KINETICS OF CRYSTAL GROWTH LIMITED BY RANDOM VELOCITY FIELDS

2008 ◽  
Vol 18 (09) ◽  
pp. 2673-2679 ◽  
Author(s):  
M. NIEMIEC ◽  
W. OLCHAWA ◽  
L. SCHIMANSKY-GEIER ◽  
J. ŁUCZKA
Keyword(s):  
Random Field ◽  
Growth Kinetics ◽  
Gaussian Random Field ◽  
Planck Equation ◽  
Type Equation ◽  
Gaussian Field ◽  
Interface Evolution ◽  
Velocity Fluctuations ◽  
Spatially Correlated ◽  
Fokker Planck

A spherical growth process controlled by velocity fluctuations of particles of a saturated solution is investigated. Velocity fluctuations are modeled by a Gaussian random field. The interface evolution is determined by a Langevin-type equation with a multiplicative random field, which in the case of the quasi-homogeneous random Gaussian field is equivalent to Fokker–Planck dynamics. We analyze numerically the Fokker–Planck equation and compare growth kinetics in the case of noisy (i.e. space-independent) fluctuations. It is shown that for a large class of spatially correlated velocity fluctuations, the growth kinetics is universal, i.e. it does not depend on the details of statistics of fluctuations.

scholarly journals Continuum dynamics of the intention field under weakly cohesive social interaction

2017 ◽  
Vol 27 (01) ◽  
pp. 159-182 ◽  
Author(s):  
Pierre Degond ◽  
Jian-Guo Liu ◽  
Sara Merino-Aceituno ◽  
Thomas Tardiveau
Keyword(s):  
Planck Equation ◽  
Type Equation ◽  
Opinion Formation ◽  
Time Dynamics ◽  
First Case ◽  
Long Time ◽  
The Mean ◽  
Continuum Dynamics ◽  
Long Time Dynamics ◽  
Fokker Planck

We investigate the long-time dynamics of an opinion formation model inspired by a work by Borghesi, Bouchaud and Jensen. First, we derive a Fokker–Planck-type equation under the assumption that interactions between individuals produce little consensus of opinion (grazing collision approximation). Second, we study conditions under which the Fokker–Planck equation has non-trivial equilibria and derive the macroscopic limit (corresponding to the long-time dynamics and spatially localized interactions) for the evolution of the mean opinion. Finally, we compare two different types of interaction rates: the original one given in the work of Borghesi, Bouchaud and Jensen (symmetric binary interactions) and one inspired from works by Motsch and Tadmor (non-symmetric binary interactions). We show that the first case leads to a conservative model for the density of the mean opinion whereas the second case leads to a non-conservative equation. We also show that the speed at which consensus is reached asymptotically for these two rates has fairly different density dependence.

Jetstream Formation through Inelastic Collisions

1971 ◽  
Vol 12 ◽  
pp. 319-326
Author(s):  
David C. Baxter ◽  
William B. Thompson
Keyword(s):  
Inelastic Collision ◽  
Planck Equation ◽  
Type Equation ◽  
Collision Integral ◽  
Inelastic Collisions ◽  
Radial Density ◽  
Fokker Planck Equation ◽  
Density Clustering ◽  
Fokker Planck

An inelastic collision integral is used in a Boltzmann-type equation for a distribution of particles in Kepler orbits. A Fokker-Planck equation is found that leads to radial density clustering.

scholarly journals Economic Segregation Under the Action of Trading Uncertainties

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1390
Author(s):  
Elena Ballante ◽  
Chiara Bardelli ◽  
Mattia Zanella ◽  
Silvia Figini ◽  
Giuseppe Toscani
Keyword(s):  
Statistical Study ◽  
Wealth Distribution ◽  
Planck Equation ◽  
Type Equation ◽  
Statistical Information ◽  
Uncertain Parameters ◽  
Social Forces ◽  
Economic Segregation ◽  
Distribution Of Wealth ◽  
Fokker Planck

We study the distribution of wealth in a market economy in which the trading propensity of the agents is uncertain. Our approach is based on kinetic models for collective phenomena, which, at variance with the classical kinetic theory of rarefied gases, has to face the lack of fundamental principles, which are replaced by empirical social forces of which we have at most statistical information. The proposed kinetic description allows recovering emergent wealth distribution profiles, which are described by the steady states of a Fokker–Planck-type equation with uncertain parameters. A statistical study of the stationary profiles of the Fokker–Planck equation then shows that the wealth distribution can develop a multimodal shape in the presence of observable highly stressful economic situations.

AN APPLICATION OF FOKKER–PLANCK EQUATION TO JOSEPHSON JUNCTION

1989 ◽  
Vol 9 (1) ◽  
pp. 109-120
Author(s):  
G. Liao ◽  
A.F. Lawrence ◽  
A.T. Abawi
Keyword(s):  
Josephson Junction ◽  
Planck Equation ◽  
Fokker Planck Equation ◽  
Fokker Planck

Quadratic Discriminant Analysis of Spatially Correlated Data

2001 ◽  
Vol 6 (2) ◽  
pp. 15-28 ◽  
Author(s):  
K. Dučinskas ◽  
J. Šaltytė
Keyword(s):  
Discriminant Function ◽  
Error Rate ◽  
Gaussian Random Field ◽  
Correlated Data ◽  
Covariance Matrices ◽  
Classification Rule ◽  
Spatial Correlations ◽  
Linear Quadratic ◽  
Spatial Correlation Function ◽  
Spatially Correlated

The problem of classification of the realisation of the stationary univariate Gaussian random field into one of two populations with different means and different factorised covariance matrices is considered. In such a case optimal classification rule in the sense of minimum probability of misclassification is associated with non-linear (quadratic) discriminant function. Unknown means and the covariance matrices of the feature vector components are estimated from spatially correlated training samples using the maximum likelihood approach and assuming spatial correlations to be known. Explicit formula of Bayes error rate and the first-order asymptotic expansion of the expected error rate associated with quadratic plug-in discriminant function are presented. A set of numerical calculations for the spherical spatial correlation function is performed and two different spatial sampling designs are compared.

scholarly journals Time-changed fractional Ornstein-Uhlenbeck process

2020 ◽  
Vol 23 (2) ◽  
pp. 450-483 ◽  
Author(s):  
Giacomo Ascione ◽  
Yuliya Mishura ◽  
Enrica Pirozzi
Keyword(s):  
Planck Equation ◽  
Uhlenbeck Process ◽  
Fokker Planck Equation ◽  
Ornstein Uhlenbeck Process ◽  
Fokker Planck

AbstractWe define a time-changed fractional Ornstein-Uhlenbeck process by composing a fractional Ornstein-Uhlenbeck process with the inverse of a subordinator. Properties of the moments of such process are investigated and the existence of the density is shown. We also provide a generalized Fokker-Planck equation for the density of the process.

scholarly journals Fokker-Planck Models for Rotating Stellar Systems

1996 ◽  
Vol 174 ◽  
pp. 363-364 ◽  
Author(s):  
Christian Einsel ◽  
Rainer Spurzem
Keyword(s):  
Initial Conditions ◽  
Planck Equation ◽  
Rotational Energy ◽  
Momentum Transport ◽  
Core Collapse ◽  
Initial Model ◽  
Fundamental Parameters ◽  
Angular Momentum Transport ◽  
Collapse Phase ◽  
Fokker Planck

Observations of Globular Cluster ellipticity distributions related to some fundamental parameters give strong evidence for a decay of rotational energy in these systems with time. In order to study the effectiveness of angular momentum transport (or loss, resp.) a code has been written which solves the Fokker-Planck equation in (E, Jz)-space and follows the evolution from some initial conditions through core collapse (and possibly gravothermal oscillations) up to the post-collapse phase. For the purpose of comparability with N-body simulations rotating initial model configurations according to the prescriptions of Lupton & Gunn (1987) have been constructed. These models are intended to continue previous work by Goodman (1983, Fokker-Planck) and Akiyama & Sugimoto (1989, N-Body). In this contribution the derivation of the flux coefficients is given.

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