Differential entropy and tiling

This paper relates the differential entropy of a sufficiently nice probability density functionp on Euclideann-space to the problem of tilingn-space by the translates of a given compact symmetric convex setS with nonempty interior. The relationship occurs via the concept of the epsilon entropy ofn-space under the norm induced byS, with probability induced byp. An expression is obtained for this entropy as approaches 0, which equals the differential entropy ofp, plusn times the logarithm of 2/, plus the logarithm of the reciprocal of the volume ofS, plus a constantC(S) depending only onS, plus a term approaching zero with. The constantC(S) is called the entropic packing constant ofS; the main results of the paper concern this constant. It is shown thatC(S) is between 0 and 1; furthermore,C(S) is zero if and only if translates ofS tile all ofn-space.This paper presents the results of one phase of research carried out at the Jet Propulsion Laboratory, California Institute of Technology, under Contract No. NAS 7-100, sponsored by the National Aeronautics and Space Administration.     

Topographic organization of Hebbian neural connections by synchronous wave activity

Experimental studies have revealed that the refinement of early, imprecise connections in the developing visual system involves activity in the retina before the onset of vision. We study the evolution of initially random unidirectional connections between two excitable layers of FitzHugh-Nagumo neurons with simulated spontaneous activity in the input layer. Lateral coupling within the layers yields synchronous neural wave activity that serves as a template for the Hebbian learning process, which establishes topographically precise interlayer connections. (c) 2001 American Institute of Physics.     

Hybrid photoactive assemblies: electron injection from host-guest complexes into semiconductor nanoparticles

Novel ternary assemblies consisting of fully encapsulated host-guest complexes (hemicarceplexes) and wide band gap semiconductor nanoparticles were investigated. The water-soluble amphiphilic host (octacarboxyhemicarcerand) traps the hydrophobic chromophore within its cavity and binds to the surface of metal oxide nanoparticles. Fluorescence quenching and fast charge injection, kforward >/= 7 x 109 s-1, from the S2 state of encapsulated azulene were observed. Charge recombination proceeds at a much lower rate of 2 x 107 s-1. Interestingly, the recombination kinetics is homogeneous, suggesting that electron tunneling through the wall of the "molecular container" is the rate-limiting step of the process.     

An ordered array of cadmium clusters assembled in zeolite A

We report the assembly of a cubic array of cationic cadmium clusters encapsulated in zeolite A, and its characterization through Rietveld analysis of powder synchrotron X-ray diffraction data and high resolution transmission electron microscopy.     

Jamming concepts in cold polymeric glasses

The purpose of the present paper is to propose an idea to construct the volume function W for polymer glasses and calculate the volume of polymer glasses as a function of the compactivity X utilizing a statistical-mechanical method developed for semiflexible polymers. We also discuss the analogue for glasses of "tapping" experiments which show the validity of statistical mechanics and the entropy concept in powders.     

Effect of drop size on the degradation of VX in concrete

The effect of drop size on the degradation rate of VX, O-ethyl S-[2-(diisopropylamino)ethyl]methylphosphonothioate, in fresh concrete has been examined using (31)P NMR. Drops of neat VX, ranging in size from 4 microL to 0.2 microL, applied to small concrete coupons (8 mm x 15 mm) were observed to degrade at different rates, with the 1 microL and smaller drops reacting in less than 4 days, and the larger droplets reacting in less than 11 days. Additionally, 4 microL VX predissolved in hexane to evenly spread it over the concrete coupon likewise reacted faster, degrading in less than 5 days. The fresh concrete, less than 2 months old, exhibited significantly faster VX degradation for all drop sizes than that observed for "aged" concrete in a previous study where VX persisted for months. The enhanced reactivity of the "fresh" concrete for VX was maintained for at least a 1-year period. The pH of water containing crushed "fresh" and "aged" concrete was 10.0 and 9.0, respectively. The higher pH of the "fresh" concrete is one reason for its enhanced reactivity toward VX. An additional contribution to the enhanced reactivity of the "fresh" concrete is suggested by the increased mobility of its sorbed VX as evidenced by its significantly narrower peak in (31)P NMR spectra.     

Ionization and recombination in intense, short electric field pulses

We investigate ionization and excitation of H(1s) in the limit of very short electric field pulses, analytically and numerically and both in the limit of small and extremely large peak electric fields. We identify a process of recombination akin to Rabi flopping from the continuum and give an analytic expression for this process after a single-cycle strong-field pulse.     

Double layers and interparticle forces in colloid science and biology: analytic results for the effect of ionic dispersion forces

We study analytically two of the central problems of colloid science: the structure of the double layer surrounding a charged particle and the forces between two such particles. Traditionally, these have been understood using a combination of electrostatic forces acting on the ions and the entropy of the same ions. Here we derive explicit formulas showing how the often dominant dispersion forces between ions and the surfaces can dramatically change the structure of the double layer and the forces.     

Investigation of ultrafast laser-driven radiative blast waves

We have examined the evolution of cylindrically symmetric blast waves produced by the deposition of femtosecond laser pulses in gas jets. In high- Z gases radiative effects become important. We observe the production of an ionization precursor ahead of the shock front and deceleration parameters below the adiabatic value of 1/2 (for a cylinder), an effect expected when the blast wave loses energy by radiative cooling. Despite significant radiative cooling, the blast waves do not appear to develop thin shell instabilities expected for strongly radiative waves. This is believed to be due to the stabilizing effect of a relatively thick blast wave shell resulting in part from electron thermal conduction effects.