Related papers: Invisibility and Inverse Problems
An elliptical invisible cloak is proposed using a coordinate transformation in the elliptical-cylindrical coordinate system, which crushes the cloaked object to a line segment instead of a point. The elliptical cloak is reduced to a…
This is a survey article, to appear in the Proceedings of the 2018 International Congress of Mathematicians. (Revised, with added and updated references.)
A brief summary of recent developments in mathematical diffraction theory is given. Particular emphasis is placed on systems with aperiodic order and continuous spectral components. We restrict ourselves to some key results and refer to the…
Transformation Acoustics emerged in the mid-2000s, initiating a new paradigm of metamaterial designs. One of the most compelling designs, the invisibility cloak, holds promise for stealth and noise reduction applications in aviation.…
We consider the inverse problem of determining an optical mask that produces a desired circuit pattern in photolithography. We set the problem as a shape design problem in which the unknown is a two-dimensional domain. The relationship…
Conventional cloaking based on Euclidean transformation optics requires that the speed of light should tend to infinity on the inner surface of the cloak. Non-Euclidean cloaking still needed media with superluminal propagation. Here we show…
Invisibility cloaks have become one of the most outstanding developments among the wide range of applications in the field of metamaterials. So far, most efforts in invisibility science have been devoted to achieving practically realizable…
One of the most remarkable predictions to emerge out of the exact infinite-dimensional solution of the glass problem is the Gardner transition. Although this transition was first theoretically proposed a generation ago for certain…
We discuss some open problems and recent progress related to the 4th order Paneitz operator and Q curvature in dimensions other than 4.
A kind of transformation media, which we shall call the "anti-cloak", is proposed to partially defeat the cloaking effect of the invisibility cloak. An object with an outer shell of "anti-cloak" is visible to the outside if it is coated…
Transformation optics (TO) has recently become a useful methodology in the design of unusual optical devices, such as novel metamaterial lenses and invisibility cloaks. Very recently Danner et al. [1] have suggested theoretical extension of…
The author reports his recollections of what transpired. These may or may not prove consistent with the contributions to be published in the proceedings. Corrections are welcome.
The aim of this work is to prove inverse formulas for Laplace transform on semilattices of open-and-compact sets in a both discrete and non-discrete cases. These are partial answers to a question posed by Yu.~I.~Lyubich.
Inverse scattering and spectral one-dimensional problems are discussed systematically in a self-contained way. Many novel results, due to the author are presented. The classical results are often presented in a new way. Several highlights…
We first review classical results on cloaking and mirage effects for electromagnetic waves. We then show that transformation optics allows the masking of objects or produces mirages in diffusive regimes. In order to achieve this, we…
Conformal transformation optics provides a simple scheme for manipulating light rays with inhomogeneous isotropic dielectrics. However, there is usually discontinuity for refractive index profile at branch cuts of different virtual Riemann…
Transformational optics are shown to markedly enhance the control of the electromagnetic wave trajectories within metamaterials with unconventional functionalities such as a beam splitter, a toroidal carpet, a Luneburg lens and a black…
These are the notes for the lecture given by the author at the "Current Events" Special Session of the AMS meeting in Baltimore on January 17, 2003. Topics reviewed include the Langlands correspondence for GL(n) in the function field case…
We discuss a recent line of research investigating inverse theorems with respect to general k-wise correlations, and explain how such correlations arise in different contexts in mathematics. We outline some of the results that were…
We review various combinatorial problems with underlying classical or quantum integrable structures. (Plenary talk given at the International Congress of Mathematical Physics, Aalborg, Denmark, August 10, 2012.)