Related papers: A shape evolution model under affine transformatio…
Soft colloids allow to explore high density states well beyond random close packing. An important open question is whether softness controls the dynamics under these dense conditions. While experimental works reported conflicting results,…
A theory of double affine and special double affine bundles, i.e. differential manifolds with two compatible (special) affine bundle structures, is developed as an affine counterpart of the theory of double vector bundles. The motivation…
The ability of soft matter such as drops and bubbles to change shape dynamically during interaction can give rise to counter-intuitive behaviour that may be expected of rigid materials. Here we show that dimple formation on approach and the…
Collective cell motions underlie structure formation during embryonic development. Tissues exhibit emergent multicellular characteristics such as jamming, rigidity transitions, and glassy dynamics, but there remain questions about how those…
We consider two minimal models of active fluid droplets that exhibit complex dynamics including steady motion, deformation, rotation and oscillating motion. First we consider a droplet with a concentration of active contractile matter…
We study a shape evolution framework in which the deformation of shapes from time t to t + dt is governed by a regularized anisotropic elasticity model. More precisely, we assume that at each time shapes are infinitesimally deformed from a…
Pinning and depinning of wavefronts are ubiquitous features of spatially discrete systems describing a host of phenomena in physics, biology, etc. A large class of discrete systems is described by overdamped chains of nonlinear oscillators…
This note deals with certain properties of convex functions. We provide results on the convexity of the set of minima of these functions, the behaviour of their subgradient set under restriction, and optimization of these functions over an…
Active particles under soft confinement such as droplets or vesicles present intriguing phenomena, as collective motion emerges alongside the deformation of the environment. A model is employed to systematically investigate droplet…
In this article we review classical and recent results in anomalous diffusion and provide mechanisms useful for the study of the fundamentals of certain processes, mainly in condensed matter physics, chemistry and biology. Emphasis will be…
We consider uniformly strongly elliptic systems of the second order with bounded coefficients. First, sufficient conditions for the invariance of convex bodies obtained for linear systems without zero order term in bounded domains and…
We show that the principal types of the closed terms of the affine fragment of $\lambda$-calculus, with respect to a simple type discipline, are structurally isomorphic to their interpretations, as partial involutions, in a natural Geometry…
In this work we define the trajectory coset of an affine map and use it to study the similarity classes of affine maps. We use the trajectory coset, a tool which allows us to gain a deeper understanding of the interplay between geometry…
We investigate discrete spin transformations, a geometric framework to manipulate surface meshes by controlling mean curvature. Applications include surface fairing -- flowing a mesh onto say, a reference sphere -- and mesh extrusion --…
A canonical formalism and constraint analysis for discrete systems subject to a variational action principle are devised. The formalism is equivalent to the covariant formulation, encompasses global and local discrete time evolution moves…
We study iterations of two classical constructions, the evolutes and involutes of plane curves, and we describe the limiting behavior of both constructions on a class of smooth curves with singularities given by their support functions.…
In this survey on local additive invariants of real and complex definable singular germs we systematically present classical or more recent invariants of different nature as emerging from a tame degeneracy principle. For this goal, we…
Automorphisms of finite order and real forms of "smooth" affine Kac-Moody algebras are studied, i.e. of 2-dimensional extensions of the algebra of smooth loops in a simple Lie algebra. It is shown that they can be parametrized by certain…
An increasingly important area of interest for mathematicians is the study of Abelian differentials. This growing interest can be attributed to the interdisciplinary role this subject plays in modern mathematics, as various problems of…
We investigate flexibility of affine varieties with an action of a linear algebraic group. Flexibility of a smooth affine variety with only constant invertible functions and a locally transitive action of a reductive group is proved. Also…