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The interaction of compact objects with an infinitely extended mirror plane due to quantum fluctuations of a scalar or electromagnetic field that scatters off the objects is studied. The mirror plane is assumed to obey either Dirichlet or…
In this study, the impact of non-inertial effects, caused by rotational motion, on the cylindrical perfect cloak is simulated. Also, the interactions between plane waves, Gaussian sine, and Gaussian pulse are investigated. it is shown that…
We describe a method that uses total internal reflection at the water-air interface inside a large, transparent tank, to measure the interface's deflections. Using this configuration, we obtain an optical set-up where the liquid surface…
A perturbative technique, the low-temperature expansion, is developed for matrix models of random surfaces. It can be applied to models with arbitrary target spaces, including ones with c>1. As a simple illustration, the series is worked…
We have investigated the effects of resonant scattering of emission lines on the image morphology and intensity from coronal loop structures. It has previously been shown that line of sight effects in optically thin line emission can yield…
The main objects under consideration in this thesis are called maps, a certain class of graphs embedded on surfaces. Our problems have a powerful relatively recent tool in common, the so-called topological recursion (TR) introduced by…
In this paper, we investigate sufficient condition for the invariance of a rectifying curve on a smooth surface immersed in Euclidean 3-space under isometry by using Darboux frame $\left\lbrace T, P, U\right\rbrace$. Further, we find the…
The need for fast, effective and accurate surveys have become increasingly necessary. A major part of the research is supported by photographic surveys which are used for capturing expansive natural surfaces using a wide range of sensors --…
The world is composed of objects, the ground, and the sky. Visual perception of objects requires solving two fundamental challenges: segmenting visual input into discrete units, and tracking identities of these units despite appearance…
The determination of density profiles with knowing the phase information of complex reflection coefficient for neutron specularly reflected from a film, yields unique results. Recently it has been shown that the phase can be determined by…
We examine domino tilings of rectangular boards, which are in natural bijection with perfect matchings of grid graphs. This leads to the study of their associated perfect matching polytopes, and we present some of their properties, in…
The aim of this study is to analyze the properties of harmonic fields in the vicinity of rough boundaries where either a constant potential or a zero flux is imposed, while a constant field is prescribed at an infinite distance from this…
An approach to diffraction tomography is investigated for two-dimensional image reconstruction of objects surrounded by an arbitrarily-shaped curve of sources and receivers. Based on the integral theorem of Helmholtz and Kirchhoff, the…
Graphs on surfaces is an active topic of pure mathematics belonging to graph theory. It has also been applied to physics and relates discrete and continuous mathematics. In this paper we present a formal mathematical description of the…
Shear localization in granular materials is studied experimentally and numerically. The system consists of two material layers with different effective frictions. The presence of the material interface leads to a special type of "total…
On a compact Riemannian manifold with boundary, we study how Ricci curvature of the interior affects the geometry of the boundary. First we establish integral inequalities for functions defined solely on the boundary and apply them to…
In this paper we observe that information theoretical concepts are valuable tools for extracting information from images and, in particular, information on image symmetries. It is shown that the problem of detecting reflectional and…
The method of wavefront shaping to control optical properties of opaque media is a promising technique for authentication applications. One of the main challenges of this technique is the sensitivity of the wavefront-sample coupling to…
Optical trapping can be used to manipulate the three-dimensional (3-D) motion of spherical particles based on the simple prediction of optical forces and the responding motion of samples. However, controlling the 3-D behaviour of…
In this article we study the deformation of finite maps and show how to use this deformation theory to construct varieties with given invariants in a projective space. Among other things, we prove a criterion that determines when a finite…