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121.
We derive scaling forms for the thermodynamic and correlation quantities for the turn-weighted fully and partially directed self-avoiding walks on the hypercubic lattices ind2. In the grand canonical (fixed fugacity per step) ensemble, the conformational rod-to-coil transition sets up in the regimew¯N=O(1), wherew is the weight of each 90° turn and¯N is the (fugacity-dependent) average number of steps. Contrary to the conventional critical phenomena wisdom, the scaling functions for the two different walk models, directed and partially directed, become universal only in the limitd. 相似文献
122.
In his celebrated paper, Polya has considered the random walk in the three-dimensional (cubic) lattice and showed that the probability of return to the origin is less than 1. Subsequent authors have shown that the probability is %34.053.... Here we consider the same random walk, with the restriction that the drunkard is only allowed to stay inxyz. It is shown that his probability of returning to the originand staying in the allowed region is %6.4844.... 相似文献
123.
P. J. Forrester 《Journal of statistical physics》1989,56(5-6):767-782
The vicious random walker problem on a line is studied in the limit of a large number of walkers. The multidimensional integral representing the probability that thep walkers will survive a timet (denotedP
t
(p)
) is shown to be analogous to the partition function of a particular one-component Coulomb gas. By assuming the existence of the thermodynamic limit for the Coulomb gas, one can deduce asymptotic formulas forP
t
(p)
in the large-p, large-t limit. A straightforward analysis gives rigorous asymptotic formulas for the probability that after a timet the walkers are in their initial configuration (this event is termed a reunion). Consequently, asymptotic formulas for the conditional probability of a reunion, given that all walkers survive, are derived. Also, an asymptotic formula for the conditional probability density that any walker will arrive at a particular point in timet, given that allp walkers survive, is calculated in the limittp. 相似文献
124.
Fabio Martinelli Enzo Olivieri Elisabetta Scoppola 《Journal of statistical physics》1989,55(3-4):477-504
We apply previous results on the pathwise exponential loss of memory of the initial condition for stochastic differential equations with small diffusion to the problem of the asymptotic distribution of the first exit times from an attracted domain. We show under general hypotheses that the suitably rescaled exit time converges in the zero-noise limit to an exponential random variable. Then we extend the results to an infinite-dimensional case obtained by adding a small random perturbation to a nonlinear heat equation. 相似文献
125.
Wansoo T Rhee 《Operations Research Letters》1985,4(3):121-123
Consider independent identically distributed random variables (Xi) valued in [0,1]. Let B(n) be the optimal (minimum) number of unit size bins needed to pack n items of size X1, X2,…,Xn. We prove that there exists a numerical constant C such that for t > 0, The constant C does not depend on the distribution of X. 相似文献
126.
127.
Summary {\rtf1\ansi\ansicpg1250\deff0\deflang1038\deflangfe1038\deftab708{\fonttbl{\f0\froman\fprq2\fcharset238{\*\fname Times New Roman;}Times New Roman CE;}}
\viewkind4\uc1\pard\f0\fs20 New explanations are given for two types of irregular thermogravimetric (TG) data. A TG relationship between mass and temperature is derived on the basis of migration behavior of bubbles generated in bulk of sample system, and superposed on that derived on the basis of kinetics of the 4\super th\nosupersub order event, which is superposed on the experimental TG data obtained from three reference papers. This suggests that these TG data are reflecting migration of bubbles. A dependence of TG behavior on heating rate, which is contrary to usual that, is shown and is explained in terms of event-rate determination by boiling.
\par } 相似文献
128.
It is proven that the canonical Gibbs measure associated with a gas of vortices of intensity ± converges, in the limitN, 0,Nconst, to a Gaussian measure, which is invariant for the two-dimensional Euler equation.On leave from Dipartimento di Matematica Università di Roma Tor Vergata Roma, Italy.On leave from Dipartimento di Matematica Università di Roma La Sapienza, Roma, Italy. 相似文献
129.
Derrida's generalized random energy model is considered. Almost sure andL
p convergence of the free energy at any inverse temperature are proven for an arbitrary numbern of hierarchical levels. The explicit form of the free energy is given in the most general case and the limitn is discussed. 相似文献
130.
Raoul Kopelman 《Journal of statistical physics》1986,42(1-2):185-200
Heterogeneous kinetics are shown to differ drastically from homogeneous kinetics. For the elementary reaction A + A products we show that the diffusion-limited reaction rate is proportional tot
– h[A]2 or to [A]x, whereh=1- d
s/2, X=1+2/d
s
=(h-2)(h-1), andd
s
is the effective spectral dimension. We note that ford = d
s
=1, h =1/2 andX = 3, for percolating clustersd
s = 4/3,h = 1/3 andX = 5/2, while for dust ds <1, 1 >h > 1/2 and >X > 3. Scaling arguments, supercomputer simulations and experiments give a consistent picture. The interplay of energetic and geometric heterogeneity results in fractal-like kinetics and is relevant to excitation fusion experiments in porous membranes, films, and polymeric glasses. However, in isotopic mixed crystals, the geometric fractal nature (percolation clusters) dominates. 相似文献