Related papers: Slider-pinning Rigidity: a Maxwell-Laman-type Theo…
We establish global existence and uniqueness of the dynamics of classical electromagnetism with extended, rigid charges and fields which need not to be square integrable. We consider also a modified theory of electromagnetism where no…
We study the flexibility of suspensions (polyhedra having the combinatorial structure of dipyramids) that have an even number of vertexes and provide arguments that there are least five distinct types of flexible suspensions.
We outline various developments of affine and general Landau Ginzburg models in physics. We then describe the A-twisting and coupling to gravity in terms of Algebraic Geometry. We describe constructions of various path integral measures…
Cyclic contractions generalize the usual contractivities in metric spaces and $b$-MSs. In this paper, we enhance several fixed point theorems related to cyclic (i) Banach self-maps, (ii) Chatterjea contractivities, (iii) Kannan…
This paper extends sliding-mode control theory to nonlinear systems evolving on smooth manifolds. Building on differential geometric methods, we reformulate Filippov's notion of solutions, characterize well-defined vector fields on quotient…
We propose a new type of state sum model for two-dimensional surfaces that takes into account topology and spin. The definition used - new to the literature - provides a rich class of extended models called spin models. Both examples and…
A linkage mechanism consists of rigid bodies assembled by joints which can be used to translate and transfer motion from one form in one place to another. In this paper, we are particularly interested in a family of spacial linkage…
A coarse-grained molecular simulation approach originally developed for entangled polymeric liquids is extended to model the mechanical behavior of long-fiber networks. The model, based on the slip-link picture of chain entanglements,…
We discuss several rigidity and flexibility phenomena in the context of Poisson geometry.
We study the set of all pseudoline arrangements with contact points which cover a given support. We define a natural notion of flip between these arrangements and study the graph of these flips. In particular, we provide an enumeration…
We study the deformation theory of projective Stanley-Reisner schemes associated to combinatorial manifolds. We achieve detailed descriptions of first order deformations and obstruction spaces. Versal base spaces are given for certain…
Substrate defects crucially influence the onset of sliding drop motion under lateral driving. A finite force is necessary to overcome the pinning influence even of microscale heterogeneities. The depinning dynamics of three-dimensional…
Spin networks appear in a number of areas, for instance in lattice gauge theories and in quantum gravity. They describe the contraction of intertwiners according to the underlying network. We show that a certain generating function of…
We report an instability of a slider slowly dragged at the surface of a granular bed in a quasistatic regime. The boat-shaped slider sits on the granular medium under its own weight and is free to translate vertically and to rotate around…
We prove some boundary rigidity results for the hemisphere under a lower bound for Ricci curvature. The main result can be viewed as the Ricci version of a conjecture of Min-Oo.
This thesis is divided into two parts. In the first part we study completely integrable systems, and their underlying structures, in detail. We study their deformation theory and the different equivalence relations surrounding it. We…
The exhaustive study of the rigid symmetries of arbitrary free field theories is motivated, along several lines, as a preliminary step in the completion of the higher-spin interaction problem in full generality. Some results for the…
We study geometric rigidity of a class of fractals, which is slightly larger than the collection of self-conformal sets. Namely, using a new method, we shall prove that a set of this class is contained in a smooth submanifold or is totally…
In this paper, we first establish an $S^1$-equivariant index theorem for Spin$^c$ Dirac operators on $\mathbb{Z}/k$ manifolds, then combining with the methods developed by Taubes \cite{MR998662} and Liu-Ma-Zhang \cite{MR1870666,MR2016198},…
We study linear functionals on a Clifford algebra (algebra of Ma- joranas) equipped with a reflection automorphism. For Hamiltonians that are functions of Majoranas or of spins, we find necessary and sufficient conditions on the coupling…