Noncommutative Vortex Solitons

We consider the noncommutative Abelian-Higgs theory and investigate general static vortex configurations including recently found exact multi-vortex solutions. In particular, we prove that the self-dual BPS solutions cease to exist once the noncommutativity scale exceeds a critical value. We then study the fluctuation spectra about the static configuration and show that the exact non BPS solutions are unstable below the critical value. We have identified the tachyonic degrees as well as massless moduli degrees. We then discuss the physical meaning of the moduli degrees and construct exact time-dependent vortex configurations where each vortex moves independently. We finally give the moduli description of the vortices and show that the matrix nature of moduli coordinates naturally emerges.Comment: 22 pages, 1 figure, typos corrected, a comment on the soliton size is adde

Elliptic supertube and a Bogomol'nyi-Prasad-Sommerfield D2-brane--anti-D2-brane Pair

An exact solution, in which a D2-brane and an anti-D2-brane are connected by an elliptically tubular D2-brane, is obtained without any junction condition. The solution is shown to preserve one quarter of the supersymmetries of the type-IIA Minkowski vacuum. We show that the configuration cannot be obtained by "blowing-up" from some inhomogeneously D0-charged superstrings. The BPS bound tells us that it is rather composed of D0-charged D2-brane-anti-D2-brane pair and a strip of superstrings connecting them. We obtain the correction to the charges of the string end points in the constant magnetic background.Comment: v3. 12 pages, journal version; title changed, length trimmed to fit for Rapid Communication forma

Platelet Collapse Model of Pulsar Glitches

A platelet collapse model of starquakes is introduced. It displays self-organized criticality with a robust power-law behavior. The simulations indicate a near-constant exponent, whenever scaling is present.Comment: Figures available by sending request to Ivan Schmidt: [email protected]

A Heavenly Example of Scale Free Networks and Self-Organized Criticality

The sun provides an explosive, heavenly example of self-organized criticality. Sudden bursts of intense radiation emanate from rapid rearrangements of the magnetic field network in the corona. Avalanches are triggered by loops of flux that reconnect or snap into lower energy configurations when they are overly stressed. Our recent analysis of observational data reveals that the loops (links) and footpoints (nodes), where they attach on the photosphere, embody a scale free network. The statistics of the avalanches and of the network structure are unified through a simple dynamical model where the avalanches and network co-generate each other into a complex, critical state. This particular example points toward a general dynamical mechanism for self-generation of complex networks.Comment: Submitted to proceedings for the Latin American Workshop on Nonlinear Phenomena, Salvador, Brazil (2003

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/

Noncommutative Electrodynamics with covariant coordinates

We study Noncommutative Electrodynamics using the concept of covariant coordinates. We propose a scheme for interpreting the formalism and construct two basic examples, a constant field and a plane wave. Superposing these two, we find a modification of the dispersion relation. Our results differ from those obtained via the Seiberg-Witten map.Comment: 5 pages, published versio

Analytical treatment of critical collapse in 2+1 dimensional AdS spacetime: a toy model

We present an exact collapsing solution to 2+1 gravity with a negative cosmological constant minimally coupled to a massless scalar field, which exhibits physical properties making it a candidate critical solution. We discuss its global causal structure and its symmetries in relation with those of the corresponding continously self-similar solution derived in the $\Lambda=0$ case. Linear perturbations on this background lead to approximate black hole solutions. The critical exponent is found to be $\gamma = 2/5$.Comment: 22 pages, 6 figures. Major changes in the discussions of Sects. 2 and 5. The value of the critical exponent has been revised to \gamma = 2/

Word Processors with Line-Wrap: Cascading, Self-Organized Criticality, Random Walks, Diffusion, Predictability

We examine the line-wrap feature of text processors and show that adding characters to previously formatted lines leads to the cascading of words to subsequent lines and forms a state of self-organized criticality. We show the connection to one-dimensional random walks and diffusion problems, and we examine the predictability of catastrophic cascades.Comment: 6 pages, LaTeX with RevTeX package, 4 postscript figures appende

Complete Supersymmetric Quantum Mechanics of Magnetic Monopoles in N=4 SYM Theory

We find the most general low energy dynamics of 1/2 BPS monopoles in the N=4 supersymmetric Yang-Mills theories (SYM) when all six adjoint Higgs expectation values are turned on. When only one Higgs is turned on, the Lagrangian is purely kinetic. When all six are turned on, however, this moduli space dynamics is augmented by five independent potential terms, each in the form of half the squared norm of a Killing vector field on the moduli space. A generic stationary configuration of the monopoles can be interpreted as stable non BPS dyons, previously found as non-planar string webs connecting D3-branes. The supersymmetric extension is also found explicitly, and gives the complete quantum mechanics of monopoles in N=4 SYM theory. We explore its supersymmetry algebra.Comment: Errors in the SUSY algebra corrected. The version to appear in PR

Energy-Momentum Conservation in General Relativity

We discuss general properties of the conservation law associated with a local symmetry. Using Noether's theorem and a generalized Belinfante symmetrization procedure in 3+1 dimensions, a symmetric energy-momentum (pseudo) tensor for the gravitational Einstein-Hilbert action is derived and discussed in detail. In 2+1 dimensions, expressions are obtained for energy and angular momentum arising in the $ISO(2,1)$ gauge theoretical formulation of Einstein gravity. In addition, an expression for energy in a gauge theoretical formulation of the string-inspired 1+1 dimensional gravity is derived and compared with the ADM definition of energy.Comment: 18 pages in Plain TeX, MIT-CTP-224