The uncoupling limit of identical Hopf bifurcations with an application to perceptual bistability

We study the dynamics arising when two identical oscillators are coupled near a Hopf bifurcation where we assume a parameter $\epsilon$ uncouples the system at $\epsilon=0$. Using a normal form for $N=2$ identical systems undergoing Hopf bifurcation, we explore the dynamical properties. Matching the normal form coefficients to a coupled Wilson-Cowan oscillator network gives an understanding of different types of behaviour that arise in a model of perceptual bistability. Notably, we find bistability between in-phase and anti-phase solutions that demonstrates the feasibility for synchronisation to act as the mechanism by which periodic inputs can be segregated (rather than via strong inhibitory coupling, as in existing models). Using numerical continuation we confirm our theoretical analysis for small coupling strength and explore the bifurcation diagrams for large coupling strength, where the normal form approximation breaks down

Probing for Instanton Quarks with epsilon-Cooling

We use epsilon-cooling, adjusting at will the order a^2 corrections to the lattice action, to study the parameter space of instantons in the background of non-trivial holonomy and to determine the presence and nature of constituents with fractional topological charge at finite and zero temperature for SU(2). As an additional tool, zero temperature configurations were generated from those at finite temperature with well-separated constituents. This is achieved by "adiabatically" adjusting the anisotropic coupling used to implement finite temperature on a symmetric lattice. The action and topological charge density, as well as the Polyakov loop and chiral zero-modes are used to analyse these configurations. We also show how cooling histories themselves can reveal the presence of constituents with fractional topological charge. We comment on the interpretation of recent fermion zero-mode studies for thermalized ensembles at small temperatures.Comment: 26 pages, 14 figures in 33 part

Instanton classical solutions of SU(3) fixed point actions on open lattices

We construct instanton-like classical solutions of the fixed point action of a suitable renormalization group transformation for the SU(3) lattice gauge theory. The problem of the non-existence of one-instantons on a lattice with periodic boundary conditions is circumvented by working on open lattices. We consider instanton solutions for values of the size (0.6-1.9 in lattice units) which are relevant when studying the SU(3) topology on coarse lattices using fixed point actions. We show how these instanton configurations on open lattices can be taken into account when determining a few-couplings parametrization of the fixed point action.Comment: 23 pages, LaTeX, 4 eps figures, epsfig.sty; some comments adde

Diffusivity and Weak Clustering in a Quasi 2D Granular Gas

We present results from a detailed simulation of a quasi-2D dissipative granular gas, kept in a non-condensed steady state via vertical shaking over a rough substrate. This gas shows a weak power-law decay in the tails of its Pair Distribution Functions (PDF's), indicating fractality and therefore a tendency to form clusters over several size scales. This clustering depends monotonically on the dissipation coefficient, and disappears when the sphere-sphere collisions are conservative. Clustering is also sensitive to the packing fraction. This gas also displays the standard nonequilibrium characteristics of similar systems, including non-Maxwellian velocity distributions. The diffusion coefficients are calculated over all the conditions of the simulations, and it is found that diluted gases are more diffusive for smaller restitution coefficients.Comment: 14 pages, 11 figure

Submillimeter H2O masers in water-fountain nebulae

We report the first detection of submillimeter water maser emission toward water-fountain nebulae, which are post-AGB stars that exhibit high-velocity water masers. Using APEX we found emission in the ortho-H2O (10_29-9_36) transition at 321.226 GHz toward three sources: IRAS 15445-5449, IRAS 18043-2116 and IRAS 18286-0959. Similarly to the 22 GHz masers, the submillimeter water masers are expanding with a velocity larger than that of the OH masers, suggesting that these masers also originate in fast bipolar outflows. In IRAS 18043-2116 and IRAS 18286-0959, which figure among the sources with the fastest water masers, the velocity range of the 321 GHz masers coincides with that of the 22 GHz masers, indicating that they likely coexist. Towards IRAS 15445-5449 the submillimeter masers appear in a different velocity range, indicating that they are tracing different regions. The intensity of the submillimeter masers is comparable to that of the 22 GHz masers, implying that the kinetic temperature of the region where the masers originate should be Tk > 1000 K. We propose that the passage of two shocks through the same gas can create the conditions necessary to explain the presence of strong high-velocity 321 GHz masers coexisting with the 22 GHz masers in the same region.Comment: 4 pages, 1 figure. Accepted for publication in A&A Letter

Collective motions in globally coupled tent maps with stochastic updating

We study a generalization of globally coupled maps, where the elements are updated with probability $p$. When $p$ is below a threshold $p_c$, the collective motion vanishes and the system is the stationary state in the large size limit. We present the linear stability analysis.Comment: 6 pages including 5 figure

The role of stellar radial motions in shaping galaxy surface brightness profiles

Aims. The physics driving features such as breaks observed in galaxy surface brightness (SB) profiles remains contentious. Here, we assess the importance of stellar radial motions in shaping their characteristics. Methods. We use the simulated Milky Way-mass cosmological discs from the Ramses Disc Environment Study (RaDES) to characterise the radial redistribution of stars in galaxies displaying type-I (pure exponentials), II (downbending), and III (upbending) SB profiles. We compare radial profiles of the mass fractions and the velocity dispersions of different sub-populations of stars according to their birth and current location. Results. Radial redistribution of stars is important in all galaxies regardless of their light profiles. Type-II breaks seem to be a consequence of the combined effects of outward-moving and accreted stars. The former produce shallower inner profiles (lack of stars in the inner disc) and accumulate material around the break radius and beyond, strengthening the break; the latter can weaken or even convert the break into a pure exponential. Further accretion from satellites can concentrate material in the outermost parts, leading to type-III breaks that can coexist with type-II breaks, but situated further out. Type-III galaxies would be the result of an important radial redistribution of material throughout the entire disc, as well as a concentration of accreted material in the outskirts. In addition, type-III galaxies display the most efficient radial redistribution and the largest number of accreted stars, followed by type-I and II systems, suggesting that type-I galaxies may be an intermediate case between types-II and III. In general, the velocity dispersion profiles of all galaxies tend to flatten or even increase around the locations where the breaks are found. The age and metallicity profiles are also affected, exhibiting different inner gradients depending on their SB profile, being steeper in the case of type-II systems (as found observationally). The steep type-II profiles might be inherent to their formation rather than acquired via radial redistribution

Dynamical Critical Phenomena and Large Scale Structure of the Universe: the Power Spectrum for Density Fluctuations

As is well known, structure formation in the Universe at times after decoupling can be described by hydrodynamic equations. These are shown here to be equivalent to a generalization of the stochastic Kardar--Parisi--Zhang equation with time-- dependent viscosity in epochs of dissipation. As a consequence of the Dynamical Critical Scaling induced by noise and fluctuations, these equations describe the fractal behavior (with a scale dependent fractal dimension) observed at the smaller scales for the galaxy--to--galaxy correlation function and $also$ the Harrison--Zel'dovich spectrum at decoupling. By a Renormalization Group calculation of the two--point correlation function between galaxies in the presence of (i) the expansion of the Universe and (ii) non--equilibrium, we can account, from first principles, for the main features of the observed shape of the power spectrum.Comment: 13 pages with 2 encapsulated PostScript figures included, gzipped tar forma