Search results for "statistical [methods]"
showing 10 items of 1664 documents
Equilibrium between a Droplet and Surrounding Vapor: A Discussion of Finite Size Effects
2017
In a theoretical description of homogeneous nucleation one frequently assumes an "equilibrium" coexistence of a liquid droplet with surrounding vapor of a density exceeding that of a saturated vapor at bulk vapor-liquid two-phase coexistence. Thereby one ignores the caveat that in the thermodynamic limit, for which the vapor would be called supersaturated, such states will at best be metastable with finite lifetime, and thus not be well-defined within equilibrium statistical mechanics. In contrast, in a system of finite volume stable equilibrium coexistence of droplet and supersaturated vapor at constant total density is perfectly possible, and numerical analysis of equilibrium free energie…
Is nuclear viscosity dependent on temperature?
2018
Nuclear viscosity is an indispensable ingredient of the nuclear fission collective dynamical models. It governs the exchange of energy between the collective variables and the thermal bath. Its dependence on the shape and temperature is a matter of controversy. By using systems of intermediate fissility we have demonstrated in a recent study that the viscosity parameters is larger for compact shapes, and decreases for larger deformations of the fissioning system, at variance with the conclusions of the statistical model modified to include empirically viscosity and time scales. In this contribution we propose an experimental scenario to highlight the possible dependence of the viscosity fro…
Diffusion in Flashing Periodic Potentials
2005
The one-dimensional overdamped Brownian motion in a symmetric periodic potential modulated by external time-reversible noise is analyzed. The calculation of the effective diffusion coefficient is reduced to the mean first passage time problem. We derive general equations to calculate the effective diffusion coefficient of Brownian particles moving in arbitrary supersymmetric potential modulated: (i) by external white Gaussian noise and (ii) by Markovian dichotomous noise. For both cases the exact expressions for the effective diffusion coefficient are derived. We obtain acceleration of diffusion in comparison with the free diffusion case for fast fluctuating potentials with arbitrary profil…
TRANSIENT DYNAMICS AND ASYMPTOTIC POPULATIONS IN A DRIVEN METASTABLE QUANTUM SYSTEM
2013
The transient dynamics of a periodically driven metastable quantum system, interacting with a heat bath, is investigated. The time evolution of the populations, within the framework of the Feynman–Vernon influ- ence functional and in the discrete variable representation, is analyzed by varying the parameters of the external driving. The results display strong non-monotonic behaviour of the populations with respect to the driving frequency.
Moment Equations for a Spatially Extended System of Two Competing Species
2005
The dynamics of a spatially extended system of two competing species in the presence of two noise sources is studied. A correlated dichotomous noise acts on the interaction parameter and a multiplicative white noise affects directly the dynamics of the two species. To describe the spatial distribution of the species we use a model based on Lotka-Volterra (LV) equations. By writing them in a mean field form, the corresponding moment equations for the species concentrations are obtained in Gaussian approximation. In this formalism the system dynamics is analyzed for different values of the multiplicative noise intensity. Finally by comparing these results with those obtained by direct simulat…
Model-free determination of dissociation energies of polyatomic systems.
2001
We describe and apply a new procedure that allows a direct determination of dissociation energies of polyatomic systems (clusters, fullerenes, polymers, and other molecules) without any modeling of the systems under investigation. As an example, we have determined the dissociation energies of a series of gold clusters Au(+)n. A comparison with values obtained from statistical models of unimolecular dissociation shows that these models significantly fail to describe the data. In contrast, the new method yields values which are an order of magnitude more accurate, thus allowing one to experimentally set benchmarks for any theory which attempts to describe activated processes.
Point field models for the galaxy point pattern modelling the singularity of the two-point correlation function
2002
There is empirical evidence that the two-point correlation function of the galaxy distribution follows, for small scales, reasonably well a power-law expression $\xi(r)\propto r^{-\gamma}$ with $\gamma$ between 1.5 and 1.9. Nevertheless, most of the point field models suggested in the literature do not have this property. This paper presents a new class of models, which is produced by modifying point fields commonly used in cosmology to mimic the galaxy distribution, but where $\gamma=2$ is too large. The points are independently and randomly shifted, leading to the desired reduction of the value of $\gamma$.
Experimental investigation of resonant activation
2000
We experimentally investigate the escape from a metastable state over a fluctuating barrier of a physical system. The system is switching between two states under electronic control of a dichotomous noise. We measure the escape time and its probability density function as a function of the correlation rate of the dichotomous noise in a frequency interval spanning more than 4 frequency decades. We observe resonant activation, namely a minimum of the average escape time as a function of the correlation rate. We detect two regimes in the study of the shape of the escape time probability distribution: (i) a regime of exponential and (ii) a regime of non-exponential probability distribution.
Modular Schrödinger equation and dynamical duality.
2008
We discuss quite surprising properties of the one-parameter family of modular (Auberson and Sabatier (1994)) nonlinear Schr\"{o}dinger equations. We develop a unified theoretical framework for this family. Special attention is paid to the emergent \it dual \rm time evolution scenarios which, albeit running in the \it real time \rm parameter of the pertinent nonlinear equation, in each considered case, may be mapped among each other by means of an "imaginary time" transformation (more seriously, an analytic continuation in time procedure).
Levy flights and nonlocal quantum dynamics
2013
We develop a fully fledged theory of quantum dynamical patterns of behavior that are nonlocally induced. To this end we generalize the standard Laplacian-based framework of the Schr\"{o}dinger picture quantum evolution to that employing nonlocal (pseudodifferential) operators. Special attention is paid to the Salpeter (here, $m\geq 0$) quasirelativistic equation and the evolution of various wave packets, in particular to their radial expansion in 3D. Foldy's synthesis of "covariant particle equations" is extended to encompass free Maxwell theory, which however is devoid of any "particle" content. Links with the photon wave mechanics are explored.