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991.
992.
The almost sure asymptotic stability of higher-dimensional linear stochastic systems and of a special class of nonlinear stochastic systems with homogeneous drift and diffusion coefficients of order one is studied. Based on the well-known Khasminskii's theorem, a new approach for obtaining the regions of almost sure asymptotic stability and instability without evaluating the stationary probability density of the diffusion process defined on unit hypersphere is proposed. Two examples of two and three degree-of-freedom linear stochastic systems are given to illustrate the application and effectiveness of the proposed approach combined with stochastic averaging. 相似文献
993.
谭忠 《厦门大学学报(自然科学版)》1995,34(6):887-892
研究了R ̄N上具有临界Sobolev指数的双调和方程,且非平凡解的存在性.这里a(x)≥0且;应用形变引理和拓扑度方法证明了当充分小时,上述方程至少有一个不变号的非平凡解. 相似文献
994.
张翼 《浙江大学学报(理学版)》1995,22(2):139-142
本文讨论了拟线性椭圆型方程-Δpu=λ|u|^p-2u,x∈Ω;u=0,x∈Ω非平凡解的存在性,其中Ω是有界光滑区域。 相似文献
995.
Akira Sakai 《Journal of statistical physics》2002,106(1-2):201-211
The contact process and oriented percolation are expected to exhibit the same critical behavior in any dimension. Above their upper critical dimension d
c, they exhibit the same critical behavior as the branching process. Assuming existence of the critical exponents, we prove a pair of hyperscaling inequalities which, together with the results of refs. 16 and 18, implies d
c=4. 相似文献
996.
Sergio Caracciolo Giorgo Parisi Andrea Pelissetto 《Journal of statistical physics》1994,77(3-4):519-543
We introduce a model of self-repelling random walks where the short-range interaction between two elements of the chain decreases as a power of the difference in proper time. The model interpolates between the lattice Edwards model and the ordinary random walk. We show by means of Monte Carlo simulations in two dimensions that the exponentv
MF obtained through a mean-field approximation correctly describes the numerical data and is probably exact as long as it is smaller than the corresponding exponent for self-avoiding walks. We also compute the exponent and present a numerical study of the scaling functions. 相似文献
997.
This investigation presents an analysis of the critical behavior of mixtures of oligomers of propylene glycol, PG17, and ethylene glycol, EGn, withn=3, 4, 5, 6.4, 8.7, 12.1 and 22.1. The critical coordinates,
c andT
c were determined from the phase diagrams. The critical compositions compare very well with the Huggins-Flory predictions. The interaction parameter
n is around one for EG3, EG4 and EG5 and it increases up to two for the higher oligomers. The break in the interaction parameter also corresponds to a minimum in the critical temperature. The phase diagrams and the interfacial tension were used to get the critical exponents and , respectively. The data were analysed with two approaches. First, from the temperature dependence of the length of the tie-lines and of the interfacial tension up to the upper critical solution temperature, UCST. Second, with the data at 30°C using the critical temperature of the systems as the variable. The first method led to =0.39±0.05 in good agreement with the result of the second method, =0.37±0.04. The exponents for the interfacial tension, , determined with the first method for PG17 with EG6.4, EG8.7 and EG12.1 are =1.66±0.11, 1.46±0.25 and 1.73±0.18, respectively. The second method led to =1.17±0.14. The critical exponents are compared to mean field and ising-3D predictions. 相似文献
998.
We study a class of twist maps where the functiong()=(1–|2|
z–1) is nonanalytic (C
1) and endowed with a varying degree of inflectionz. Whenz>3, reappearance of a KAM torus after its breakup has been observed. We introduce an inverse residue criterion to determine the reappearance point. Scaling behavior at the transition points is also studied. For 2z<3 the scaling exponents are found to vary withz, whereas forz3 they are independent ofz. In this sensez=3 plays a role quite similar to that of the upper critical dimension in phase transitions. 相似文献
999.
The uniform nearest particle system (UNPS) is studied, which is a continuoustime Markov process with state space
. The rigorous upper bound
(mf)
= ( – 1)/ for the order parameter
2, is given by the correlation identity and the FKG inequality. Then an improvement of this bound
(mf)
is shown in a similar fashion;
C( – 1)/|log( – 1) for >1. Recently, Mountford proved that the critical value c=1. Combining his result and our improved bound implies that if the critical exponent exists, it is strictly greater than the mean-field value 1 in the weak sense. 相似文献
1000.
M. Muthukumar 《Journal of statistical physics》1983,30(2):457-465
A simple method based on Wilson's renormalization group ideas is applied to calculate the dynamical critical exponentz for polymer chains in different dynamical regimes. It is shown that the Doi-Edwards reptating chain does not belong to the same dynamical universality class as the Rouse chain. The earlier results based on (4 –d, d space dimensionality) expansion for chains with excluded volume effect are recovered without any expansion. When combined with the Monte Carlo techniques, this method results in a simple scheme for calculating the static and dynamic exponents for a polymer chain with a prescribed dynamics. Numerical results suggest that the slithering snake model of Wall and Mandel for the dynamics is in a different dynamic universality class than the Rouse chain.Presented at the Symposium on Random Walks, Gaithersburg, MD, June 1982.Research supported in part by the National Science Foundation (Grant No. DMR-8112968) and the Petroleum Research Fund, administered by the American Chemical Society. 相似文献