636 research outputs found

    Matter X waves

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    We predict that an ultra-cold Bose gas in an optical lattice can give rise to a new form of condensation, namely matter X waves. These are non-spreading 3D wave-packets which reflect the symmetry of the Laplacian with a negative effective mass along the lattice direction, and are allowed to exist in the absence of any trapping potential even in the limit of non-interacting atoms. This result has also strong implications for optical propagation in periodic structuresComment: 5 pages, 2 figure

    Stochastics theory of log-periodic patterns

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    We introduce an analytical model based on birth-death clustering processes to help understanding the empirical log-periodic corrections to power-law scaling and the finite-time singularity as reported in several domains including rupture, earthquakes, world population and financial systems. In our stochastics theory log-periodicities are a consequence of transient clusters induced by an entropy-like term that may reflect the amount of cooperative information carried by the state of a large system of different species. The clustering completion rates for the system are assumed to be given by a simple linear death process. The singularity at t_{o} is derived in terms of birth-death clustering coefficients.Comment: LaTeX, 1 ps figure - To appear J. Phys. A: Math & Ge

    Making On-Demand Routing Efficient with Route-Request Aggregation

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    In theory, on-demand routing is very attractive for mobile ad hoc networks (MANET), because it induces signaling only for those destinations for which there is data traffic. However, in practice, the signaling overhead of existing on-demand routing protocols becomes excessive as the rate of topology changes increases due to mobility or other causes. We introduce the first on-demand routing approach that eliminates the main limitation of on-demand routing by aggregating route requests (RREQ) for the same destinations. The approach can be applied to any existing on-demand routing protocol, and we introduce the Ad-hoc Demand-Aggregated Routing with Adaptation (ADARA) as an example of how RREQ aggregation can be used. ADARA is compared to AODV and OLSR using discrete-event simulations, and the results show that aggregating RREQs can make on-demand routing more efficient than existing proactive or on-demand routing protocols

    Excitation Thresholds for Nonlinear Localized Modes on Lattices

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    Breathers are spatially localized and time periodic solutions of extended Hamiltonian dynamical systems. In this paper we study excitation thresholds for (nonlinearly dynamically stable) ground state breather or standing wave solutions for networks of coupled nonlinear oscillators and wave equations of nonlinear Schr\"odinger (NLS) type. Excitation thresholds are rigorously characterized by variational methods. The excitation threshold is related to the optimal (best) constant in a class of discr ete interpolation inequalities related to the Hamiltonian energy. We establish a precise connection among dd, the dimensionality of the lattice, 2σ+12\sigma+1, the degree of the nonlinearity and the existence of an excitation threshold for discrete nonlinear Schr\"odinger systems (DNLS). We prove that if σ2/d\sigma\ge 2/d, then ground state standing waves exist if and only if the total power is larger than some strictly positive threshold, νthresh(σ,d)\nu_{thresh}(\sigma, d). This proves a conjecture of Flach, Kaldko& MacKay in the context of DNLS. We also discuss upper and lower bounds for excitation thresholds for ground states of coupled systems of NLS equations, which arise in the modeling of pulse propagation in coupled arrays of optical fibers.Comment: To appear in Nonlinearit
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