Localisation of Fermions to brane: Codimension d≥2d \geq 2

We investigate $4+d$ dimensional fermionic models in which the system in codimension-$d$ supports a topologically stable solution, and in which the fermion may be localised to the brane, with power law in 'instanton' backgrounds and exponentially in 'soliton' backgrounds. When the fermions are isoscalars, the mechanism fails, while for isospinor fermions it is successful. As backgrounds we consider instantons of Yang--Mills and sigma models in even codimensions, solitons of sigma models in odd codimensions, as well as solitons of Higgs and Goldstone models in all codimensions.Comment: 20 pages latex; expande

The impact of diffusion on confined oscillated bubbly fluid

We consider the dynamics of monodisperse bubbly fluid confined by two plane solid walls and subjected to small-amplitude high-frequency transversal oscillations. The frequency these oscillations is assumed to be high in comparison with typical relaxation times for a single bubble, but comparable with the eigenfrequency of volume oscillations. A time-averaged description accounting for mutual coupling of the phases and the diffusivity of bubbles is applied. We find nonuniform steady states with the liquid quiescent on average. At relatively low frequencies accumulation of bubbles either at the walls or in planes oriented parallel to the walls is detected. These one-dimensional states are shown to be unstable. At relatively high frequencies the bubbles accumulate at the central plane and the solution is stable.Comment: 12 pages, 9 figures, submitted to Phys. Fluid

The effect of substituted benzene dicarboxylic acid linkers on the optical band gap energy and magnetic coupling in manganese trimer metal organic frameworks

We have systematically studied a series of eight metal-organic frameworks (MOFs) in which the secondary building unit is a manganese trimer cluster, and the linkers are differently substituted benzene dicarboxylic acids (BDC). The optical band gap energy of the compounds vary from 2.62 eV to 3.57 eV, and theoretical studies find that different functional groups result in new states in the conduction band, which lie in the gap and lower the optical band gap energy. The optical absorption between the filled Mn 3d states and the ligands is weak due to minimal overlap of the states, and the measured optical band gap energy is due to transitions on the BDC linker. The Mn atoms in the MOFs have local moments of 5 mu B, and selected MOFs are found to be antiferromagnetic, with weak coupling between the cluster units, and paramagnetic above 10 K

Intelligent systems in the context of surrounding environment

We investigate the behavioral patterns of a population of agents, each controlled by a simple biologically motivated neural network model, when they are set in competition against each other in the Minority Model of Challet and Zhang. We explore the effects of changing agent characteristics, demonstrating that crowding behavior takes place among agents of similar memory, and show how this allows unique `rogue' agents with higher memory values to take advantage of a majority population. We also show that agents' analytic capability is largely determined by the size of the intermediary layer of neurons. In the context of these results, we discuss the general nature of natural and artificial intelligence systems, and suggest intelligence only exists in the context of the surrounding environment (embodiment). Source code for the programs used can be found at http://neuro.webdrake.net/

The dynamics of vortices on S^2 near the Bradlow limit

The explicit solutions of the Bogomolny equations for N vortices on a sphere of radius R^2 > N are not known. In particular, this has prevented the use of the geodesic approximation to describe the low energy vortex dynamics. In this paper we introduce an approximate general solution of the equations, valid for R^2 close to N, which has many properties of the true solutions, including the same moduli space CP^N. Within the framework of the geodesic approximation, the metric on the moduli space is then computed to be proportional to the Fubini- Study metric, which leads to a complete description of the particle dynamics.Comment: 17 pages, 9 figure

Three-Wave Modulational Stability and Dark Solitons in a Quadratic Nonlinear Waveguide with Grating

We consider continuous-wave (CW) states and dark solitons (DSs) in a system of two fundamental-frequency (FF) and one second-harmonic (SH) waves in a planar waveguide with the quadratic nonlinearity, the FF components being linearly coupled by resonant reflections on the Bragg grating. We demonstrate that, in contrast with the usual situation in quadratic spatial-domain models, CW states with the phase shift between the FF and SH components are modulationally stable in a broad parameter region in this system, provided that the CW wavenumber does not belong to the system's spectral gap. Stationary fundamental DSs are found numerically, and are also constructed by means of a specially devised analytical approximation. Bound states of two and three DSs are found too. The fundamental DSs and two-solitons bound states are stable in all the cases when the CW background is stable, which is shown by dint of calculation of the corresponding eigenvalues, and verified in direct simulations. Tilted DSs are found too. They attain a maximum contrast at a finite value of the tilt, that does not depend on the phase mismatch. At a maximum value of the tilt, which grows with the mismatch, the DS merges into the CW background. Interactions between the tilted solitons are shown to be completely elastic.Comment: 10 pages, 12 figures; Journal of Optics A, in pres

Evolution and anti-evolution in a minimal stock market model

We present a novel microscopic stock market model consisting of a large number of random agents modeling traders in a market. Each agent is characterized by a set of parameters that serve to make iterated predictions of two successive returns. The future price is determined according to the offer and the demand of all agents. The system evolves by redistributing the capital among the agents in each trading cycle. Without noise the dynamics of this system is nearly regular and thereby fails to reproduce the stochastic return fluctuations observed in real markets. However, when in each cycle a small amount of noise is introduced we find the typical features of real financial time series like fat-tails of the return distribution and large temporal correlations in the volatility without significant correlations in the price returns. Introducing the noise by an evolutionary process leads to different scalings of the return distributions that depend on the definition of fitness. Because our realistic model has only very few parameters, and the results appear to be robust with respect to the noise level and the number of agents we expect that our framework may serve as new paradigm for modeling self generated return fluctuations in markets.Comment: 13 pages, 5 figure

Symmetric and asymmetric solitons in linearly coupled Bose-Einstein condensates trapped in optical lattices

We study spontaneous symmetry breaking in a system of two parallel quasi-one-dimensional traps, equipped with optical lattices (OLs) and filled with a Bose-Einstein condensate (BEC). The cores are linearly coupled by tunneling. Analysis of the corresponding system of linearly coupled Gross-Pitaevskii equations (GPEs) reveals that spectral bandgaps of the single GPE split into subgaps. Symmetry breaking in two-component BEC solitons is studied in cases of the attractive (AA) and repulsive (RR) nonlinearity in both traps; the mixed situation, with repulsion in one trap and attraction in the other (RA), is considered too. In all the cases, stable asymmetric solitons are found, bifurcating from symmetric or antisymmetric ones (and destabilizing them), in the AA and RR systems, respectively. In either case, bi-stability is predicted, with a nonbifurcating stable branch, either antisymmetric or symmetric, coexisting with asymmetric ones. Solitons destabilized by the bifurcation tend to rearrange themselves into their stable asymmetric counterparts. The impact of a phase mismatch, between the OLs in the two cores is also studied. Also considered is a related model, for a binary BEC in a single-core trap with the OL, assuming that the two species (representing different spin states of the same atom) are coupled by linear interconversion. In that case, the symmetry-breaking bifurcations in the AA and RR models switch their character, if the inter-species nonlinear interaction becomes stronger than the intra-species nonlinearity.Comment: 21 pages + 24 figs, accepted to Phys. Rev.