Optimal Estimates for the Electric Field in Two-Dimensions

The purpose of this paper is to set out optimal gradient estimates for solutions to the isotropic conductivity problem in the presence of adjacent conductivity inclusions as the distance between the inclusions goes to zero and their conductivities degenerate. This difficult question arises in the study of composite media. Frequently in composites, the inclusions are very closely spaced and may even touch. It is quite important from a practical point of view to know whether the electric field (the gradient of the potential) can be arbitrarily large as the inclusions get closer to each other or to the boundary of the background medium. In this paper, we establish both upper and lower bounds on the electric field in the case where two circular conductivity inclusions are very close but not touching. We also obtain such bounds when a circular inclusion is very close to the boundary of a circular domain which contains the inclusion. The novelty of these estimates, which improve and make complete our earlier results published in Math. Ann., is that they give an optimal information about the blow-up of the electric field as the conductivities of the inclusions degenerate.Comment: 26 page

Defective development of gamma/delta T cells in interleukin 7 receptor-deficient mice is due to impaired expression of T cell receptor gamma genes.

Mice lacking the interleukin 7 receptor (IL-7R) generate alpha/beta T cells at a detectable but greatly reduced rate, but gamma/delta T cells are completely absent. The special role of IL-7R signaling in gamma/delta T cell development has remained unclear. IL-7Ralpha(-/-) mice exhibit a paucity of gamma gene rearrangements. This striking observation can be explained by a defect in T cell receptor (TCR)-gamma gene rearrangement, a defect in TCR-gamma gene transcription leading to death of gamma/delta lineage cells, and/or a requirement for IL-7R in commitment of cells to the gamma/delta lineage. To determine the role of IL-7R signaling in gamma/delta T cell development, we examined transcription of a prerearranged TCR-gamma transgene in IL-7Ralpha(-/-) mice, as well as the effects of IL-7 on transcription of endogenous, rearranged TCR-gamma genes in alpha/beta lineage cells. The results demonstrate that IL-7R-mediated signals are necessary for the normal expression of rearranged TCR-gamma genes. Equally significant, the results show that the poor expression of TCR-gamma genes in IL-7Ralpha(-/-) mice is responsible for the selective deficit in gamma/delta cells in these mice, since a high copy TCR-gamma transgene exhibited sufficient residual expression in IL-7Ralpha(-/-) mice to drive gamma/delta cell development. The results indicate that the absence of gamma/delta T cells in IL-7Ralpha(-/-) mice is due to insufficient TCR-gamma gene expression

Electronic structure of YbB6_{6}: Is it a Topological Insulator or not?

To resolve the controversial issue of the topological nature of the electronic structure of YbB$_{6}$, we have made a combined study using density functional theory (DFT) and angle resolved photoemission spectroscopy (ARPES). Accurate determination of the low energy band topology in DFT requires the use of modified Becke-Johnson exchange potential incorporating the spin-orbit coupling and the on-site Coulomb interaction $U$ of Yb $4f$ electrons as large as 7 eV. We have double-checked the DFT result with the more precise GW band calculation. ARPES is done with the non-polar (110) surface termination to avoid band bending and quantum well confinement that have confused ARPES spectra taken on the polar (001) surface termination. Thereby we show definitively that YbB$_{6}$ has a topologically trivial B 2$p$-Yb 5$d$ semiconductor band gap, and hence is a non-Kondo non-topological insulator (TI). In agreement with theory, ARPES shows pure divalency for Yb and a $p$-$d$ band gap of 0.3 eV, which clearly rules out both of the previous scenarios of $f$-$d$ band inversion Kondo TI and $p$-$d$ band inversion non-Kondo TI. We have also examined the pressure-dependent electronic structure of YbB$_{6}$, and found that the high pressure phase is not a Kondo TI but a \emph{p}-\emph{d} overlap semimetal.Comment: The main text is 6 pages with 4 figures, and the supplementary information contains 6 figures. 11 pages, 10 figures in total To be appeared in Phys. Rev. Lett. (Online publication is around March 16 if no delays.

Efficiency of Nonlinear Particle Acceleration at Cosmic Structure Shocks

We have calculated the evolution of cosmic ray (CR) modified astrophysical shocks for a wide range of shock Mach numbers and shock speeds through numerical simulations of diffusive shock acceleration (DSA) in 1D quasi- parallel plane shocks. The simulations include thermal leakage injection of seed CRs, as well as pre-existing, upstream CR populations. Bohm-like diffusion is assumed. We model shocks similar to those expected around cosmic structure pancakes as well as other accretion shocks driven by flows with upstream gas temperatures in the range $T_0=10^4-10^{7.6}$K and shock Mach numbers spanning $M_s=2.4-133$. We show that CR modified shocks evolve to time-asymptotic states by the time injected particles are accelerated to moderately relativistic energies (p/mc \gsim 1), and that two shocks with the same Mach number, but with different shock speeds, evolve qualitatively similarly when the results are presented in terms of a characteristic diffusion length and diffusion time. For these models the time asymptotic value for the CR acceleration efficiency is controlled mainly by shock Mach number. The modeled high Mach number shocks all evolve towards efficiencies $\sim 50$%, regardless of the upstream CR pressure. On the other hand, the upstream CR pressure increases the overall CR energy in moderate strength shocks ($M_s \sim {\rm a few}$). (abridged)Comment: 23 pages, 12 ps figures, accepted for Astrophysical Journal (Feb. 10, 2005

A new survivability measure for military communication networks

A new measure for survivability of military communication networks based upon topological structures is presented. The proposed measure can be used to evaluate and enhance the survivability of military communication networks, which is illustrated through case studies. The computer simulation results have shown that the new measure can well reflect the survivability of networks. It can be used as a reliable criterion for estimating the survivability of networks and designing networks with high survivability