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101.
F. den Hollander 《Journal of statistical physics》1994,75(5-6):891-918
Some fifteen years ago, Shuler formulated three conjectures relating to the large-time asymptotic properties of a nearest-neighbor random walk on 2 that is allowed to make horizontal steps everywhere but vertical steps only on a random fraction of the columns. We give a proof of his conjectures for the situation where the column distribution is stationary and satisfies a certain mixing codition. We also prove a strong form of scaling to anisotropic Brownian motion as well as a local limit theorem. The main ingredient of the proofs is a large-deviation estimate for the number of visits to a random set made by a simple random walk on . We briefly discuss extensions to higher dimension and to other types of random walk.Dedicated to Prof. K. E. Shuler on the occasion of his 70th birthday, celebrated at a Symposium in his honor on July 13, 1992, at the University of California at San Diego, La Jolla, California. 相似文献
102.
Ute Ebert 《Journal of statistical physics》1996,82(1-2):183-265
We study the diffusion of polymers through quenched short-range correlated random media by renormalization group (RG) methods, which allow us to derive universal predictions in the limit of long chains and weak disorder. We take local quenched random potentials with second momentv and the excluded-volume interactionu of the chain segments into account. We show that our model contains the relevant features of polymer diffusion in random media in the RG sense if we focus on the local entropic effects rather than on the topological constraints of a quenched random medium. The dynamic generating functional and the general structure of its perturbation expansion inu andv are derived. The distribution functions for the center-of-mass motion and the internal modes of one chain and for the correlation of the center of mass motions of two chains are calculated to one-loop order. The results allow for sufficient cross-checks to have trust in the one-loop renormalizability of the model. The general structure as well as the one-loop results of the integrated RG flow of the parameters are discussed. Universal results can be found for the effective static interactionwu–v0 and for small effective disorder coupling
on the intermediate length scalel. As a first physical prediction from our analysis, we determine the general nonlinear scaling form of the chain diffusion constant and evaluate it explicitly as for
. 相似文献
103.
We consider the covariance matrix,G
mm
=q
2<(x,m);(y,m)>, of thed-dimensionalq-states Potts model, rewriting it in the random cluster representation of Fortuin and Kasteleyn. In any of theq ordered phases, we identify the eigenvalues of this matrix both in terms of representations of the unbroken symmetry group of the model and in terms of random cluster connectivities and covariances, thereby attributing algebraic significance to these stochastic geometric quantities. We also show that the correlation length corresponding to the decay rate of one of the eigenvalues is the same as the inverse decay rate of the diameter of finite clusers. For dimensiond=2, we show that this correlation length and the correlation length of the two-point function with free boundary conditions at the corresponding dual temperature are equal up to a factor of two. For systems with first-order transitions, this relation helps to resolve certain inconsistencies between recent exact and numerical work on correlation lengths at the self-dual point o. For systems with second order transitions, this relation implies the equality of the correlation length exponents from above and below threshold, as well as an amplitude ratio of two. In the course of proving the above results, we establish several properties of independent interest, including left continuity of the inverse correlation length with free boundary conditions and upper semicontinuity of the decay rate for finite clusters in all dimensions, and left continuity of the two-dimensional free boundary condition percolation probability at o. We also introduce DLR equations for the random cluster model and use them to establish ergodicity of the free measure. In order to prove these results, we introduce a new class of events which we call decoupling events and two inequalities for these events. The first is similar to the FKG inequality, but holds for events which are neither increasing nor decreasing; the second is similar to the van den Berg-Kesten inequality in standard percolation. Both inequalities hold for an arbitrary FKG measure. 相似文献
104.
Yasunari Fukai Kô hei Uchiyama 《Transactions of the American Mathematical Society》1996,348(10):4131-4152
This paper establishes a criterion for whether a -dimensional random walk on the integer lattice visits a space-time subset infinitely often or not. It is a precise analogue of Wiener's test for regularity of a boundary point with respect to the classical Dirichlet problem. The test obtained is applied to strengthen the harder half of Kolmogorov's test for the random walk.
105.
We examine the steady-state flux of particles diffusing in a one-dimensional finite chain with Sinai-type disorder, i.e., the system in which in addition to the thermal noise, particles are subject to a stationary random-correlated in space Gaussian force. For this model we calculate the disorder average (over configurations of the random force) flux exactly for arbitrary values of system's parameters, such as chain lengthN, strength of the force, and temperature. We prove that within the limitN1 the average flux decreases withN as J(N)=C/N and thus confirm our recent predictions that the flux in the discrete-space Sinai model is anomalous. 相似文献
106.
We study the Hopfield model of an autoassociative memory on a random graph onN vertices where the probability of two vertices being joined by a link isp(N). Assuming thatp(N) goes to zero more slowly thanO(1/N), we prove the following results: (1) If the number of stored patternsm(N) is small enough such thatm(N)/Np(N) 0, asN, then the free energy of this model converges, upon proper rescaling, to that of the standard Curie-Weiss model, for almost all choices of the random graph and the random patterns. (2) If in additionm(N) < ln N/ln 2, we prove that there exists, forT< 1, a Gibbs measure associated to each original pattern, whereas for higher temperatures the Gibbs measure is unique. The basic technical result in the proofs is a uniform bound on the difference between the Hamiltonian on a random graph and its mean value. 相似文献
107.
含吲哚核端基多甲川菁染料的合成及性能 总被引:6,自引:0,他引:6
我们曾合成了具有桥环的硫三碳菁及多甲川苯乙烯菁,并测定了光学性能。本文报道吲哚环为端基的桥链三碳菁和四甲川苯乙烯菁的合成及在有机溶剂中电子吸收光谱及溶解性能的测定。所用仪器同前,7种多甲川菁染料的合成反应如下: 相似文献
108.
The electrochemical and in-situ surface-enhanced Raman spectroscopy (SERS) techniques were used to investigate the electrooxidation behavior of methanol in acidic, neutral and alkaline media at a Pt-Ru nanoparticle modified glassy carbon (Pt-Ru/GC) electrode. The results showed that methanol could be dissociated spontaneously at the Pt-Ru/GC electrode to produce a strongly adsorbed intermediate, CO. It was found that CO could be oxidized more easily in the alkaline medium than in the acidic and neutral media. The peak potential of methanol oxidation was shifted from 0.663 and 0.708 V in the acidic and neutral media to -0.030 V in the alkaline medium, which is due to that the adsorption strength of CO on the Pt surface in the alkaline medium is weaker than that in the acidic and neutral media. The final product of the methanol oxidation is CO2. However, in the alkaline medium, CO2 produced would form CO3^2- and HCO3^- resulting in the decrease in the alkaline concentration and then in the decrease in the performance of DMFC. Therefore, the performance of the alkaline DMFC is not Stable. 相似文献
109.
Conformational statistics of polymer chain terminally attached to wall (Ⅲ)——NRW model loop chain 总被引:1,自引:0,他引:1
When the two end groups of a linear polymer chain are absorbed on a solid surface,the polymer chain forms the "loop" conformation.Investigation has been made on the conformational statistics of a model loop chain by the normal landom walk (NRW) on a lattice confined in the half-infinite space.Based on the conformational distribution function of the NRW model tail chain,it is easy to deduce an analytical formula expressing the conforma-tional number of the model loop chain.It was found that the ratio of the conformational number of the model loop chain to that of the free chain varies with the power function N-2/3 when the chain length N→∞ The same result was obtained by means of the recursion equation.The ratio of the mean square end-to-end distance h2 for the model loop chain to its mean square bond length I2 is 2N/3 Compared with the free chain with the same length N,the mean square end-to-end distance of the model loop chain contracts to a certain extent.The basic relationships deduced were support 相似文献
110.
B. A. Arbuzov Z. G. Isaeva M. G. Belyaeva V. V. Ratner O. N. Kataeva I. A. Litvinov V. A. Naumov 《Russian Chemical Bulletin》1992,41(1):117-119
Oxidation of 2-carene by lead tetraacetate in acetic acid afforded p-menth-1(10),2-dien-7-ol, 2-acetyl-6,6-dimethylbicyclo[3.1.0]hexane, p-menth-2-ene-1,7-diol, p-menth-1-ene-3,7-diol, and 2-(m-tolyl)propanol-2.Deceased.A. M. Butlerov Scientific Research Chemical Institute, V. I. Ul'yanov-Lenin Kazan' State University, 420008 Kazan. Translated from Izvestiya Akademii Nauk, Seriya Khimicheskaya, No. 1, pp. 147–150, January, 1992. 相似文献