Related papers: Shrinking targets on Bedford-McMullen carpets
Reduced k-means clustering is a method for clustering objects in a low-dimensional subspace. The advantage of this method is that both clustering of objects and low-dimensional subspace reflecting the cluster structure are simultaneously…
Recently, invisible cloaks have attracted much attention due to their exciting property of invisibility, which are based on a solid theory of transformation optics and quasi-conformal mapping. Two kinds of cloaks have been proposed:…
In this paper we compute the Assouad and lower spectra of Bedford--McMullen sponges in $\mathbb{R}^3$ explicitly. According to the formulae established, we discover that the spectra are not determined by the ratio set, and the box, lower…
We investigate the rotation sets of billiards on the $m$-dimensional torus with one small convex obstacle and in the square with one small convex obstacle. In the first case the displacement function, whose averages we consider, measures…
By introducing a concept of "minifying layer", we propose a universal device to hide the position of an object by shifting its scattering without scaling effect for a distance, independent of the direction of incident wave and observation.…
The authors present an impedance-matched reduced version of acoustic cloaking whose mass is in a reasonable range. A layered cloak design with isotropic material is also proposed for the reduced cloak. Numerical calculations from the…
We prove that any non-degenerate Bedford-McMullen carpet does not admit oblique self-embedding similitudes; that is, if $f$ is a similitude sending the carpet into itself, then the image of the $x$-axis under $f$ must be parallel to one of…
The possibility of using plasmonic covers to drastically reduce the total scattering cross section of spherical and cylindrical objects is discussed. While it is intuitively expected that increasing the physical size of an object may lead…
We investigate the scattering of 2D cylindrical invisibility cloaks with simplified constitutive parameters with the assistance of scattering coefficients. We show that the scattering of the cloaks originates not only from the boundary…
Let $F\subseteq [0,1]^2$ be a Bedford-McMullen carpet defined by exponents $m>n$, that projects to $[0,1]$ on the $y$-axis. We show that under mild conditions on $F$, there are many non principle lines $\ell$ such that $\dim^* F\cap \ell =…
Limiting the total weight of an acoustic cloak is of fundamental importance in underwater applications, where buoyancy of the cloaked object is desirable. Unfortunately, it is well known that traditional cloaking strategies imply either a…
Although negative-refractive-index metamaterials have successfully achieved subwavelength focusing, image resolution is limited by the presence of losses. In this Letter, a metal transmission screen with subwavelength spaced slots is…
Shrinking target problems in the context of iterated function systems have received an increasing amount of interest in the past few years. The classical shrinking target problem concerns points returning infinitely many times to a sequence…
We study the smallest intersecting and enclosing ball problems in Euclidean spaces for input objects that are compact and convex. They link and unify many problems in computational geometry and machine learning. We show that both problems…
Soft membranes are commonly employed in shape-morphing applications, where the material is programmed to achieve a target shape upon activation by an external trigger, and as coating layers that alter the surface characteristics of bulk…
Concealing objects by making them invisible to an external electromagnetic probe is coined by the term cloaking. Cloaking devices, having numerous potential applications, are still face challenges in realization, especially in the visible…
Carpet or ground-plane invisibility cloaks hide an object in reflection and inhibit transmission by construction. This concept has significantly reduced the otherwise demanding material requirements and has hence enabled various…
Metamaterial cloaking has been proposed and studied in recent years following several interesting approaches. One of them, the scattering-cancellation technique, or plasmonic cloaking, exploits the plasmonic effects of suitably designed…
A rectangular "shifting cloak", which visually shifts the cloaked object for a certain distance from the original place, is proposed. Comparing with the previously proposed similar cloaks, this rectangular shifting cloak has a much simpler…
In this paper we show that if $p$ is a polynomial which bifurcates then the product map $(z,w)\mapsto(p(z),q(w))$ can be approximated by polynomial skew products possessing special dynamical objets called blenders. Moreover, these objets…