Discrete instability in nonlinear lattices

The discrete multiscale analysis for boundary value problems in nonlinear discrete systems leads to a first order discrete modulational instability above a threshold amplitude for wave numbers beyond the zero of group velocity dispersion. Applied to the electrical lattice [Phys. Rev. E, 51 (1995) 6127 ], this acurately explains the experimental instability at wave numbers beyond 1.25 . The theory is also briefly discussed for sine-Gordon and Toda lattices.Comment: 1 figure, revtex, published: Phys. Rev. Lett. 83 (1999) 232

Fusion in the entwined category of Yetter--Drinfeld modules of a rank-1 Nichols algebra

We rederive a popular nonsemisimple fusion algebra in the braided context, from a Nichols algebra. Together with the decomposition that we find for the product of simple Yetter-Drinfeld modules, this strongly suggests that the relevant Nichols algebra furnishes an equivalence with the triplet W-algebra in the (p,1) logarithmic models of conformal field theory. For this, the category of Yetter-Drinfeld modules is to be regarded as an \textit{entwined} category (the one with monodromy, but not with braiding).Comment: 36 pages, amsart++, times, xy. V3: references added, an unnecessary assumption removed, plus some minor change

Fourier transform and the Verlinde formula for the quantum double of a finite group

A Fourier transform S is defined for the quantum double D(G) of a finite group G. Acting on characters of D(G), S and the central ribbon element of D(G) generate a unitary matrix representation of the group SL(2,Z). The characters form a ring over the integers under both the algebra multiplication and its dual, with the latter encoding the fusion rules of D(G). The Fourier transform relates the two ring structures. We use this to give a particularly short proof of the Verlinde formula for the fusion coefficients.Comment: 15 pages, small errors corrected and references added, version to appear in Journal of Physics

Removing Orbital Debris with Lasers

Orbital debris in low Earth orbit (LEO) are now sufficiently dense that the use of LEO space is threatened by runaway collisional cascading. A problem predicted more than thirty years ago, the threat from debris larger than about 1 cm demands serious attention. A promising proposed solution uses a high power pulsed laser system on the Earth to make plasma jets on the objects, slowing them slightly, and causing them to re-enter and burn up in the atmosphere. In this paper, we reassess this approach in light of recent advances in low-cost, light-weight modular design for large mirrors, calculations of laser-induced orbit changes and in design of repetitive, multi-kilojoule lasers, that build on inertial fusion research. These advances now suggest that laser orbital debris removal (LODR) is the most cost-effective way to mitigate the debris problem. No other solutions have been proposed that address the whole problem of large and small debris. A LODR system will have multiple uses beyond debris removal. International cooperation will be essential for building and operating such a system.Comment: 37 pages, 15 figures, in preparation for submission to Advances in Space Researc

Modulational instability of bright solitary waves in incoherently coupled nonlinear Schr\"odinger equations

We present a detailed analysis of the modulational instability (MI) of ground-state bright solitary solutions of two incoherently coupled nonlinear Schr\"odinger equations. Varying the relative strength of cross-phase and self-phase effects we show existence and origin of four branches of MI of the two-wave solitary solutions. We give a physical interpretation of our results in terms of the group velocity dispersion (GVD) induced polarization dynamics of spatial solitary waves. In particular, we show that in media with normal GVD spatial symmetry breaking changes to polarization symmetry breaking when the relative strength of the cross-phase modulation exceeds a certain threshold value. The analytical and numerical stability analyses are fully supported by an extensive series of numerical simulations of the full model.Comment: Physical Review E, July, 199

Ultrashort filaments of light in weakly-ionized, optically-transparent media

Modern laser sources nowadays deliver ultrashort light pulses reaching few cycles in duration, high energies beyond the Joule level and peak powers exceeding several terawatt (TW). When such pulses propagate through optically-transparent media, they first self-focus in space and grow in intensity, until they generate a tenuous plasma by photo-ionization. For free electron densities and beam intensities below their breakdown limits, these pulses evolve as self-guided objects, resulting from successive equilibria between the Kerr focusing process, the chromatic dispersion of the medium, and the defocusing action of the electron plasma. Discovered one decade ago, this self-channeling mechanism reveals a new physics, widely extending the frontiers of nonlinear optics. Implications include long-distance propagation of TW beams in the atmosphere, supercontinuum emission, pulse shortening as well as high-order harmonic generation. This review presents the landmarks of the 10-odd-year progress in this field. Particular emphasis is laid to the theoretical modeling of the propagation equations, whose physical ingredients are discussed from numerical simulations. Differences between femtosecond pulses propagating in gaseous or condensed materials are underlined. Attention is also paid to the multifilamentation instability of broad, powerful beams, breaking up the energy distribution into small-scale cells along the optical path. The robustness of the resulting filaments in adverse weathers, their large conical emission exploited for multipollutant remote sensing, nonlinear spectroscopy, and the possibility to guide electric discharges in air are finally addressed on the basis of experimental results.Comment: 50 pages, 38 figure

Ret is essential to mediate GDNF’s neuroprotective and neuroregenerative effect in a Parkinson disease mouse model

Glial cell line-derived neurotrophic factor (GDNF) is a potent survival and regeneration-promoting factor for dopaminergic neurons in cell and animal models of Parkinson disease (PD). GDNF is currently tested in clinical trials on PD patients with so far inconclusive results. The receptor tyrosine kinase Ret is the canonical GDNF receptor, but several alternative GDNF receptors have been proposed, raising the question of which signaling receptor mediates here the beneficial GDNF effects. To address this question we overexpressed GDNF in the striatum of mice deficient for Ret in dopaminergic neurons and subsequently challenged these mice with 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine (MPTP). Strikingly, in this established PD mouse model, the absence of Ret completely abolished GDNF’s neuroprotective and regenerative effect on the midbrain dopaminergic system. This establishes Ret signaling as absolutely required for GDNF’s effects to prevent and compensate dopaminergic system degeneration and suggests Ret activation as the primary target of GDNF therapy in PD

Repeated administration of the GABAB receptor positive modulator BHF177 decreased nicotine self-administration, and acute administration decreased cue-induced reinstatement of nicotine seeking in rats

Abstract: Rationale $\gamma$-Aminobutyric acid (GABA) is the major inhibitory neurotransmitter in the brain and is implicated in the modulation of central reward processes. Acute or chronic administration of GABA$_B$ receptor agonists or positive modulators decreased self-administration of various drugs of abuse. Furthermore, GABA$_B$ receptor agonists inhibited cue-induced reinstatement of nicotine- and cocaine-seeking behavior. Because of their fewer adverse side effects compared with GABA$_B$ receptor agonists, GABA$_B$ receptor positive modulators are potentially improved therapeutic compounds for the treatment of drug dependence compared with agonists. Objectives and methods: We examined whether the acute effects of the GABA$_B$ receptor positive modulator N-[(1R,2R,4S)-bicyclo[2.2.1]hept-2-yl]-2-methyl-5-[4-(trifluoromethyl)phenyl]-4-pyrimidinamine (BHF177) on nicotine self- administration and food-maintained responding under a fixed-ratio 5 schedule of reinforcement were maintained after repeated administration. The effects of acute BHF177 administration on cue-induced nicotine- and food-seeking behavior, a putative animal model of relapse, were also examined. Results: Repeated administration of BHF177 for 14 days decreased nicotine self-administration, with small tolerance observed during the last 7 days of treatment, whereas BHF177 minimally affected food-maintained responding. Acute BHF177 administration dose-dependently blocked cue-induced reinstatement of nicotine-, but not food-, seeking behavior after a 10-day extinction period. Conclusions: These results showed that BHF177 selectively blocked nicotine self-administration and prevented cueinduced reinstatement of nicotine seeking, with minimal effects on responding for food and no effect on cue-induced reinstatement of food seeking. Thus, GABA$_B$ receptor positive modulators could be useful therapeutics for the treatment of different aspects of nicotine dependence by facilitating smoking cessation by decreasing nicotine intake and preventing relapse to smoking in humans