Related papers: On the passage from atomistic systems to nonlinear…
We derive a collisionless kinetic theory for an ensemble of molecules undergoing nonholonomic rolling dynamics. We demonstrate that the existence of nonholonomic constraints leads to problems in generalizing the standard methods of…
We introduce positive elastic potentials in the harmonic approximation leading by Hamilton's variational principle to fractional Laplacian matrices having the forms of power law matrix functions of the simple local Bornvon Karman Laplacian.…
We derive von-K\'arm\'an plate theory from three dimensional, purely atomistic models with classical particle interaction. This derivation is established as a $\Gamma$-limit when considering the limit where the interatomic distance…
We present an alternative to the Kohn-Sham formulation of density functional theory for the ground-state properties of strongly interacting electronic systems. The idea is to start from the limit of zero kinetic energy and systematically…
We suggest to include the density of electron charge explicitly in the electron potential of density functional theory, rather than implicitly via exchange-correlation functionals. The advantages of the approach are conceptual and…
The subject of this paper is the study of the asymptotic behaviour of the equilibrium configurations of a nonlinearly elastic thin rod, as the diameter of the cross-section tends to zero. Convergence results are established assuming…
We extend the theory of structured deformations to the setting of linearized elasticity by providing an integral representation for the underlying energy that features bulk and surface contributions. Our derivation is obtained both via a…
A new reference state for density functional theory, termed the independent atom ansatz, is introduced in this work. This ansatz allows for the exact representation of electron density in terms of non-interacting, atom-localized orbitals.…
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…
We consider a general problem of inelastic collision of particles interacting with power-law potentials. Using quantum defect theory we derive an analytical formula for the energy-dependent complex scattering length, valid for arbitrary…
We obtain linear elasticity as $\Gamma$-limit of finite elasticity under incompressibility assumption and Dirichlet boundary conditions. The result is shown for a large class of energy densities for rubber-like materials.
Clapeyron's Theorem in classical linear elasticity provides a way to explicitly express the energy stored in an equilibrium configuration in terms of the work of the forces applied on the boundary. We derive several new integral relations…
This article presents a systematic methodology for modeling a class of flexible multidimensional mechanical structures defined by linear elastic relations that directly allows to obtain their infinite-dimensional port-Hamiltonian…
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…
The limits of linear electrodynamics are reviewed, and possible directions of nonlinear extension are explored. The central theme is that the qualitative character of the empirical successes of quantum electrodynamics must be used as a…
We use molecular simulations to study the nonadhesive and adhesive atomic-scale contact of rough spheres with radii ranging from nanometers to micrometers over more than ten orders of magnitude in applied normal load. At the lowest loads,…
We consider an atomistic model defined through an interaction field satisfying a variational principle, and can therefore be considered a toy model of (orbital free) density functional theory. We investigate atomistic-to-continuum coupling…
Variational solutions of the Boltzmann equation usually rely on the concept of linear response. We extend the variational approach for tight-binding models at high entropies to a regime far beyond linear response. We analyze both weakly…
The nonrelativistic limit of a semilinear field equation is considered in a uniform and isotropic space.The scale-function of the space is constructed based on the Einstein equation.The Cauchy problem of the limit-equation is considered,and…
Large deformations play a central role in the shape transformations of slender active and biological structures. A classical example is the eversion of the Volvox embryo, which demonstrates the need for shell theories that can describe…