相关论文: Shrinking targets on Bedford-McMullen carpets
We introduce darning of compact sets (darning and gluing of finite unions of compact sets), which are not thin at any of their points, in a potential-theoretic framework which may be described, analytically, in terms of harmonic…
We propose to compute approximations to general invariant sets in dynamical systems by minimizing the distance between an appropriately selected finite set of points and its image under the dynamics. We demonstrate, through computational…
This paper proves shrinking target results for IETs. Let {a_1\geq a_2 \geq...} be a sequence of positive real numbers with divergent sum. Then for almost every IET T, the limsup of B(T^ix,a_i) has full Lebesgue measure (where B(z, e) is the…
The cloaking performance of two microwave cloaks, both based on the recently proposed transmission-line approach, are studied using commercial full-wave simulation software. The cloaks are shown to be able to reduce the total scattering…
We present a rigorous derivation of dimensionally reduced theories for thin sheets of nematic elastomers, in the finite bending regime. Focusing on the case of twist nematic texture, we obtain 2D and 1D models for wide and narrow ribbons…
We study the size of \emph{dynamical covering sets} on a self-similar set. Dynamical covering sets are limsup sets generated by placing shrinking target sets around points along an orbit in a dynamical system. In the case when the target…
We construct a sequence of smooth minimizing surfaces in a sequence of metrics converging to the standard Euclidean metric, so that they have diverging $L^2$ norm of second fundamental form.
We provide efficient constant factor approximation algorithms for the problems of finding a hierarchical clustering of a point set in any metric space, minimizing the sum of minimimum spanning tree lengths within each cluster, and in the…
Metamaterial is promising for enhancing the capability of plasmonic devices. We consider a cylindrical waveguide with three-level \Lambda\ atoms embedded in the dielectric core. By comparing metal cladding vs metamaterial cladding of a…
Model sets (or cut and project sets) provide a familiar and commonly used method of constructing and studying nonperiodic point sets. Here we extend this method to situations where the internal spaces are no longer Euclidean, but instead…
Existing designs of transformation acoustic cloaks are not easy to implement in many practical situations because of their large dimensions, while scattering cancellation cloaks do not protect the inner cloak volume. Here we report…
Overlay measurements are a critical part of modern semiconductor fabrication, but overlay targets have not scaled down in the way devices have. In this work, we produce overlay targets with very small footprint, consisting of just a few…
The scattering cancellation technique (SCT) has proved to be an effective way to render static objects invisible to electromagnetic and acoustic waves. However, rotating cylindrical or spherical objects possess additional peculiar…
Transformation-based cylindrical cloaks and concentrators are illuminated with non-monochromatic waves and unusual effects are observed with interesting potential applications. The transient responses of the devices are studied numerically…
We study the special fibers of a certain class of absolutely simple abelian varieties over number fields with endomorphism rings $\bz$ and possessing $l$-adic monodromy groups of the least possible rank. We also study the Dirichlet density…
We propose a composite optical transformation to design an illusion device which can move the image of a target from one place to another place. Enclosed by such an illusion device, an arbitrary object located at one place appears to be at…
Defining the $m$-th stratum of a closed subset of an $n$ dimensional Euclidean space to consist of those points, where it can be touched by a ball from at least $n-m$ linearly independent directions, we establish that the $m$-th stratum is…
Reduced-Order Modelling of the Bending of an Array of An array of micromirrors for beam steering optical switching has been designed in a thick polysilicon technology. A novel semi-analytical method to calculate the static characteristics…
We propose multilayer cylindrical invisibility cloaks that are optimized for oblique incidences through combination of analytic formalism of scattering and genetic optimization. We show that by using only four layers of homogeneous and…
Experimental data on thin films of cylinder-forming block copolymers (BC) -- free-standing BC membranes as well as supported BC films -- strongly suggest that the local orientation of the BC patterns is coupled to the geometry in which the…