Gross–Pitaevskii dynamics of Bose–Einstein condensates and superfluid turbulence

The Gross–Pitaevskii equation, also called the nonlinear Schrödinger equation (NLSE), describes the dynamics of low-temperature superflows and Bose–Einstein Condensates (BEC). We review some of our recent NLSE-based numerical studies of superfluid turbulence and BEC stability. The relations with experiments are discussed.     

Some mixing properties of time series models

Sufficient conditions are given for linear processes and ARMA processes to have the Gaswirth and Rubin mixing condition. The mixing rates are also determined.     

On the regularity condition for the extremal problem under locally Lipschitz inclusion constraints

This paper deals with a regularity assumption for the existence of Lagrange Multipliers for an optimization problem in Hilbert spaces. First some results of [6] are extended; then a class of discrete systems in a Hilbert Space is considered where the regularity assumption automatically holds and the Discrete Maximum Principle is obtained.This research was partly supported by the Computer and Automation Institute of the Hungarian Academy of Sciences.     

Pulsed laser deposition of PZT/Pt composite thin films with high dielectric constants

PbZr_0.53Ti_0.47O₃ (PZT) thin films containing nanoparticles of Pt (3–10 nm) were produced using pulsed laser deposition (PLD). The Pt content can be tuned by varying the energy density of the laser beam. Phase and microstructure analysis of the thin films was performed using XRD, SEM, TEM and AFM. The electrical properties were investigated by C–V and I–V measurements. The effective dielectric constant of the composite films increased substantially through the Pt dispersion. These films are promising candidates, for instance, for high-density dynamic random access memory (DRAM) devices. PACS 77.22.Ch; 77.84.Lf; 81.15.Fg     

Contribution of the triangle graphs to the neutron electric dipole moment

In the Kobayashi-Maskawa model we compute a new contribution to the neutron electric dipole moment induced byCP violating flavour-changing transitions of the typess→d+gluon+γ through heavy quark loops. This contribution, essentially given by the triangle anomaly graph, is by itself gauge invariant. We obtain from this mechanismD _n /e=3.10^?32 cm, one order of magnitude below our previous estimate from usual penguin diagram contributions.     

A dynamical theory for the off-shell continuation of the πN t-matrix: M. J. Reiner. Physics Department,Virginia Polytechnic Institute and State University,Blacksburg, Virginia 24061 and Department of Physics and Astronomy,University of Rochester,Rochester, New York 14627

First-order gluon radiative corrections to the rate of weak decay of a quark into three quarks are calculated taking full account of all the masses involved. Using dimensional regularization techniques, the infrared divergences inherent to the problem cancel out, and the finite parts in convenient analytic forms which tend to the correct zero-mass limits are obtained. The total correction to the decay rate always exceeds its (negative) zero-mass limit and changes sign as the masses increase. Thus, except for small mass values, it is positive and acts in a direction opposite to that expected when the masses vanish.     

The diazo route to 2-vinylcyclopropylidenes

2-Vinylcyclopropylidene(2),3-methyl-2-vinylcyclopropylidenes(79,81)and2-(1-propenyl)cyclopropylidenes (95,97) were generated from the corresponding nitrosoureas in methanol at room temperature. The diazo route is initiated by the formation of 2-vinylcyclopropanediazonium ions (e.g.43) which do not undergo 1,3-carbon shifts. No cyclopentenyl products were found in weakly basic methanol where the diazonium ions prevail. Ring opening of the diazonium ions gives pentadienyl cations and products derived therefrom. Delocalisation of the pentadienyl cations was demonstrated by the distribution of deuterium and methyl labels. In the presence of strong base, 1-diazo-2-vinylcyclopropanes (e.g.48) arise by deprotonation of the diazonium ions. Rearrangement of 48 was excluded by independent generation of the potential product, 4-diazocyclopentene (103). Substantial quantities of 3-methoxycyclopentene (108) were obtained from 103, but not from 48. The 2-vinylcyclopropylidenes 2,79 and 95, arising by loss of nitrogen from the corresponding diazo compounds, undergo allene formation and Skattebøl rearrangement competitively. Cis-oriented methyl groups at either C-2(81) or C-2'(97) prevent the Skattebøl rearrangement. The cyclopentenylidenes 3 and 83 yield 4-methoxycyclopentenes (52,86) in excess over cyclopentadiens (4,84). In the presence of methyl vinyl ether, cycloaddition of 3 and electrophilic addition of 3-cyclopentenyl cation (51) occurred in a 1:14 ratio. Stereospecific formation of 52 indicates protonation of a ‘foiled carbene’ (3a) to give a bishomocyclopropenyl ion (51a). Our studies confirm that the various routes to 2-vinylcyclopropylidenes converge at the carbene stage.