We study a general class of nonlinear mean field
Fokker-Planck equations in relation with an effective generalized
thermodynamical (E.G.T.) formalism. We show that these equations describe
several physical systems such as: chemotaxis of bacterial
populations, Bose-Einstein condensation in the canonical ensemble,
porous media, generalized Cahn-Hilliard equations, Kuramoto model,
BMF model, Burgers equation, Smoluchowski-Poisson system for
self-gravitating Brownian particles, Debye-Hückel theory of
electrolytes, two-dimensional turbulence... In particular, we show
that nonlinear mean field Fokker-Planck equations can provide
generalized Keller-Segel models for the chemotaxis of
biological populations. As an example, we introduce a new model of
chemotaxis incorporating both effects of anomalous diffusion and
exclusion principle (volume filling). Therefore, the notion of
generalized thermodynamics can have applications for concrete
physical systems. We also consider nonlinear mean field
Fokker-Planck equations in phase space and show the passage from
the generalized Kramers equation to the generalized Smoluchowski
equation in a strong friction limit. Our formalism is simple and
illustrated by several explicit examples corresponding to Boltzmann,
Tsallis, Fermi-Dirac and Bose-Einstein entropies among others. 相似文献
This paper studies the mean first passage time (or exit time, or escape time) over the non-fluctuating potential harrier for a system driven only by a dichotomous noise. It finds that the dichotomous noise can make the particles escape over the potential barrier, in some circumstances; but in other circumstances, it can not. In the case that the particles escape over the potential harrier, a resonant activation phenomenon for the mean first passage time over the potential barrier is obtained. 相似文献
Considering a single-mode laser system with cross-correlated additive colored noise and multiplicative colored noise, we study the effects of correlation among noises on the normalized intensity correlation function C(s).C(s) is derived by means of the projection operator method. 相似文献
A new charge measurement method, time over threshold (TOT), has been used in some gas detectors lately. Here TOT is studied for TOF system, made of plastic scintillator counter, which can simplify the electronics of the system. The signal characteristics are measured and analyzed with a high quality oscilloscope, including noise, pedestal, signal amplitude, total charge, rise time and the correlation between them. The TOT and charge are related and can be fitted by some empirical formula. The charge measurement resolution by TOT is given and this will help the design of TOF electronics. 相似文献
Low-frequency noise, in the range 1–500 Hz, is measured at room temperature in samples of Au/PS/SCS/Al structure with a layer of porous silicon. Numerical values of the Hooge parameter αH are estimated and the dependence of αH on the composition of the gaseous environment, where the sample is placed, is determined. Possible reasons of observed high values of αH for the samples in air and of the increase in αH in conditions of gas adsorption are discussed. Introducing of carbon oxide in air changes the shape of spectrum. 相似文献
We study a stochastic neural-network model in which neurons and synapses change with a priori probability p and 1–p, respectively, in the limit p0. This implies neuron activity competing with fast fluctuations of the synaptic connections—in fact, random oscillations around values given by a learning (for example, Hebb's) rule. The consequences for the system performance of a dynamics constantly checking at random the set of memorized patterns is thus studied both analytically and numerically. We describe various nonequilibrium phase transitions whose nature depends on the properties of fluctuations. We find, in particular, that under rather general conditions locally stable mixture states do not occur, and pattern recognition and retrieval processes are substantially improved for some classes of synaptic fluctuations. 相似文献
The diffusion of hard-core particles subject to a global bias is described by a nonlinear, anisotropic generalization of the diffusion equation with conserved, local noise. Using renormalization group techniques, we analyze the effect of an additional noise term, with spatially long-ranged correlations, on the long-time, long-wavelength behavior of this model. Above an upper critical dimension dLR, the long-ranged noise is always relevant. In contrast, for d<dLR, we find a weak noise regime dominated by short-range noise. As the range of the noise correlations increases, an intricate sequence of stability exchanges between different fixed points of the renormalization group occurs. Both smooth and discontinuous crossovers between the associated universality classes are observed, reflected in the scaling exponents. We discuss the necessary techniques in some detail since they are applicable to a much wider range of problems. 相似文献
In univariate Padé approximation we learn from the Froissart phenomenon that Padé approximants to perturbed Taylor series exhibit almost cancelling pole–zero combinations that are unwanted. The location of these pole–zero doublets was recently characterized for rational functions by the so‐called Froissart polynomial. In this paper the occurrence of the Froissart phenomenon is explored for the first time in a multivariate setting. Several obvious questions arise. Which definition of Padé approximant is to be used? Which multivariate rational functions should be investigated? When considering univariate projections of these functions, our analysis confirms the univariate results obtained so far in [13], under the condition that the noise is added after projection. At the same time, it is apparent from section 4 that for the unprojected multivariate Froissart polynomial no conjecture can be formulated yet.