Minimum Distance Between the Faces of Two Convex Polyhedra: A Sufficient Condition

The problem of finding the Euclidean distance between two convex polyhedra can be reduced to the combinatorial optimization problem of finding the minimum distance between their faces. This paper presents a global optimality criterion for this problem. An algorithm (QLDPA) for the fast computation of the distance between convex and bounded polyhedra is proposed as an application of it. Computer experiments show its fast performance, especially when the total number of vertices is large.     

The benefit of practice for sound localization without sight

An experiment was designed to determine whether normally sighted human subjects would be able to adapt to the handicapping effects of sudden deprivation of visual cues on horizontal plane sound localization. Two groups of sighted normal-hearing young adults participated. One group was allowed the benefit of sight. The other group was blindfolded. Measurements of accuracy and the time to respond were made daily over the course of five consecutive days, in a semi-reverberant sound proof booth that modeled listening in a small office. Sound localization was assessed using an array of eight speakers that surrounded the subject in space. Each day, one block of 120 trials was presented for each of three stimuli, two one-third octave noise bands, centred at 0.5 and 4 kHz, and broadband noise, to assess the utilization of interaural temporal difference cues, interaural level difference cues and binaural and spectral cues in combination. Blindfolded subjects were relatively less accurate than sighted subjects. Both groups showed gains with practice, the blindfolded group to a greater degree, largely due to improvements in the use of spectral cues. The blindfolded group took longer to respond than the sighted group, but showed greater decrements in response time with practice.     

Effect of superfluidity on the structure of the inner crust of neutron stars

A self-consistent, completely quantum calculation of the structure of the inner crust of neutron stars is carried out in the Wigner-Seitz approximation with a realistic phenomenological nuclear energy functional, where pair correlations of neutrons and protons are included in the explicit form. It has been shown that the superfluidity of neutrons and protons affects the structure of the ground state of the crust.     

Moment Inequalities and High-Energy Tails for Boltzmann Equations with Inelastic Interactions

Journal of Statistical Physics - We study high-energy asymptotics of the steady velocity distributions for model kinetic equations describing various regimes in dilute granular flows. The main...     

Recording and decay of transient gratings in a system of saturable three-level centers

The kinetics of formation and relaxation of transient holographic gratings recorded in a system of saturable three-level centers is studied. Distortions in the shape of the profile of recorded and decaying structures of population and of the refractive index are taken into account. The analysis of the time dependences of diffraction efficiencies of different orders is performed for phase (thermal) and amplitude (concentration) gratings.     

Vanadium(III) chloride catalyzed Biginelli condensation: solution phase library generation of dihydropyrimidin-(2H)-ones

The three component condensation of an aldehyde, a β-keto ester and urea (thiourea) in the presence of a catalytic amount of VCl₃ is disclosed for the solution phase synthesis of dihydropyrimidinones. The ease of synthesis and work-up allowed the parallel synthesis of a 48-membered library of dihydropyrimidinones quickly and efficiently in good yields.     

Fourier-Feynman transform, convolution and first variation

We examine several interesting relationships and expressions involving Fourier-Feynman transform, convolution product and first variation for functionals in the Fresnel class F(B) of an abstract Wiener space B. We also prove a translation theorem and Parseval's identity for the analytic Feynman integral. This revised version was published online in June 2006 with corrections to the Cover Date.     

Dynamical significance in alkali metasilicate glasses

In this work, we elucidate the effect of the less mobile ions on the dynamics of the more mobile ions by molecular dynamics simulations of lithium ions motion in lithium metasilicate glass by freezing some randomly chosen lithium ions (5%, 10% and 25%) at their initial locations at 700 K. A remarkable slowing down of the dynamics of the majority mobile Li ions was observed both in the self-part of the density–density correlation function, F_s(k,t), and in the diffusion coefficients. On the other hand, there is no significant change in the structure. These results show many similarities to the mixed alkali effect (MAE) with mixing of the small content of foreign alkali (10% and 25% of K₂O), where large reduction of the dynamics was also observed in both experiments and MD simulations. This immobilization of faster ions causes the large MAE as already discussed in relation to the mechanism of the cooperative ion jump motions. Although of lesser importance, the ion dynamics are influenced by the matrix of oxygen atoms, because the jump motions of Li ions are assisted by the localized motions of oxygen atoms.