相关论文: On regularized full- and partial-cloaks in acousti…
Cloaking using complementary media was suggested by Lai et al. in [8]. The study of this problem faces two difficulties. Firstly, this problem is unstable since the equations describing the phenomenon have sign changing coefficients, hence…
We conjecture that the set of homogeneous probability measures on the maximal Satake compactification of an arithmetic locally symmetric space $S=\Gamma\backslash G/K$ is compact. More precisely, given a sequence of homogeneous probability…
We briefly review the basics ideas and results of a recently proposed statistical mechanical approach to granular materials. Using lattice models from standard Statistical Mechanics and results from a mean field replica approach and Monte…
In this letter, we propose a conceptual device to perform subwavelength imaging with positive refraction. The key to this proposal is that a drain is no longer a must for some cases. What's more, this device is an isotropic omnidirectional…
Transformation optics constructions have allowed the design of cloaking devices that steer electromagnetic, acoustic and quantum waves around a region without penetrating it, so that this region is hidden from external observations. The…
We outline a general method of constructing finite-range cloaking potentials which render a given finite-range real or complex potential $v(x)$ unidirectionally reflectionless or invisible at a wavenumber $k_0$ of our choice. We give…
The weak lensing surveys have the potential to probe directly the clustering statistics of dark matter in the universe. Recent studies have shown that it is possible to predict analytically the whole probability distribution function (pdf)…
The generalized smooth condition, $(L_{0},L_{1})$-smoothness, has triggered people's interest since it is more realistic in many optimization problems shown by both empirical and theoretical evidence. Two recent works established the…
The acoustic cloaking theory of Norris (2008) permits considerable freedom in choosing the transformation function f from physical to virtual space. The standard process for defining cloak materials is to first define f and then evaluate…
We construct finite time blow-up solutions to the 3-dimensional harmonic map flow into the sphere $S^2$, \begin{align*} u_t & = \Delta u + |\nabla u|^2 u \quad \text{in } \Omega\times(0,T) \\ u &= u_b \quad \text{on } \partial…
Invariant transformation for quantum mechanical systems is proposed. A cloaking of matter wave can be realized at given energy by designing the potential and effective mass of the matter waves in the cloaking region. The general conditions…
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 propose a finite elements algorithm to solve a fourth order partial differential equation governing the propagation of time-harmonic bending waves in thin elastic plates. Specially designed perfectly matched layers are implemented to…
The electromagnetic characteristics of plane-transformed invisibility cloaks are quantitatively studied in this paper. We take elliptical cylindrical cloak as the example, and use an elliptical cylindrical wave expansion method to obtain…
We consider the scattering of light in participating media composed of sparsely and randomly distributed discrete particles. The particle size is expected to range from the scale of the wavelength to the scale several orders of magnitude…
We complete the `paraxial' (small-angle) ray optics cloaking formalism presented previously [Choi and Howell, Opt. Express 22, 29465 (2014)], by extending it to the full-field of light. Omnidirectionality is then the only relaxed parameter…
The attempt to solve inverse scattering problems often leads to optimization and sampling problems that require handling moderate to large amounts of partial differential equations acting as constraints. We focus here on determining…
We analyze a semi-implicit finite volume scheme for the Gray--Scott system, a model for pattern formation in chemical and biological media. We prove unconditional well-posedness of the fully discrete problem and establish qualitative…
A new recipe for concealing objects from detection is suggested. Different with traditional cloak which deflects light around the core of the cloak to make the object inside invisible, our cloak guides the light to penetrate the core of the…
We deal with the linearized model of the acoustic wave propagation generated by small bubbles in the harmonic regime. We estimate the waves generated by a cluster of $M$ small bubbles, distributed in a bounded domain $\Omega$, with relative…