Search results for "statistical [methods]"
showing 10 items of 1664 documents
Optical wave turbulence: Toward a unified nonequilibrium thermodynamic formulation of statistical nonlinear optics
2014
International audience; The nonlinear propagation of coherent optical fields has been extensively explored in the framework of nonlinear optics, while the linear propagation of incoherent fields has been widely studied in the framework of statistical optics. However, these two fundamental fields of optics have been mostly developed independently of each other, so that a satisfactory understanding of statistical nonlinear optics is still lacking. This article is aimed at reviewing a unified theoretical formulation of statistical nonlinear optics on the basis of the wave turbulence theory, which provides a nonequilibrium thermodynamic description of the system of incoherent nonlinear waves. W…
NOISE EFFECTS IN POLYMER DYNAMICS
2008
The study of the noise induced effects on the dynamics of a chain molecule crossing a potential barrier, in the presence of a metastable state, is presented. A two-dimensional stochastic version of the Rouse model for a flexible polymer has been adopted to mimic the molecular dynamics and to take into account the interactions between adjacent monomers. We obtain a nonmonotonic behavior of the mean first passage time and its standard deviation, of the polymer centre of inertia, with the noise intensity. These findings reveal a noise induced effect on the mean crossing time. The role of the polymer length is also investigated.
Transient behavior of a population dynamical model
2005
The transient behavior of an ecosystem with N random interacting species in the presence of a multiplicative noise is analyzed. The multiplicative noise mimics the interaction with the environment. We investigate different asymptotic dynamical regimes and the role of the external noise on the probability distribution of the local field.
Crumpling of a stiff tethered membrane.
2003
first-principles numerical simulation model for crumpling of a stiff tethered membrane is introduced. In our model membranes, wrinkles, ridge formation, ridge collapse, as well as the initiation of stiffness divergence, are observed. The ratio of the amplitude and wave length of the wrinkles, and the scaling exponent of the stiffness divergence, are consistent with both theory and experiment. We observe that close to the stiffness divergence there appears a crossover beyond which the elastic behavior of a tethered membrane becomes similar to that of dry granular media. This suggests that ridge formation in membranes and force-chain network formation in granular packings are different manife…
A Second Order Accurate Kinetic Relaxation Scheme for Inviscid Compressible Flows
2013
In this paper we present a kinetic relaxation scheme for the Euler equations of gas dynamics in one space dimension. The method is easily applicable to solve any complex system of conservation laws. The numerical scheme is based on a relaxation approximation for conservation laws viewed as a discrete velocity model of the Boltzmann equation of kinetic theory. The discrete kinetic equation is solved by a splitting method consisting of a convection phase and a collision phase. The convection phase involves only the solution of linear transport equations and the collision phase instantaneously relaxes the distribution function to an equilibrium distribution. We prove that the first order accur…
On the existence of kinetic equations
1974
The existence of the Boltzmann equation and its generalizations is studied by analysing the order of magnitude of their terms. As a consequence we conclude that the reduced distribution functions are not analytic in the density.
Sine-Gordon Statistical Mechanics
1984
The Classical partition-function $$ Z = \int {D\Pi {\text{ }}D\phi {\text{ }}\exp - } \beta H\left[ \phi \right]$$ (1) in which \( {\beta ^{{ - 1}}} = {k_{B}}T{\text{ and }}H\left[ \phi \right]\) is the sine-Gordon (s-G) Hamiltonian $$ H\left[ \phi \right] = {\Upsilon _{0}}^{{ - 1}}\int {\left[ {\frac{1}{2}{\Upsilon _{0}}^{2}{\Pi ^{2}} + \frac{1}{2}{\phi _{z}}^{2} + {m^{2}}\left( {1 - \cos \phi } \right)} \right]} dz $$ (2) has been evaluated by transfer integral methods [1,2].
Verhulst model with Lévy white noise excitation
2008
The transient dynamics of the Verhulst model perturbed by arbitrary non-Gaussian white noise is investigated. Based on the infinitely divisible distribution of the Levy process we study the nonlinear relaxation of the population density for three cases of white non-Gaussian noise: (i) shot noise, (ii) noise with a probability density of increments expressed in terms of Gamma function, and (iii) Cauchy stable noise. We obtain exact results for the probability distribution of the population density in all cases, and for Cauchy stable noise the exact expression of the nonlinear relaxation time is derived. Moreover starting from an initial delta function distribution, we find a transition induc…
Wetting in fluid systems. Wetting and capillary condensation of lattice gases in thin film geometry
1994
Monte Carlo studies of lattice gas models with attractive interactions between nearest neighbors on a simple cubic lattice are carried out for a L×L×D geometry with two hard walls of size L×L and periodic boundary conditions parallel to the wall. Two types of short-range forces at the walls are considered: (i) Both walls are of the same type and exert an attractive force of the same strength (in Ising model terminology, surface fields HD = H1 occur). (ii) The walls differ, one attracts and the other repels particles, again with the same strength (HD = −H1). In the first case, capillary condensation occurs at a chemical potential differing from its value for phase coexistence in the bulk, an…
Characterisation and mitigation of beam-induced backgrounds observed in the ATLAS detector during the 2011 proton-proton run
2013
This paper presents a summary of beam-induced backgrounds observed in the ATLAS detector and discusses methods to tag and remove background contaminated events in data. Triggerrate based monitoring of beam-related backgrounds is presented. The correlations of backgrounds with machine conditions, such as residual pressure in the beam-pipe, are discussed. Results from dedicated beam-background simulations are shown, and their qualitative agreement with data is evaluated. Data taken during the passage of unpaired, i.e. non-colliding, proton bunches is used to obtain background-enriched data samples. These are used to identify characteristic features of beam-induced backgrounds, which then are …