Lagrangian Formalism for nonlinear second-order Riccati Systems: one-dimensional Integrability and two-dimensional Superintegrability

The existence of a Lagrangian description for the second-order Riccati equation is analyzed and the results are applied to the study of two different nonlinear systems both related with the generalized Riccati equation. The Lagrangians are nonnatural and the forces are not derivable from a potential. The constant value $E$ of a preserved energy function can be used as an appropriate parameter for characterizing the behaviour of the solutions of these two systems. In the second part the existence of two--dimensional versions endowed with superintegrability is proved. The explicit expressions of the additional integrals are obtained in both cases. Finally it is proved that the orbits of the second system, that represents a nonlinear oscillator, can be considered as nonlinear Lissajous figuresComment: 25 pages, 7 figure

Irrotational binary neutron stars in quasiequilibrium

We report on numerical results from an independent formalism to describe the quasi-equilibrium structure of nonsynchronous binary neutron stars in general relativity. This is an important independent test of controversial numerical hydrodynamic simulations which suggested that nonsynchronous neutron stars in a close binary can experience compression prior to the last stable circular orbit. We show that, for compact enough stars the interior density increases slightly as irrotational binary neutron stars approach their last orbits. The magnitude of the effect, however, is much smaller than that reported in previous hydrodynamic simulations.Comment: 4 pages, 2 figures, revtex, accepted for publication in Phys. Rev.

Fully quantum mechanical dynamic analysis of single-photon transport in a single-mode waveguide coupled to a traveling-wave resonator

We analyze the dynamics of single photon transport in a single-mode waveguide coupled to a micro-optical resonator using a fully quantum mechanical model. We examine the propagation of a single-photon Gaussian packet through the system under various coupling conditions. We review the theory of single photon transport phenomena as applied to the system and we develop a discussion on the numerical technique we used to solve for dynamical behavior of the quantized field. To demonstrate our method and to establish robust single photon results, we study the process of adiabatically lowering or raising the energy of a single photon trapped in an optical resonator under active tuning of the resonator. We show that our fully quantum mechanical approach reproduces the semi-classical result in the appropriate limit and that the adiabatic invariant has the same form in each case. Finally, we explore the trapping of a single photon in a system of dynamically tuned, coupled optical cavities.Comment: 24 pages, 10 figure

On Rapidly Rotating Magnetic Core-Collapse Supernovae

We have analyzed the magnetic effects that may occur in rapidly rotating core collapse supernovae. We consider effects from both magnetic turbulence and the formation of magnetic bubbles. For magnetic turbulence we have made a perturbative analysis for our spherically symmetric core-collapse supernova model that incorporates the build up of magnetic field energy in the matter accreting onto the proto-neutron star shortly after collapse and bounce. This significantly modifies the pressure profile and increases the heating of the material above the proto-neutron star resulting in an explosion even in rotating stars that would not explode otherwise. Regarding magnetic bubbles we show that a model with a modest initial uniform magnetic field and uniform angular velocity of ~0.1 rad/s can form magnetic bubbles due to the very non homologous nature of the collapse. It is estimated that the buoyancy of the bubbles causes matter in the proto-neutron star to rise, carrying neutrino-rich material to the neutron-star surface. This increases the neutrino luminosity sufficiently at early times to achieve a successful neutrino-driven explosion. Both magnetic mechanisms thus provide new means for initiating a Type II core-collapse supernova.Comment: 12 pages, 9 figure

Revised Relativistic Hydrodynamical Model for Neutron-Star Binaries

We report on numerical results from a revised hydrodynamic simulation of binary neutron-star orbits near merger. We find that the correction recently identified by Flanagan significantly reduces but does not eliminate the neutron-star compression effect. Although results of the revised simulations show that the compression is reduced for a given total orbital angular momentum, the inner most stable circular orbit moves to closer separation distances. At these closer orbits significant compression and even collapse is still possible prior to merger for a sufficiently soft EOS. The reduced compression in the corrected simulation is consistent with other recent studies of rigid irrotational binaries in quasiequilibrium in which the compression effect is observed to be small. Another significant effect of this correction is that the derived binary orbital frequencies are now in closer agreement with post-Newtonian expectations.Comment: Submitted to Phys. Rev.

Enhancing the efficiency of formal low-cost houses by the development of a new low-cost ceiling system

Existing formal low-cost houses in South Africa have been shown to be very thermally and energy inefficient. This could be problematic for the country since the government has promised to build roughly 3 million more of these houses in the near future. Inefficiency in these houses can be effectively addressed by installing ceilings, but the cost thereof is unfortunately too high to be affordable to the applicable sector of the population. New options need to be considered to reduce costs. Research has shown that practically any material can be used as a ceiling if it provides a barrier to heat flow and eliminates infiltration. The material should ideally possess good thermal properties and comply with standard building regulations, but most importantly, it must be very cheap and easy to install. The low-cost ceiling proposed in this paper has all of these attributes, and installation thereof could result in substantial energy savings, improved indoor comfort, and a better quality of lif

Self-Generated Magnetic Fields in Galactic Cooling Flows

Interstellar magnetic fields in elliptical galaxies are assumed to have their origin in stellar fields that accompany normal mass loss from an evolving population of old stars. The seed fields are amplified by interstellar turbulence driven by stellar mass loss and supernova events. These disordered fields are further amplified by time-dependent compression in the inward moving galactic cooling flow and are expected to dominate near the galactic core. Under favorable circumstances, fields similar in strength to those observed $B \sim 1-10~(r/10~kpc)^{-1.2}\mu$G can be generated solely from these natural galactic processes. In general the interstellar field throughout elliptical galaxies is determined by the outermost regions in the interstellar gas where the turbulent dynamo process can occur. Because of the long hydrodynamic flow times in galactic cooling flows, currently observed magnetic fields may result from periods of intense turbulent field amplification that occurred in the outer galaxy in the distant past. Particularly strong fields in ellipticals may result from ancient galactic mergers or shear turbulence introduced at the boundary between the interstellar gas and ambient cluster gas.Comment: 21 pages in AASTEX LaTeX with 2 figures; accepted by Astrophysical Journa