The Spectral Gap of the 2-D Stochastic Ising Model with Nearly Single-Spin Boundary Conditions

We establish upper bounds for the spectral gap of the stochastic Ising model at low temperature in an N×N box, with boundary conditions which are plus except for small regions at the corners which are either free or minus. The spectral gap decreases exponentially in the size of the corner regions, when these regions are of size at least of order logN. This means that removing as few as O(logN) plus spins from the corners produces a spectral gap far smaller than the order N ^–2 gap believed to hold under the all-plus boundary condition. Our results are valid at all subcritical temperatures.     

The Spectral Gap of the 2-D Stochastic Ising Model with Mixed Boundary Conditions

We establish upper bounds for the spectral gap of the stochastic Ising model at low temperatures in an l×l box with boundary conditions which are not purely plus or minus; specifically, we assume the magnitude of the sum of the boundary spins over each interval of length l in the boundary is bounded by l, where <1. We show that for any such boundary condition, when the temperature is sufficiently low (depending on ), the spectral gap decreases exponentially in l.     

Structure of 72,74Se at high spin

Lifetimes of high spin states up to { }=22⁺ in the yrast positive parity bands have been measured to investigate the shape evolution with increasing spin in ^{72, 74}Se. The Q _t values derived from these measurements indicate that prolate shape stabilizes for ⁷²Se, while a triaxial shape develops for ⁷⁴Se at higher spins. Comparison of the observed trend in Q _t with spin for ^{72, 74}Se with that of the corresponding kryptones isotones emphasizes the stability provided by N=38 prolate shell gap even at high rotational frequency.     

A system with three contiguous planar tetracoordinate carbons is viable: a computational study on a C6H6 isomer

Ab initio and density functional theory calculations indicate that a benzene dication isomer (1: C₆H₆²⁼) with three contiguous planar tetracoordinate carbons is at a minimum on the potential energy surface. The remarkable preference for the planar structure for 1 is traced to the aromatic stabilization present in the three membered ring formed by the three planar tetracoordinate carbon atoms.     

Enhanced fluorescence of remote functionalized diaminodicyanoquinodimethanes in the solid state and fluorescence switching in a doped polymer by solvent vapors

Remote functionalized zwitterionic diaminodicyanoquinodimethanes are found to exhibit a dramatic enhancement of light emission in the solid state and when doped in polymer films, as compared to the solution state. Crystal structure analysis of prototypical molecules reveals the role of the remote functionality in the solid state molecular organization. Semiempirical quantum chemical computations provide a viable model to explain the interesting phenomenon of fluorescence enhancement as arising from the inhibition of geometry relaxation of the vertical excited state to a nonemitting state. The reversible switching of a doped polymer film fluorescence triggered by solvent vapors is demonstrated.     

Duality gaps in nonconvex stochastic optimization

We consider multistage stochastic optimization models containing nonconvex constraints, e.g., due to logical or integrality requirements. We study three variants of Lagrangian relaxations and of the corresponding decomposition schemes, namely, scenario, nodal and geographical decomposition. Based on convex equivalents for the Lagrangian duals, we compare the duality gaps for these decomposition schemes. The first main result states that scenario decomposition provides a smaller or equal duality gap than nodal decomposition. The second group of results concerns large stochastic optimization models with loosely coupled components. The results provide conditions implying relations between the duality gaps of geographical decomposition and the duality gaps for scenario and nodal decomposition, respectively.Mathematics Subject Classification (1991): 90C15Acknowledgments. This work was supported by the Priority Programme Online Optimization of Large Scale Systems of the Deutsche Forschungsgemeinschaft. The authors wish to thank Andrzej Ruszczyski (Rutgers University) for helpful discussions.     

Duality gap in convex programming

In this paper, we consider general convex programming problems and give a sufficient condition for the equality of the infimum of the original problem and the supremum of its ordinary dual. This condition may be seen as a continuity assumption on the constraint sets (i.e. on the sublevel sets of the constraint function) under linear perturbation. It allows us to generalize as well as treat previous results in a unified framework. Our main result is in fact based on a quite general constraint qualification result for quasiconvex programs involving a convex objective function proven in the setting of a real normed vector space.Mathematics Subject Classification (2000):90C25, 90C26, 90C30, 90C31     

Theoretical study of relative width of photonic band gap for the 3-D dielectric structure

Calculations for the relative width (Δω/ω₀) as a function of refractive index and relative radius of the photonic band gap for the fcc closed packed 3-D dielectric microstructure are reported and comparison of experimental observations and theoretical predictions are given. This work is useful for the understanding of photonic crystals and occurrence of the photonic band gap.     

Ultrashort in-plane semiconductor microlasers with high-reflectivity microstructured mirrors

We present very compact, as short as 20 m long, low-threshold in-plane semiconductor lasers operating at a wavelength of 980 nm, in which microstructured mirrors have been formed at both cavity ends by deep reactive ion etching (RIE). The back mirror consists of a seven-period third order Bragg reflector with a measured reflectivity of 95%. The front mirror has a similar configuration, but consists of three periods with a lower reflectivity (80%) in order to allow output coupling. Lasing has been achieved from 20 m long and 8 m wide devices exhibiting a current threshold of 7 mA. These are among the shortest in-plane Fabry–Perot electrically pumped lasers demonstrated to date. Design issues are discussed, along with experimental data from which values for the reflectivity of the mirrors are derived. State-of-the-art electron beam lithography (EBL) and high-aspect-ratio RIE have been used for device fabrication, while additional strategies are proposed for the further improvement of the device performance.     

Efficiency of Using an Analyzed Substance in Arc and Spark Light Sources

In order to evaluate the efficiency of application of an analyzed substance in electrode light sources for spectral analysis, it is suggested to use the ratio between the intensity of the concentrationsensitive spectral line of a chemical element and the product of the mass of the substance brought from the sample during exposure and the energy of a single pulse of a light source. It is established that annealing and sparking may favor stable selective entry of a substance into a plasma.