Related papers: Geometry of Thin Films
A rigidity theory is developed for frameworks in a metric space with two types of distance constraints. Mixed sparsity graph characterisations are obtained for the infinitesimal and continuous rigidity of completely regular bar-joint…
We survey some recent developments in the quest for global surfaces of section for Reeb flows in dimension three using methods from Symplectic Topology. We focus on applications to geometry, including existence of closed geodesics and sharp…
This paper concentrates on optical Hamiltonian systems of $T*\T^n$, i.e. those for which $\Hpp$ is a positive definite matrix, and their relationship with symplectic twist maps. We present theorems of decomposition by symplectic twist maps…
We propose an approach for investigation of interaction of thin material films with quantum electrodynamic fields. Using main principles of quantum electrodynamics (locality, gauge invariance, renormalizability) we construct a single model…
We prove that homological mirror symmetry for very affine hypersurfaces respects certain natural symplectic operations (as functors between partially wrapped Fukaya categories), verifying conjectures of Auroux. These conjectures concern…
When the thickness of the layer is smaller than the electrons mean free path, the morphology affects the conductivity directly based on the layer thickness. This issue provides basis in order to estimate the thickness of the layer by…
We study the dynamics of a cosmological bubble wall beyond the approximation of an infinitely thin wall. In a previous paper, we discussed the range of validity of this approximation and estimated the first-order corrections due to the…
We study the optical paths of the light rays propagating inside a nonlinear moving dielectric media. For the rapidly moving dielectrics we show the existence of a distinguished surface which resembles, as far as the light propagation is…
The following are notes on the geometry of the bidisk. In particular, we examine the properties of equidistant surfaces in the bidisk.
The purpose of this article is to study the behavior of a heterogeneous thin film whose microstructure oscillates on a scale that is comparable to that of the thickness of the domain. The argument is based on a 3D-2D dimensional reduction…
The versatility of quantum gas experiments greatly benefits from the ability to apply variable potentials. Here we describe a method which allows the preparation of potential structures for microcavity photons via spatially selective…
A reflection mapping is a singular holomorphic mapping obtained by restricting the quotient mapping of a complex reflection group. We study the analytic structure of double point spaces of reflection mappings. In the case where the image is…
It is proved that a bijection between two compact hyperbolic surfaces with boundary is an isometry if it and its inverse map each geodesic onto some geodesic.
The derivation of a quantum Markovian model for an opto-mechanical system consisting of a quantum mechanical mirror interacting with quantum optical input fields via radiation pressure is difficult problem which ultimately involves the…
We find a system of two polynomial equations in two unknowns, whose solution allows to give an explicit expression of the conformal representation of a simply connected three sheeted compact Riemann surface onto the extended complex plane.…
This article has been written for an educational magazine whose target audience consists of students and teachers of mathematics in universities, colleges and schools. It concerns a notion of duality between rectangles. A proof is given…
Given a finite collection of two-dimensional tile types, the field of study concerned with covering the plane with tiles of these types exclusively has a long history, having enjoyed great prominence in the last six to seven decades. Much…
Two-dimensional mirror symmetry enriched topological (SET) orders can be studied using the folding approach: it can be folded along the mirror axis and turned into a bilayer system on which the mirror symmetry acts as a $\mathbb Z_2$…
We investigate the effects of the relativistic movement of an optical medium on the conditions of constructive and destructive interference, reflection and transmission pattern, and performance of spectroscopes. First, we consider the case…
We study complex analytic (possibly singular) projective connections on the plane. We characterize some of them in terms of their families of integral curves. We also give a beginning of classification of second order odes polynomial in the…