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871.
Randomization time for the overhand shuffle 总被引:1,自引:0,他引:1
Robin Pemantle 《Journal of Theoretical Probability》1989,2(1):37-49
This paper analyzes repeated shuffling of a deck ofN cards. The measure studied is a model for the popularoverhand shuffle introduced by Aldous and Diaconis. It is shown that convergence to the uniform distribution requires at least orderN
2 shuffles, and that orderN
2 log(N) shuffles suffice. For a 52-card deck, more than 1000 shuffles are needed. 相似文献
872.
Asymptotic Stability for a Class of Neutral Systems with Discrete and Distributed Time Delays 总被引:4,自引:0,他引:4
In this note, the asymptotic stability for a class of neutral systems with discrete time and distributed time delays is considered. Delay-dependent criteria are proposed to guarantee the stability for such systems. Some numerical examples are given to illustrate that our results are less conservative than previous results. 相似文献
873.
Thomas Lorenz 《Set-Valued Analysis》2006,14(3):209-247
The well-known Reynold's Transport Theorem deals with the integral over a time-dependent set (that is evolving along a smooth vector field) and specifies its semiderivative with respect to time. Here reachable sets of differential inclusions are considered instead. Dispensing with any assumptions about the regularity of the compact initial set, we give sufficient conditions on the differential inclusion for the absolute continuity (of the integral) with respect to time and its weak derivative is formulated as a Hausdorff integral over the topological boundary. 相似文献
874.
This paper concerns large time behavior of a regular weak solution for non-Newtonian flow equations. It is shown that the decay of the solution is of exponential type when the force term is equal to zero and the domain is bounded. Moreover, the ratio of the enstrophy over the energy has a limit as time tends to infinity, which is an eigenvalue of the Stokes operator. 相似文献
875.
Danxia Wang Yanan Li Hongen Jia 《Numerical Methods for Partial Differential Equations》2023,39(2):1251-1265
In this paper, we present a two-grid finite element method for the Allen-Cahn equation with the logarithmic potential. This method consists of two steps. In the first step, based on a fully implicit finite element method, the Allen-Cahn equation is solved on a coarse grid with mesh size H. In the second step, a linearized system whose nonlinear term is replaced by the value of the first step is solved on a fine grid with mesh size h. We give the energy stabilities of the traditional finite element method and the two-grid finite element method. The optimal convergence order of the two-grid finite element method in H1 norm is achieved when the mesh sizes satisfy h = O(H2). Numerical examples are given to demonstrate the validity of the proposed scheme. The results show that the two-grid method can save the CPU time while keeping the same convergence rate. 相似文献
876.
Based on the theoretical framework of adaptive dynamics, the evolution of the predator-prey model with functional response of group defense effect on the predator handling time, was investigated. Firstly, in view of the interaction of predator populations with interspecific competition, the evolutionary conditions for a single predator population to split into 2 populations with different strategies through evolutionary branching were given. Secondly, when the ecological equilibrium of the model is unstable and the system has a limit cycle, the population will have strong coexistence under large mutation, but this coexistence will be evolutionarily unstable. Finally, the conclusions for the model with Holling-Ⅱ type functional response were compared. The results indicate that, with a sufficiently large prey carrying capacity, group defense effects can evolutionarily lead to the extinction of predators. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved. 相似文献
877.
Changshi Li Yuhui Liu Fengru Wang Jerry Zhijian Yang & Cheng Yuan 《高等学校计算数学学报(英文版)》2023,16(2):433-452
We proposed absorbing interface conditions for the simulation of linear
wave propagation on non-uniform meshes. Based on the superposition principle of
second-order linear wave equations, we decompose the interface condition problem into two subproblems around the interface: for the first one the conventional
artificial absorbing boundary conditions is applied, while for the second one, the
local analytic solutions can be derived. The proposed interface conditions permit
a two-way transmission of low-frequency waves across mesh interfaces which can
be supported by both coarse and fine meshes, and perform a one-way absorption
of high-frequency waves which can only be supported by fine meshes when they
travel from fine mesh regions to coarse ones. Numerical examples are presented to
illustrate the efficiency of the proposed absorbing interface conditions. 相似文献
878.
Input-to-state stability (ISS) analysis and stabilization are concerned in this paper for switched nonlinear positive systems (SNPS), where the deterministic and random switching are both included. For general SNPS, switched affine nonlinear positive systems (SANPS) and switched linear positive systems (SLPS) with deterministic and some kinds of random ”slow” switching, some criterions on ISS are provided. From the criterions for SANPS and SLPS, the ISS properties can be judged just by the differential, algebraic and switching characteristics of the systems. Further, based on the criterions for SANPS and SLPS, some state feedback controllers are designed such that the closed-loop systems be positive, ISS or ISS in some stochastic senses. Four simulation examples verify the validity of our results. 相似文献
879.
Jet quenching has successfully served as a hard probe to study the properties of Quark-Gluon Plasma (QGP). As a multi-particle system, jets require time to develop from a highly virtual parton to a group of partons close to mass shells. In this study, we present a systematical analysis on the effects of this formation time on jet quenching in relativistic nuclear collisions. Jets from initial hard scatterings were simulated with Pythia, and their interactions with QGP were described using a Linear Boltzmann Transport (LBT) model that incorporates both elastic and inelastic scatterings between jet partons and the thermal medium. Three different estimations of the jet formation time were implemented and compared, including instantaneous formation, formation from single splitting, and formation from sequential splittings, before which no jet-medium interaction was assumed. We found that deferring the jet-medium interaction with a longer formation time not only affects the overall magnitude of the nuclear modification factor of jets but also its dependence on the jet transverse momentum. 相似文献
880.
We prepose a 5-bit lattice Boltzmann model for KdV equation. Using Chapman-Enskog expansion and multiscale technique, we obtained
high order moments of equilibrium distribution function, and the 3rd dispersion coefficient and 4th order viscosity. The parameters
of this scheme can be determined by analysing the energy dissipation.
The project supported by the Foundation of the Laboratory for Nonlinear Mechanics of Continuous Media, Institute of Mechanics,
Chinese Academy of Sciences 相似文献