纤维型物质的输送机理

本文对纤维状物料的气力输送机理进行了探讨.文中将物料对空气的相对运动看作为空气在松散纤维状物料群体所组成的多孔介质中的渗流问题.由此推得的理论结果与以往所测的实验数据比较,大致符合.     

各向异性液体-多孔饱和介质在机械荷载作用下的弹性动力分析

将一个各向异性液体-多孔饱和介质的弹性动力分析,归结为一个横观各向同性液体-多孔饱和介质在机械荷载作用下的变形问题.自然界中有些物理问题,仅在一个方向发生变形,例如,与变形结构和变形柱有关的问题.土力学中,通常假设只有竖向沉降,从而归结为一维多孔弹性模型.采用各向异性液体-多孔饱和介质的一维变形模型,研究了在不同时间和距离下扰动的变化.给出了在不同类型荷载作用下,介质的各向异性对位移分布和应力分布的影响.     

饱和多孔介质粘弹性理论

本文讨论了饱和多孔介质的粘弹体本构关系。把Lee的弹性和粘弹性比拟理论,拓展到饱和多孔介质领域内。用比拟理论解出了饱和粘性土的常载和变载的一维固结问题,并利用比拟理论的属性,可以由简单的粘弹性本构关系来推求复杂的本构关系,得到了粘弹性地基上的粘弹性梁板问题的解答。由此初步形成了饱和多孔介质粘弹性比拟法的完整理论。     

修正的临界多孔介质方程Hlder连续解的正则性

本文研究具耗散的修正临界多孔介质方程弱解的正则性问题.利用时空Besov空间理论结合能量估计方法,得到了该方程具Hlder连续的弱解是光滑解.多孔介质方程本质上是具非局部零散度速度场的输运扩散方程,与已有大量研究的准地转方程有许多相似之处.从数学角度看,多孔介质方程是准地转方程的一个推广.本文研究3维具耗散的修正临界多孔介质方程弱解的正则性问题.利用时空Besov空间理论结合经典的能量估计方法,得到了该方程具Hlder连续的弱解是光滑解.利用同样的方法可以证明,该结论对于3维修正的临界准地转方程也是成立的.     

具有加权非局部边界条件的多孔介质方程组的临界指标问题（英文）

本文研究了具有非局部边界条件和非线性内部源的多孔介质抛物型方程组问题.利用比较原理,获得了权函数和系数对整体解和爆破解的影响,并得到了解的爆破临界指标,推广了先前的研究结果.     

基于三维CFD-DEM的多孔介质流场数值模拟

将多孔介质局部细观流动与基于Darcy定律的宏观物理模型相结合，应用三维CFD-DEM对多孔介质流场进行局部细观数值模拟，得到多孔介质的惯性阻力系数和粘性阻力系数.并将其作为参数提供给基于Darcy定律的CFD多孔介质模型，从而可用于更大规模的多孔介质流场计算.应用Voronoi多面体作为网格单元，解决了CFD DEM中网格孔隙率精确计算的困难.文中发展的多尺度结合应用的研究方法，在计算精度和计算效率的矛盾中找到了较好的平衡，对于工程应用而言，有节约实验成本、提高计算结果可靠性的功效.     

不可压饱和多孔弹性杆动力响应的多辛方法

研究了不可压饱和多孔弹性杆的一维动力响应问题.基于多孔介质理论,在流相和固相微观不可压、固相骨架小变形的假定下,建立了不可压流体饱和多孔弹性杆一维轴向动力响应的数学模型.利用Hamilton空间体系的多辛理论,构造了不可压饱和多孔弹性杆轴向振动方程的多辛形式及其多种局部守恒律.采用中点Box离散方法得到轴向振动方程的多辛离散格式和局部能量守恒律以及局部动量守恒律的离散格式;数值模拟了不可压饱和多孔弹性杆的轴向振动过程,记录了每一时间步的局部能量数值误差和局部动量数值误差.结果表明,已构造的多辛离散格式具有很高的精确性和较长时间的数值稳定性,这为解决饱和多孔介质的动力响应问题提供了新的途径.     

非线性边界条件下具有空变系数和吸收项的非局部多孔介质抛物方程解的爆破现象

本文研究了非线性边界条件下具有空变系数和吸收项的非局部多孔介质抛物方程解的爆破问题.运用微分不等式技巧,得到了高维空间上非线性边界条件下具有空变系数和吸收项的非局部多孔介质抛物方程全局解的条件.同时,通过构造能量表达式,应用Sobolev不等式等技巧,推出了爆破发生时解的爆破时间上界和下界估计.     

具有非局部边界的多孔介质抛物方程组解的整体存在及爆破

研究了一类具有加权非局部边界和非线性内部源的多孔介质抛物型方程组解的整体存在及爆破问题,通过构造方程组的上、下解及引用比较定理,得到了由幂函数和指数函数完全耦合的多孔介质抛物型方程组解的整体存在及解在有限时刻爆破的充分条件,并推广了已有的结果.     

多孔介质方程在一般几何流演化下的梯度估计

本文研究了多孔介质方程在一般几何流下的梯度估计.通过Aroson和Bénilan对多孔介质方程的研究结果以及运用Li-Yau梯度估计的方法,获得了对多孔介质方程的正解对于Laplace算子以及drifing Laplace算子在一般几何流演化下的一些梯度估计,推广了Zhu Xiao-bao和Deng Yi-hua的结果...     

Bipartite flocking for multi-agent systems

This paper addresses the bipartite flock control problem where a multi-agent system splits into two clusters upon internal or external excitations. Using structurally balanced signed graph theory, LaSalle’s invariance principle and Barbalat’s Lemma, we prove that the proposed algorithm guarantees a bipartite flocking behavior. In each of the two disjoint clusters, all individuals move with the same direction. Meanwhile, every pair of agents in different clusters moves with opposite directions. Moreover, all agents in the two separated clusters approach a common velocity magnitude, and collision avoidance among all agents is ensured as well. Finally, the proposed bipartite flock control method is examined by numerical simulations. The bipartite flocking motion addressed by this paper has its references in both natural collective motions and human group behaviors such as predator–prey and panic escaping scenarios.     

Boundary-value problem for density-velocity model of collective motion of organisms

The collective motion of organisms is observed at almost all levels of biological systems. In this paper the density-velocity model of the collective motion of organisms is analyzed. This model consists of a system of nonlinear parabolic equations, a forced Burgers equation for velocity and a mass conservation equation for density. These equations are supplemented with the Neumann boundary conditions for the density and the Dirichlet boundary conditions for the velocity. The existence, uniqueness and regularity of solution for the density-velocity problem is proved in a bounded 1D domain. Moreover, a priori estimates for the solutions are established, and existence of an attractor is proved. Finally, some numerical approximations for asymptotical behavior of the density-velocity model are presented.     

The motion of a particle in a viscous fluid under gravity,vibration and Basset's force

The sedimentation of a heavy solid spherical particle from a state of rest in an incompressible viscous fluid in a vessel with a vibrating bottom is investigated. Taking the Basset force into account, the problem is reduced to solving a Cauchy problem for a linear integro-differential equation. An exact solution of this problem and simple asymptotic formulae are obtained and a complete analysis of the effect of the Basset force on the oscillations and sedimentation of the particles is carried out. It is shown that a consideration of the Basset force introduces a considerable correction to the classical amplitude-frequency relation, reducing its value and also considerably slowing the arrival of the amplitude at a constant value. When there are no vibrations, it follows from the solution of the problem that there is a slow establishment of the limiting velocity (inversely proportional to the square root of the time), which differs considerably from the case of the sedimentation of particles in accordance with Stokes's law (the establishment of the limiting velocity occurs exponentially).     

Emergence of coherent motion in aggregates of motile coupled maps

In this paper we study the emergence of coherence in collective motion described by a system of interacting motiles endowed with an inner, adaptative, steering mechanism. By means of a nonlinear parametric coupling, the system elements are able to swing along the route to chaos. Thereby, each motile can display different types of behavior, i.e. from ordered to fully erratic motion, accordingly with its surrounding conditions. The appearance of patterns of collective motion is shown to be related to the emergence of interparticle synchronization and the degree of coherence of motion is quantified by means of a graph representation. The effects related to the density of particles and to interparticle distances are explored. It is shown that the higher degrees of coherence and group cohesion are attained when the system elements display a combination of ordered and chaotic behaviors, which emerges from a collective self-organization process.     

Modeling of Phase Transitions in Weakly Bound Molecular Clusters

The method of molecular dynamics was used for modeling the isomerization of a hydrogen bonding network in small water clusters (hexamer and octamer). The collective modes of the particles moving in the clusters were determined by applying principal component analysis. An entropy criterion for phase transitions in water clusters was suggested. This criterion can be used to study phase transitions in weakly bound atomic and molecular clusters.     

相似理论和泥沙的垂直分布

本文利用相似性原理处理了二维渠道均匀定常挟沙水流,在湍流脉动速度和含沙量涨落值相似的条件下,我们得到了泥沙垂直于挟沙水流的流动方向的含沙量分布.这个含沙量分布和扩散理论得到的含沙量分布略有差别,而和重力理论得到的含沙量分布则差别较大.     

The Stokesian Dynamics Method and the Settling behaviour of Particle-Fibre-Mixtures

Sedimentation of fibres and particles can be observed manifold in industrial application. In waste water treatment, the water is clarified from solid particles and fibres utilizing sedimentation. Some filtration processes use fibres as an aid to improve the filtration quality. Finally, in the paper recycling process, one tries to separate cellulose fibres from inorganic particles used as filling material or in printing colours. For all these applications, it is necessary to understand the hydrodynamic interactions between single particles as well as particle and fibre collectives. In the present paper, the sedimentation behaviour of fibres and particles is considered in detail. Mathematic modelling is used to investigate inter particle influences in detail. In particular, a method called Stokesian Dynamics is used to simulate the settling of fibres and particles. The main challenge of the modelling is the dependence of the direction of each fibre on its sedimentation velocity and the different sizes of the particles in a poly-modal particle size distribution. Additionally fibres, particles and the fluid are influencing each other in a significant manner and in a long range. Therefore, while calculating the force on a particle, one has to take into account the influences of many particles. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Fokker-planck equation for brownian motion of rotating spherical particles : PMM vol. 40, n 6, 1976, pp. 1127–1131

The Langevin equation to derive the Fokker-Planck equation is used for the Brownian motion of particles in translational motion. The Fokker-Planck equation for the Brownian motion of particles which have, in addition to the translational velocity also an angular velocity, has not, so far, been derived. This can apparently be explained by the fact that in the case of the rotational motion, the Langevin equation for the translational motion velocity vector must be supplemented by a corresponding equation for an angular velocity vector. The latter equation must contain, in addition to the systematic moment of reaction linearly dependent on the angular velocity of rotation itself, a random moment rapidly varying with time. Moreover, to ensure the compatibility of two differential vector equations within the system, additional relations which must be introduced, must connect not only the coefficients of the systematic reactions, but also the. random vectors varying rapidly with time.In [1],the Boltzmann's equation for a mixture of two gases was used to derive a Fokker-Planck equation for a translational motion of Brownian particles. The same method can be applied to the Brownian motion of spherical particles which have, in addition to the translational velocities, angular velocities of self-rotations. In this case there is no need to introduce additional relations connecting the random rapidly varying vectors.In the present paper we derive the Fokker-Planck equations for a new model of rotating spherical molecules which was used in [2].     

The energy-optimal motion of a vibration-driven robot in a resistive medium

The rectilinear motion of a two-mass system in a resistive medium is considered. The motion of the system as a whole occurs by longitudinal periodic motion of one body (the internal mass) relative to the other body (the shell). The problem consists of finding the periodic law of motion of the internal mass that ensures velocity-periodic motion of the shell at a specified average velocity and minimum energy consumption. The initial problem reduces to a variational problem with isoperimetric conditions in which the required function is the velocity of the shell. It is established that, with optimal motion, the shell velocity is a piecewise-constant time function taking two values (a positive value and a negative value). The magnitudes of these velocities and the overall size of the intervals in which they are taken are uniquely defined, while the optimal motion itself is non-uniquely defined. The simplest optimal motion, for which the period is divided into two sections – one with a positive velocity and the other with a negative velocity of motion of the shell – is investigated in detail. It is shown that, among all the optimal motions, this simplest motion is characterized by the maximum amplitude of oscillations of the internal mass relative to the shell. © Elsevier Ltd. All rights reserved.     

Correlated Brownian Motions as an Approximation to Deterministic Mean-Field Dynamics

We analyze the transition from deterministic mean-field dynamics of several large particles and infinitely many small particles to a stochastic motion of the large particles. In this transition the small particles become the random medium for the large particles, and the motion of the large particles becomes stochastic. Under the assumption that the empirical velocity distribution of the small particles is governed by a probability density ψ, the mean-field force can be represented as the negative gradient of a scaled version of ψ. The stochastic motion is described by a system of stochastic ordinary differential equations driven by Gaussian space-time white noise and the mean-field force as a shift-invariant integral kernel. The scaling preserves a small parameter in the transition, the so-called correlation length. In this set-up, the separate motion of each particle is a classical Brownian motion (Wiener process), but the joint motion is correlated through the mean-field force and the noise. Therefore, it is not Gaussian. The motion of two particles is analyzed in detail and a diffusion equation is deduced for the difference in the positions of the two particles. The diffusion coefficient in the latter equation is spatially dependent, which allows us to determine regions of attraction and repulsion of the two particles by computing the probability fluxes. The result is consistent with observations in the applied sciences, namely that Brownian particles get attracted to one another if the distance between them is smaller than a critical small parameter. In our case, this parameter is shown to be proportional to the aforementioned correlation length. __________ Published in Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 6, pp. 757–769, June, 2005.