Symmetry breaking and other phenomena in the optimization of eigenvalues for composite membranes

We consider the following eigenvalue optimization problem: Given a bounded domain $\Omega\subset\R^n$ and numbers $\alpha\geq 0$, $A\in [0,|\Omega|]$, find a subset $D\subset\Omega$ of area $A$ for which the first Dirichlet eigenvalue of the operator $-\Delta + \alpha \chi_D$ is as small as possible. We prove existence of solutions and investigate their qualitative properties. For example, we show that for some symmetric domains (thin annuli and dumbbells with narrow handle) optimal solutions must possess fewer symmetries than $\Omega$; on the other hand, for convex $\Omega$ reflection symmetries are preserved. Also, we present numerical results and formulate some conjectures suggested by them.Comment: 24 pages; 3 figures (as separate files); (shortened previous version); to appear in Comm. Math. Phy

Evolution of mixing state of black carbon particles: Aircraft measurements over the western Pacific in March 2004

We report the evolution of the mixing state of black carbon (BC) particles in urban plumes measured by an airborne single particle soot photometer. The aircraft observations were conducted over the ocean near the coast of Japan in March 2004. The number fiaction of coated BC particles with a core diameter of 180 mn increased from 0.35 to 0.63 within 12 hours (h), namely 2.3% h-1, after being emitted from the Nagoya urban area in Japan. BC particles with a core diameter of 250 nm increased at the slower rate of 1.0% h-1. The increase in coated BC particles was associated with increases in non-sea salt sulfate and water-soluble organic carbon by a factor of approximately two, indicating that these compounds contributed to the coating on the BC particles. These results give direct evidence that BC particles become internally mixed on a time scale of 12 h in urban plumes. Copyright 2007 by the American Geophysical Union

Disorder-induced topological change of the superconducting gap structure in iron pnictides

In superconductors with unconventional pairing mechanisms, the energy gap in the excitation spectrum often has nodes, which allow quasiparticle excitations at low energies. In many cases, e.g. $d$-wave cuprate superconductors, the position and topology of nodes are imposed by the symmetry, and thus the presence of gapless excitations is protected against disorder. Here we report on the observation of distinct changes in the gap structure of iron-pnictide superconductors with increasing impurity scattering. By the successive introduction of nonmagnetic point defects into BaFe$_2$(As$_{1-x}$P$_x$)$_2$ crystals via electron irradiation, we find from the low-temperature penetration depth measurements that the nodal state changes to a nodeless state with fully gapped excitations. Moreover, under further irradiation the gapped state evolves into another gapless state, providing bulk evidence of unconventional sign-changing $s$-wave superconductivity. This demonstrates that the topology of the superconducting gap can be controlled by disorder, which is a strikingly unique feature of iron pnictides.Comment: 5 pages, 4 figure

Feedback regulation of the heat shock response in E. coli

Survival of organisms in extreme conditions has necessitated the evolution of stress response networks that detect and respond to environmental changes. Among the extreme conditions that cells must face is the exposure to higher than normal temperatures. In this paper, we propose a detailed biochemical model that captures the dynamical nature of the heat-shock response in Escherichia coli. Using this model, we show that both feedback and feedforward control are utilized to achieve robustness, performance, and efficiency of the response to the heat stress. We discuss the evolutionary advantages that feedback confers to the system, as compared to other strategies that could have been implemented to get the same performance

Threshold electronic structure at the oxygen K edge of 3d transition metal oxides: a configuration interaction approach

It has been generally accepted that the threshold structure observed in the oxygen K edge X-ray absorption spectrum in 3d transition metal oxides represents the electronic structure of the 3d transition metal. There is, however, no consensus about the correct description. We present an interpretation, which includes both ground state hybridization and electron correlation. It is based on a configuration interaction cluster calculation using a MO6 cluster. The oxygen K edge spectrum is calculated by annihilating a ligand hole in the ground state and is compared to calculations representing inverse photoemission experiments in which a 3d transition metal electron is added. Clear differences are observed related to the amount of ligand hole created in the ground state. Two "rules" connected to this are discussed. Comparison with experimental data of some early transition metal compounds is made and shows that this simple cluster approach explains the experimental features quite well.Comment: 10 pages, submitted to Phys. Rev. B, tried to make a better PS file