This article analyzes modulated phases in liquid crystals, from the long-established cholesteric and blue to recently discovered twist-bend, splay-bend, splay nematic phases, as well twist-grain-boundary (TGB) helical nanofilament variations on smectic phases. The analysis uses concept of four fundamental modes director deformation: twist, bend, splay, a fourth mode related saddle-splay. Each i...

We study local deformations of time-frequency and timescale representations, in the framework of the so-called reassignment methods, which aim at deblurringg time-frequency representations. We focus on deformations generated by appropriate vector elds deened on time-frequency or time scale plane, and constructed on the basis of geometric and group-theoretical arguments. Such vector elds may be ...

We prove that any flat G-bundle, where G is a complex connected reductive algebraic group, on the punctured disc admits the structure of an oper. This result is important in the local geometric Langlands correspondence proposed in [7]. Our proof uses certain deformations of the affine Springer fibers which could be of independent interest. As a byproduct, we construct representations of affine ...

We classify all functions satisfying non-trivial families of PVIα equations. It turns out that all of these 23 solutions are of geometric origin: they are related to deformations of elliptic surfaces as proved earlier by Doran. Similarly, we prove that the same solutions can be obtained from deformations of three-sheeted covers of P1 with branching locus consisting of four points. e-mail: basse...

At the present work we consider infinitesimal deformations f : x → x + εz(x) of a space LN with non-symmetric affine connection L i jk . Based on the non-symmetry of the connection, we use four kinds of covariant derivative to express the Lie derivative and the deformations. Rigidity of geometric objects (connection, tensors, curvature) is defined by virtue of Lie derivative. AMS Subj. Class.: ...

The elastic properties of materials constrain the motion and dynamics of objects in the real world, hence modeling and simulating the physical characteristics of these objects is essential to obtain realistic computer modeling for graphics, vision and animation. This type of modeling is referred to as physically-based modeling and is the main focus of this chapter. A major problem for physicall...

Building a portfolio of deformations is the key step for building better defect models for the test and yield learning domain. A viable approach to achieve this goal is through geometric characterization and classification of failure patterns found on memory fail bitmaps. In this paper, we present preliminary results on how to build such a portfolio of deformations for an IC technology of inter...

W algebras arise in the study of various nonlinear integrable systems such as: self-dual gravity, the KP and Toda hierarchies, their quasi-classical (or dispersionless) limit, etc. Twistor theory provides a geometric background for these algebras. Present state of these topics is overviewed. A few ideas on possible deformations of self-dual gravity (including quantum deformations) are presented...

The goal of the present paper is to construct examples of global deformations of vector field Lie algebras in a conceptual way. Fialowski and Schlichermaier [8] constructed global deformations of the infinitesimally and formally rigid Lie algebra of polynomial vector fields on the circle and of its central extension, the Virasoro algebra. The Lie algebra of polynomial vector fields on the circl...