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

Spin-Driven Nematic Instability of the Multi-Orbital Hubbard Model: Application to Iron-Based Superconductors

Nematic order resulting from the partial melting of density-waves has been proposed as the mechanism to explain nematicity in iron-based superconductors. An outstanding question, however, is whether the microscopic electronic model for these systems -- the multi-orbital Hubbard model -- displays such an ordered state as its leading instability. In contrast to usual electronic instabilities, such as magnetic and charge order, this fluctuation-driven phenomenon cannot be captured by the standard RPA method. Here, by including fluctuations beyond RPA in the multi-orbital Hubbard model, we derive its nematic susceptibility and contrast it with its ferro-orbital order susceptibility, showing that its leading instability is the spin-driven nematic phase. Our results also demonstrate the primary role played by the $d_{xy}$ orbital in driving the nematic transition, and reveal that high-energy magnetic fluctuations are essential to stabilize nematic order in the absence of magnetic order.Comment: 8 pages, 6 figure

Effect of Charge Fluctuations on the Persistent Current through a Quantum Dot

We study coherent charge transfer between an Aharonov-Bohm ring and a side-attached quantum dot. The charge fluctuation between the two sub-structures is shown to give rise to algebraic suppression of the persistent current circulating the ring as the size of the ring becomes relatively large. The charge fluctuation at resonance provides transition between the diamagnetic and the paramagnetic states. Universal scaling, crossover behavior of the persistent current from a continuous to a discrete energy limit in the ring is also discussed.Comment: 5 pages, 4 figure