Related papers: Tame the flexibility of circle patterns
The deformation of a loaded bike tire has been analyzed with a model consisting of a toroid of thin inextensible walls mounted on a central rim. If the tire radius is much shorter than the rim radius, the deflection, d, of the tire can be…
By using higher K-theory, we study deformation theory of K-theoretic cycles. As an application, we answer two questions posed by Mark Green and Philip Griffiths: (1). How to define tangent spaces to cycle class groups in general? (2).…
Given a distribution of defects on a structured surface, such as those represented by 2-dimensional crystalline materials, liquid crystalline surfaces, and thin sandwiched shells, what is the resulting stress field and the deformed shape?…
Shells, when confined, can deform in a broad assortment of shapes and patterns, often quite dissimilar to what is produced by their flat counterparts (plates). In this work we discuss the morphological landscape of shells deposited on a…
We illustrate the use of intersection types as a semantic tool for showing properties of the lattice of lambda theories. Relying on the notion of easy intersection type theory we successfully build a filter model in which the interpretation…
The Andreev-Thurston Circle Packing Theorem is generalized to packings of convex bodies in planar simply connected domains. This turns out to be a useful tool for constructing conformal and quasiconformal mappings with interesting geometric…
In this work we use the deformation procedure and explore the route to obtain distinct field theory models that present similar stability potentials. Starting from systems that interact polynomially or hyperbolically, we use a deformation…
Working in any model theoretic structure, we single out a class of definable bipartite graphs that admit definable, close to perfect matchings. We use this result to prove a strengthening of Tarski's theorem for the definable setting.
This paper focuses on state-of-the art of various approaches for the modelling of deformation behavior of soils when subjected to cyclic loading. The various approaches are broadly classified into implicit and explicit. Models within each…
This paper examines the intuitive meaning of the Saint--Venant compatibility equation known from the linear theory of deformations. The linearized theory is typically obtained from the relations of finite deformation theory by neglecting…
In this paper, we study the occurrence of patterns in the cycle structures of permutations.
Hexagonal circle patterns with constant intersection angles are introduced and studied. It is shown that they are described by discrete integrable systems of Toda type. Conformally symmetric patterns are classified. Circle pattern analogs…
Let $S$ be a closed, orientable surface of genus $g\geq 2$. We consider Delaunay circle patterns on $S$ equipped with a complex projective structure. We prove that the space of complex projective structures on $S$ equipped with a Delaunay…
We propose a general theory for surface patterning in many different biological systems, including mite and insect cuticles, pollen grains, fungal spores, and insect eggs. The patterns of interest are often intricate and diverse, yet an…
We prove a conjecture of Freed and Hopkins, which relates deformation classes of reflection positive, invertible, $d$-dimensional extended field theories with fixed symmetry type to a certain generalized cohomology of a Thom spectrum. Along…
This monograph is on convex real projective structures on strongly tame n-orbifolds with some appropriate conditions on ends.
We prove a perturbative inversion theorem for the map between the interacting and the noninteracting Fermi surface for a class of many fermion systems with strictly convex Fermi surfaces and short-range interactions between the fermions.…
A formula for the radii and positions of four circles in the plane for an arbitrary linearly independent circle configuration is found. Among special cases is the recent extended Descartes Theorem on the Descartes configuration and an…
A variational framework is introduced to describe how a surface bends when it is subject to local constraints on its geometry. This framework is applied to describe the patterns of a folded sheet of paper. The unstretchability of paper…
In this paper, we mainly study the compactness and local structure of immersing surfaces in $\mathbb{R}^n$ with local uniform bounded area and small total curvature $\int_{\Sigma\cap B_1(0)} |A|^2$. A key ingredient is a new quantity which…