Remodeling of the synaptic extracellular matrix (ECM) and its dynamic relationship with nerve terminal plasticity have been demonstrated in normal frog neuromuscular junctions (NMJs) in vivo (Chen et al., 1991). Our previous work has led to a hypothesis that extension of synaptic ECM precedes nerve terminal growth during synaptic remodeling. To test this hypothesis, the present study examined t...

The instability of strained films for island formation is examined through an approach incorporating both discrete microscopic details and continuum mechanics. A linear relationship between the island wave number and misfit strain is found for large strains, while only in the small strain limit is a crossover to the continuum elasticity result obtained. A universal scaling relation accommodatin...

We survey new extensions of continuum mechanics incorporating spontaneous violations of the Second Law (SL), which involve the viscous flow and heat conduction. First, following an account of the Fluctuation Theorem (FT) of statistical mechanics that generalizes the SL, the irreversible entropy is shown to evolve as a submartingale. Next, a stochastic thermomechanics is formulated consistent wi...

A number of topics from continuum mechanics are presented that are useful in developing mathematical models of brain neuromechanics. Part I reviews basic concepts used to describe deformation or distortion of brain tissue, strains, stresses, their connection and material stiffness. Part II presents concepts from viscoelasticity used to describe the time dependent response of brain tissue such a...

Volumetric strain can be divided into two parts: strain due to bond distance change and strain due to vacancy sources and sinks. In this paper, efforts are focused on studying the atomic lattice strain due to a vacancy in an FCC metal lattice with molecular dynamics simulation (MDS). The result has been compared with that from a continuum mechanics method. It is shown that using a continuum mec...

Atomic-scale modeling of self-positioning GaAs-InAs nanostructures is performed. Curvature radius values obtained by the atomic-scale finite element method are compared with a continuum mechanics solution under plane strain conditions. Atomic-scale modeling and continuum mechanics solution predict same curvature radius for structures with large thickness. However, atomic-scale modeling shows si...

This paper shows that the stress field in the classical theory of continuum mechanics may be taken to be a covector-valued differential two-form. The balance laws and other fundamental laws of continuum mechanics may be neatly rewritten in terms of this geometric stress. A geometrically attractive and covariant derivation of the balance laws from the principle of energy balance in terms of this...

A parametrization of the Hamiltonian of the generalized Witten model of the SUSY QM by a single arbitrary function in d = 1 has been obtained for an arbitrary number of the supersymmetries N . Possible applications of this formalism have been discussed. It has been shown that the N = 1 and 2 conformal SUSY QM is generalized for any N . Submitted to the Physics Letters B.

The work can be considered as an essay on mathematical and conceptual structure of nonrelativistic quantum mechanics (QM) which is related here to some other (more general, but also to more special – “approximative”) theories. QM is here primarily equivalently reformulated in the form of a Poisson system on the phase space consisting of density matrices, where the “observables”, as well as “sym...

Continuing in the vein of a recently developed generalization of continuum thermomechanics, in this paper we extend fracture mechanics and beam mechanics to materials described by fractional integrals involving D, d and R. By introducing a product measure instead of a Riesz measure, so as to ensure that the mechanical approach to continuum mechanics is consistent with the energetic approach, sp...