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991.
Recent results of Monte Carlo simulations of the ant-in-the-labyrinth method in three-dimensional percolation lattices are reanalyzed in the light of more accurate corrections to scaling ansatz, motivated by inconsistent results that have appeared in the literature. The results are observed to be sensitive to the form of the scaling correction terms. Using a single correction term, we estimate the valuek=0.197±0.004 for the anomalous diffusion exponent at criticality. When two correction terms are included,k=0.200±0.002 is obtained. These new estimates are consistent with known theoretical bounds, with recent series expansion results, and with numerical calculations of the conductance of random resistor networks above criticality. 相似文献
992.
GENERALIZED SOLUTION OF SINGULARLY PERTURBED PROBLEMS FOR REACTION DIFFUSION EQUATIONS 总被引:2,自引:0,他引:2
Yao Jingsun Mo Jiaqi 《Annals of Differential Equations》2006,22(1):81-86
The singularly perturbed initial boundary value problem for reaction diffusion equation is considered. Under suitable conditions the existence, uniqueness and asymptotic behavior of the generalized solution for the problems are studied. 相似文献
993.
A. Frei Yu. Sobolev I. Altarev K. Eberhardt A. Gschrey E. Gutsmiedl R. Hackl G. Hampel F. J. Hartmann W. Heil J. V. Kratz Th. Lauer A. Liźon Aguilar A. R. Müller S. Paul Yu. Pokotilovski W. Schmid L. Tassini D. Tortorella N. Trautmann U. Trinks N. Wiehl 《The European Physical Journal A - Hadrons and Nuclei》2007,34(2):119-127
The production rates of ultracold neutrons (UCN) with a solid deuterium converter have been measured at the pulsed reactor
TRIGA Mainz. Exposed to a thermal neutron fluence of
n·cm^-2·pulse^-1, the number of detected very cold and ultracold neutrons ranges up to 200 000 at 7mol of solid deuterium
(sD2) in combination with a pre-moderator (mesitylene). About 50% of the measured neutrons can be assigned to UCN with energies
E of
where V
F(sD
2) = 105 neV and V
F(guide) = 190 neV are the Fermi potentials of the sD2 converter and our stainless steel neutron guides, respectively. Thermal cycling of solid deuterium, which was frozen out
from the gas phase, considerably improved the UCN yield, in particular at higher amounts of sD2. 相似文献
994.
Sonia Mazzucchi Valter Moretti Ivan Remizov Oleg Smolyanov 《Mathematische Nachrichten》2023,296(3):1244-1284
Chernoff approximations of Feller semigroups and the associated diffusion processes in Riemannian manifolds are studied. The manifolds are assumed to be of bounded geometry, thus including all compact manifolds and also a wide range of non-compact manifolds. Sufficient conditions are established for a class of second order elliptic operators to generate a Feller semigroup on a (generally non-compact) manifold of bounded geometry. A construction of Chernoff approximations is presented for these Feller semigroups in terms of shift operators. This provides approximations of solutions to initial value problems for parabolic equations with variable coefficients on the manifold. It also yields weak convergence of a sequence of random walks on the manifolds to the diffusion processes associated with the elliptic generator. For parallelizable manifolds this result is applied in particular to the representation of Brownian motion on the manifolds as limits of the corresponding random walks. 相似文献
995.
本文针对带非线性源项的Riesz回火分数阶扩散方程,利用预估校正方法离散时间偏导数,并用修正的二阶Lubich回火差分算子逼近Riesz空间回火的分数阶偏导数,构造出一类新的数值格式.给出了数值格式在一定条件下的稳定性与收敛性分析,且该格式的时间与空间收敛阶均为二阶.数值试验表明数值方法是有效的. 相似文献
996.
Weizhu Bao Harald Garcke Robert Nürnberg Quan Zhao 《Numerical Methods for Partial Differential Equations》2023,39(1):759-794
We consider the evolution of curve networks in two dimensions (2d) and surface clusters in three dimensions (3d). The motion of the interfaces is described by surface diffusion, with boundary conditions at the triple junction points lines, where three interfaces meet, and at the boundary points lines, where an interface meets a fixed planar boundary. We propose a parametric finite element method based on a suitable variational formulation. The constructed method is semi-implicit and can be shown to satisfy the volume conservation of each enclosed bubble and the unconditional energy-stability, thus preserving the two fundamental geometric structures of the flow. Besides, the method has very good properties with respect to the distribution of mesh points, thus no mesh smoothing or regularization technique is required. A generalization of the introduced scheme to the case of anisotropic surface energies and non-neutral external boundaries is also considered. Numerical results are presented for the evolution of two-dimensional curve networks and three-dimensional surface clusters in the cases of both isotropic and anisotropic surface energies. 相似文献
997.
Pradip Roul V. M. K. Prasad Goura Roberto Cavoretto 《Numerical Methods for Partial Differential Equations》2023,39(1):45-64
This paper presents an efficient numerical technique for solving a class of time-fractional diffusion equation. The time-fractional derivative is described in the Caputo form. The L1 scheme is used for discretization of Caputo fractional derivative and a collocation approach based on sextic B-spline basis function is employed for discretization of space variable. The unconditional stability of the fully-discrete scheme is analyzed. Two numerical examples are considered to demonstrate the accuracy and applicability of our scheme. The proposed scheme is shown to be sixth order accuracy with respect to space variable and (2 − α)-th order accuracy with respect to time variable, where α is the order of temporal fractional derivative. The numerical results obtained are compared with other existing numerical methods to justify the advantage of present method. The CPU time for the proposed scheme is provided. 相似文献
998.
999.
This paper is concerned with the large time behavior of the solutions for 1D radiation hydrodynamic limit model without viscosity and its asymptotic stability of the viscous contact discontinuity wave under the smallness assumption of the strength of the contact wave and initial perturbations. The present pressure includes a fourth-order term about the absolute temperature from radiation effect which brings the main difficulty. Furthermore, the dissipative of the system is weaker for the lack of viscosity. All these make the problem more challenging. The prove is mainly based on the energy method, including normal and radial directions energy estimates. 相似文献
1000.
In this paper we address the large-time behavior of solutions of bistable and multistable reaction–diffusion equation with discontinuities around the stable steady states. We show that the solution always converges to a special solution, which may either be a traveling wave in the bistable case, or more generally a terrace (i.e. a collection of stacked traveling waves with ordered speeds) in the multistable case. 相似文献