Related papers: Unified Framework for Dislocation-Based Defect Ene…
This paper develops a comprehensive mathematical framework for energy-based modeling of physical systems, with particular emphasis on preserving fundamental structural properties throughout the modeling and discretization process. The…
This paper develops an algorithmic framework for real-time optimization of distribution-level distributed energy resources (DERs). The proposed framework optimizes the operation of both DERs that are individually controllable and groups of…
The ratio of symmetry energy coefficient to temperature $C_{sym}/T$ is extracted from different prescriptions using the isotopic as well as the isobaric yield distributions obtained in different projectile fragmentation reactions. It is…
The maximum-weight matching problem and the behavior of its energy landscape is numerically investigated. We apply a perturbation method adapted from the analysis of spin glasses. This gives inside into the complexity of the energy…
We analyze the dislocation content of grain boundary (GB) phase junctions, i.e., line defects separating two different GB phases coexisting on the same GB plane. While regular GB disconnections have been characterized for a variety of…
In this paper we introduce Peierls-Nabarro type models for edge dislocations at semi-coherent interfaces between two heterogeneous crystals, and prove the optimality of uniformly distributed edge dislocations. Specifically, we show that the…
This paper studies the boundary behaviour at mechanical equilibrium at the ends of a finite interval of a class of systems of interacting particles with monotone decreasing repulsive force. Our setting covers pile-ups of dislocations,…
The energetic cost of creating a defect within a host material is given by the formation energy. Here we present a formulation allowing the calculation of formation energies in one-dimensional nanostructures, which overcomes the…
In this article, we study scaling laws for singularly perturbed two-well energies with prescribed Dirichlet boundary data in settings where the wells and/or the boundary data are incompatible. Our main focus is the geometrically linear…
In this paper, Neumann cracks in elastic bodies are considered. We establish a rigorous asymptotic expansion for the boundary perturbations of the displacement (and traction) vectors that are due to the presence of a small elastic linear…
The formation energy of a solid surface can be extracted from slab calculations if the bulk energy per atom is known. It has been pointed out previously that the resulting surface energy will diverge with slab thickness if the bulk energy…
A novel energy minimization formulation of electrostatics that allows computation of the electrostatic energy and forces to any desired accuracy in a system with arbitrary dielectric properties is presented. An integral equation for the…
A new bound dark energy, BDE, cosmology has been proposed where the dark energy is the binding energy between light meson fields that condense a few tens of years after the big bang. It is reported that the correct dark energy density…
Sequences of experimental ground-state energies are mapped onto concave patterns cured from convexities due to pairing and/or shell effects. The same patterns, completed by a list of excitation energies, can be used to give numerical…
Rock formations are very often characterized by the presence of fractures that have grown subcritically over geological time scales and under evolving stress fields. In mechanically layered systems, such fractures can either become…
We analyze fully implicit and linearly implicit backward difference formula (BDF) methods for quasilinear parabolic equations, without making any assumptions on the growth or decay of the coefficient functions. We combine maximal parabolic…
In this paper we study the evolution of cosmological perturbations in the presence of dynamical dark energy, and revisit the issue of dark energy perturbations. For a generally parameterized equation of state (EoS) such as w_D(z) =…
Epitaxially grown heterogeneous nanowires present dislocations at the interface between the phases if their radius is big. We consider a corresponding variational discrete model with quadratic pairwise atomic interaction energy. By…
In the 50's Read and Shockley proposed a formula for the energy of small angle grain boundaries in polycrystals based on linearised elasticity and an ansazt on the distribution of incompatibilities of the lattice at the interface. In this…
We consider a discrete model of planar elasticity where the particles, in the reference configuration, sit on a regular triangular lattice and interact through nearest neighbor pairwise potentials, with bonds modeled as linearized elastic…