Polymer emissivity

The thermal emission characteristics of polypyromellitimides have been examined as a function of temperature by measurement of the power required to maintain steady-state temperatures in an evacuated system. The emissivity was derived and found to increase with increasing temperature up to a saturation limit of above 0.9 at temperatures above 475°K. The effect is explained as a thermal population of excited infrared transitions. Power emitted is dominated by the most intense bands which are common to absorption and emission spectra.     

Achieving peak brightness in an atom laser

In this Letter we present experimental results and a simple analytic theory on the first continuous (long pulse) Raman atom laser. We analyze the flux and brightness of a generic two state atom laser with an analytic model that shows excellent agreement with our experiments. We show that, for the same source size, the brightness achievable with a Raman atom laser is at least 3 orders of magnitude greater than achievable in any other demonstrated continuously outcoupled atom laser.     

Structure Results for Multiple Tilings in 3D

We study multiple tilings of 3-dimensional Euclidean space by a convex body. In a multiple tiling, a convex body $P$ is translated with a discrete multiset $\Lambda $ in such a way that each point of ${\mathbb {R}}^d$ gets covered exactly $k$ times, except perhaps the translated copies of the boundary of $P$ . It is known that all possible multiple tilers in ${\mathbb {R}}^3$ are zonotopes. In ${\mathbb {R}}^2$ it was known by the work of Kolountzakis (Discrete Comput Geom 23(4):537–553, 2000) that, unless $P$ is a parallelogram, the multiset of translation vectors $\Lambda $ must be a finite union of translated lattices (also known as quasi periodic sets). In that work (Kolountzakis, Discrete Comput Geom 23(4):537–553, 2000) the author asked whether the same quasi-periodic structure on the translation vectors would be true in ${\mathbb {R}}^3$ . Here we prove that this conclusion is indeed true for ${\mathbb {R}}^3$ . Namely, we show that if $P$ is a convex multiple tiler in ${\mathbb {R}}^3$ , with a discrete multiset $\Lambda $ of translation vectors, then $\Lambda $ has to be a finite union of translated lattices, unless $P$ belongs to a special class of zonotopes. This exceptional class consists of two-flat zonotopes $P$ , defined by the Minkowski sum of two 2-dimensional symmetric polygons in ${\mathbb {R}}^3$ , one of which may degenerate into a single line segment. It turns out that rational two-flat zonotopes admit a multiple tiling with an aperiodic (nonquasi-periodic) set of translation vectors $\Lambda $ . We note that it may be quite difficult to offer a visualization of these 3-dimensional non-quasi-periodic tilings, and that we discovered them by using Fourier methods.     

Soft Dynamics simulation. 1. Normal approach of two deformable particles in a viscous fluid and optimal-approach strategy

Discrete simulation methods are efficient tools to investigate the behaviors of complex fluids such as dry granular materials or dilute suspensions of hard particles. By contrast, materials made of soft and/or concentrated units (emulsions, foams, vesicles, dense suspensions) can exhibit both significant elastic particle deflections (Hertz-like response) and strong viscous forces (squeezed liquid). We point out that the gap between two particles is then not determined solely by the positions of their centers, but rather exhibits its own dynamics. We provide the first ingredients of a new discrete numerical method, named Soft Dynamics, to simulate the combined dynamics of particles and contacts. As an illustration, we present the results for the approach of two particles. We recover the scaling behaviors expected in three limits: the Stokes limit for very large gaps, the Poiseuille-lubricated limit for small gaps and even smaller surface deflections, and the Hertz limit for significant surface deflections. We find that for each gap value, an optimal force achieves the fastest approach velocity. The principle of larger-scale simulations with this new method is provided. They will consitute a promising tool for investigating the collective behaviors of many complex materials.     

Noise reduction in a mode-locked semiconductor laser by coherent photon seeding

We have used coherent photon seeding to reduce the noise in an actively mode-locked extended-cavity semiconductor laser. Feedback is provided by an auxiliary cavity terminated either by a wedge plate or by a phase-conjugate mirror. Both conventional and phase-conjugate feedback can reduce the low-frequency noise components (0-5 MHz) by as much as 36 dB, hence drastically reducing the pulse fluctuations. A noise reduction of as much as 18 dB is also observed in the 0.01-3.0-GHz frequency range. We obtained these results while preserving the pulse duration (26 ps) and improving the time-bandwidth product.     

Frobenius Problem and the Covering Radius of a Lattice

Let and let be relatively prime integers. The Frobenius number of this N-tuple is defined to be the largest positive integer that cannot be expressed as are non-negative integers. The condition that implies that such a number exists. The general problem of determining the Frobenius number given N and is NP-hard, but there have been a number of different bounds on the Frobenius number produced by various authors. We use techniques from the geometry of numbers to produce a new bound, relating the Frobenius number to the covering radius of the null-lattice of this N-tuple. Our bound is particularly interesting in the case when this lattice has equal successive minima, which, as we prove, happens infinitely often.     

Trifluoromethylation of alkenyl bromides and iodides (including 5-iodouracils) with (CF3)2Hg and Cu ("trifluoromethylcopper")

Bromo- and iodoalkenes undergo trifluoromethylation efficiently in DMA with "CF3Cu" generated from (CF3)2Hg and Cu. Variable stereochemical inversion is observed with substrates having a gem-carbonyl group. Substrates having gem-hydrogen, -alkyl, or -alkenyl groups give products with stereochemical retention.     

Scaling violation and shadowing corrections at HERA

We study the value of shadowing corrections (SC) in the HERA kinematic region in the Glauber–Mueller approach. Since the Glauber–Mueller approach was proven in perturbative quantum chromodynamics (QCD) in the double-logarithmic approximation (DLA), we develop the DLA approach for the deep inelastic structure function which takes into account the SC. Our estimates show small SC for in the HERA kinematic region while they turn out to be sizable for the gluon structure function. We compare our estimates with those for gluon distribution in leading order (LO) and next to leading order (NLO) in the DGLAP evolution equations. Received: 21 September 1998 /Published online: 14 January 1999