Related papers: Mechanical stability conditions for 3D and 2D crys…
Based on the Suzuki product-formula approach, we construct a family of unconditionally stable algorithms to solve the time-dependent Maxwell equations. We describe a practical implementation of these algorithms for one-, two-, and…
The ideal Magnetohydrodynamics (MHD) equations are challenging because one needs to maintain the divergence free condition, $\nabla \cdot \Bv = 0$. Many numerical methods have been developed to enforce this condition. In this work, we…
We study the stability of 5D gravitational solutions containing an arbitrary number of scalar fields. A closed set of equations is derived which governs the background and perturbations of N scalar fields and the metric, for arbitrary bulk…
We develop and analyze a stabilization term for cut finite element approximations of an elliptic second order partial differential equation on a surface embedded in $\mathbb{R}^d$. The new stabilization term combines properly scaled normal…
Machine Learning (ML) techniques are revolutionizing the way to perform efficient materials modeling. Nevertheless, not all the ML approaches allow for the understanding of microscopic mechanisms at play in different phenomena. To address…
We introduce a new class of mixed finite element methods for 2D and 3D compressible nonlinear elasticity. The independent unknowns of these conformal methods are displacement, displacement gradient, and the first Piola-Kirchhoff stress…
We prove the stability under lamination of a set of real, symmetric 3$\times$3 matrices that can be viewed as a subset of the effective conductivities of a polycrystal. Constructed in a companion paper, such set in combination with several…
In this paper we investigate the dependence of the magnetic states of heterophase particles on mechanical multiaxial stresses. It is shown that for such particles, there are four possible states, and the conditions of stability of these…
We consider the problems of characterizing and testing the stability of cellular automata configurations that evolve on a two-dimensional torus according to threshold rules with respect to the von-Neumann neighborhood. While stable…
In the present work we suggest a general covariant theory which can be used to study the stability of any physical system treated geometrically. Stability conditions are connected to the magnitude of the deviation vector. This theory is a…
Material strength is a classical concept with renewed importance in fracture mechanics, particularly in crack nucleation in brittle solids. We formulate material strength in finite elasticity and examine its geometric, constitutive, and…
We prove stability for a class of heterogeneous catalysis models in the $L_p$-setting. We consider a setting in a finite three-dimensional pore of cylinder-like geometry, with the lateral walls acting as a catalytic surface. Under a…
The complex physics of self-assembly in colloidal crystals on deformable interfaces and surfaces poses interesting possibilities for the designability and synthesis of next-generation metamaterials. The goal of this article is to…
We introduce conformal mixed finite element methods for $2$D and $3$D incompressible nonlinear elasticity in terms of displacement, displacement gradient, the first Piola-Kirchhoff stress tensor, and pressure, where finite elements for the…
The stability of the fundamental defects of an unstretchable flat sheet is examined. This involves expanding the bending energy to second order in deformations about the defect. The modes of deformation occur as eigenstates of a…
The world of two-dimensional crystals is of great significance for the design and study of structural and functional materials with novel properties. The world of two-dimensional crystals is of great significance for the design and study of…
Proceeded from the gravitation equations proposed by one of authors it was argued in a previous paper that there can exist supermassive compact configurations of degenerated Fermi-gas without events horizon. In the present paper we consider…
We study the space of stability conditions on the total space of the canonical line bundle over the three dimensional projective space. We construct a family of geometric stability conditions and some subset of the boudary of them, which…
The purpose of the study is to further investigate the classical Gibbs analysis of the heterogeneous system "stressed crystal - melt." It is demonstrated that each equilibrium configuration is stable with respect to a special class of…
We study nematic configurations within three-dimensional (3D) cuboids, with planar degenerate boundary conditions on the cuboid faces, in the Landau-de Gennes framework. There are two geometry-dependent variables: the edge length of the…