Abstract:
Shock wave formation and propagation in two-dimensional granular materials under vertical vibration are studied by digital high speed photography. The steepen density and temperature wave fronts form near the plate as granular layer collides with vibrating plate and propagate upward through the layer. The temperature front is always in the transition region between the upward and downward granular flows. The effects of driving parameters and particle number on the shock are also explored.

Abstract:
If a dissipative anisotropic dielectric material, characterized by the permittivity matrix $\underline{\underline{\epsilon}}$, supports Voigt-wave propagation, then so too does the analogous active material characterized by the permittivity matrix $\underline{\underline{{\tilde{\epsilon}}}}$, where $\underline{\underline{{\tilde{\epsilon}}}}$ is the hermitian conjugate of $\underline{\underline{\epsilon}}$. Consequently, a dissipative material that supports Voigt-wave propagation can give rise to a material that supports the propagation of Voigt waves with attendant linear gain in amplitude with propagation distance, by infiltration with an active dye.

Abstract:
We study wave propagation in periodic and frequency dependent materials. The approach in this paper leads to spectral analysis of a quadratic operator pencil where the spectral parameter relates to the quasimomentum and the frequency is a parameter. We show that the underlying operator has a discrete spectrum, where the eigenvalues are symmetrically placed with respect to the real and imaginary axis. Moreover, we discretize the operator pencil with finite elements and use a Krylov space method to compute eigenvalues of the resulting large sparse matrix pencil.

Abstract:
This paper investigates the characteristics of electromagnetic wave propagation in biaxially anisotropic left-handed materials (BA-LHMs) theoretically and numerically. We discuss under what conditions the anomalous refraction or reflection will occur at the interface when a plane wave passes from one isotropic right-handed material into another BA-LHM. Meanwhile the refraction angle of the wave vector and that of the Poynting power are presented when the anomalous refraction takes place. According to the theoretical analysis,sev eral sets of constitutive parameters of BA-LHMs are considered. Then the anomalous refraction or reflection of the continuous-wave (CW) Gaussian Beam passing from free space into BA-LHMs are simulated by the finite difference time domain (FDTD) method based on the Drude dispersive models. The simulated results are in agreement with theoretical results,which validates the theoretical analysis.

Abstract:
We have developed a method to simulate behavior of nanoporous materials in a molecular dynamics code. The nanoporous solid is produced via a spinodal decomposition of a material brought from a supercritical fluid into the two phase (liquid-vapor) region and then quenching and freezing the liquid into an interconnected nanoporous solid. We have simulated, at the atomic level, compression in crystal/nanoporous configurations, demonstrating that this is a powerful technique for studying the equation-of-state of cold and warm dense matter. By performing compression simulations relevant to high energy density physics experiments, we have been able to elucidate experimental measurement by identifying governing microscopic mechanisms.

Abstract:
Some physically interesting properties and effects of wave propagation in biaxially anisotropic left-handed materials are investigated in this paper. We show that in the biaxially gyrotropic left-handed material, the left-right coupling of circularly polarized light arises due to the negative indices in permittivity and permeability tensors of gyrotropic media. It is well known that the geometric phases of photons inside a curved fiber in previous experiments often depend on the cone angles of solid angles subtended by a curve traced by the direction of wave vector of light, at the center of photon momentum space. Here, however, for the light propagating inside certain anisotropic left-handed media we will present a different geometric phase that is independent of the cone angles. The extra phases of electromagnetic wave resulting from the instantaneous helicity inversion at the interfaces between left- and right- handed (LRH) media is also studied in detail by using the Lewis-Riesenfeld invariant theory. Some interesting applications (e.g., controllable position-dependent frequency shift, detection of quantum-vacuum geometric phases and helicity reversals at the LRH interfaces etc.) of above effects and phenomena in left-handed media is briefly discussed.

A theoretical model for the
propagation of acoustic waves in dry granular media is presented within the
framework of the nonlinear granular elasticity. An essential ingredient is the
dependence of the elastic moduli on compression. For the purpose of
illustration, we analyze the case of a time-harmonic plane wave propagation
under isotropic compression. We derive explicit relations for the wave speed
dependence with the confining pressure. The present approach provides an
accurate description of acoustic wave propagation in granular packings and
represents a powerful tool to interpret the results of current experiments.

Abstract:
We investigate the propagation of electromagnetic waves in stratified anisotropic dielectric-magnetic materials using the integral equation method (IEM). Based on the superposition principle, we use Hertz vector formulations of radiated fields to study the interaction of wave with matter. We derive in a new way the dispersion relation, Snell's law and reflection/transmission coefficients by self-consistent analyses. Moreover, we find two new forms of the generalized extinction theorem. Applying the IEM, we investigate the wave propagation through a slab and disclose the underlying physics which are further verified by numerical simulations. The results lead to a unified framework of the IEM for the propagation of wave incident either from a medium or vacuum in stratified dielectric-magnetic materials.

Abstract:
Amplification/attenuation of light waves in artificial materials with a gain/loss modulation on the wavelength scale can be sensitive to the propagation direction. We give a numerical proof of the high anisotropy of the gain/loss in two dimensional periodic structures with square and rhombic lattice symmetry by solving the full set of Maxwell's equations using the finite difference time domain method. Anisotropy of amplification/attenuation leads to the narrowing of the angular spectrum of propagating radiation with wavevectors close to the edges of the first Brillouin Zone. The effect provides a novel and useful method to filter out high spatial harmonics from noisy beams.

Abstract:
The polarization direction of an electromagnetic field changes and eventually reaches a steady state when propagating through a birefringent material with off axis absorption or gain. The steady state orientation direction depends on the magnitude of the absorption (gain) and the phase retardation rate. The change in the polarization direction is experimentally demonstrated in weakly doped ($0.05\%$) Pr$^{3+}$:Y$_2$SiO$_5$ crystals, where the light polarization, if initially aligned along the most strongly absorbing principal axis, gradually switch to a much less absorbing polarization state during the propagation. This means that the absorption coefficient, $\alpha$, in birefringent materials generally varies with length. This is important for, e.g., laser crystal gain media, highly absorbing and narrow band spectral filters and quantum memories.