The transmission or scattering of elastic waves by an inhomogeneity of simple geometry: A comparison of theories

The extended method of equivalent inclusion developed is applied to study the specific wave problems of the transmission of elastic waves in an infinite medium containing a layer of inhomogeneity, and of the scattering of elastic waves in an infinite medium containing a perfect spherical inhomogeneity. The eigenstrains are expanded as a geometric series and the method of integration for the inhomogeneous Helmholtz operator given by Fu and Mura is adopted. The results obtained by using a limited number of terms in the eigenstrain expansion are compared with exact solutions for the layer problem and for a perfect sphere. Two parameters are singled out for this comparison: the ratio of elastic moduli, and the ratio of the mass densities. General trends for three different situations are shown

Semi-Finite Forms of Bilateral Basic Hypergeometric Series

We show that several classical bilateral summation and transformation formulas have semi-finite forms. We obtain these semi-finite forms from unilateral summation and transformation formulas. Our method can be applied to derive Ramanujan's $_1\psi_1$ summation, Bailey's $_2\psi_2$ transformations, and Bailey's $_6\psi_6$ summation.Comment: 8 pages. accepted by Proc. Amer. Math. So

Surface States of the Topological Insulator Bi_{1-x}Sb_x

We study the electronic surface states of the semiconducting alloy BiSb. Using a phenomenological tight binding model we show that the Fermi surface of the 111 surface states encloses an odd number of time reversal invariant momenta (TRIM) in the surface Brillouin zone confirming that the alloy is a strong topological insulator. We then develop general arguments which show that spatial symmetries lead to additional topological structure, and further constrain the surface band structure. Inversion symmetric crystals have 8 Z_2 "parity invariants", which include the 4 Z_2 invariants due to time reversal. The extra invariants determine the "surface fermion parity", which specifies which surface TRIM are enclosed by an odd number of electron or hole pockets. We provide a simple proof of this result, which provides a direct link between the surface states and the bulk parity eigenvalues. We then make specific predictions for the surface state structure for several faces of BiSb. We next show that mirror invariant band structures are characterized by an integer "mirror Chern number", n_M. The sign of n_M in the topological insulator phase of BiSb is related to a previously unexplored Z_2 parameter in the L point k.p theory of pure Bi, which we refer to as the "mirror chirality", \eta. The value of \eta predicted by the tight binding model for Bi disagrees with the value predicted by a more fundamental pseudopotential calculation. This explains a subtle disagreement between our tight binding surface state calculation and previous first principles calculations on Bi. This suggests that the tight binding parameters in the Liu Allen model of Bi need to be reconsidered. Implications for existing and future ARPES experiments and spin polarized ARPES experiments will be discussed.Comment: 15 pages, 7 figure

On the origin and energy of oscillatory earthquake waves

A critical survey of the different modes of generation of oscillatory earthquake waves is given. The consequences of the failure of Hooke's law on the dispersion of waves is indicated. The energy of an earthquake is considered from the theory of elasticity with a discussion of Sezawa's result

On seismic rays and waves (Part One)

The equations of motion of an elastico-viscous medium in which the material constants vary with position are deduced. These can be put into the form of a wave equation only when the gradients of the constants are small. By the method of Sommerfeld and Runge these equations are compared with the equation of the characteristic function, whence the condition for the validity of the ray method is obtained. It is similar to De Broglie's criterion in wave mechanics. Expressed in terms of measurable quantities in seismology, the condition is applied to the data recently obtained by Gutenberg for the upper layers of the earth's crust. The equation of the characteristic function is used in deriving the forms of the ray paths for several particular velocity functions, following a method previously used by Epstein

Optimal nonlocal multipartite entanglement concentration based on projection measurements

We propose an optimal nonlocal entanglement concentration protocol (ECP) for multi-photon systems in a partially entangled pure state, resorting to the projection measurement on an additional photon. One party in quantum communication first performs a parity-check measurement on her photon in an N-photon system and an additional photon, and then she projects the additional photon into an orthogonal Hilbert space for dividing the original $N$-photon systems into two groups. In the first group, the N parties will obtain a subset of $N$-photon systems in a maximally entangled state. In the second group, they will obtain some less-entangled N-photon systems which are the resource for the entanglement concentration in the next round. By iterating the entanglement concentration process several times, the present ECP has the maximal success probability which is just equivalent to the entanglement of the partially entangled state. That is, this ECP is an optimal one.Comment: 5 pages, 4 figure

Comparison between the Torquato-Rintoul theory of the interface effect in composite media and elementary results

We show that the interface effect on the properties of composite media recently proposed by Torquato and Rintoul (TR) [Phys. Rev. Lett. 75, 4067 (1995)] is in fact elementary, and follows directly from taking the limit in the dipolar polarizability of a coated sphere: the TR ``critical values'' are simply those that make the dipolar polarizability vanish. Furthermore, the new bounds developed by TR either coincide with the Clausius-Mossotti (CM) relation or provide poor estimates. Finally, we show that the new bounds of TR do not agree particularly well with the original experimental data that they quote.Comment: 13 pages, Revtex, 8 Postscript figure