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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.
I. Peshko G. Galich M. Lopiychuk A. Khizhnyak V. Nakvasuk 《Optics & Laser Technology》1997,29(4):211-215
A laser system containing four CW Nd:YAG double-rod lasers, transforming optics and a fibre with input-output optics has been designed and investigated. It is shown that reduction of the beam parameter product of the non-Gaussian beams in the image space of the lens has made it possible to collect the emission of four lasers to the same fibre. Independent laser operation has provided the output power control in the range of 10–900 W with a stable light spot size on the input end of the fibre. 相似文献
73.
A. Debussche 《Journal de Mathématiques Pures et Appliquées》1998,77(10):967-988
The notion of random attractor for a dissipative stochastic dynamical system has recently been introduced. It generalizes the concept of global attractor in the deterministic theory. It has been shown that many stochastic dynamical systems associated to a dissipative partial differential equation perturbed by noise do possess a random attractor. In this paper, we prove that, as in the case of the deterministic attractor, the Hausdorff dimension of the random attractor can be estimated by using global Lyapunov exponents. The result is obtained under very natural assumptions. As an application, we consider a stochastic reaction-diffusion equation and show that its random attractor has finite Hausdorff dimension. 相似文献
74.
Considerthediferenceequationwithavariabledelayxn-xn-1=F(xn,xr(n),n=n0,n0+1,…(1)where(H1):F∈C(R×R,R),F(u,v)isdecreasingwithres... 相似文献
75.
This paper presents a unified analysis of decomposition algorithms for continuously differentiable optimization problems defined on Cartesian products of convex feasible sets. The decomposition algorithms are analyzed using the framework of cost approx imation algorithms. A convergence analysis is made for three decomposition algorithms: a sequential algorithm which extends the classical Gauss-Seidel scheme, a synchronized parallel algorithm which extends the Jacobi method, and a partially asynchronous parallel algorithm. The analysis validates inexact computations in both the subproblem and line search phases, and includes convergence rate results. The range of feasible step lengths within each algorithm is shown to have a direct correspondence to the increasing degree of parallelism and asynchronism, and the resulting usage of more outdated information in the algorithms. 相似文献
76.
In this paper we show that the Boltzmann weights of the three-dimensional Baxter-Bazhanov model give representations of the braid group if some suitable spectral limits are taken. In the trigonometric case we classify all possible spectral limits which produce braid group representations. Furthermore, we prove that for some of them we get cyclotomic invariants of links and for others we obtain tangle invariants generalizing the cyclotomic ones. 相似文献
77.
We consider an optimal growth (multi-sector) model with nonconvex technology. Using the Clarke results on generalized gradients, we prove that the value function has left and right derivatives with respect to the initial capital stock, without requiring supermodularity assumptions. 相似文献
78.
本文证明了周期单元中带有某些硬相互作用的相对论Boltzmann方程初值问题在初值满足质量、能量和熵有限的条件下具有一个整体温和解. 相似文献
79.
The purpose of this paper is to give the Reid ``Roundabout Theorem' for quadratic functionals with general boundary conditions.
In particular, we describe the so-called coupled point and regularity condition introduced in [16] in terms of Riccati equation
solutions.
Accepted 27 February 1996 相似文献
80.
1IntroductionThebrainofmankindhasmanycognitivefunctionssuchaslearning,asociationandoptimizationetc..Theneuronisthemostfoundam... 相似文献