Search results for "stochastic"

Size effect in phase transition kinetics

1988

The growth of a spontaneous lattice average magnetization in a magnetic system which is suddenly brought below the transition temperature is a stochastic process in which the very small fluctuations of the initial magnetization are amplified to a macroscopic size. The initial magnetization fluctuates in time around the zero average value because of the finite size of the system. As a consequence of the fluctuation-amplification phenomenon the nonlinear relaxation of the finite system is qualitatively different from that of the infinite one. The present paper studies this feature of phase-transition kinetics in the framework of a very simple model: the dynamical generalization of the spheric…

Noise-Induced Phase Transitions

2009

Killing (absorption) versus survival in random motion

2017

We address diffusion processes in a bounded domain, while focusing on somewhat unexplored affinities between the presence of absorbing and/or inaccessible boundaries. For the Brownian motion (L\'{e}vy-stable cases are briefly mentioned) model-independent features are established, of the dynamical law that underlies the short time behavior of these random paths, whose overall life-time is predefined to be long. As a by-product, the limiting regime of a permanent trapping in a domain is obtained. We demonstrate that the adopted conditioning method, involving the so-called Bernstein transition function, works properly also in an unbounded domain, for stochastic processes with killing (Feynman-…

STOCHASTIC ANALYSIS OF ONE-DIMENSIONAL HETEROGENEOUS SOLIDS WITH LONG-RANGE INTERACTIONS

2011

Random mass distribution in one-dimensional (1D) elastic solids in the presence of long-range interactions is studied in this paper. Besides the local Cauchy contact forces among adjacent elements, long-range forces depending on the product of interacting masses, as well as on their relative displacements, are considered. In this context, the random fluctuations of the mass distribution involve a stochastic model of the nonlocal interactions, and the random displacement field of the body is provided as the solution of a stochastic integro-differential equation. The presence of the random field of mass distribution is reflected in the random kernel of the solving integro-differential equatio…

The Stochastic Limit of the Fröhlich Hamiltonian: Relations with the Quantum Hall Effect

2003

We propose a model of an approximatively two-dimensional electron gas in a uniform electric and magnetic field and interacting with a positive background through the Fröhlich Hamiltonian. We consider the stochastic limit of this model and we find the quantum Langevin equation and the generator of the master equation. This allows us to calculate the explicit form of the conductivity and the resistivity tensors and to deduce a fine tuning condition (FTC) between the electric and the magnetic fields. This condition shows that the x-component of the current is zero unless a certain quotient, involving the physical parameters, takes values in a finite set of physically meaningful rational number…

Stochastic models for heterogeneous relaxation: Application to inhomogeneous optical lineshapes

2001

Dynamic heterogeneity has often been modeled by assuming that a single-particle observable, fluctuating at a molecular scale, is influenced by its coupling to environmental variables fluctuating on a second, perhaps slower, time scale. Starting from the most simple Gaussian Markov process we model the exchange between 'slow' and 'fast' environments by treating the fluctuating single-particle variable as a projection from a higher-dimensional Markov process. The moments of the resulting stochastic process are calculated from the corresponding Master equations or Langevin equations, depending on the model. The calculations show the importance of the way to treat exchange processes. The result…

Restoring the valence-shell stabilization in Nd 140

2020

A projectile Coulomb-excitation experiment was performed at the radioactive-ion beam facility HIE-ISOLDE at CERN to obtain E2 and M1 transition matrix elements of Nd-140 using the multistep Coulomb-excitation code GOSIA. The absolute M1 strengths, B(M1; 2(2)(-) -> 2(1)(+)) = 0.033(8)mu(2)(N), B(M1 ; 2(3)(+) -> 2(1)(+)) = 0.26(-0.10)(+0.11)mu(2)(N), and B(M1; 2(4)+ -> 2(1)(+)) <0.04 mu(2)(N) identify the 2(3)(+) state as the main fragment of the one-quadrupole-phonon proton-neutron mixed-symmetry state of Nd-140. The degree of F-spin mixing in Nd-140 was quantified with the determination of the mixing matrix element VF-mix <7(-7)(-13) keV. Peer reviewed

Strongly super-Poisson statistics replaced by a wide-pulse Poisson process: The billiard random generator

2021

Abstract In this paper we present a study on random processes consisting of delta pulses characterized by strongly super-Poisson statistics and calculate its spectral density. We suggest a method for replacing a strongly super-Poisson process with a wide-pulse Poisson process, while demonstrating that these two processes can be set in such a way to have similar spectral densities, the same mean values, and the same correlation times. We also present a billiard system that can be used to generate random pulse noise of arbitrary statistical properties. The particle dynamics is considered in terms of delta and wide pulses simultaneously. The results of numerical experiments with the billiard s…

Non-stationary spectral moments of base excited MDOF systems

1988

The paper deals with the evaluation of non-stationary spectral moments of multi-degree-of-freedom (MDOF) line systems subjected to seismic excitations. The spectral moments of the response are evaluated in incremental form solution by means of an unconditionally stable step-by-step procedure. As an application, the statistics of the largest peak of the response are also evaluated.

How Does the Relaxation of a Supercooled Liquid Depend on Its Microscopic Dynamics?

1998

Using molecular dynamics computer simulations we investigate how the relaxation dynamics of a simple supercooled liquid with Newtonian dynamics differs from the one with a stochastic dynamics. We find that, apart from the early beta-relaxation regime, the two dynamics give rise to the same relaxation behavior. The increase of the relaxation times of the system upon cooling, the details of the alpha-relaxation, as well as the wave vector dependence of the Edwards-Anderson-parameters are independent of the microscopic dynamics.