Dynamics of liquid membranes. I: Non-adaptive finite difference methods

A non-adaptive method and a Lagrangian-Eulerian finite difference technique are used to analyse the dynamic response of liquid membrancs to imposed pressure variations. The non-adaptive method employs a fixed grid and upwind differences for the convection terms, whereas the Lagrangian-Eulerian technique uses operator splitting and decomposes the mixed convection-diffusion system of equations into a sequence of convection and diffusion operators. The convection operator is solved exactly by means of the method of characteristics, and its results are interpolated onto the fixed (Eulerian) grid used to solve the diffusion operator. It is shown that although the method of characteristics eliminates the numerical diffusion associated with upwinding the convection terms in a fixed Eulerian grid, the Lagrangian-Eulerian method may yield overshoots and undershoots near steep flow gradients or when rapid pressure gradients are imposed, owing to the interpolation of the results of the convection operator onto the fixed grid used to solve the diffusion operator. This interpolation should be monotonic and positivity-preserving and should satisfy conservation of mass and linear momentum. It is also shown that both the non-adaptive and Lagrangian-Eulerian finite difference methods produce almost identical (within 1%) results when liquid membranes are subjected to positive and negative step and ramp changes in the pressure coefficient. However, because of their non-adaptive character, these techniques require an estimate of the (unknown) length of the membrane and do not use all the grid points in the calculations. The liquid membrane dynamic response is also analysed as a function of the Froude number, convergence parameter and nozzle exit angle for positive and negative step and ramp changes in the pressure coefficient.     

Cross-Properties Relations in 3D Percolation Networks: I. Network Characteristic Length Determination

This work developed efficient methods to determine the hydraulic characteristic length of percolation networks. The proposed methods are based on the determination of the percolation threshold using the Hoshen–Kopelman algorithm extended to 3D networks. The methods were tested with simple cubic site-bond network models with and without spatial correlations. It was shown that the proposed methods outperformed the algorithms based on the simulation of the porosimetry curve.*Author for correspondence: Fax +55-21-2562-8300; e-mail: paulo@peq.coppe.ufrj.br     

Dynamics of Geometrically Nonlinear Rods: I. Mechanical Models and Equations of Motion

Slender thread like bodies (like cables, ropes, textilethreads or belts) are often used in technical applications. Becauseof their dimensions the one-dimensional continuum is the appropriatemechanical model for bodies of this type. Making use of the basicrelations of three-dimensional continua as a starting point the paperdevelops the general kinematic and kinetic relations of one-dimensionalcontinua for the case that the cross-sections will remain plane (Bernoullihypothesis), that large deflections are possible but the strains remainsmall and that the material is homogeneous and isotropic and behaveslinearly elastic. This results in the equations of motion of shearableand extensible rods (Timoshenko-beams). By neglection of shear deformationand of the rotational inertia of the cross-sections (assumptions thatcan be done in most technical applications) the equations of motionof Euler–Bernoulli-beams are derived in standard and concentratedform. The Euler–Bernoulli-beam equations contain the equations ofmotion of threads with zero bending and torsional stiffness. It isshown that the neglection of bending and torsional stiffness is onlyvalid if the tension is always positive. The second part of this paper[1] selects and develops appropriate numerical solution methods.The derived algorithms are used to solve problems from space and marineengineering.     

Stopping a Viscous Fluid by a Feedback Dissipative Field: I. The Stationary Stokes Problem

We consider a planar stationary flow of an incompressible viscous fluid in a semiinfinite strip governed by the Stokes system with a body forces field. We show how this fluid can be stopped at a finite distance of the entrance of the semi-infinite strip by means of a feedback field depending in a sub-linear way on the velocity field. This localization effect is proved reducing the problem to a non-linear bi-harmonic type one for which the localization of solutions is obtained by means of the application of a suitable energy method. Since the presence of the non-linear terms defined through the body forces field is not standard in the fluid mechanics literature, we establish also some results about the existence and uniqueness of weak solutions for this problem.     

Nonlinear Dynamics of a Rigid Unbalanced Rotor in Journal Bearings. Part I: Theoretical Analysis

The dynamic behaviour of a rigid rotor supported on plain journal bearings was studied, focusing particular attention on its nonlinear aspects. Under the hypothesis that the motion of the rotor mass center is plane, the rotor has five Lagrangian co-ordinates which are represented by the co-ordinates of the mass center and the three angular co-ordinates needed to express the rotor's rotation with respect to its center of mass. In such conditions, the system is characterised not only by the nonlinearity of the bearings but also by the nonlinearity due to the trigonometric functions of the three assigned angular co-ordinates. However, if two angular co-ordinates have values that are generally quite small because of the small radial clearances in the bearings, the system is de facto linear in these angular co-ordinates. Moreover, if the third angular co-ordinate is assumed to be cyclic [18], the number of degrees of freedom in the system is reduced to four and nonlinearity depends solely on the presence of the journal bearings, whose reactions were predicted with the -film, short bearing model. After writing the equations of motion in this way and determining a numerical routine for a Runge–Kutta integration the most significant aspects of the dynamics of a symmetrical rotor were studied, in the presence of either pure static or pure couple unbalance and also when both types of unbalance were present. Two categories of rotors, whose motion is prevailingly a cylindrical whirl or a conical whirl, were put under investigation.     

Dynamics of rigid and flexible polymer chains in confined geometries. part I: steady simple shear flow

This paper describes exact solutions to the response of both the elastic and rigid dumbbell models to a steady simple shear flow in a channel having a length scale comparable to the dumbbells themselves. Results are given for rheological properties over the entire range of the ratio of the channel width to the length of the dumbbell. It is found that both models lead to a decrease in viscosity as the channel is reduced in size with the elastic dumbbell predicting a stronger dependence on that parameter compared with the rigid dumbbell. The elastic dumbbell predicts shear independent rheological properties whereas the rigid dumbell predicts shear thinning as in the case of unbounded flows. The rate of shear thinning, however, decreases with decreasing channel width.     

String Pendulum Dynamics. Control in the Single-Axis Azimuth-Free Gyro Mode

An implementation of a generalized Foucault pendulum, where the basic mechanical elements are a massive solid ball and two weightless strings, is considered. A two-dimensional electromechanical model of the gyro is constructed. Channels for inertial data acquisition and for vibration control are formed. The stability of the reference manifold for the chosen operation mode is shown.     

Orientation-Dependent Morphology and Evolution of Interfacial Dislocation Networks in Ni-Based Single-Crystal Superalloys:A Molecular Dynamics Simulation

In this paper,the morphology and evolution of interfacial dislocation networks of(100),(110)and(111)interphases of Ni-based single-crystal superalloys are studied by molecular dynamics(MD)simulations.Three-dimensional cubic-type and sandwich-type models are chosen to explore the orientation-dependent morphology of dislocation networks,and their respective advantages and disadvantages are compared.From the simulations,it is observed that various lattice orientations and model types lead to different morphologies of dislocation networks.Based on the analysis of average atomic energy and dislocation characteristics,the(100)orientation model has a more regular dislocation network,lower energy and better stability than the(110)and(111)orientation models after MD relaxation,which are supported by previous experimental and numerical simulations.Moreover,the cubic-type model has lower energy and better stability than the sandwich-type model.This will be helpful for choosing a more appropriate and reasonable model for simulating the interfacial dislocation networks of Ni-based single-crystal superalloys.     

Microelectromechanical Systems for Nanomechanical Testing: Displacement- and Force-Controlled Tensile Testing with Feedback Control

Experimental Mechanics - Background: MEMS-based nanomechanical testing has received much interests. However, it remains challenging to perform displacement- and force-controlled nanomechanical...     

Time-Stepping Approximation of Rigid-Body Dynamics with Perfect Unilateral Constraints. I: The Inelastic Impact Case

We consider a discrete mechanical system with a non-trivial mass matrix, subjected to perfect unilateral constraints described by the geometrical inequalities ${f_{\alpha} (q) \geqq 0, \alpha \in \{1, \dots, \nu\} (\nu \geqq 1)}$ . We assume that the transmission of the velocities at impact is governed by Newton’s Law with a coefficient of restitution e = 0 (so that the impact is inelastic). We propose a time-discretization of the second order differential inclusion describing the dynamics, which generalizes the scheme proposed in Paoli (J Differ Equ 211:247–281, 2005) and, for any admissible data, we prove the convergence of approximate motions to a solution of the initial-value problem.     

Dynamics of crack penetration vs. branching at a weak interface: An experimental study

In this paper, the dynamic crack-interface interactions and the related mechanics of crack penetration vs. branching at a weak interface are studied experimentally. The interface is oriented perpendicular to the incoming mode-I crack in an otherwise homogeneous bilayer. The focus of this investigation is on the effect of interface location and the associated crack-tip parameters within the bilayer on the mechanics of the ensuing fracture behavior based on the optical methodologies laid down in Ref. Sundaram and Tippur (2016). Time-resolved optical measurement of crack-tip deformations, velocity and stress intensity factor histories in different bilayer configurations is performed using Digital Gradient Sensing (DGS) technique in conjunction with high-speed photography. The results show that the crack path selection at the interface and subsequently the second layer are greatly affected by the location of the interface within the geometry. Using optically measured fracture parameters, the mechanics of crack penetration and branching are explained. Counter to the intuition, a dynamically growing mode-I approaching a weak interface at a lower velocity and stress intensity factor penetrates the interface whereas a higher velocity and stress intensity factor counterpart gets trapped by the interface producing branched daughter cracks until they kink out into the next layer. An interesting empirical observation based on measured crack-tip parameters for crack penetration and branching is also made.     

Dynamics of a Rigid Unbalanced Rotor with Nonlinear Elastic Restoring Forces. Part I: Theoretical Analysis

In a previous paper, the dynamic behaviour of a Jeffcott rotor was studied in the presence of pure static unbalance and nonlinear elastic restoring forces. The present paper extends the analysis to a rigid rotor with an axial length such as to make the transverse moment of inertia greater than the axial one. As in the previous investigation, the elastic restoring forces are assumed to be nonlinear and the effects of couple unbalance are also included but, unlike the Jeffcott rotor, the system exhibits six degrees-of-freedom. The Lagrangian coordinates were fixed so as to coincide with the three coordinates of the centre of mass of the rotor and the three angular coordinates needed in order to express the rotor's rotations with respect to a reference frame having its origin in the centre of mass. The precession motions of such a rotor turn out to be cylindrical at low angular speeds and exhibit a conical aspect when operating at higher speeds. The motion equations of the rotor were written with reference to a system that was subsequently adopted for the experimental analysis. The particular feature of this system was the use of a steel wire (piano wire) for the rotor shaft, suitably constrained and with the possibility of regulating the tension of the wire itself, in order to increase or reduce the nonlinear character of the system. The numerical analysis performed with integration of the motion equations made it possible to point out that chaotic solutions were manifested only when the tension in the wire was given the lowest values – i.e. when the system was strongly nonlinear – in the presence of considerable damping and rotor unbalance values that were so high as to lose any practical significance. Under conditions commonly shared by analogous real systems characterised by poor damping, where the contribution to nonlinearity is almost entirely due to elastic restoring forces, the analysis pointed out that precession motions may be manifested with a periodic character, whether synchronous or not, or a quasi-periodic character, but in no case is the solution chaotic.     

Engine Control using Neural Networks: A New Method in Engine Management Systems

To be able to meet the demands of low emissions and fuel consumption ofmodern combustion engines, new ways have to be found to control thecombustion. We use new sensors to measure the pressure in the combustionchamber and analyze this signal with a neural network in order to receiveseveral form factors which can be used to control the ignition timing. Theneural network is trained off line with measured data and used on line toderive the form factors. The proposed algorithm can be computed in real timeon conventional digital signal processors and adapted to new engines withvery little effort.     

神经系统疾病与认知动力学 (I) : 癫痫发作的动力学与控制

研究表明癫痫发作过程与神经系统本身的非线性动力学行为密切相关. 因此, 开展癫痫发作的非线性网络动力学建模与调控问题的研究, 有助于理解癫痫临床表征的动力学机理和定位致痫灶网络, 进而设计有效的网络调控策略. 本文回顾了癫痫脑神经疾病网络动力学与控制方面的研究进展, 系统总结了本文作者近年来在癫痫发作动力学建模分析及其调控等方面取得的研究成果. 首先, 基于海马齿状回CA3区环路神经元网络模型, 分析了影响颞叶癫痫发作的分子和网络结构因素, 阐释了癫痫发作转迁的动力学机制. 其次, 由于脑神经系统的集群编码特性, 基于神经场模型和平均场模型建模方法完善了皮质?基底节?丘脑环路网络动力学理论框架, 并基于此框架分析了失神癫痫发作转迁的动力学分岔机制, 探讨了不同类型癫痫发作的转迁路径, 发现了失神癫痫发作转迁的多稳态共存现象, 揭示了时滞对失神癫痫同步发作的控制效果, 设计了丰富有效的癫痫深脑刺激调控策略, 给出了电刺激调控失神癫痫发作的动力学解释. 最后, 通过数据驱动的统计建模和神经元群模型动力学建模分析, 提出了局灶癫痫致痫灶定位及寻找有效控制癫痫发作网络关键节点的理论新方法. 这些研究成果为理解难治性癫痫发作动力学本质及在临床诊疗的应用方面提供重要理论支撑. 最后对进一步研究给出若干建议.      

Heat and mass transfer in unsaturated porous media at a hot boundary: I. One-dimensional analytical model

We present a model of heat and mass transfer in an unsaturated zone of sand and silty clay soils, taking into account the effects of temperature gradients on the advective flux, and of the enhancement of thermal conduction by the process of latent heat transfer through vapor flow. The motivation for this study is to supply information for the planned storage of thermal energy in unsaturated soils and for hot waste storage. Information is required on the possibility of significant drying at a hot boundary, as this would reduce the thermal conductivity of a layer adjacent to the boundary and, thus, prevent effective heat transfer to the soil. This study indicates the possibility that the considered system may be unstable, with respect to the drying conditions, with the occurrence of drying depending on the initial and the boundary conditions. An analysis performed for certain boundary conditions of heat transfer and for given soil properties, disregarding the advective flux of energy, indicated that there are initial conditions of water content for which heating will not cause significant drying. Under these conditions, fine soils may be better suited for heat transfer at the hot boundary, due to their higher field capacity, although their heat conduction coefficients at saturation are lower than those of sandy soils. At present, these conclusions are limited to the range of 50–80°C. Potential effects of solute concentration at the hot boundary are indicated.     

Crack propagation at material interfaces: I. Experimental technique to determine crack profiles

The analysis of the strength of adhesively bonded joints depends to a large degree on concepts of linear fracture mechanics. This discipline rests on appropriate fracture criteria and their evaluation in terms of the linearized theory of (visco) elasticity. We document here the technique and the instrumentation that allows close experimental scrutiny of the linearity assumption as well as an exploration of criteria for interfacial unbonding.     

Continuum and discrete models of dislocation pile-ups. I. Pile-up at a lock

A mathematical methodology for analysing pile-ups of large numbers of dislocations is described. As an example, the pile-up of n identical screw or edge dislocations in a single slip plane under the action of an external force in the direction of a locked dislocation in that plane is considered. As n→∞ there is a well-known formula for the number density of the dislocations, but this density is singular at the lock and it cannot predict the stress field there or the force on the lock. This poses the interesting analytical and numerical problem of matching a local discrete model near the lock to the continuum model further away.     

A formulation of anisotropic continuum elastoplasticity at finite strains. Part I: Modelling

A constitutive model for anisotropic elastoplasticity at finite strains is developed together with its numerical implementation. An anisotropic elastic constitutive law is described in an invariant setting by use of structural tensors and the elastic strain measure C_e. The elastic strain tensor as well as the structural tensors are assumed to be invariant in relation to superimposed rigid body rotations. An anisotropic Hill-type yield criterion, described by a non-symmetric Eshelby-like stress tensor and further structural tensors, is developed, where use is made of representation theorems for functions with non-symmetric arguments. The model also considers non-linear isotropic hardening. Explicit results for the specific case of orthotropic anisotropy are given. The associative flow rule is employed and the features of the inelastic flow rule are discussed in full. It is shown that the classical definition of the plastic material spin is meaningless in conjunction with the present formulation. Instead, the study motivates an alternative definition, which is based on the demand that such a quantity must be dissipation-free, as the plastic material spin is in the case of isotropy. Equivalent spatial formulations are presented too. The full numerical treatment is considered in Part II.     

Chaotic Phenomena and Fractional-Order Dynamics in the Trajectory Control of Redundant Manipulators

Redundant manipulators have some advantages when compared with classicalarms because they allow the trajectory optimization, both on the freespace and on the presence of obstacles, and the resolution ofsingularities. For this type of arms the proposed kinematic controlalgorithms adopt generalized inverse matrices but, in general, thecorresponding trajectory planning schemes show important limitations.Motivated by these problems this paper studies the chaos revealed by thepseudoinverse-based trajectory planning algorithms, using the theory offractional calculus.     

Small and Moderate Prandtl Number Chaotic Convection in Porous Media in the Presence of Feedback Control

Feedback control on thermal convection in a fluid-saturated porous medium is investigated based on the dynamical systems approach. A low dimensional Lorenz-like model was obtained using the Galerkin-truncated approximation. The possible suppression or enhancement of chaotic convection is demonstrated when the fluid layer is subjected to feedback control in a low-dimensional framework.