相关论文: Non-laminate Microstructures in Monoclinic-I Marte…

We prove that the rank-one convex hull of finitely many $2\times 2$ triangular matrices is a semialgebraic set, defined by linear and quadratic polynomials. We present explicit constructions for five-point configurations and offer evidence…

This paper presents an efficient algorithm for the approximation of the rank-one convex hull in the context of nonlinear solid mechanics. It is based on hierarchical rank-one sequences and simultaneously provides first and second derivative…

With the goal of identifying optimal elastic single-scale microstructures for multiple loading situations, the paper shows that qualified starting guesses, based on knowledge of optimal rank-3 laminates, significantly improves chances of…

We address the questions (P1), (P2) asked in Kirchheim-M\"{u}ller-\v{S}ver\'{a}k (2003) concerning the structure of the Rank-$1$ convex hull of a submanifold $\mathcal{K}_1\subset M^{3\times 2}$ that is related to weak solutions of the two…

We provide quantitative inner and outer bounds for the symmetric quasiconvex hull $Q^e(\mathcal{U})$ on linear strains generated by three-well sets $\mathcal{U}$ in $\mathbb{R}^{2\times 2}_{sym}$. In our study, we consider all possible…

In the paper we consider convex cones in infinite-dimensional real vector spaces which are endowed with no topology. The main purpose is to study an internal geometric structure of convex cones and to obtain an analytical description of…

We study three-dimensional path geometries with nontrivial torsion of maximal rank. We introduce the notion of constant torsion and show that such path geometries are in one-to-one correspondence with certain cone structures modeled on…

We study sets defined as the intersection of a rank-1 constraint with different choices of linear side constraints. We identify different conditions on the linear side constraints, under which the convex hull of the rank-1 set is polyhedral…

We introduce and study three different notions of tropical rank for symmetric and dissimilarity matrices in terms of minimal decompositions into rank 1 symmetric matrices, star tree matrices, and tree matrices. Our results provide a close…

In this work we derive the state of strain or stress under symmetry conserving conditions in pseudomorphic lattices with monoclinic symmetry. We compare surface vectors across the template epitaxial layer interface and impose conditions of…

Martensitic materials show a complex, hierarchical microstructure containing structural domains separated by various types of twin boundaries. Several concepts exist to describe this microstructure on each length scale, however, there is no…

Let T be the unit circle in the complex plane C. This paper proves the existence of analytic structure in a compact subset K of T X C^n, where K has so-called "lineally convex" or "hypoconvex" fibers over T. It also addresses a related…

Inspired by recent work of Kopparty-Moshkovitz-Zuiddam and motivated by problems in combinatorics and hypergraphs, we introduce the notion of the symmetric geometric rank of a symmetric tensor. This quantity is equal to the codimension of…

The atomic topology and magnetic microstructure of individual, highly mobile Type I and Type II twin boundaries in 10M Ni-Mn-Ga martensite were investigated by transmission electron microscopy (TEM). The twin boundaries established in a…

This monograph starts with an upper triangular matrix with integer entries and 1's on the diagonal. It develops from this a spectrum of structures, which appear in different contexts, in algebraic geometry, representation theory and the…

Smectic liquid crystals are remarkable, beautiful examples of materials microstructure, with ordered patterns of geometrically perfect ellipses and hyperbolas. The solution of the complex problem of filling three-dimensional space with…

We analyze generic sequences for which the geometrically linear energy \[E_\eta(u,\chi):= \eta^{-\frac{2}{3}}\int_{B_{0}(1)} \left| e(u)- \sum_{i=1}^3 \chi_ie_i\right|^2 d x+\eta^\frac{1}{3} \sum_{i=1}^3 |D\chi_i|(B_{0}(1))\] remains…

Dense packings of nonoverlapping bodies in three-dimensional Euclidean space are useful models of the structure of a variety of many-particle systems that arise in the physical and biological sciences. Here we investigate the packing…

We construct 1-parameter families of non-periodic embedded minimal surfaces of infinite genus in $T \times \mathbb{R}$, where $T$ denotes a flat 2-tori. Each of our families converges to a foliation of $T \times \mathbb{R}$ by $T$. These…

Antimony telluroiodide (SbTeI) is predicted to be a promising material in many technological applications based on theoretical simulations, however the bulk structure solution remains elusive. We consolidate SbTeI belonging to the…