Numerical Approximation of Asymptotically Disappearing Solutions of Maxwell's Equations

This work is on the numerical approximation of incoming solutions to Maxwell's equations with dissipative boundary conditions whose energy decays exponentially with time. Such solutions are called asymptotically disappearing (ADS) and they play an importarnt role in inverse back-scatering problems. The existence of ADS is a difficult mathematical problem. For the exterior of a sphere, such solutions have been constructed analytically by Colombini, Petkov and Rauch [7] by specifying appropriate initial conditions. However, for general domains of practical interest (such as Lipschitz polyhedra), the existence of such solutions is not evident. This paper considers a finite-element approximation of Maxwell's equations in the exterior of a polyhedron, whose boundary approximates the sphere. Standard Nedelec-Raviart-Thomas elements are used with a Crank-Nicholson scheme to approximate the electric and magnetic fields. Discrete initial conditions interpolating the ones chosen in [7] are modified so that they are (weakly) divergence-free. We prove that with such initial conditions, the approximation to the electric field is weakly divergence-free for all time. Finally, we show numerically that the finite-element approximations of the ADS also decay exponentially with time when the mesh size and the time step become small.Comment: 15 pages, 3 figure

Positional disorder of Ba in the thermoelectric germanium clathrate Ba6Ge25

The local structure of Ba6Ge25 has been studied by x-ray diffraction and the atomic pair distribution function technique at 40 K and room temperature. Unambiguous evidence has been found that two out of three types of Ba atoms in Ba6Ge25 move off their positions and become locked in split sites at low temperatures.Comment: 5 pages and 4 figures, submitted to Solid State Communication

Fabrication of salt–hydrogel marbles and hollow-shell microcapsules by an aerosol gelation technique

We designed a new method for preparation of liquid marbles by using hydrophilic particles. Salt–hydrogel marbles were prepared by atomising droplets of hydrogel solution in a cold air column followed by rolling of the collected hydrogel microbeads in a bed of micrometre sized salt particles. Evaporation of the water from the resulting salt marbles with a hydrogel core yielded hollow-shell salt microcapsules. The method is not limited to hydrophilic particles and could potentially be also applied to particles of other materials, such as graphite, carbon black, silica and others. The structure and morphology of the salt–hydrogel marbles were analysed by SEM and their particle size distributions were measured. We also tested the dissolution times of the dried salt marbles and compared them with those of table salt samples under the same conditions. The high accessible surface area of the shell of salt microcrystals allows a faster initial release of salt from the hollow-shell salt capsules upon their dissolution in water than from the same amount of table salt. The results suggest that such hollow-shell particles could find applications as a table salt substitute in dry food products and salt seasoning formulations with reduced salt content without the loss of saltiness

Probability for Primordial Black Holes in Multidimensional Universe with Nonlinear Scalar Curvature Terms

We investigate multi-dimensional universe with nonlinear scalar curvature terms to evaluate the probability of creation of primordial black holes. For this we obtain Euclidean instanton solution in two different topologies: (a) $S^{D-1}$ - topology which does not accommodate primordial black holes and (b) $S^1\times S^{D-2}$-topology which accommodates a pair of black holes. The probability for quantum creation of an inflationary universe with a pair of black holes has been evaluated assuming a gravitational action which is described by a polynomial function of scalar curvature with or without a cosmological constant ($\Lambda$) using the framework of semiclassical approximation of Hartle-Hawking boundary conditions. We discuss here a class of new gravitational instantons solution in the $R^4$-theory which are relevant for cosmological model building.Comment: 18 pages, no figure. accepted in Phys. Rev.

Evidence for shape coexistence in 98^{98}Mo

A $\gamma\gamma$ angular correlation experiment has been performed to investigate the low-energy states of the nucleus $^{98}$Mo. The new data, including spin assignments, multipole mixing ratios and lifetimes reveal evidence for shape coexistence and mixing in $^{98}$Mo, arising from a proton intruder configuration. This result is reproduced by a theoretical calculation within the proton-neutron interacting boson model with configuration mixing, based on microscopic energy density functional theory. The microscopic calculation indicates the importance of the proton particle-hole excitation across the Z=40 sub-shell closure and the subsequent mixing between spherical vibrational and the $\gamma$-soft equilibrium shapes in $^{98}$Mo.Comment: 6 pages, 5 figures, 3 tables; published in Phys. Rev.