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71.
Luis L. Bonilla 《Journal of statistical physics》1987,46(3-4):659-678
A nonlinear Fokker-Planck equation is derived to describe the cooperative behavior of general stochastic systems interacting via mean-field couplings, in the limit of an infinite number of such systems. Disordered systems are also considered. In the weak-noise limit; a general result yields the possibility of having bifurcations from stationary solutions of the nonlinear Fokker-Planck equation into stable time-dependent solutions. The latter are interpreted as non-equilibrium probability distributions (states), and the bifurcations to them as nonequilibrium phase transitions. In the thermodynamic limit, results for three models are given for illustrative purposes. A model of self-synchronization of nonlinear oscillators presents a Hopf bifurcation to a time-periodic probability density, which can be analyzed for any value of the noise. The effects of disorder are illustrated by a simplified version of the Sompolinsky-Zippelius model of spin-glasses. Finally, results for the Fukuyama-Lee-Fisher model of charge-density waves are given. A singular perturbation analysis shows that the depinning transition is a bifurcation problem modified by the disorder noise due to impurities. Far from the bifurcation point, the CDW is either pinned or free, obeying (to leading order) the Grüner-Zawadowki-Chaikin equation. Near the bifurcation, the disorder noise drastically modifies the pattern, giving a quenched average of the CDW current which is constant. Critical exponents are found to depend on the noise, and they are larger than Fisher's values for the two probability distributions considered. 相似文献
72.
73.
We investigate a new interpretation for the Navier-Stokes corrections to the hydrodynamic equation of asymmetric interacting particle systems. We consider a system that starts from a measure associated with a profile that is constant along the drift direction. We show that under diffusive scaling the macroscopic behavior of the process is described by a nonlinear parabolic equation whose diffusion coefficient coincides with the diffusion coefficient of the hydrodynamic equation of the symmetric version of the process. 相似文献
74.
本文是[1,12]的继续,研究描述架中概念的结构;本文讨论后半部分,内容涉及概念内涵与外延的转换,清晰关系的内投影与内变换,概念的结构*以及有关问题的注记。 相似文献
75.
UCINSKI DARIUSZ; JAI ABDELHAQ EL 《IMA Journal of Mathematical Control and Information》1997,14(2):153-174
In this paper, the concept of weak spreadability is introduced.It constitutes an extension of the idea developed by El Jai& Kassara. In the case of linear distributed systems weconsider quadratic control techniques with a conveniently penalizedcriterion which makes the system weakly spreadable. The approachis outlined for a convectiondiffusion system, and theresults of a numerical study are also included to illustratethe main features of the considered problem. 相似文献
76.
In [5] Phillips proved that one can obtain the additive group of any nonstandard model *? of the ring ? of integers by using a linear mod 1 function h : F ?, where F is the α-dimensional vector space over ? when α is the cardinality of *?. In this connection it arises the question whether there are linear mod 1 functions which are neither addition nor quasi-linear. We prove that this is the case. 相似文献
77.
E. Hatta H. Hosoi H. Akiyama T. Ishii K. Mukasa 《The European Physical Journal B - Condensed Matter and Complex Systems》1998,2(3):347-349
We have observed a remarkable two-armed spiral in the collapse process of a floating monolayer at the air-water interface
by phase contrast microscopy. This demonstrates that the floating monolayer as a form of soft condensed matter reorganizes
itself due to a certain kind of macroscopic or collective behavior of molecules as it collapses. This pattern formation is
caused by the breakdown of a critical dynamical balance between the deformation of solid domain and the applied surface pressure.
The fragility as well as the flexibility of the floating monolayer can be associated with the observed pattern growth. There
are also observed interesting, periodically arranged collections of molecules in numerous collapsed regions.
Received: 8 July 1997 / Accepted: 4 November 1997 相似文献
78.
79.
An effective residual interaction between particles and holes for shell model calculations around 208Pb, derived from the interaction between free nucleons, is compared with the measured properties of proton-hole neutron states
in 208Tl and the interaction between proton holes is adjusted to newly measured level energies in 206Hg. These interaction elements are particularly relevant for neutron-rich nuclei. The adjustment of two mixing elements reproduces
the known γ-decay data in 208Tl.
Received: 2 April 2002 / Accepted: 2 May 2002 相似文献
80.