For a class of systems obeying Euler's equation of motion the existence of a quantity to be named "proper mechanical energy" (PME) is shown which, together with internal energy, results in a quantity to be named "proper energy" (PE), which is conserved under conditions of time-dependent potentials. The appertaining formal structure for the continuum mechanics of such systems is the counterpart ...

In one-dimensional case, it is shown that the basic principles of quantum mechanics are properties of the set of intermediate cardinal-ity. The concept of discrete space is not a unique alternative of the continuous space. Since discrete space is a countable set, there is an intermediate possibility connected with the continuum problem: space may be neither continuous nor discrete. The commonly...

In continuum mechanics, the equations of motion for mixtures were derived through the use of a variational principle by Bedford and Drumheller in [1978]. Only immiscible mixtures were investigated. We have chosen a different approach. In this paper, we first write the equations of motion for each constituent of an inviscid miscible mixture of fluids without chemical reactions or diffusion. The ...

2014 The continuum mechanics framevork for analyzing necking and shear band instabilities is discussed. The predicted onset of instability depends sensitively on the material’s constitutive characterization, not only through properties, such as strain hardening and strain rate sensitivity, that can be measured in proportional loading tests, but also through the material’s response to a change i...

An entropic formulation of relativistic continuum mechanics is developed in the Landau-Lifshitz frame. We introduce two spatial scales, one being the small scale representing the linear size of each material particle and the other the large scale representing the linear size of a large system which consists of material particles and is to linearly regress to the equilibrium. We propose a local ...

This paper presents a variational and multisymplectic formulation of both compressible and incompressible models of continuum mechanics on general Riemannian manifolds. A general formalism is developed for non-relativistic first-order multisymplectic field theories with constraints, such as the incompressibility constraint. The results obtained in this paper set the stage for multisymplectic re...

We present an overview of hybridizable discontinuous Galerkin methods for solving partial differential equations (PDEs) in continuum mechanics [1, 2, 3, 4]. The essential ingredients are a local Galerkin projection of the underlying PDEs at the element level onto spaces of polynomials of degree k to parametrize the numerical solution in terms of the numerical trace; a judicious choice of the nu...

The era of commodity computing brings a profound change in the use of numerical analysis of continuum mechanics problems in science and engineering. Teraflop-rate computing facility, until recently available only to chosen few is becoming commonplace in an industrial setting. Range and complexity of problems where numerical methods are applied is also expanding. Here, massive reduction in the c...

Understanding the kinematics of the tongue during normal speech will provide important information both for accurate modeling of the acoustics of the vocal tract and for clinical diagnosis and enhanced treatment of persons with abnormal speech due to tongue motion impediments. Measuring tongue motion can be done using magnetic resonance imaging (MRI) which cannot provide the temporal resolution...

The charm contribution into the proton structure function in DIS at the HERA ep-collider Abstract In the framework of perturbative QCD and a model for the production of charmed hadrons the structure function F c 2 is calculated and compared with the experimental data of H1 and ZEUS Collaborations. We show that the spectator mechanism of the D *-meson production independent of a hadronic remnant...