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Register a new userSpecial transformations for pentamode acoustic cloaking
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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 whether the materials are practically realizable. In this paper, this process is inverted by defining desirable material properties and then deriving the appropriate transformations which guarantee the cloaking effect. Transformations are derived which result in acoustic cloaks with special properties such as 1) constant density 2) constant radial stiffness 3) constant tangential stiffness 4) power-law density 5) power-law radial stiffness 6) power-law tangential stiffness 7) minimal elastic anisotropy.
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Conventional sonic crystal (SC) devices designed for acoustic imaging can focus acoustic waves from an input source into only one image but not multi-images. Furthermore the output position of formed image cannot be designed at will. In this paper, we propose the hybrid SC imaging devices to achieve multi-images from one-source-input along with the designable image-positions. The proposed hybrid devices can image acoustic waves radiated both from point source and Gaussian beam, which different from conventional SC imaging devices that only applies to point source. These multi-functional but still simple and easy-to-fabricate devices are believed to find extensive applications, particularly in ultrasonic photography and compact acoustic imaging.
A central ingredient of cloaking-by-mapping is the diffeomorphisn which transforms an annulus with a small hole into an annulus with a finite size hole, while being the identity on the outer boundary of the annulus. The resulting meta-material is anisotropic, which makes it difficult to manufacture. The problem of minimizing anisotropy among radial transformations has been studied in [4]. In this work, as in [4], we formulate the problem of minimizing anisotropy as an energy minimization problem. Our main goal is to provide strong evidence for the conjecture that for cloaks with circular boundaries, non-radial transformations do not lead to lower degree of anisotropy. In the final section, we consider cloaks with non-circular boundaries and show that in this case, non-radial cloaks may be advantageous, when it comes to minimizing anisotropy.
This is a survey of approximate cloaking using transformation optics for acoustic and electromagnetic waves.
We consider the propagation of acoustic waves in a 2D waveguide unbounded in one direction and containing a compact obstacle. The wavenumber is fixed so that only one mode can propagate. The goal of this work is to propose a method to cloak the obstacle. More precisely, we add to the geometry thin outer resonators of width $varepsilon$ and we explain how to choose their positions as well as their lengths to get a transmission coefficient approximately equal to one as if there were no obstacle. In the process we also investigate several related problems. In particular, we explain how to get zero transmission and how to design phase shifters. The approach is based on asymptotic analysis in presence of thin resonators. An essential point is that we work around resonance lengths of the resonators. This allows us to obtain effects of order one with geometrical perturbations of width $varepsilon$. Various numerical experiments illustrate the theory.
A birational transformation f: P^n --> Z, where Z is a nonsingular variety of Picard number 1, is called a special birational transformation of type (a, b) if f is given by a linear system of degree a, its inverse is given by a linear system of degree b and the base locus S subset P^n of f is irreducible and nonsingular. In this paper, we classify special birational transformations of type (2,1). In addition to previous works Alzati-Sierra and Russo on this topic, our proof employs natural C^*-actions on Z in a crucial way. These C^*-actions also relate our result to the problem studied in our previous work on smooth projective varieties with nonzero prolongations.
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