Structural differences in wave propagation in discrete and continuous systems

Summary The harmonic and transient behaviours of one-dimensional discrete semi-infinite cascades of masses and springs have been derived from analytical pulse response solutions [1]. The investigation shows structural differences between the dynamic behaviour of models with distributions of mass over the finite elements as compared to continuous models. Two generally accepted ideas are scrutinized. Firstly, that the dynamic behaviour of a discrete model after a refinement of the mesh converges to the response of the underlying continuous model. Secondly, that a symmetric mass distribution over the element results in a better convergence. Both ideas need some adjustment.This paper has been presented at the 2nd ESMC, Genua, Italy, 1994.     

Method for determining the coupling parameters for complex linear systems with discrete couplings between subsystems

Complex systems whose subsystems interact at finitely many points are considered. The couplings are given by linear homogeneous differential relations.     

High-speed roll coating with complex rheology fluids

The flow of high solids content suspensions and coating colors through the deformable gap of counter-rotating rolls at high speed was investigated. Measurements of nip pressure profiles in a laboratory film coater were conducted and flow visualization experiments downstream the nip were carried out. A high-speed video system allowed showing the formation, elongation and break up of filaments that yield the misting droplets. The role of rheology on misting was also investigated using shear and extensional data. Results show that misting, mainly generated by film splitting, is reduced when the extensional viscosity of the color is larger.     

Viscous fluids with hidden variables and hyperbolic systems

The behaviour of viscous fluids is described through a hidden variable approach which leads to a hyperbolic quasi-linear system. Such a system accounts even for transverse weak discontinuities which are shown to be exceptional waves.     

复杂机构的控制与结构同步优化设计

本文研究了非线性机构控制与结构同步优化设计问题。提出了一种复杂系统敏度分析的数值求解方法,该方法首先通过滑模控制器将非线性动力学方程化简为一个线性微分方程;然后,利用Newmark积分法,获得系统对设计变量敏度的数值解;最后,以Stewart平台为例,介绍了该方法的应用过程。数值结果说明了方法的有效性。     

Conductance in discrete dynamical systems

We will cover results related to the study of the conductance on digraphs arising from discrete dynamical systems. Several definitions of conductance are known and we present a study which gives a comparison between them in order to choose the appropriate definition to applications. The study makes a strong use of symbolic dynamics. As an application, we analyze the mechanical system of the nonlinear pendulum.     

Steady shear banding in complex fluids

Shear banding (SB) is manifested by the abrupt “demixing” of the flow into regions of high and low shear rate. In this paper, we first relate analytically the rheological parameters of the fluid with the range of shear rates and stresses of SB occurrence. For this, we accept that the origin of shear banding is constitutive, and adopt a non-linear viscoelastic expression able to accommodate the double-valuedness of the stress with flow intensity, under certain conditions. We then implement the model for the case of pressure driven flow through a cylindrical pipe; we derive approximate expressions for the velocity profile in the two-banded regions (core and outer annular), the overall throughput in the presence or absence of “spurt”, and the radial location limits of the shear rate discontinuity.     

Slip of complex fluids in viscometry

Concentrating on viscometry, the concept of (apparent) slip in rotational viscometers requires an angular slip velocity. This, as well as the customary concept of a slip velocity for unidirectional viscometric flow, is estimated by means of dimensional reasoning. It is demonstrated that slip is very well possible, despite the fact that experiments might indicate no slip.     

Inhomogeneous flows in sheared complex fluids

Using dynamic light scattering in heterodyne mode, we measure velocity profiles in two complex fluids known to exhibit stress plateau behaviour under shear: a wormlike micelle solution and a lamellar phase. In both cases, our data provide evidence for the simplest shear-banding scenario, according to which the effective viscosity drop in the system is due to the nucleation and growth of a highly sheared band in the gap. We point out that the position of the interface between the two structures is stable at a fixed local shear stress *.This paper was presented at the first Annual European Rheology Conference (AERC) held in Guimarães, Portugal, September 11-13, 2003.     

Topology optimization of fluids in Stokes flow

We consider topology optimization of fluids in Stokes flow. The design objective is to minimize a power function, which for the absence of body fluid forces is the dissipated power in the fluid, subject to a fluid volume constraint. A generalized Stokes problem is derived that is used as a base for introducing the design parameterization. Mathematical proofs of existence of optimal solutions and convergence of discretized solutions are given and it is concluded that no regularization of the optimization problem is needed. The discretized state problem is a mixed finite element problem that is solved by a preconditioned conjugate gradient method and the design optimization problem is solved using sequential separable and convex programming. Several numerical examples are presented that illustrate this new methodology and the results are compared to results obtained in the context of shape optimization of fluids. Copyright © 2003 John Wiley & Sons, Ltd.     

Modeling particle sedimentation in viscous fluids with a coupled immersed boundary method and discrete element method

Numerical techniques have increasingly been used to model fluid–particle two-phase flows. Coupling the immersed boundary method (IBM) and discrete element method (DEM) is one promising approach for modeling particulate flows. In this study, IBM was coupled with DEM to improve the reliability and accuracy of IBM for determining the positions of particles during the sedimentation process within viscous fluids. The required ratio of the particle diameter to the grid size (D/dx) was determined by comparing the simulation results with the analytical solution and experimental data. A dynamic mesh refinement model was utilised in the IBM model to refine the computational fluid dynamics grid near the particles. In addition, an optimum coupling interval between the IBM and DEM models was determined based on the experimental results of a single particle sedimentation within silicon oil at a Reynolds number of 1.5. The experimental results and the analytical solution were then utilised to validate the IBM–DEM model at Reynolds numbers of 4.1, 11.6, and 31.9. Finally, the validated model was utilised to investigate the sedimentation process for more than one particle by modeling the drafting-kissing-tumbling process and the Boycott phenomenon. Benchmark tests showed that the IBM–DEM technique preserves the advantages of DEM for tracking a group of particles, while the IBM provides a reliable and accurate approach for modeling the particle–fluid interaction.     

Configurational forces in discrete elastic systems

The concept of configurational forces is applied to a simple, one-dimensional problem that is solved by finite elements. Both the exact solution and its finite-element approximation are provided in closed form. The total energy according to the approximate solution depends on the choice of the nodes. Any virtual shift of a node results in a virtual change of energy, which can be interpreted as the virtual work done by a configurational force acting on that node. It is shown that, in the case of equidistant nodes, the configurational forces acting on the interior nodes vanish. Also, the relation between the nodal configurational forces and the Eshelby stress resultant along the rod is investigated.     

Perspectives on shear banding in complex fluids

In this review, I present an idiosyncratic view of the current state of shear banding in complex fluids. Particular attention is paid to some of the outstanding issues and questions facing the field, including the applicability of models that have “traditionally” been used to model experiments; future directions and challenges for experimentalists; and some of the issues surrounding vorticity banding, which has been discussed theoretically and whose experiments are fewer in number yet, in many ways, more varied in character.     

Extensions of nondissipative continuum mechanics toward complex fluids and complex solids

Nondissipative classical continuum mechanics, in both Eulerian and Lagrangian formulations, is extended to complex fluids and complex solids. The extensions involve extra fields characterizing microstructure, preserve the Hamiltonian structure of the classical theory, and are rigorously derived from Hamiltonian formulations of the particle mechanics and statistical mechanics.     

Lag synchronization between discrete chaotic systems with diverse structure

A lag synchronization controller is designed in studying discrete chaotic systems with diverse structures to realize synchronization between Henon and Ikeda sys- terns. The structure of the lag synchronization controller and the error equations of state variables between discrete chaotic systems are presented based on the stability theory. The designed controller has unique structures for different chaotic systems. Lag synchro- nization between any discrete chaotic systems with diverse structures can be achieved. Simulation results show that this control method is effective and feasible.