Spatial pattern formation of a ratio-dependent predator—prey model     

林望 《海洋学报(英文版)》2010,29(9)

This paper presents a theoretical analysis of evolutionary process that involves organisms distribution and their interaction of spatially distributed population with diffusion in a Holling-III ratio-dependent predator--prey model, the sufficient conditions for diffusion-driven instability with Neumann boundary conditions are obtained. Furthermore, it presents novel numerical evidence of time evolution of patterns controlled by diffusion in the model, and finds that the model dynamics exhibits complex pattern replication, and the pattern formation depends on the choice of the initial conditions. The ideas in this paper may provide a better understanding of the pattern formation in ecosystems.  相似文献   

A benchmark comparison of numerical methods for infinite Prandtl number thermal convection in two-dimensional Cartesian geometry     

B. J. Travis  C. Anderson  J. Baumgardner  C. W. Gable  B. H. Hager  R. J. O'Connell 《地球物理与天体物理流体动力学》2013,107(3-4):137-160

Abstract

A comparison is made between seven different numerical methods for calculating two-dimensional thermal convection in an infinite Prandtl number fluid. Among the seven methods are finite difference and finite element techniques that have been used to model thermal convection in the Earth's mantle. We evaluate the performance of each method using a suite of four benchmark problems, ranging from steady-state convection to intrinsically time-dependent convection with recurring thermal boundary layer instabilities. These results can be used to determine the accuracy of other computational methods, and to assist in the development of new ones.  相似文献   

Effective block diagonal preconditioners for Biot's consolidation equations in piled‐raft foundations     

K. B. Chaudhary  K. K. Phoon  K. C. Toh 《国际地质力学数值与分析法杂志》2013,37(8):871-892

The finite element (FE) simulation of large‐scale soil–structure interaction problems (e.g. piled‐raft, tunnelling, and excavation) typically involves structural and geomaterials with significant differences in stiffness and permeability. The symmetric quasi‐minimal residual solver coupled with recently developed generalized Jacobi, modified symmetric successive over‐relaxation (MSSOR), or standard incomplete LU factorization (ILU) preconditioners can be ineffective for this class of problems. Inexact block diagonal preconditioners that are inexpensive approximations of the theoretical form are systematically evaluated for mitigating the coupled adverse effects because of such heterogeneous material properties (stiffness and permeability) and because of the percentage of the structural component in the system in piled‐raft foundations. Such mitigation led the proposed preconditioners to offer a significant saving in runtime (up to more than 10 times faster) in comparison with generalized Jacobi, modified symmetric successive over‐relaxation, and ILU preconditioners in simulating piled‐raft foundations. Copyright © 2012 John Wiley & Sons, Ltd.  相似文献   

静力平衡近似下大气中非线性对称运动的稳定性、分岔和突变     

彭晓林  罗德海 《成都信息工程学院学报》1991,(Z1)

本文在考虑基本气流具有非线性切变情况下,导出了对称运动所满足的非线性常微分方程,并用非线性系统的稳定、分岔、突变理论,严格地讨论了非线性对称运动的稳定性、分岔和突变问题,获得了一个推广的对称不稳定判据,找到了突变产生的条件。  相似文献   

An explanation of the dimensions of penumbral filaments     

Zhou Dao-qi 《Chinese Astronomy and Astrophysics》1991,15(4):453-460

Unstable pertubation modes exist in the magnetic field of penumbral electric current and I think the penumbral filaments are formed from the development of such modes. Under the short wave approximation the non-adiabatic dispersion equation is solved in the radial and transverse directions of the sunspot. From the condition of instability the length and width of the penumbral filament can be evaluated and it is found that the filament mode is static in the direction of the length and is non-moving in the direction of the width, that the penumbral filaments are a feature of the sunspot magnetic flow under gravity and that the presence of the filaments implies the existence of a twisted magnetic field.  相似文献   

Plasma instability at the inner edge of the accretion disk—I     

S. C. Tripathy  C. B. Dwivedi  A. C. Das  A. R. Prasanna 《Journal of Astrophysics and Astronomy》1993,14(2):103-114

In this paper, the analytical and numerical results of the stability analysis of the accretion disk at the inner boundary is presented. Including the effect of finite conductivity in the disk dynamics, a simple calculation considering only the radial perturbation has been carried out. Within local approximation, it is concluded that the disk is stable to Kelvin-Helmholtz and resistive electromagnetic modes whereas the magnetosonic mode can destabilise the disk structure.  相似文献   

Plasma instability at the inner edge of the accretion disk— II     

S. C. Tripathy  C. B. Dwivedi  A. C. Das  A. R. Prasanna 《Journal of Astrophysics and Astronomy》1993,14(3-4):167-179

A two-dimensional instability analysis for a magneto-keplerian disk flow around a compact object is presented here. Using the eigenvalue technique, linearly coupled perturbed equations have been numerically solved within the local approximation. It is concluded that Kelvin-Helmholtz, magnetosonic (fast and slow) and resistive electromagnetic modes exist. However, only the magnetosonic mode can destabilise the disk structure. Further, we discuss the properties of different modes as a function of disk parameters and plot the eigenmode structures for different physical quantities.  相似文献   

基于复杂网络的岩土颗粒材料分散性失稳先兆研究     

杨晓娟  马刚  周恒  陆希  李易奥  周伟 《岩土力学》2022,43(7):1978-1988

岩土颗粒材料在达到Mohr-Coulomb塑性极限之前可能已经发生了没有明显局部损伤的全域准均匀破坏,即分散性失稳。近年来,网络科学工具在颗粒材料环境中的应用为研究其失稳破坏现象提供了有趣新颖的洞见。采用离散单元法对不同初始密实度的颗粒体系进行等体积应变加载路径的数值试验,发现初始状态越松散的颗粒体系越有可能发生分散性失稳;采用网络科学的理论和方法分析颗粒接触网络的拓扑结构特性和演化规律,发现颗粒材料分散性失稳的结构根源是颗粒接触网络完全崩塌。将颗粒体系划分为强、弱接触系统以构建强接触子网络、弱接触子网络和强−弱接触子网络,研究颗粒接触网络及其3个子网络的特征量演化,结果表明：当颗粒材料开始处于不稳定状态时,易受扰动的弱接触系统的部分接触先失效,导致强接触系统失去其稳定支撑作用而降低承载能力。随着加载的继续,系统通过非局部的自组织过程导致接触结构的全面崩塌,最终触发整体分散性失稳。因此,先于整体失稳的部分弱接触的失效,可视为颗粒材料分散性失稳的关键性临界征兆。  相似文献   

裂隙黄土边坡三维稳定性极限分析     

朱学亮  邵生俊  沈晓钧  邵帅  刘小康 《岩土力学》2022,43(10):2735-2743

黄土边坡中竖直裂隙的发育往往会对边坡稳定产生影响。相对于平面应变机制,建立三维破坏机制下边坡稳定性分析方法更能接近实际边坡失稳情况。基于塑性极限分析上限法,考虑预先存在竖直裂隙的三维黄土边坡不同破坏机制（坡面破坏、坡脚破坏和坡底破坏）,建立能量平衡方程及其无量纲临界高度值γH/c表达式,采用随机搜索法得到了临界高度的上限解。分析了约束宽度、边坡坡度、内摩擦角以及裂隙深度对三维竖直裂隙黄土边坡临界高度值的影响。结果表明：对于坡脚破坏机制,临界高度值随着裂隙深度的增加而减小,减小至临界裂隙深度 (δ /H)_min后,裂隙深度的增加不再影响临界高度值;临界裂隙深度随着坡度β 的增大而增大,随着内摩擦角φ 的增大而减小。当约束宽度B/H<0.8时,大多数破坏机制为坡面破坏。当约束宽度B/H=0.8、内摩擦角φ =10° 及约束宽度B/H=0.6、内摩擦角φ =15° 时,边坡的破坏从坡面破坏机制逐渐过渡到坡脚破坏机制。存在竖直裂隙的黄土边坡比完整边坡具有更小的临界高度,约束宽度及内摩擦角会对三维黄土边坡破坏机制产生影响。  相似文献   

俯冲带地震诱发机制:研究进展综述   总被引：4，自引：0，他引：4  

邵同宾  嵇少丞 《地质论评》2015,61(2):245-268

俯冲带作为地球循环体系的关键部位,具有构造活跃、地震多发以及地质条件复杂等特征。基于震源位置,俯冲带地震既可划分为板间和板内地震,也可分为浅源、中源和深源地震。俯冲带内的浅源地震包括板间地震和浅源板内地震,而中源和深源地震皆属于板内地震。在地球浅部,温度与压力低,浅源地震是由岩石发生脆性破裂或沿着先存断层发生不稳定摩擦滑移造成的。随着深度增加,温度和压力的增加使得流行于浅部的脆性和摩擦行为在无水条件下被强烈抑制,岩石从而表现为可抑制地震的韧性行为,使得中-深源地震的诱发机制有别于常规的脆性行为。随着研究的逐渐深入,人们了解到中源地震的诱发机制主要是脱水或与流体相关的致脆以及塑性剪切失稳,而深源地震的成因主要是相变致裂。然而,中-深源地震很可能是两种或两种以上机制共同作用的结果。例如,在中源深度既可能是流体相关的致脆导致脱水源区的脆性围岩产生地震,亦可能是脱水的蛇纹岩本身可能在流体孔隙压的作用下作粘滑滑移,而前者比后者更为重要。孕震带宽度大于"反裂隙模型"预测的亚稳态橄榄石冷核宽度的深源地震可能是由第一阶段的相变致裂和第二阶段的塑性剪切失稳诱发,而孕震带的实际宽度与预测宽度相当的深源地震则可能仅由相变致裂引起。只要过渡带内名义无水矿物中的结构水能释放出来,脱水致脆同样可能触发一些深源地震;而塑性剪切失稳不仅能在中-深源地震触发后的扩展阶段起着主导作用,而且还能单独触发一些中-深源地震,因此能够解释大多数反复发生的中-深源地震活动。  相似文献