The continuum theory of micromagnetism is used to study ultrathin films with magnetic anisotropy varying laterally on the nanometer scale. A series of infinitely long stripes with alternating inand out-of-plane uniaxial anisotropy is considered as a model for patterned ferromagnetic films. The analytical solution based on an effective anisotropy description of the dipolar energy is given as a f...

We discuss properties of dipolar SLEκ under conditioning. We show that κ = 2, which describes continuum limits of loop erased random walks, is characterized as being the only value of κ such that dipolar SLE conditioned to stop on an interval coincides with dipolar SLE on that interval. We illustrate this property by computing a new bulk passage probability for SLE2. 1 Institut de Physique Théo...

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...

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...

This Chapter describes the concurrent coupling of atomistic methods with continuum mechanics. Such models are useful in the study of phenomena such as fracture and dislocation dynamics, where molecular mechanics and/or quantum mechanics models are required for phenomena such as bond breaking, but the relevant configuration is far too large to permit a completely atomic description. To make such...