Global and exploding solutions in a model of self-gravitating systems

We study asymptotic properties of solutions to an extension to arbitrary dimensions of the astrophysical model proposed by Chavanis et al. to explain phenomena of gravitational collapse in clouds of self-gravitating particles. In particular, we show that in the two-dimensional case the solutions can be continued to global ones, while in three space dimensions large data of negative energy blow up in a finite time. Relations between isothermal, Streater's energy-transport and the present models are also studied.     

Poloidal–toroidal decomposition in a finite cylinder. I: Influence matrices for the magnetohydrodynamic equations

The Navier–Stokes equations and magnetohydrodynamics equations are written in terms of poloidal and toroidal potentials in a finite cylinder. This formulation insures that the velocity and magnetic fields are divergence-free by construction, but leads to systems of partial differential equations of higher order, whose boundary conditions are coupled. The influence matrix technique is used to transform these systems into decoupled parabolic and elliptic problems. The magnetic field in the induction equation is matched to that in an exterior vacuum by means of the Dirichlet-to-Neumann mapping, thus eliminating the need to discretize the exterior. The influence matrix is scaled in order to attain an acceptable condition number.     

Computational studies of the cyclization of thiosemicarbazides

While typically cyclodehydration of thiosemicarbazides in acidic media leads to 1,3,4‐thiadiazoles, we have recently shown that under reflux conditions in anhydrous acetic acid the cyclization yields an imidazolidine derivative. The mechanism of this reaction has been characterized theoretically. Calculations indicate that this direction, facilitated by the presence of the ? CH₂CO₂? moiety in the N4 substituent is favored over the direction leading toward the thiadiazole product. Formation of the C? N bond that closes the five‐member ring appears to be concerted with the departure of ethanol molecule, although the proton transfer from the nitrogen atom to oxygen atom is much more advanced in the transition state. Copyright © 2007 John Wiley & Sons, Ltd.     

On subgame perfect equilibria in quantum Stackelberg duopoly with incomplete information

The Li–Du–Massar quantum duopoly model is one of the generally accepted quantum game schemes. It has applications in a wide range of duopoly problems. Our purpose is to study Stackelberg's duopoly with incomplete information in the quantum domain. The result of Lo and Kiang has shown that the correlation of players' quantities caused by the quantum entanglement enhances the first-mover advantage in the game. Our work demonstrates that there is no first-mover advantage if the players' actions are maximally correlated. Furthermore, we proved that the second mover gains a higher equilibrium payoff than the first one.     

Arbiter as the Third Man in Classical and Quantum Games

We study the possible influence of a not necessarily sincere arbiter on the course of classical and quantum 2×2 games and we show that this influence in the quantum case is much bigger than in the classical case. Extreme sensitivity of quantum games on initial states of quantum objects used as carriers of information in a game shows that a quantum game, contrary to a classical game, is not defined by a payoff matrix alone but also by an initial state of objects used to play a game. Therefore, two quantum games that have the same payoff matrices but begin with different initial states should be considered as different games.     

Boson-fermion duality in four dimensions: Comments on the paper of luther and schotte

The Fock space for the fermion field can be identified with the Fock space for the boson field, provided the overall numbers of internal degrees of freedom are the same. As a consequence, the respective free field Hamiltonian systems are equivalent (dual): the four-component neutrino model is thus equivalent to the doublet of independent (electric and magnetic, respectively) Maxwell fields, which are quantized in the Coulomb gauge. This statement arises on the field theory level, and seems to make doubtful the claim that realistic photons can be constructed from (bound) neutrino pairs: each (anti)neutrino degree should be represented by the photon-type (electric and magnetic, respectively) degree of freedom.     

The spectrum of theP-wave baryons and hadronic loops

In current QCD inspired analyses of the hadron spectrum nonperturbative quark loops are generally neglected. We study the validity of this assumption by estimating mass splittings and mixings induced by hadronic mass renormalization to the (70,1^?) baryon multiplet. All intermediate states in the loop composed of a ground state meson (0^?+, 1^??) and a ground state baryon (1/2⁺, 3/2⁺) are included. We use a³ P ₀ type model for the partial decay widths and spectral functions. Using unitarity and analyticity one finds a definite prediction for the masses and mixings, in good agreement with experiment, even when the perturbative one-gluon exchange is completely ignored. Our result thus allows for a smaller one-gluon exchange overall contribution, which would resolve the difficulty of the apparent smallness of the observed spin-orbit coupling. In particular if one adds the (nonperturbative) unitarity corrections to the one-gluon exchange contribution the gluon coupling constant can be reduced by a factor of 3 giving a reasonable value α_s≈0.3.     

Mechanism for flow-rate controlled breakup in confined geometries: a route to monodisperse emulsions

This Letter describes a quasistationary breakup of an immiscible, inviscid fluid at low capillary numbers. The breakup proceeds in a coflowing, viscous liquid, in a confined geometry of a long and narrow orifice. In contrast to the capillary instability in an unbounded fluid, the collapse proceeds through a series of equilibria, each yielding the minimum interfacial energy of the fluid-fluid interface. The process is slow in comparison to typical relaxation speeds of the interface, and it is reversible. Its quasistatic character of collapse forms the basis for controlled, high-throughput generation of monodisperse fluid dispersions.     

Time-resolved streak camera system with solid state laser and optical parametric generator in different spectroscopic applications

Apparatus to study time-evolution of emission spectra over very wide time and spectral range is described. Excitation part of the equipment consists of solid state Nd:YAG laser and optical parametric generator. The heart of the detection system consists of spectrograph and streak camera. The significance of optics and electronics built in the system for proper, fast and convenient measurements is underlined. The results of donor-acceptor energy transfer in a rigid polyvinyl alcohol matrix serve here as an example of application our equipment to study complex systems.