Related papers: Continuum limits of atomistic energies allowing sm…
In the stationary case, atomistic interaction energies can be proved to $\Gamma$-converge to classical elasticity models in the simultaneous atomistic-to-continuum and linearization limit [19],[40]. The aim of this note is that of extending…
Nematic elastomers and glasses deform spontaneously when subjected to temperature changes. This property can be exploited in the design of heterogeneously patterned thin sheets that deform into a non-trivial shape when heated or cooled. In…
In this paper we show the emergence of polycrystalline structures as a result of elastic energy minimisation. For this purpose, we introduce a variational model for two-dimensional systems of edge dislocations, within the so-called core…
We derive the atomistic representations of the elastic tensors appearing in the linearized theory of first strain-gradient elasticity for an arbitrary multi-lattice. In addition to the classical (2nd-Piola) stress and elastic moduli…
In this work we improve upon previous results on the expansion of the interaction energy of two atoms. On the one hand we prove the van der Waals-London's law, assuming that only one of the ground state eigenspaces of the atoms is…
Using the density functional formalism we derive expression for the distortion free energy for systems with continuous broken symmetry and use it to derive expression for the elastic constants of smectic phases in which director is tilted…
Some issues that arise when modeling elastic energy for binary alloys are discussed within the context of a Keating model and density functional calculations. The Keating model is based on atomistic modeling of elastic interactions in…
We make use of continuum elasticity theory to investigate the collective modes that propagate along the edge of a two-dimensional electron liquid or crystal in a magnetic field. An exact solution of the equations of motion is obtained with…
An analytical framework is proposed to describe the elasticity, viscosity and fragility of metallic glasses in relation to their atomic-level structure and the effective interatomic interaction. The bottom-up approach starts with forming an…
Discrete models of dislocations in cubic crystal lattices having one or two atoms per unit cell are proposed. These models have the standard linear anisotropic elasticity as their continuum limit and their main ingredients are the elastic…
The method of many body Green's functions is used to derive algebraic expressions for the different elastic and thermodynamical quantities such as the free energy, internal energy, entropy, heat capacity, elastic constants (adiabatic and…
A finite-deformation crystal-elasticity membrane model for Transition Metal Dichalcogenide (TMD) monolayers is presented. Monolayer TMDs are multi-atom-thick two-dimensional (2D) crystalline membranes having atoms arranged in three parallel…
Starting from a general classical model of many interacting particles we present a well defined step by step procedure to derive the continuum-mechanics equations of nonlinear elasticity theory with fluctuations which describe the…
A weak notion of elastic energy for (not necessarily regular) rectifiable curves in any space dimension is proposed. Our $p$-energy is defined through a relaxation process, where a suitable $p$-rotation of inscribed polygonals is adopted.…
We derive the trapping energy of a colloidal particle at a liquid interface with contact angle h and principal curvatures c1 and c2. The boundary conditions at the particle surface are significantly simplified by introducing the shift e of…
We consider a simple model for the assembly of chiral molecules in two dimensions driven by maximization of the contact area. We derive a macroscopic model described by a parameter taking nine possible values corresponding to the possible…
A discrete-to-continuum analysis for free-boundary problems related to crystalline films deposited on substrates is performed by $\Gamma$-convergence. The discrete model here introduced is characterized by an energy with two contributions,…
Energies and equilibrium equations for thin elastic plates are discussed, with emphasis on several issues pertinent to recent approaches in soft condensed matter. Consequences of choice of basis, choice of invariant strain measures, and of…
Metals in one spatial dimension are described at the lowest energy scales by the Luttinger liquid theory. It is well understood that this free theory, and even interacting integrable models, can support ballistic transport of conserved…
We analyze a two-dimensional phase field model designed to describe the dynamics of crystalline grains. The phenomenological free energy is a functional of two order parameters. The first one reflects the orientational order while the…