Related papers: Auxetic deformations and elliptic curves
In the assessment of wood charring, it was believed for a long time that physicochemical processes were responsible for the creation of cracking patterns on the charring wood surface. This implied no possibility to rigorously explain the…
The issue of symmetry and symmetry breaking is fundamental in all areas of science. Symmetry is often assimilated to order and beauty while symmetry breaking is the source of many interesting phenomena such as phase transitions,…
Many algorithms for the computation of correspondences between deformable shapes rely on some variant of nearest neighbor matching in a descriptor space. Such are, for example, various point-wise correspondence recovery algorithms used as a…
We give an efficient, deterministic algorithm to decide if two abelian varieties over a number field are isogenous. From this, we derive an algorithm to compute the endomorphism ring of an elliptic curve over a number field.
Analytic methods are emerging in solid and configuration modeling, while providing new insights into a variety of shape and motion related problems by exploiting tools from group morphology, convolution algebras, and harmonic analysis.…
We study deformation theory of elliptic fibre bundles over curves in positive characteristics. As applications, we give examples of non-liftable elliptic surfaces in charactertic two and three, which answers a question of Katsura and Ueno.…
Isogenies, the mappings of elliptic curves, have become a useful tool in cryptology. These mathematical objects have been proposed for use in computing pairings, constructing hash functions and random number generators, and analyzing the…
Emerging multi-material 3D printing techniques have paved the way for the rational design of metamaterials with not only complex geometries but also arbitrary distributions of multiple materials within those geometries. Varying the spatial…
Geometrical properties of two-dimensional mixtures near the jamming transition point are numerically investigated using harmonic particles under mechanical training. The configurations generated by the quasi-static compression and…
The Epstein deformation space parameterizes marked rational maps with prescribed combinatorial and dynamical structure. For the family of quadratic rational maps with a periodic critical cycle of order 4 and an extra critical point not…
Fix an elliptic curve $E_0$ without CM and a non-isotrivial elliptic scheme over a smooth irreducible curve, both defined over the algebraic numbers. Consider the union of all images of a fixed finite-rank subgroup (of arbitrary rank) of…
We propose a systematic approach to the construction of invariant union of polytopes (IUP) in expanding piecewise affine mappings whose linear components are isotropic scalings. The approach relies on using empirical information embedded in…
Topological materials present unconventional electronic properties that make them attractive for both basic science and next-generation technological applications. The majority of currently known topological materials have been discovered…
Recent advances in nanoscale fabrication enable atomic-scale manipulation of two-dimensional (2D) materials by introducing engineered pores and perforations. This provides new opportunities to tailor functional properties of 2D materials…
We formulate a cut finite element method for linear elasticity based on higher order elements on a fixed background mesh. Key to the method is a stabilization term which provides control of the jumps in the derivatives of the finite element…
PhD thesis investigating homological quantum codes derived from curved and higher dimensional geometries. In the first part we will consider closed surfaces with constant negative curvature. We show how such surfaces can be constructed and…
Computing the diameter of the intersection graphs of objects is a basic problem in computational geometry. Previous works showed that the complexity of computing the diameter mainly depends on the object types: for unit disks and squares in…
Understanding the orientation of geological structures is crucial for analyzing the complexity of the Earths' subsurface. For instance, information about geological structure orientation can be incorporated into local anisotropic…
We study the quadratic invariants of the elasticity tensor in the framework of its unique irreducible decomposition. The key point is that this decomposition generates the direct sum reduction of the elasticity tensor space. The…
The fast marching algorithm, and its variants, solves numerically the generalized eikonal equation associated to an underlying riemannian metric. A major challenge for these algorithms is the non-isotropy of the riemannian metric.…