Related papers: Geometry of Thin Films
The spherical symmetry Black holes are considered in expanding background. The singularity line and the marginally trapped tube surface behavior are discussed. In particular, we address the conditions of whether a dynamical horizon forms…
The transition of the binary gravitational lens from the equal mass case to small (planetary) mass ratios q is studied. It is shown how the limit of a (pure shear) Chang-Refsdal lens is approached, under what conditions the Chang-Refsdal…
In this book chapter we study the Riemannian Geometry of the density registration problem: Given two densities (not necessarily probability densities) defined on a smooth finite dimensional manifold find a diffeomorphism which transforms…
Two planar embedded circle patterns with the same combinatorics and the same intersection angles can be considered to define a discrete conformal map. We show that two locally finite circle patterns covering the unit disc are related by a…
We study the realization of the (super) conformal topological symmetry in two-dimensional field theories. The mirror automorphism of the topological algebra is represented as a reflection in the space of fields. As a consequence, a double…
Aspects of duality and mirror symmetry in string theory are discussed. We emphasize, through examples, the importance of loop spaces for a deeper understanding of the geometrical origin of dualities in string theory. Moreover we show that…
We study X-ray diffraction in smectic liquid crystal multilayers. Such systems are fabricated as freely suspended films and have a unique layered structure. As such, they can be described as organic Bragg mirrors with sub-nanometer…
We analyse a mechanical system in two-dimensional relative motion with friction. Although the system is simple, the peculiar interplay between two kinetic friction forces and gravity leads to the wide range of admissible solutions exceeding…
The works of William Rowan Hamilton in Geometrical Optics are presented, with emphasis on the Malus-Dupin theorem. According to that theorem, a family of light rays depending on two parameters can be focused to a single point by an optical…
We compare the flat geometry associated to a quadratic differential with the hyperbolic geometry associated to the underlying Riemann surface. We show that if a curve is contained in a thick subsurface, then its hyperbolic length is…
In this paper we explore how light propagates from thin elements into a volume for viewing. In particular, devices that are typically connected with geometric optics, like parallax barriers, differ in treatment with those that obey physical…
A concrete analysis of the general properties and numerical characteristics of different atomic and nuclear shell systems and subnuclear particles is carried out on the base of the solution scheme for an introduced in part I physical graph…
The dynamical properties, especially the symmetric orbits, of the 2-parameter family of circle maps called off-center reflection is studied.
One can often see caustic by reflection in nature, but it is rather hard to understand the way of how caustic arise and which geometric properties of a mirror surface define the geometry of the caustic. The caustic by reflection has…
Wave effects can be important for the gravitational lensing of gravitational waves. In such a case, wave optics must be used in stead of geometric optics. We consider a plane wave entering a lens object and solve numerically the wave…
In the study of holomorphic maps, the term "rigidity" refers to certain types of results that give us very specific information about a general class of holomorphic maps owing to the geometry of their domains or target spaces. Under this…
We provide a comprehensive study of atomic Raman and Bragg diffraction when coupling to a pair of counterpropagating light gratings (double diffraction) or to a single one (single diffraction) and discuss the transition from one case to the…
The B-side of Kontsevich's Homological Mirror Symmetry Conjecture is discussed. We give first a self-contained study of derived categories and their homological algebra, and later restrict to the bounded derived category of schemes and…
The geometry of a light wavefront, evolving from a initial flat wavefront in the 3-space associated with a post-Newtonian relativistic spacetime, is studied numerically by means of the ray tracing method. For a discretization of the…
Thin polymer films have striking dynamical properties that differ from their bulk counterparts. With the simple geometry of a stepped polymer film on a substrate, we probe mobility above and below the glass transition temperature…