Zobrazeno 1 - 10
of 371
pro vyhledávání: '"74G65"'
A review on the classical Plateau problem is presented. Then, the state of the art about the Kirchhoff-Plateau problem is illustrated as well as some possible future directions of research.
Externí odkaz:
http://arxiv.org/abs/2410.06179
Autor:
Bétermin, Laurent, Furlanetto, Camille
We investigate two-dimensional crystallization phenomena, i.e. minimality of a lattice's patch for interaction energies, with pair potentials of type $(x,y)\mapsto V(\|x-y\|)$ where $\|\cdot\|$ is an arbitrary norm on $\mathbb{R}^2$ and $V:\mathbb{R}
Externí odkaz:
http://arxiv.org/abs/2407.20762
Autor:
Shu, Ruiwen
In this paper we give a quantitative stability result for the discrete interaction energy on the multi-dimensional torus, for the periodic Riesz potential. It states that if the number of particles $N$ is large and the discrete interaction energy is
Externí odkaz:
http://arxiv.org/abs/2407.18395
Autor:
Kalayanamit, Panas
We study the existence and regularity of minimizers of the neo-Hookean energy in the closure of classes of deformations without cavitation. The exclusion of cavitation is imposed in the form of the divergence identities, which is equivalent to the we
Externí odkaz:
http://arxiv.org/abs/2405.12156
A static variational model for shape formation in heteroepitaxial crystal growth is considered. The energy functional takes into account surface energy, elastic misfit-energy and nucleation energy of dislocations. A scaling law for the infimal energy
Externí odkaz:
http://arxiv.org/abs/2403.13646
In this note we show Ahlfors-regularity for a large class of quasiminimizers of the Griffith functional. This allows us to prove that, for a range of free discontinuity problems in linear elasticity with anisotropic, cohesive, or heterogeneous behavi
Externí odkaz:
http://arxiv.org/abs/2402.09396
Autor:
Larsen, Christopher J.
The seminal paper of Francfort and Marigo [FM] introduced a variational formulation for Griffith fracture that has resulted in substantial theoretical and practical progress in modeling and simulating fracture. In particular, it led to the phase-fiel
Externí odkaz:
http://arxiv.org/abs/2402.08633
Autor:
Llerena, Randy, Piovano, Paolo
In this paper we introduce a variational model for the study of multilayer films that allows for the treatment of both coherent and incoherent interfaces between layers. The model is designed in the framework of the theory of Stress Driven Rearrangem
Externí odkaz:
http://arxiv.org/abs/2401.14866
We consider two-dimensional systems of point particles located on rectangular lattices and interacting via pairwise potentials. The goal of this paper is to investigate the phase transitions (and their nature) at fixed density for the minimal energy
Externí odkaz:
http://arxiv.org/abs/2312.01395
Autor:
Tenpas, Nathaniel
We utilize recently introduced linear programming bounds for the energy of periodic configurations in $\mathbb{R}^d$ to construct periodic configurations $\omega^*_\beta+L_\beta$, each of which is universally optimal among all configurations of the f
Externí odkaz:
http://arxiv.org/abs/2311.05594