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.     

Variational inference in neural functional prior using normalizing flows: application to differential equation and operator learning problems

Physics-informed deep learning has recently emerged as an effective tool for leveraging both observational data and available physical laws. Physics-informed neural networks(PINNs) and deep operator networks(DeepONets) are two such models. The former encodes the physical laws via the automatic differentiation, while the latter learns the hidden physics from data. Generally, the noisy and limited observational data as well as the over-parameterization in neural networks(NNs) result in uncertainty...     

Concavity techniques with application to shock problems

The problem of the impact of a point mass on the end of an elastic straight rod which is clamped at the other end, can be studied with the aid of a Concavity Method.The motion of the system is described by the behaviour of a positive function on the solution.This technique can be extended to more complicate cases, for instance to the case in which the material of the rod is non-linear elastic or viscoelastic.

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Zusammenfassung Das problem des Stosses einer Punktmasse auf das eine Ende eines elastischen geraden Stabes, an dem anderen Ende eingespannt ist, kann mit Hilfe einer Konkavitäts-Methode untersucht werden.Die Bewegung des Systems wird beschrieben durch das Verhalten einer positiven Funktion auf der Lösung.Diese Technik lässt sich auf kompliziertere Fälle übertragen, z.B. wenn das Material, aus dem der Stab besteht, nicht linear-elastisch oder visko-elastisch ist.

     

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.     

Machine learning of synaptic structure with neurons to promote tumor growth

In this paper, we use machine learning techniques to form a cancer cell model that displays the growth and promotion of synaptic and electrical signals. Here, such a technique can be applied directly to the spiking neural network of cancer cell synapses.The results show that machine learning techniques for the spiked network of cancer cell synapses have the powerful function of neuron models and potential supervisors for different implementations. The changes in the neural activity of tumor micr...     

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.     

Bifurcation for non-differentiable operators with an application to elasticity

We consider operator equations of the form

Modeling of dielectric viscoelastomers with application to electromechanical instabilities

Soft dielectrics are electrically-insulating elastomeric materials, which are capable of large deformation and electrical polarization, and are used as smart transducers for converting between mechanical and electrical energy. While much theoretical and computational modeling effort has gone into describing the ideal, time-independent behavior of these materials, viscoelasticity is a crucial component of the observed mechanical response and hence has a significant effect on electromechanical actuation. In this paper, we report on a constitutive theory and numerical modeling capability for dielectric viscoelastomers, able to describe electromechanical coupling, large-deformations, large-stretch chain-locking, and a time-dependent mechanical response. Our approach is calibrated to the widely-used soft dielectric VHB 4910, and the finite-element implementation of the model is used to study the role of viscoelasticity in instabilities in soft dielectrics, namely (1) the pull-in instability, (2) electrocreasing, (3) electrocavitation, and (4) wrinkling of a pretensioned three-dimensional diaphragm actuator. Our results show that viscoelastic effects delay the onset of instability under monotonic electrical loading and can even suppress instabilities under cyclic loading. Furthermore, quantitative agreement is obtained between experimentally measured and numerically simulated instability thresholds. Our finite-element implementation will be useful as a modeling platform for further study of electromechanical instabilities and for harnessing them in design and is provided as online supplemental material to aid other researchers in the field.     

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...     

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.