between the particles, which is not sufficient for chemically detailed systems with many-body potentials such as angles and torsions. We introduce a method to calculate local pressures in systems with n-body interactions (n=2,3,4, . . .) based on a micromechanical definition of the pressure tensor. The local pressure consists of a kinetic contribution from the linear momentum of the particles and an internal contribution from dissected many-body interactions by infin…
Finite-size effects in dynamics of zero-range processes
2010
The finite-size effects prominent in zero-range processes exhibiting a condensation transition are studied by using continuous-time Monte Carlo simulations. We observe that, well above the thermodynamic critical point, both static and dynamic properties display fluid-like behavior up to a density {\rho}c (L), which is the finite-size counterpart of the critical density {\rho}c = {\rho}c (L \rightarrow \infty). We determine this density from the cross-over behavior of the average size of the largest cluster. We then show that several dynamical characteristics undergo a qualitative change at this density. In particular, the size distribution of the largest cluster at the moment of relocation,…
Linear and nonlinear experimental regimes of stochastic resonance
2000
We investigate the stochastic resonance phenomenon in a physical system based on a tunnel diode. The experimental control parameters are set to allow the control of the frequency and amplitude of the deterministic modulating signal over an interval of values spanning several orders of magnitude. We observe both a regime described by the linear response theory and the nonlinear deviation from it. In the nonlinear regime we detect saturation of the power spectral density of the output signal detected at the frequency of the modulating signal and a dip in the noise level of the same spectral density. When these effects are observed we detect a phase and frequency synchronization between the st…
Extinction statistics in N random interacting species
2008
A randomly interacting N-species Lotka-Volterra system in the presence of a Gaussian multiplicative noise is analyzed. The investigation is focused on the role of this external noise into the statistical properties of the extinction times of the populations. The distributions show a Gaussian shape for each noise intensity value investigated. A monotonic behavior of the mean extinction time as a function of the noise intensity is found, while a nonmonotonic behavior of the width of the extinction time probability distribution characterizes the dynamical evolution.
Classical Statistical Mechanics
2003
Some aspects of statistical mechanics that are particularly important for computer simulation approaches are recalled. Using Ising and classical Heisenberg models as examples, various statistical ensembles and appropriate thermodynamic potentials are introduced, and concepts such as Legendre transformations between ensembles and the thermodynamic integration method to obtain the entropy are mentioned. Probability distributions characterizing statistical fluctuations are discussed, fluctuation relations for response functions are derived, and the behavior of these quantities at first and second order phase transitions are described qualitatively. Also the general consequences of phase coexis…
Transitions between imperfectly ordered crystalline structures: A phase switch Monte Carlo study
2012
A model for two-dimensional colloids confined laterally by ``structured boundaries'' (i.e., ones that impose a periodicity along the slit) is studied by Monte Carlo simulations. When the distance $D$ between the confining walls is reduced at constant particle number from an initial value ${D}_{0}$, for which a crystalline structure commensurate with the imposed periodicity fits, to smaller values, a succession of phase transitions to imperfectly ordered structures occur. These structures have a reduced number of rows parallel to the boundaries (from $n$ to $n\ensuremath{-}1$ to $n\ensuremath{-}2$, etc.) and are accompanied by an almost periodic strain pattern, due to ``soliton staircases'' …
Statistical Properties of Statistical Ensembles of Stock Returns
1999
We select n stocks traded in the New York Stock Exchange and we form a statistical ensemble of daily stock returns for each of the k trading days of our database from the stock price time series. We analyze each ensemble of stock returns by extracting its first four central moments. We observe that these moments are fluctuating in time and are stochastic processes themselves. We characterize the statistical properties of central moments by investigating their probability density function and temporal correlation properties.
Variety and volatility in financial markets
2000
We study the price dynamics of stocks traded in a financial market by considering the statistical properties both of a single time series and of an ensemble of stocks traded simultaneously. We use the $n$ stocks traded in the New York Stock Exchange to form a statistical ensemble of daily stock returns. For each trading day of our database, we study the ensemble return distribution. We find that a typical ensemble return distribution exists in most of the trading days with the exception of crash and rally days and of the days subsequent to these extreme events. We analyze each ensemble return distribution by extracting its first two central moments. We observe that these moments are fluctua…
Statistics of nonlinear stochastic dynamical systems under Lévy noises by a convolution quadrature approach
2010
This paper describes a novel numerical approach to find the statistics of the non-stationary response of scalar non-linear systems excited by L\'evy white noises. The proposed numerical procedure relies on the introduction of an integral transform of Wiener-Hopf type into the equation governing the characteristic function. Once this equation is rewritten as partial integro-differential equation, it is then solved by applying the method of convolution quadrature originally proposed by Lubich, here extended to deal with this particular integral transform. The proposed approach is relevant for two reasons: 1) Statistics of systems with several different drift terms can be handled in an efficie…