相关论文: Invisible obstacles
Within this chapter, we discuss control in the coefficients of an obstacle problem. Utilizing tools from H-convergence, we show existence of optimal solutions. First order necessary optimality conditions are obtained after deriving…
We consider reshaping a scattering obstacle virtually by using transformation optics in acoustic and electromagnetic scattering. Among the general virtual reshaping results, the virtual minification and virtual magnification are…
We consider a polyhedron with zero classical resistance, i.e., a polyhedron invisible to an observer viewing only the paths of geometrical optics rays. The corresponding problem of scattering of plane waves by the polyhedron is studied. The…
We study a question arising in inverse scattering theory: given a penetrable obstacle, does there exist an incident wave that does not scatter? We show that every penetrable obstacle with real-analytic boundary admits such an incident wave.…
This paper deals with the accomplishment of total area coverage of an arbitrary region using sensors with a finite sensing radius of rs. For a given region, we aim to obtain a deterministic placement of sensors which, apart from ensuring…
We consider the propagation of acoustic waves at a given wavenumber in a waveguide which is unbounded in one direction. We explain how to construct penetrable obstacles characterized by a physical coefficient $\rho$ which are invisible in…
The problem of practical preparing small impedance particles with a prescribed boundary impedance is formulated and its importance in physics and technology is discussed. It is shown that if this problem is solved then one can easily…
An inverse obstacle problem for the wave equation in a two layered medium is considered. It is assumed that the unknown obstacle is penetrable and embedded in the lower half-space. The wave as a solution of the wave equation is generated by…
We prove existence of weak solutions to the obstacle problem for semilinear wave equations (including the fractional case) by using a suitable approximating scheme in the spirit of minimizing movements. This extends the results in [9],…
The possibility of making an optically large (many wavelengths in diameter) object appear invisible has been a subject of many recent studies. Exact invisibility scenarios for large (relative to the wavelength) objects involve…
Here we demonstrate existence of a piecewise smooth obstacle having connected interior and invisible from a point in the framework of geometric optics.
Motivated by questions in inverse scattering theory, we develop free boundary methods in obstacle problems where both the solution and the right hand side of the equation may have varying sign. The key condition that prevents the appearance…
Given a graph $G$, an {\em obstacle representation} of $G$ is a set of points in the plane representing the vertices of $G$, together with a set of connected obstacles such that two vertices of $G$ are joined by an edge if and only if the…
A mathematical method for through-wall imaging via wave phenomena in the time domain is introduced. The method makes use of a single reflected wave over a finite time interval and gives us a criterion whether a penetrable obstacle exists or…
Penetration of two coupled particles through a repulsive barrier is considered. A simple mechanism of the appearance of barrier resonances is demonstrated that makes the barrier anomalously transparent as compared to the probability of…
When a quantum object -- a particle as we call it in a non-rigorous way -- is described by a multi-branched wave- function, with the corresponding wave-packets occupying separated regions of the time-space, a frequently asked question is…
Transformation optics offers an unconventional approach to the control of electromagnetic fields. A transformation optical structure is designed by first applying a form-invariant coordinate transform to Maxwell's equations, in which part…
We consider the reflection-transmission problem in a waveguide with obstacle. At certain frequencies, for some incident waves, intensity is perfectly transmitted and the reflected field decays exponentially at infinity. In this work, we…
Quantum mechanics predicts an exponentially small probability that a particle with energy greater than the height of a potential barrier will nevertheless reflect from the barrier in violation of classical expectations. This process can be…
We construct a function for almost-complex Riemannian manifolds. Non-vanishing of the function for the almost-complex structure implies the almost-complex structure is not integrable. Therefore the constructed function is an obstruction for…