Avalanches in the Weakly Driven Frenkel-Kontorova Model

A damped chain of particles with harmonic nearest-neighbor interactions in a spatially periodic, piecewise harmonic potential (Frenkel-Kontorova model) is studied numerically. One end of the chain is pulled slowly which acts as a weak driving mechanism. The numerical study was performed in the limit of infinitely weak driving. The model exhibits avalanches starting at the pulled end of the chain. The dynamics of the avalanches and their size and strength distributions are studied in detail. The behavior depends on the value of the damping constant. For moderate values a erratic sequence of avalanches of all sizes occurs. The avalanche distributions are power-laws which is a key feature of self-organized criticality (SOC). It will be shown that the system selects a state where perturbations are just able to propagate through the whole system. For strong damping a regular behavior occurs where a sequence of states reappears periodically but shifted by an integer multiple of the period of the external potential. There is a broad transition regime between regular and irregular behavior, which is characterized by multistability between regular and irregular behavior. The avalanches are build up by sound waves and shock waves. Shock waves can turn their direction of propagation, or they can split into two pulses propagating in opposite directions leading to transient spatio-temporal chaos. PACS numbers: 05.70.Ln,05.50.+q,46.10.+zComment: 33 pages (RevTex), 15 Figures (available on request), appears in Phys. Rev.

Counting Supertubes

The quantum states of the supertube are counted by directly quantizing the linearized Born-Infeld action near the round tube. The result is an entropy $S = 2\pi \sqrt{2 (Q_{D0}Q_{F1}-J)}$, in accord with conjectures in the literature. As a result, supertubes may be the generic D0-F1 bound state. Our approach also shows directly that supertubes are marginal bound states with a discrete spectrum. We also discuss the relation to recent suggestions of Mathur et al involving three-charge black holes.Comment: 15 pages, v2: reference corrected; v3: few corrections and explicit derivation of a relation are added to appendix

Unitary Quantum Physics with Time-Space Noncommutativity

In this work quantum physics in noncommutative spacetime is developed. It is based on the work of Doplicher et al. which allows for time-space noncommutativity. The Moyal plane is treated in detail. In the context of noncommutative quantum mechanics, some important points are explored, such as the formal construction of the theory, symmetries, causality, simultaneity and observables. The dynamics generated by a noncommutative Schrodinger equation is studied. We prove in particular the following: suppose the Hamiltonian of a quantum mechanical particle on spacetime has no explicit time dependence, and the spatial coordinates commute in its noncommutative form (the only noncommutativity being between time and a space coordinate). Then the commutative and noncommutative versions of the Hamiltonian have identical spectra.Comment: 18 pages, published versio

Boundary States for Supertubes in Flat Spacetime and Godel Universe

We construct boundary states for supertubes in the flat spacetime. The T-dual objects of supertubes are moving spiral D1-branes (D-helices). Since we can obtain these D-helices from the usual D1-branes via null deformation, we can construct the boundary states for these moving D-helices in the covariant formalism. Using these boundary states, we calculate the vacuum amplitude between two supertubes in the closed string channel and read the open string spectrum via the open closed duality. We find there are critical values of the energy for on-shell open strings on the supertubes due to the non-trivial stringy correction. We also consider supertubes in the type IIA Godel universe in order to use them as probes of closed timelike curves. This universe is the T-dual of the maximally supersymmetric type IIB PP-wave background. Since the null deformations of D-branes are also allowed in this PP-wave, we can construct the boundary states for supertubes in the type IIA Godel universe in the same way. We obtain the open string spectrum on the supertube from the vacuum amplitude between supertubes. As a consequence, we find that the tachyonic instability of open strings on the supertube, which is the signal of closed time like curves, disappears due to the stringy correction.Comment: 26 pages, 3 figures, v2: explanations added, references added, v3: explanations adde

AdS_3 OM theory and the self-dual string or Membranes ending on the Five-brane

We describe properties of the M-theory five-brane containing $Q$ coincident self-dual strings on its worldvolume. This is the five-brane description of Q membranes ending on the five-brane. In particular, we consider a Maldacena-like low energy limit in the six-dimensional worldvolume which yields a near `horizon' description of the self-dual string using light open membranes, i.e. OM theory, in an AdS_3 x S^3 geometry.Comment: 13 pages, latex, v2: corrected open membrane metric prefactor + typo

Avalanches and the Renormalization Group for Pinned Charge-Density Waves

The critical behavior of charge-density waves (CDWs) in the pinned phase is studied for applied fields increasing toward the threshold field, using recently developed renormalization group techniques and simulations of automaton models. Despite the existence of many metastable states in the pinned state of the CDW, the renormalization group treatment can be used successfully to find the divergences in the polarization and the correlation length, and, to first order in an $\epsilon = 4-d$ expansion, the diverging time scale. The automaton models studied are a charge-density wave model and a ``sandpile'' model with periodic boundary conditions; these models are found to have the same critical behavior, associated with diverging avalanche sizes. The numerical results for the polarization and the diverging length and time scales in dimensions $d=2,3$ are in agreement with the analytical treatment. These results clarify the connections between the behaviour above and below threshold: the characteristic correlation lengths on both sides of the transition diverge with different exponents. The scaling of the distribution of avalanches on the approach to threshold is found to be different for automaton and continuous-variable models.Comment: 29 pages, 11 postscript figures included, REVTEX v3.0 (dvi and PS files also available by anonymous ftp from external.nj.nec.com in directory /pub/alan/cdwfigs

Orbiting Membranes in M-theory on AdS_7 x S^4 Background

We study classical solutions describing rotating and boosted membranes on AdS_7 x S^4 background in M-theory. We find the dependence of the energy on the spin and R-charge of these solutions. In the flat space limit we get E ~ S^{2/3}, while for AdS at leading order E-S grows as S^{1/3}. The membranes on AdS_4 x S^7 background have briefly been studied as well.Comment: 13 pages, latex, v2: a note and refs. added, some typos correcte

AdS and pp-wave D-particle superalgebras

We derive anticommutators of supercharges with a brane charge for a D-particle in AdS(2) x S(2) and pp-wave backgrounds. A coset GL(2|2)/(GL(1))^4 and its Penrose limit are used with the supermatrix-valued coordinates for the AdS and the pp-wave spaces respectively. The brane charges have position dependence, and can be absorbed into bosonic generators by shift of momenta which results in closure of the superalgebras.Comment: 15 page

Steady-State Dynamics of the Forest Fire Model on Complex Networks

Many sociological networks, as well as biological and technological ones, can be represented in terms of complex networks with a heterogeneous connectivity pattern. Dynamical processes taking place on top of them can be very much influenced by this topological fact. In this paper we consider a paradigmatic model of non-equilibrium dynamics, namely the forest fire model, whose relevance lies in its capacity to represent several epidemic processes in a general parametrization. We study the behavior of this model in complex networks by developing the corresponding heterogeneous mean-field theory and solving it in its steady state. We provide exact and approximate expressions for homogeneous networks and several instances of heterogeneous networks. A comparison of our analytical results with extensive numerical simulations allows to draw the region of the parameter space in which heterogeneous mean-field theory provides an accurate description of the dynamics, and enlights the limits of validity of the mean-field theory in situations where dynamical correlations become important.Comment: 13 pages, 9 figure

Magnetic Reversal on Vicinal Surfaces

We present a theoretical study of in-plane magnetization reversal for vicinal ultrathin films using a one-dimensional micromagnetic model with nearest-neighbor exchange, four-fold anisotropy at all sites, and two-fold anisotropy at step edges. A detailed "phase diagram" is presented that catalogs the possible shapes of hysteresis loops and reversal mechanisms as a function of step anisotropy strength and vicinal terrace length. The steps generically nucleate magnetization reversal and pin the motion of domain walls. No sharp transition separates the cases of reversal by coherent rotation and reversal by depinning of a ninety degree domain wall from the steps. Comparison to experiment is made when appropriate.Comment: 12 pages, 8 figure