Particle Lagrangian Tracking with Hydrodynamic Interactions and Collisions

Hydrodynamic interactions between particle pairs are included in a Lagrangian approach for the simulation of the turbulent dispersion of a discrete particle. Several particles are simultaneously followed, and the set of equations of motion involves a coupling between particles through the use of a resistance matrix pertaining to the sedimentation theory. Results are presented for particle behavior in low turbulence fields, where collisions between particle pairs are assumed to be perfectly elastic. The influence of the turbulence anisotropy is considered and the anisotropy of the particle fluctuating motion is shown to be reduced by collisions.     

Collisions and Regularization for the 3-Vortex Problem

We study the dynamics of 3 point-vortices on the plane for a fluid governed by Euler’s equations, concentrating on the case when the moment of inertia is zero. We prove that the only motions that lead to total collisions are self-similar and that there are no binary collisions. Also, we give a regularization of the reduced system around collinear configurations (excluding binary collisions) which smoothes out the dynamics. Both authors gratefully acknowledge support from DGAPA-UNAM under project PAPIIT IN101902 and from CONACyT under grant 32167-E. The second author thanks the hospitality of IIMAS-UNAM during the preparation of this paper.     

The Geometry of Binary Collisions and Generalized Radon Transforms

Elastic collisions are characterized by the conservation of momentum and energy. We consider some geometrical aspects of such collisions, when the energy of one particle can be expressed in terms of the moments as . The geometry of elastic collisions is essential for the regularizing property of the gain term in the Boltzmann equation, which was proved by P.-L. Lions. We show how such results can be deduced from a regularity theorem for generalized Radon transforms by Sogge & Stein. This is possible for and for ; we also show that the same technique cannot be used with other choices of . (Accepted May 20, 1996)     

The analytical predictive criteria for chaos and escape in nonlinear oscillators: A survey

The purpose of this paper is to provide a brief summary of the various analytical predictive criteria in order for strange phenomena to occur in a class of softening nonlinear oscillators, oscillators which may exhibit escape from a potential well. Implications of Melnikov's criteria are discussed first and transient chaos in the twin-well potential oscillator is illustrated. Three different heuristic criteria for steady state chaos or escape solution, proposes by F. Moon, G. Schmidt and W. Szempliskia-Stupnicka, are then presented and compared to computer simulation results.     

A novel ADP based model-free predictive control

Dynamic programming is a very useful tool in solving optimization and optimal control problems. Here, the Approximate Dynamic Programming (ADP) and the notion of neural networks based predictive control are combined with a model-free control method based on SPSA (Simultaneous perturbation stochastic approximation), and a novel ADP based model-free predictive control strategy for nonlinear systems is proposed. Dynamic programming is used to adjust the control parameters in the novel model-free control method and the notion of predictive control is introduced to modify the whole control structure. Finally, the proposed ADP based model-free predictive control strategy is applied to solve nonlinear tracking problems and the effectiveness of this novel control method is fully illustrated though simulation tests on two typical nonlinear systems.     

Rayleigh wave existence theory: A supplementary remark

It is shown explicitly that the matrix B, which plays a central role in surface wave existence theory, is positive definite at zero velocity.     

Quantifying the extent of crushing in granular materials: A probability-based predictive method

Grain crushing is one of the micromechanisms that governs the stress-strain behaviour of a granular material, and also its permeability by altering the grain size distribution. It is therefore advantageous to be able to predict the point of onset of crushing and to quantify the subsequent evolution of crushing. This paper uses the data of Discrete Element Method (DEM) simulations to inform a statistical model of granular crushing. Distributions of normalised contact forces are first obtained. If the statistical distribution of the crushing strength of the grains is then known, the onset of crushing within an assembly of grains should be predictable. Two different cases, one in which grain strength was statistically independent of grain size and one showing an arbitrary trend, were used to compare with DEM results and so confirm the validity of the statistical method.     

A hyperchaotic time-delayed system with single-humped nonlinearity: theory and experiment

In this paper, two different concepts of multiple task motion planning algorithm for nonholonomic systems are considered. The egalitarian approach treats all the tasks equivalently and tries to solve all the tasks simultaneously. In contrast, the prioritarian approach arranges the tasks with decreasing priorities in such a way that the solution of the lower order task should not influence the solution of the higher order task. This paper contains the derivation of the egalitarian motion planning algorithm and the prioritarian motion planning algorithm. Moreover, the definitions of the three types of basic subtasks are also included. The efficiency of the egalitarian and prioritarian algorithms is presented with the simulation of the nonholonomic model of the unmanned surface vessel. The simulation results provide the data to perform a comparison of the egalitarian versus the prioritarian approach.     

A predictive mechano-biological model of the bone-implant healing

The quality of the fixation orthopaedic implant to its surrounding bone determines its clinical longevity. Up to 20% of hip replacement operations are currently revisions for aseptic loosening. While this fixation quality is determined primarily by the bone and tissue anchoring the implant, conditions influencing bone growth in the early post-operative period include the surgical technique and coupled mechanical and biochemical factors. The aim of the study was to propose an original mechano-biological formulation of the healing process of periprosthetic tissue. The multiphasic porous model involved the solid osseous matrix, the extracellular fluid phase, the osteoblastic cellular phase responsible from the bone formation and the growth factor phase promoting the cellular activity. To derive the non-linear convective-diffuse governing equations, mass balance was associated to cell active haptotactic and chemotactic migration, growth factor diffusion, cell proliferation (logistic law) and bone formation (reactive medium). The in-vivo application concerned a canine axisymmetric implant which was stable and mechanically unloaded. Predictive numerical results were compared to ex-vivo data from a histologic study. The generic healing pattern involving two main oscillations of the radial bone formation was well predicted. In the future, the model could assist in evaluating the role of growth factor concentrations and their temporal delivering as far as the role of pertinent sources such as bioactive coating or additional biomaterials.     

Integrability for peaffian constrained systems: A geometrical theory

There exists an Ehresmann connection on the fibred constrained sub-manifold defined by Pfaffian differential constraints. It is proved that curvature of the connection is closely related to the d-σ commutation relation in the classical nonholonomic mechanics. It is also proved that conditions of complete integrability for Pfaffian systems in Frobenius sense are equivalent to the three requirements upon the conditional variations in the classical calculus of variations: (1) the variations belong to the constrained manifold, (2) variational operators commute with differential operators, (3) variations satisfy the Chetaev's conditions. Thus this theory verifies the conjecture or experience of researchers of mechanics on the integrability conditions in terms of variation calculus. The project supported by the National Natural Science Foundation of China     

The bimodal theory of plasticity: A form-invariant generalisation

The bimodal plasticity model of fibre-reinforced materials is currently available and applicable only in association with thin-walled fibrous composites containing a family of straight fibres which are conveniently assumed parallel with the x₁-axis of an appropriately chosen Cartesian co-ordinate system. Based on reliable experimental evidence, the model suggests that plastic slip in the composite operates in two distinct modes; the so-called matrix dominated mode (MDM) which depends on a matrix yield stress, and the fibre dominated mode (FDM) which depends also on the fibre yield stress. Each mode is activated by different states of applied stress, has its own yield surface (or surfaces) in the stress space and has its own segment on the overall yield surface of the composite. This paper employs theory of tensor representations and produces a form-invariant generalisation of both modes of the model. This generalisation furnishes the model with direct applicability to relevant plasticity problems, regardless of the shape of the fibres or the orientation of the co-ordinate system. It thus provides a proper mathematical foundation that underpins important physical concepts associated with the model while it also elucidates several technical relevant issues. A most interesting of those issues is the revelation that activation of the MDM plastic regime is possible only if the applied stress state allows the fibres to act like they are practically inextensible. Moreover, activation of the more dominant, between the two MDM plastic slip branches is possible only if conditions of material incompressibility hold, in addition to the implied condition of fibre inextensibility. A direct mathematical connection is thus achieved between basic, experimentally verified concepts of the bimodal plasticity model and a relevant mathematical model originated earlier from the theory of ideal fibre-reinforced materials. An additional issue of discussion involves the number of independent yield stress parameters that the bimodal theory needs to take into consideration. Moreover, an analytical expression is provided of a relatively simple mathematical surface that possesses all known features of the FDM yield surface; currently captured with the aid of both experimental and computational means. The present study is guided by the existing relevant experimental evidence which, however, is principally associated with the plastic behaviour of solids reinforced by strong fibres. Nevertheless, several of the outlined developments are expected to be applicable to composite materials containing a single family of more compliant or even weak fibres.     

Superstatistics: theory and applications

Superstatistics is a superposition of two different statistics relevant to driven nonequilibrium systems with a stationary state and intensive parameter fluctuations. It contains Tsallis statistics as a special case. After briefly summarizing some of the theoretical aspects, we describe recent applications of this concept to three different physical problems, namely a) fully developed hydrodynamic turbulence, b) pattern formation in thermal convection states, and c) the statistics of cosmic rays.Received: 13 March 2003, Accepted: 27 May 2003, Published online: 9 December 2003PACS: 05.40.-a     

A new predictive model for fragmenting and non-fragmenting binary droplet collisions

A new predictive model for collisional interactions between liquid droplets, which is valid for moderate to high Weber numbers (>40), has been developed and validated. Four possible collision outcomes, viz., bouncing, coalescence, reflexive separation and stretching separation, are considered. Fragmentations in stretching and reflexive separations are modeled by assuming that the interacting droplets form an elongating ligament that either breaks up by capillary wave instability, or retracts to form a single satellite droplet. The outcome of a collision, number of satellites formed from separation processes and the post-collision characteristics such as velocity and drop-size are compared with available experimental data. The comparisons include colliding mono- and poly-disperse streams of droplets of different fuels under atmospheric conditions, and the results agree reasonably well.     

A micromorphic electromagnetic theory

This work is concerned with the determination of both macroscopic and microscopic deformations, motions, stresses, as well as electromagnetic fields developed in the material body due to external loads of thermal, mechanical, and electromagnetic origins. The balance laws of mass, microinertia, linear momentum, moment of momentum, energy, and entropy for microcontinuum are integrated with the Maxwell’s equations. The constitutive theory is constructed. The finite element formulation of micromorphic electromagnetic physics is also presented. The physical meanings of various terms in the constitutive equations are discussed.     

A theory of mixtures

This paper is concerned with a dynamical theory of mixtures, composed of n reactive constituents in relative motion to each other. The theory is developed in terms of the constituent ingredients using a balance of energy and an entropy production inequality for each constituent of the mixture, together with invariance requirements under superposed rigid body motions of the whole mixture. The balance of energy and the entropy production inequality for each of the constituents, which include contributions arising from interactions, combine to yield a single energy equation and a single entropy production inequality in terms of the ingredients of the mixture as a whole; the relations between the thermodynamical variables of the mixture and those of its constituents depend, in general, on the past history of the temperature and the kinematic variables. Full thermodynamical restrictions are deduced, and the theory is applied to the special case of a mixture of two ideal fluids.     

Dynamic void nucleation and growth in solids: A self-consistent statistical theory

We present a framework for a self-consistent theory of spall fracture in ductile materials, based on the dynamics of void nucleation and growth. The constitutive model for the material is divided into elastic and “plastic” parts, where the elastic part represents the volumetric response of a porous elastic material, and the “plastic” part is generated by a collection of representative volume elements (RVEs) of incompressible material. Each RVE is a thick-walled spherical shell, whose average porosity is the same as that of the surrounding porous continuum, thus simulating void interaction through the resulting lowered resistance to further void growth. All voids nucleate and grow according to the appropriate dynamics for a thick-walled sphere made of incompressible material. The macroscopic spherical stress in the material drives the response in all volume elements, which have a distribution of critical stresses for void nucleation, and the statistically weighted sum of the void volumes of all RVEs generates the global porosity. Thus, macroscopic pressure, porosity, and a distribution of growing microscopic voids are fully coupled dynamically. An example is given for a rate-independent, perfectly plastic material. The dynamics of void growth gives rise to a rate effect in the macroscopic material even though the parent material is rate independent.     

裂纹体分析的权函数理论与应用: 回顾和展望

断裂力学是工程材料和结构的疲劳与断裂分析、损伤容限设计和结构完整性评定的理论基础. 应力强度因子作为线弹性裂纹尖端奇异场的单一表征参量和裂纹扩展驱动力, 在裂纹体的断裂力学分析中发挥着关键作用. 权函数法为复杂受载裂纹体的应力强度因子求解计算提供了强有力的解析工具, 不但具有远高于各类数值解法的计算效率, 而且精度可靠, 使用方便. 本文结合笔者团队在权函数法方面的长期研究工作, 对该方法自20世纪70年代初提出至今半个世纪以来, 国际断裂界在二维和三维权函数理论与应用方面的主要研究进展作了回顾和评述, 并对其未来发展提出了展望. 主要内容涵盖: 当前国际断裂界广泛应用的3种二维裂纹解析权函数法简介和以格林函数为基准的验证评价; 三维裂纹问题的片条合成权函数法和点载荷权函数法; 权函数法在复杂受载裂纹体的应力强度因子和裂纹张开位移等关键力学参量计算、内聚力/桥连等裂纹模型分析、共线多裂纹权函数理论及其在剩余强度预测等方面的应用, 以及复杂裂纹几何的工程化权函数分析和权函数法的反向应用问题.