The well-known electro-mechanical analogy that equates current, voltage, resistance, inductance and capacitance to force, velocity, damping, spring constant and mass has a shortcoming in that mass can only be used to simulate a capacitor which has one terminal connected to ground. A new model that was previously proposed by the authors that combines a mass with a pulley (MP) is shown to simulat...

Abstract Different approaches to quantum gravity converge in predicting the existence of a minimal scale length. This raises fundamental question as whether and how an intrinsic limit spatial resolution can affect mechanical observables associated internal degrees freedom. We answer this general terms by showing that spin operator acquires momentum-dependent contribution mechanics equipped with...

We review in these lecture notes some of our recent work on modelling the response of nematic elastomers to applied mechanical loads and/or to electric fields, both in the static and in the dynamic regime. Our aim is to compare theoretical results based on mathematical analysis and on numerical simulations with the available experimental evidence, in order to examine critically the various rece...

The issue of non-perturbative background independent quantization of matrix models is addressed. The analysis is carried out by considering a simple matrix model which is a matrix extension of ordinary mechanics reduced to 0 dimension. It is shown that this model has an ordinary mechanical system evolving in time as a classical solution. But in this treatment the action principle admits a natur...

Paper in honour of Freeman Dyson on the occasion of his 80th birthday. Normal N-body systems relax to equilibrium distributions in which classical kinetic energy components are 1/2kT , but, when inter-particle forces are an inverse cubic repulsion together with a linear (simple harmonic) attraction, the system pulsates for ever. In spite of this pulsation in scale, r(t), other degrees of freedo...

The approach of defining quantum corrections on nuclear dynamics of molecular systems incorporated approximately into selected degrees of freedom, is described. The approach is based on the Madelung-de-Broglie-Bohm formulation of time-dependent quantum mechanics which represents a wavefunction in terms of an ensemble of trajectories. The trajectories follow classical laws of motion except that ...

We extend a recent computation of the dependence of the free energy, F, on the noncommutative scale θ to theories with very different UV sensitivity. The temperature dependence of F strongly suggests that a reduced number of degrees of freedom contributes to the free energy in the non-planar sector, Fnp, at high temperature. This phenomenon seems generic, independent of the UV sensitivity, and ...

INTRODUCTION In classic mechanics, degrees of freedom (DOF) are defined as the minimum number of independent coordinates needed to describe a system’s position. The human musculoskeletal system has many mechanical DOF through which countless movements are accomplished. However, natural movements are characterized by the coordination of the DOF such that few vary independently. The concept of fu...

We derive a class of mesoscopic virial equations governing energy partition between conjugate position and momentum variables of individual degrees of freedom. They are shown to apply to a wide range of nonequilibrium steady states with stochastic (Langevin) and deterministic (Nosé–Hoover) dynamics, and to extend to collective modes for models of heat-conducting lattices. A macroscopic virial t...

We use quartic oscillators system with two degrees of freedom to model Yang-Mills classical mechanics. This simple model explains qualitatively many features reported in lattice calculation of (3 + 1) dimensional classical Yang-Mills system. The largest Lyapunov exponent (λ) and the thermalization time were numerically evaluated. We also show, in our model, that λ scales with 4th root of energy...