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91.
We present and discuss how the so called Equation-free approach for multi-scale computations can be used to systematically study certain aspects of the dynamics of detailed individual-based epidemiological simulators. As our illustrative example, we choose a simple individual-based stochastic epidemic model evolving on a fixed random regular network (RRN). We show how control policies based on the isolation of the infected population can dramatically influence the dynamics of the disease resulting to big-amplitude oscillations. We also address the development of a computational framework that enables detailed epidemiological simulators to converge to their coarse-grained critical points, which mark the onset of the emergent time-dependent solutions as well as to trace branches of coarse-grained unstable equilibria. Using the individual-based simulator we construct the coarse-grained bifurcation diagrams illustrating the dependence of the solutions on the disease characteristics. 相似文献
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Efficient integration of stiff kinetics with phase change detection for reactive reservoir processes
Morten R. Kristensen Margot G. Gerritsen Per G. Thomsen Michael L. Michelsen Erling H. Stenby 《Transport in Porous Media》2007,69(3):383-409
We propose the use of implicit one-step Explicit Singly Diagonal Implicit Runge–Kutta (ESDIRK) methods for integration of
the stiff kinetics in reactive, compositional and thermal processes that are solved using operator-splitting type approaches.
To facilitate the algorithmic development we construct a virtual kinetic cell model. The model serves both as a tool for the
development and testing of tailored solvers as well as a testbed for studying the interactions between chemical kinetics and
phase behavior. As case study, two chemical kinetics models with 6 and 14 components, respectively, are implemented for in
situ combustion, a thermal oil recovery process. Through benchmark studies using the 14 component reaction model the new ESDIRK
solvers are shown to improve computational speed when compared to the widely used multi-step BDF methods DASSL and LSODE.
Phase changes are known to cause convergence problems for the integration method. We propose an algorithm for detection and
location of phase changes based on discrete event system theory. Experiments show that the algorithm improves the robustness
of the integration process near phase boundaries by lowering the number convergence and error test failures by more than 50%
compared to direct integration without the new algorithm. 相似文献
94.
本文利用边界单元法及基于Peierls-Nabarro模型的位错理论,分析了理想纳米触头下多位错的生成,得到了滑移面上多位错的构形以及表面位移与载荷的关系曲线。根据得到的计算结果分析了薄膜厚度的影响,得到了与已有实验结果相同的结论。通过把表面看成一个包含在无穷大弹性体中的无穷大弹性体中无穷大裂纹来考虑表面的影响,从而可以直接采用已有的边界积分方程。该方法在连续介质力学的计算中引入了包含原子信息的层间势能函数,为分析多尺度的力学问题提供了有效的方法。 相似文献
95.
We consider the evolution of a reactive soluble substance introduced into the Poiseuille flow in a slit channel. The reactive transport happens in presence of dominant Péclet and Damköhler numbers. We suppose Péclet numbers corresponding to Taylor’s dispersion regime. The two main results of the paper are the following. First, using the anisotropic perturbation technique, we derive rigorously an effective model for the enhanced diffusion. It contains memory effects and contributions to the effective diffusion and effective advection velocity, due to the flow and chemistry reaction regime. Error estimates for the approximation of the physical solution by the upscaled one are presented in the energy norms. Presence of an initial time boundary layer allows only a global error estimate in L 2 with respect to space and time. We use the Laplace’s transform in time to get optimal estimates. Second, we explicit the retardation and memory effects of the adsorption/desorption reactions on the dispersive characteristics and show their importance. The chemistry influences directly the characteristic diffusion width. 相似文献
96.
We present a two-step up-scaling approach that allows to derive the jump conditions that must be imposed at the interface
to account for transport phenomena in a fluid/porous domain. This general approach is first applied to a heat conduction problem
to illustrate the main steps of the analysis. The heat flux and temperature jump conditions are related to surface-excess
quantities, whose values depend on the interface location. Good agreement between the mesoscopic and macroscopic results are
obtained, whatever the position of the interface inside the transition region. The approach is then applied to the problem
of a laminar flow over a porous medium. The Beavers and Joseph relation is recovered, but only for a particular position of
the interface. 相似文献
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Wael W. MOHAMMED 《数学年刊B辑(英文版)》2018,39(1):145-162
The main goal of this paper is to approximate the Kuramoto-Shivashinsky (K-S for short) equation on an unbounded domain near a change of bifurcation, where a band of dominant pattern is changing stability. This leads to a slow modulation of the dominant pattern. Here we consider PDEs with quadratic nonlinearities and derive rigorously the modulation equation, which is called the Ginzburg-Landau (G-L for short) equation, for the amplitudes of the dominating modes. 相似文献
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