Introduction to bifurcation-theory

The theory of bifurcation from equilibria based on center-manifold reductio, and Poincare-Birkhoff normal forms is reviewed at an introductory level. Both differential equations and maps are discussed, and recent results explaining the symmetry of the normal form are derived. The emphasis is on the simplest generic bifurcations in one-parameter systems. Two applications are developed in detail: a Hopf bifurcation occurring in a model of three-wave mode coupling and steady-state bifurcations occurring in the real Landau-Ginzburg equation. The former provides an example of the importance of degenerate bifurcations in problems with more than one parameter and the latter illustrates new effects introduced into a bifurcation problem by a continuous symmetry.Physic

Homoclinic snaking in bounded domains

Homoclinic snaking is a term used to describe the back and forth oscillation of a branch of time-independent spatially localized states in a bistable, spatially reversible system as the localized structure grows in length by repeatedly adding rolls on either side. On the real line this process continues forever. In finite domains snaking terminates once the domain is filled but the details of how this occurs depend critically on the choice of boundary conditions. With periodic boundary conditions the snaking branches terminate on a branch of spatially periodic states. However, with non-Neumann boundary conditions they turn continuously into a large amplitude filling state that replaces the periodic state. This behavior, shown here in detail for the Swift-Hohenberg equation, explains the phenomenon of “snaking without bistability”, recently observed in simulations of binary fluid convection by Mercader, Batiste, Alonso and Knobloch (preprint)

Radio Continuum Study of Supernova Remnants in the Large Magellanic Cloud - SNR J0519-6926

We present the results of new high resolution ATCA observations of SNR J0519-6926. We found that this SNR exhibits a typical "horseshoe" appearance with alpha = -0.55 +- 0.08 and D=28+-1 pc. No polarization (or magnetic fields) are detected to a level of 1%. This is probably due to a relatively poor sampling of the uv plane caused be observing in "snap-shot" mode.Comment: 6 pages 4 figures, to be published in Serbian Astronomical Journa

Sexual negotiation in the AIDS era: negotiated safety revisited

Objective: To test the safety of the 'negotiated safety' strategy - the strategy of dispensing with condoms within HIV-seronegative concordant regular sexual relationships under certain conditions. Method: Data from a recently recruited cohort of homosexually active men (Sydney Men and Sexual Health cohort, n = 1037) are used to revisit negotiated safety. The men were surveyed using a structured questionnaire and questions addressing their sexual relationships and practice, their own and their regular partner's serostatus, agreements entered into by the men concerning sexual practice within and outside their regular relationship, and contextual and demographic variables. Results: The findings indicate that a significant number of men used negotiated safety as an HIV prevention strategy. In the 6 months prior to interview, of the 181 men in seroconcordant HIV-negative regular relationships, 62% had engaged in unprotected anal intercourse within their relationship, and 91% (165 men) had not engaged in unprotected anal intercourse outside their relationship. Of these 165 men, 82% had negotiated agreements about sex outside their relationship. The safety of negotiation was dependent not only on seroconcordance but also on the presence of an agreement; 82% of the men who had not engaged in unprotected anal intercourse outside their regular relationship had entered into an agreement with their partner, whereas only 56% of those who had engaged in unprotected anal intercourse had an agreement. The safety of negotiation was also related to the nature of the safety agreement reached between the men and on the acceptability of condoms. Agreements between HIV-negative seroconcordant regular partners prohibiting anal intercourse with casual partners or any form of sex with a casual partner were typically complied with, and men who had such negotiated agreements were at low risk of HIV infection. Conclusions: The adoption of the strategy of negotiated safety among men in HIV-seronegative regular relationships may help such men sustain the safety of their sexual practice

Radio-Continuum Observations Of Small, Radially Polarised Supernova Remnant J0519-6902 In The Large Magellanic Cloud

We report on new Australian Telescope Compact Array (ATCA) observations of SNR J0519-6902. The Supernova Remnant (SNR) is small in size (~8 pc) and exhibits a typical SNR spectrum of alpha = -0.53 +- 0.07, with steeper spectral indices found towards the northern limb of the remnant. SNR J0519-6902 contains a low level of radially orientated polarisation at wavelengths of 3 & 6 cm, which is characteristic of younger SNRs. A fairly strong magnetic field was estimated of ~171 microG. The remnant appears to be the result of a typical Type Ia supernovae, sharing many properties as another small and young Type Ia LMC SNR, J0509-6731.Comment: 10 pages 7 figures, submitted to Serbian Astronomical Journa

SMC SMP 24: A newly radio-detected planetary nebula in the small magellanic cloud

In this paper we report new radio-continuum detection of an extragalactic PN: SMC SMP 24. We show the radio-continuum image of this PN and present the measured radio data. The newly reduced radio observations are consistent with the multi-wavelength data and derived parameters found in the literature. SMC SMP 24 appear to be a young and compact PN, optically thick at frequencies below 2 GHz.Comment: accepted for publication in Serbian Astronomical Journa

Multifrequency Observations of One of the Largest Supernova Remnants in the Local Group of Galaxies, LMC - SNR J0450-709

We present the results of new Australia Telescope Compact Array (ATCA) observations of one of the largest supernova remnants, SNR J0450-709, in the Local Group of galaxies. We found that this Large Magellanic Cloud (LMC) ob ject exhibits a typical morphology of an old supernova remnant (SNR) with diameter D=102x75+-1 pc and radio spectral index alpha=-0.43+-0.06. Regions of high polarisation were detected with peak value of ~40%.Comment: 7 pages, 4 figures, accepted for publication in Serbian Astronomical Journa

Scaling and singularities in the entrainment of globally-coupled oscillators

The onset of collective behavior in a population of globally coupled oscillators with randomly distributed frequencies is studied for phase dynamical models with arbitrary coupling. The population is described by a Fokker-Planck equation for the distribution of phases which includes the diffusive effect of noise in the oscillator frequencies. The bifurcation from the phase-incoherent state is analyzed using amplitude equations for the unstable modes with particular attention to the dependence of the nonlinearly saturated mode $|\alpha_\infty|$ on the linear growth rate $\gamma$. In general we find $|\alpha_\infty|\sim \sqrt{\gamma(\gamma+l^2D)}$ where $D$ is the diffusion coefficient and $l$ is the mode number of the unstable mode. The unusual $(\gamma+l^2D)$ factor arises from a singularity in the cubic term of the amplitude equation.Comment: 11 pages (Revtex); paper submitted to Phys. Rev. Let

Reference manual for the Langley Research Center flight simulation computing system

The researchers at the Langley Research Center Flight Simulation Computing System are provided with an advanced real-time digital simulation capability. This capability is controlled at the user interface level by the Real Time Simulation Supervisor. The Supervisor is a group of subprograms loaded with a simulation application program. The Supervisor provides the interface between the application program and the operating system, and coordinates input and output to and from the simulation hardware. The Supervisor also performs various utility functions as required by a simulation application program