Abstract:
We propose a cloak for coupled shear and pressure waves in solids. Its elastic properties are deduced from a geometric transform that retains the form of Navier equations. The spherical shell is made of an anisotropic and heterogeneous medium described by an elasticity tensor C' (without the minor symmetries) which has 21 non-zero spatially varying coefficients in spherical coordinates. Although some entries of C, e.g. some with a radial subscript, and the density (a scalar radial function) vanish on the inner boundary of the cloak, this metamaterial exhibits less singularities than its cylindrical counterpart studied in [M. Brun, S. Guenneau, A.B. Movchan, Appl. Phys. Lett. 94, 061903 (2009).] In the latter work, C' suffered some infinite entries, unlike in our case. Finite element computations confirm that elastic waves are smoothly detoured around a spherical void without reflection.

Abstract:
In this work, we propose the generation of diffraction resistant beams by using a parabolic reflector and a source of spherical waves positioned at a point slightly displaced from its focus (away from the reflector). In our analysis, considering the reflector dimensions much greater than the wavelength, we describe the main characteristics of the resulting beams, showing their properties of resistance to the diffraction effects. Due to its simplicity, this method may be an interesting alternative for the generation of long range diffraction resistant waves.

Abstract:
Bragg diffraction of atoms by light waves has been used to create high momentum components in a Bose-Einstein condensate. Collisions between atoms from two distinct momentum wavepackets cause elastic scattering that can remove a significant fraction of atoms from the wavepackets and cause the formation of a spherical shell of scattered atoms. We develop a slowly varying envelope technique that includes the effects of this loss on the condensate dynamics described by the Gross-Pitaevski equation. Three-dimensional numerical calculations are presented for two experimental situations: passage of a moving daughter condensate through a non-moving parent condensate, and four-wave mixing of matter waves.

Abstract:
In this paper, we investigate the existence and characterizations of the Fr\'echet derivatives of the solution to time-harmonic elastic scattering problems with respect to the boundary of the obstacle. Our analysis is based on a technique - the factorization of the difference of the far-field pattern for two different scatterers - introduced by Kress and Pa\"ivarinta to establish Fr\'echet differentiability in acoustic scattering. For the Dirichlet boundary condition an alternative proof of a differentiability result due to Charalambopoulos is provided and new results are proven for the Neumann and impedance exterior boundary value problems.

Abstract:
The classical problem of diffraction of radio waves around a spherical earth is briefly reviewed, with the purpose of pointing out a mistake in the mathematical derivation of the theory which has been generally accepted. The correct way of analysis is indicated.

Abstract:
In this paper, a generalized dynamical theory of thermoelasticity is employed to study disturbances in an infinite elastic solid containing a spherical cavity which is subjected to step rise in temperature in its inner boundary and an impulsive dynamic pressure on its surface. The problem is solved by the use of the Laplace transform on time. The short time approximations for the stress, displacement and temperature are obtained to examine their discontinuities at the respective wavefronts. It is shown that the instantaneous change in pressure and temperature at the cavity wall gives rise to elastic and thermal disturbances which travel with finite velocities v1 and v2(>v1) respectively. The stress, displacement and temperature are found to experience discontinuities at the respective wavefronts. One of the significant findings of the present analysis is that there is no diffusive nature of the waves as found in classical theory.

Abstract:
We present a technique for studying the polarimetric properties of a birefringent object by means of classical ghost diffraction. The standard ghost diffraction setup is modified to include polarizers for controlling the state of polarization of the beam in various places. The object is characterized by a Jones matrix and the absolute values of the Fourier transforms of its individual elements are measured. From these measurements the original complex-valued functions can be retrieved through iterative methods resulting in the full Jones matrix of the object. We present two different placements of the polarizers and show that one of them leads to better polarimetric quality, while the other placement offers the possibility to perform polarimetry without controlling the source's state of polarization. The concept of an effective source is introduced to simplify the calculations. Ghost polarimetry enables the assessment of polarization properties as a function of position within the object through simple intensity correlation measurements.

Abstract:
The problem of diffraction of a plane elastic wave by a gradient transversely isotropic layer is considered. Using the method of overdetermined boundary value problem in combination with the Fourier transform method, the system of ordinary differential equations of the second order with boundary conditions of the third type is obtained which is solved by the grid method. Results of calculations obtained using the above-mentioned technique for the case of piecewise linear profiles for the Young modulus of the layer are given. 1. Introduction In nature, many of the geological formations form layered structures with elastic properties differing in various directions. Of all the formations and media, the special interest is often given to transversely isotropic media in which elastic modula of the media are the same in the plane normal to the axis of symmetry but differ from those of the direction along the axis of symmetry. Studies show that many sedimentary rocks indeed are transversely isotropic [1–3]. Besides, a thin-layered packet of parallel beds each of which is isotropic but properties of which differ from properties of the other beds within the packet behaves as a transversely isotropic medium at presence of deformations. Furthermore, transversely isotropic structures are normally used at production of composites. If fibers packed in parallel are used as a reinforcing agent, then the composite possesses a unidirectional structure and is treated as a transversely isotropic material in the planes normal to the direction of reinforcement [4]. Most often sheet metals are not isotropic and possess normal anisotropy (transversely isotropic). Ferroconcrete containing cracks is considered a transversely isotropic material with the plane of isotropy parallel to the plane of the crack [5]. Transversely isotropic structures also occur at production of laminated wood [6]. A number of works have been dedicated to studying processes of propagation of sound waves through anisotropic elastic layers. For example, in [7, 8], an elastic layer was considered as uniform and anisotropic whereas [9] dealt with the problem of propagation of the sound wave through a transversely isotropic nonuniform layer. A simpler case of the problem was considered by the authors of present paper earlier [10]. In the present work considered is the problem of diffraction of an elastic wave by a nonuniform transversely isotropic plate with constant elasticity characteristics along the axis of the layer and a continuous distribution of elasticity parameters in the section. Differential

Abstract:
Simulation results for head-on collisions of equal-sized spherical polymer nanodroplets using molecular dynamics are presented. Elastic behavior of an initial compressed phase for the colliding droplets is analyzed. Deformations and contact radii of the nanodroplets are compared with the Hertzian model of elastic solid balls. It is found that at least the initial phase of collision can be explained by this continuum model, except at the very moment of the beginning of collision.