In one-dimensional case, it is shown that the basic principles of quantum mechanics are properties of the set of intermediate cardinality. PACS numbers: 03.65.Bz, 02.10.Cz 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 conti...

Results of molecular-mechanics simulations of axial and torsional deformations of a single wall carbon nanotube are used to find Young’s modulus, the shear modulus, and the wall thickness of an equivalent continuum tube made of a linear elastic isotropic material. These values are used to compare the response of the continuum tube in bending and buckling with that obtained from the molecular me...

The design of composite tissue scaffolds containing an extracellular matrix (ECM) and synthetic polymer fibers is a new approach to create bioactive scaffolds that can enhance cell function. Currently, studies investigating the effects of ECM-deposition and decellularization on polymer degradation are still lacking, as are data on optimizing the stability of the ECM-containing composite scaffol...

We consider continuous media in which contact edge forces are present. Introducing the notion of quasibalanced contact force distribution, we are able to prove the conjectures made in [Noll, 1990] concerning the representation of contact edge forces. We first generalise the Noll theorem on Cauchy postulate. Then we adapt the celebrated Cauchy tetrahedron construction to find a representation th...

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...