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

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

Pattern generation by dissipative parametric instability

Nonlinear instabilities are responsible for spontaneous pattern formation in a vast number of natural and engineered systems, ranging from biology to galaxy buildup. We propose a new instability mechanism leading to pattern formation in spatially extended nonlinear systems, which is based on a periodic antiphase modulation of spectrally dependent losses arranged in a zigzag way: an effective filtering is imposed at symmetrically located wave numbers k and -k in alternating order. The properties of the dissipative parametric instability differ from the features of both key classical concepts of modulation instabilities, i.e., the Benjamin-Feir instability and the Faraday instabiltyity. We demonstrate how the dissipative parametric instability can lead to the formation of stable patterns in one- and two-dimensional systems. The proposed instability mechanism is generic and can naturally occur or can be implemented in various physical systems

Two dimensional modulational instability in photorefractive media

We study theoretically and experimentally the modulational instability of broad optical beams in photorefractive nonlinear media. We demonstrate the impact of the anisotropy of the nonlinearity on the growth rate of periodic perturbations. Our findings are confirmed by experimental measurements in a strontium barium niobate photorefractive crystal.Comment: 8 figure

Stopping of Charged Particles in a Magnetized Classical Plasma

The analytical and numerical investigations of the energy loss rate of the test particle in a magnetized electron plasma are developed on the basis of the Vlasov-Poisson equations, and the main results are presented. The Larmor rotation of a test particle in a magnetic field is taken into account. The analysis is based on the assumption that the energy variation of the test particle is much less than its kinetic energy. The obtained general expression for stopping power is analyzed for three cases: (i) the particle moves through a collisionless plasma in a strong homogeneous magnetic field; (ii) the fast particle moves through a magnetized collisionless plasma along the magnetic field; and (iii) the particle moves through a magnetized collisional plasma across a magnetic field. Calculations are carried out for the arbitrary test particle velocities in the first case, and for fast particles in the second and third cases. It is shown that the rate at which a fast test particle loses energy while moving across a magnetic field may be much higher than the loss in the case of motion through plasma without magnetic field.Comment: 14 pages, 3 figures, LaTe

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

A Minimal Model of Metabolism Based Chemotaxis

Since the pioneering work by Julius Adler in the 1960's, bacterial chemotaxis has been predominantly studied as metabolism-independent. All available simulation models of bacterial chemotaxis endorse this assumption. Recent studies have shown, however, that many metabolism-dependent chemotactic patterns occur in bacteria. We hereby present the simplest artificial protocell model capable of performing metabolism-based chemotaxis. The model serves as a proof of concept to show how even the simplest metabolism can sustain chemotactic patterns of varying sophistication. It also reproduces a set of phenomena that have recently attracted attention on bacterial chemotaxis and provides insights about alternative mechanisms that could instantiate them. We conclude that relaxing the metabolism-independent assumption provides important theoretical advances, forces us to rethink some established pre-conceptions and may help us better understand unexplored and poorly understood aspects of bacterial chemotaxis

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

Phytotherapeutic and naturopathic adjuvant therapies in otorhinolaryngology

Phytotherapeutic pharmaceuticals and herbal medicinal products with its roots in classical phytotherapeutic medicine have a well-established role in otolaryngological therapy, especially for diseases of the upper airways and acute and chronic infections. A thorough selection and application could mean huge benefit for the patient, in particular in cases with contraindications, chemo- and antibiotic resistance or patient request. Besides, it might spare other medications. Phytotherapeutic pharmaceuticals must fulfil the same criteria of quality, effectiveness and harmlessness of evidence-based medicine like chemical pharmaceuticals, although they are often prescribed due to its well established or traditional based use. This review focuses on phytotherapeutic therapies well established within the European Community for otolaryngologic disease patterns by referring to clinical studies or meta-analysis