Associated with each component of the Nash equilibria of a game are its index and degree. Its index is the local degree of the displacement map whose roots are the Nash equilibria of the game. Its degree is the local degree of the projection map from the Nash graph to the space of games. We show that the index and the degree of each component are the same. Further, they are invariant to adding ...

The equilibrium position of active maglev motorized spindle had great influence on the industrial processing accuracy, in order to improve the performance of active maglev motorized spindle and processing accuracy, a new control method and control device of active maglev was put forward based on H∞ mixed sensitivity. Firstly, a mathematical model was established among the electromagnetic force ...

In this report, I present a simple model using springs to conceptualize the relationship between ionic conductances across a cellular membrane and their effect on membrane potential. The equation describing the relationships linking membrane potential, ionic equilibrium potential, and ionic conductance is of similar form to that describing the force generated by a spring as a function of its di...

Abatmct-An extension of the hybrid stress finite element model, originally suggested for linear small displacement problems by Pian, to the large deflection problem is presented. An incremental approach and the concepts of initial stress are employed. A procedure to check the equilibrium in the reference state, prior to the addition of a further load increment, is included. An example and a dis...

In this paper, we propose upper and lower error bounding techniques for reduced order modelling applied to the computational homogenisation of random composites. The upper bound relies on the construction of a reduced model for the stress field. Upon ensuring that the reduced stress satisfies the equilibrium in the finite element sense, the desired bounding property is obtained. The lower bound...

The identification of damage variables and their growth with loading in two dimensions by using only full-field displacement measurements has been proposed in this study. The equilibrium gap method is used to estimate the damage field during a biaxial experiment on a sample made of a composite material. From the analysis of a sequence of measurements, a proposed form of constitutive law is test...

High Static Low Dynamic Stiffness (HSLDS) mounts consist of nonlinear springs that support a high static load with low static displacement, whilst maintaining locally low stiffness near equilibrium, to give a low natural frequency and consequently good isolation properties. Recent analysis has investigated such devices when the force-displacement relationship is an odd function about the equili...

The predictions of the mode-coupling theory of the glass transition (MCT) for the tagged-particle density-correlation functions and the mean-squared displacement curves are compared quantitatively and in detail to results from Newtonian- and Brownian-dynamics simulations of a polydisperse quasi-hard-sphere system close to the glass transition. After correcting for a 17% error in the dynamical l...

The effects of structural and vibrational disorder on the EXAFS signals are parameterized in terms of the Debye Waller (DW) factor. Here the vibrational contribution is addressed, which for most systems can be singled out by studying the temperature dependence of the EXAFS DW factor, which corresponds to a good accuracy to the parallel mean square relative displacement (MSRD) around the inter-a...

We study experimentally the case of steady-state simultaneous two-phase flow in a quasi-two-dimensional porous media. The dynamics is dominated by the interplay between a viscous pressure field from the wetting fluid and bubble transport of a less viscous, nonwetting phase. In contrast with more studied displacement front systems, steady-state flow is in equilibrium, statistically speaking. The...