Oscillatory evolution of collective behavior in evolutionary games played with reinforcement learning

Nonlinear Dynamics - Large-scale cooperation underpins the evolution of ecosystems and the human society, and the collective behaviors by self-organization of multi-agent systems are the key for...     

An equilibrium-based learning approach with application to robotic fish

Nonlinear Dynamics - In this work, we extend the concept of integral control to equilibrium-based learning control. As far as the plant reaches an equilibrium that deviates from the reference, a...     

An analytical solution to the heat transfer problem in thick-walled hunt flow

The flow of a liquid metal in a rectangular duct, subject to a strong transverse magnetic field is of interest in a number of applications. An important application of such flows is in the context of coolants in fusion reactors, where heat is transferred to a lead-lithium eutectic. It is vital, therefore, that the heat transfer mechanisms are understood. Forced convection heat transfer is strongly dependent on the flow profile. In the hydrodynamic case, Nusselt numbers and the like, have long been well characterised in duct geometries. In the case of liquid metals in strong magnetic fields (magnetohydrodynamics), the flow profiles are very different and one can expect a concomitant effect on convective heat transfer. For fully developed laminar flows, the magnetohydrodynamic problem can be characterised in terms of two coupled partial differential equations. The problem of heat transfer for perfectly electrically insulating boundaries (Shercliff case) has been studied previously (Bluck et al., 2015). In this paper, we demonstrate corresponding analytical solutions for the case of conducting hartmann walls of arbitrary thickness. The flow is very different from the Shercliff case, exhibiting jets near the side walls and core flow suppression which have profound effects on heat transfer.     

Transport processes in narrow channels with application to rotary exchangers

Rotary solid storage elements, combining heat and mass transfer, are used for dehumidizing air, solvents recovery or separation. The performance of the rotor mainly depends on its single channels parameters and the type of flow material combinations employed as sorbents and carrying structures. The local heat transfer along the ducts was investigated by holographic interferometry. Fundamental tests were conducted to determine the loading behaviour of different rotary heat and mass exchanger samples. In further experiments the loading progression of different samples after an increase of humidity were determined. Finally a method of the numerical simulation of the combined heat and mass transfer in rotary exchangers is described briefly. Received on 23 September 1998     

Plastic collapse in non-associated hardening materials with application to Cam-clay

This paper presents a variational formulation for the analysis of plastic collapse conditions for a class of hardening materials that accounts for some non-associated flow laws such as the modified Cam-clay model of soils. In this framework, classical statical and kinematical principles of limit analysis do not hold. The variational principle is formulated for the general class of materials whose flow equations are derived from a kind of generalized potentials named bipotentials by de Saxcé.The plastic collapse phenomenon for hardening materials is considered first and formulated as a system of equations. In particular, the case of the usual modified Cam-clay model is analyzed. The paper follows with the proposal of a minimization principle whose solution is then related to the solution of the plastic collapse problem. We demonstrate the use of this minimum principle in a simple example of triaxial compression of a modified Cam-clay material. Finally, we discuss the particular form of the proposed variational formulation for the case of associated plasticity.     

Methodology to assess integrity with application to collector copper lamellas

The performance of engineering components and structures is strongly influenced by the interaction between design, manufacture and materials. A methodology to assess the integrity of a circular collector is presented by investigating the failure of copper lamellas. The investigated circular collector, having 315 copper lamellas, is one of the main parts of an electric motor. The fracture of the copper lamellas was observed in normal operation. This unexpected fracture required an investigation of the fracture origin, in order to improve the initial design. The numerical results of the finite element analysis on the stress field in the copper lamellas for the operating regimes, and the stress concentration effects are shown. Failure assessment diagram, based on notch stress intensity factor, was considered in order to estimate if crack initiation can occur. Finally a study of crack propagation will present comparatively the numerical obtained crack path against the one observed in-service.     

Rotating cylinder drag balance with application to riblets

Experimental results are reported and discussed for a rotating cylinder drag balance designed to predict drag reduction by surfaces like riblets. The apparatus functions by measuring the torque applied to the inner cylinder by a fluid, such as water, that is set in motion by the controlled rotation of the outer cylinder. The instrument was validated by calibration for laminar flow and comparison of turbulent flow results to the those of G. I. Taylor. The ability to predict drag reduction was demonstrated by testing 114 m symmetric sawtooth riblets, which gave a maximum reduction of about 5% and an overall drag reduction range of 5<S ⁺<20, both of which are in excellent comparison to results reported in literature. The most suitable conditions for testing riblets are to apply the riblets only to the inner cylinder surface and to use cylinders for which the curvature of the flow is minimized. Received: 2 February 1999/Accepted: 1 October 1999     

Image-processing techniques in laser-speckle photography with application to hybrid stress analysis

Six techniques for analyzing speckle halo fringes for fringe spacing and orientation using a digital image analyzer are presented. Each of the techniques were tested for range, accuracy, and computer run-time through analysis of a known case of rigid-body motion. Application of these techniques to two-dimensional hybrid stress analysis is described where speckle-displacement data around the high-stress region of a notched bar in tension is used as input data to a plane-stress finite-element program. Paper was presented at the 1985 SEM Spring Conference on Experimental Mechanics held in Las Vegas, NV on June 9–14, 1985.     

Advances in the embedded-strain-gage technique with an application to contact problems

Improvements in the embedded-strain-gage technique for the measurement of strains at internal points in models of machine components are described. A New measurement module permits an experimental determination of the strain in models of epoxy resin. By its construction, the centers of the rosettes may be accurately located in the model mold, before casting. A large number of gages may be embedded with accuracy in a systematic manner. Application to the study of rolling contact is discussed. The improved technique has permitted an accurate embedment of gages at 0.043 in. below the surface of a flat model of epoxy resin which is then pressed against a spherical model having a radsius of curvature machined to 75 in. A testing machine is described and preliminary test results are presented.     

Some functional inequalities,with application to Green's function

Some elementary inequalities for functional with functional derivatives of given sign are presented and proved. These are then applied to the study of Green's functions for diffusion processes in a medium with sources and sinks (or alternately to Green's functions for the Schrödinger operator). The resulting inequalities are shown to include as quite special cases the super and sub-additive inequalities of potential theory. One consequence of the generalization is that scattering length is also shown to have sub-additive properties.This research was supported in part by the National Science Foundation and the U.S. Atomic Energy Commission.     

Pursuit on regular surfaces with application to consensus problems

Nonlinear Dynamics - In this work we develop geometric and numerical methods to analyze the behavior of a system of organisms or particles under various types of pursuit on a regular surface. We...     

Bifurcation for non-differentiable operators with an application to elasticity

We consider operator equations of the form

A generalized variational theorem in elastodynamics,with application to shell theory

Summary With a view toward the consistent derivations and numerical solutions of one- and two-dimensional approximate theories in a class of Cosserat continuum, a variational theorem is, in a straightforward manner, established by means of Hamilton's principle. By the use of this theorem, a linear theory of anisotropic shells for both extensional and flexural motions, including thermal effects, is systematically constructed. A theorem of uniqueness in this theory is then presented.

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Sommario Per mezzo del principio di Hamilton si stabilisce direttamente un teorema variazionale in vista di organiche derivazioni e soluzioni numeriche di teorie approssimate a una e a due dimensioni in una classe di continui di Cosserat. Con questo teorema si costruisce sistematicamente una teoria lineare di membrane anisotropiche per movimenti estensionali e flessionali includendo gli effetti termici. Si presenta poi in questo teorema una teoria di unicità.

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Supported by the U.S. Office of Naval Research.     

Inertial contributions to the pressure in the truncated-cone-and-plate apparatus with application to dilute polymer solutions

New measurements of the pressure distribution generated by two Newtonian liquids in the Truncated Cone-and-Plate Apparatus are presented, in order to evaluate the exact form of the inertial contribution for a range of Reynolds numbers (Re) fromRe = 140 toRe = 36,000;Re = R ² /, where and are the liquid density and viscosity respectively,R is the plate radius, and is the angular velocity of the cone. The Walters equation for lowRe, p ^w = 0.15 ² (r² – R²), is shown to be in excellent agreement with the measurements up toRe = 1000, provided an appropriate correction for the Newtonian hole pressure is made. Up toRe = 1000, the measured slope is within 1% of the theoretical value of 0.15 given by the Walters equation; as the Reynolds number increases above 1000, the data become increasingly nonlinear inr ². Other theoretical predictions made especially for largeRe begin to disagree with the data even belowRe = 1000. The application of the experimentally determined additive inertial contribution to measurements of pressure distribution in four dilute polymer solutions is found to reproduce adequately the expected form of the viscoelastic pressure distribution, even at highRe where the Walters equation is not valid. Measurements of a combination of normal-stress differencesN ₁ + 2N ₂ for polymer solutions involving specific polymer/solvent interaction sites show a difference of 45% with change of solvent, while no difference is observed in solutions of polymers without the interaction sites. The normal-stress ratio —N ₂/N ₁ for a 5% solution of cis-polybutadiene is 0.24 at a shear rate of 100 s^–1, and it appears to approach the zero shear limit of 2/7 given by the Doi-Edwards theory. The Higashitani-Pritchard-Baird-Lodge equation relating the elastic hole pressure to the normal-stress differenceN ₁ –N ₂ gives a qualitative agreement betweenN ₁ –N ₂ from the TCP Apparatus and the hole pressure from the Stressmeter; the percent difference is 0 at shear stress < 25 Pa, 35% at = 45 Pa, and 18% at the highest = 63 Pa.     

An inverse finite element method with an application to extrusion with solidification

The flow and solidification of planar jets are analysed by means of an efficient inverse isotherm finite element method. The method is based on a tessellation that is constructed by isotherms as characteristic co-ordinate lines transverse to the flow direction. Thus opposite sides of finite elements lie on isotherms. The method allows the simultaneous determination of the location of the isotherms with the primary unknowns, namely, the velocity, the pressure, the temperature and the location of the free surface. Thus the determination of the location of the solidification front (which is known to pose significant computational difficulties) is automatic. This facilitates the control of the location of the solidification front by controlling macroscopic variables such as the flow rate, the cooling rate and the capillary design. The location of the solidification may then be suitably chosen to influence the frozen-in orientation and structure in extrusion of high-performance materials such as composites and polymers, in continuous casting of metals and in growth of crystals.     

A color-coded particle tracking velocimeter with application to natural convection

This paper introduces a novel concept of the image-processing technique to visualize a two-dimensional flow field and to generate streaks with embedded time marks in real time. Grey levels of a pixel are used in this work to encode the temporal information rather than the intensity of particle trajectories used in conventional image-processing systems. To do this, the incoming video image is first binarized by a step function predefined in an input look-up table, with the height of the step varying with time to bear temporal marks. A real-time arithmetic-logic unit and an image-frame buffer are used to accumulate the images. These processes result in continuous streaks with embedded time marks which have many advantages over those recorded by conventional techniques. Pseudo-color output look-up tables and color monitor provide more direct and intuitive means for human visual perception. This color-coded particle tracking velocimetry was applied to investigate natural convection in an enclosure heated from below with an isothermal extrusion. By quantifying the color-coded streaks, velocity vectors were obtained at a discrete number of points with less labor. The present technique provides an elaborate tool for simultaneous qualitative and quantitative realizations of steady and slowly varying flow fields.A version of this paper was presented at the twenty-second Midwestern Mechanics Conference, University of Missouri-Rolla, USA, October 6–9, 1991     

Thermodynamics-based gradient plasticity theories with an application to interface models

In the framework of small deformations, the so-called residual-based gradient plasticity theory is reconsidered and improved. Using the notion of moving geometrically necessary dislocations (GNDs), suitable micromechanics interpretations are heuristically given for the higher order boundary conditions and the long distance particle interactions. Also, a comparison is made between this theory and the analogous virtual work principle (VWP)-based one, whereby their respective conceptual and methodological features are pointed out. The conditions under which the two theories lead to a same constitutive model are investigated, showing that, correspondingly, a certain indeterminacy exhibited by the VWP-based theory disappears. A phenomenological interface model is used to better point out differences and analogies of the two theories.     

Meshless analysis of plasticity with application to crack growth problems

The governing equations for classical rate-independent plasticity are formulated in the framework of meshless method. The special J₂ flow theory for three-dimensional, two-dimensional plane strain and plane stress problems are presented. The numerical procedures, including return mapping algorithm, to obtain the solutions of boundary-value problems in computational plasticity are outlined. For meshless analysis the special treatment of the presence of barriers and mirror symmetries is formulated. The crack growth process in elastic–plastic solid under plane strain and plane stress conditions is analyzed. Numerical results are presented and discussed.