Scattering of dislocated wavefronts by vertical vorticity and the Aharonov-Bohm effect II: Dispersive waves

Previous results on the scattering of surface waves by vertical vorticity on shallow water are generalized to the case of dispersive water waves. Dispersion effects are treated perturbatively around the shallow water limit, to first order in the ratio of depth to wavelength. The dislocation of the incident wavefront, analogous to the Aharonov-Bohm effect, is still observed. At short wavelengths the scattering is qualitatively similar to the nondispersive case. At moderate wavelengths, however, there are two markedly different scattering regimes according to wether the capillary length is smaller or larger than $\sqrt{3}$ times depth. The dislocation is characterized by a parameter that depends both on phase and group velocity. The validity range of the calculation is the same as in the shallow water case: wavelengths small compared to vortex radius, and low Mach number. The implications of these limitations are carefully considered.Comment: 30 pages, 11 figure

Fedosov's formal symplectic groupoids and contravariant connections

Using Fedosov's approach we give a geometric construction of a formal symplectic groupoid over any Poisson manifold endowed with a torsion-free Poisson contravariant connection. In the case of Kaehler-Poisson manifolds this construction provides, in particular, the formal symplectic groupoids with separation of variables. We show that the dual of a semisimple Lie algebra does not admit torsion-free Poisson contravariant connections.Comment: 29 page

Variations de tolérance aux pesticides agricoles des diatomées périphytiques dans une rivière contaminée : une analyse de l'échelle des communautés à celle des populations

3rd International Conference on EnvironmentalManagement, Engineering, Planning and Economics (CEMEPE 2011) & SECOTOX Conference, Skiathos, GRC, 19-/06/2011 - 24/06/2011International audiencePeriphytic diatoms are an important phototrophic component of river biofilm and are used in situ for the bioindication of pollution as well as in laboratory ecotoxicological tests to assess the toxicity of contaminants. In spring 2009, phototrophic biofilm samples composed mostly of diatoms were collected in a small river and their sensitivity to the herbicide diuron was estimated via photosynthesis bioassays. A large difference in tolerance to diuron was demonstrated between two periphytic communities from an upstream unpolluted site and a downstream site subjected to high seasonal contamination by pesticides. The comparison of diatom community structure between sites revealed important variations of the relative abundance of some species which could explain this difference. Consequently, some of these species were isolated from the river in autumn when toxic pressure was low, and kept in culture for more than six months in uncontaminated water. Acute toxicity tests of diuron based on growth inhibition were then performed on each species. Surprisingly the sensitivities of the species as estimated by EC50 were almost the same. However two strains of another species that could be isolated from each site of the river showed significant differences in tolerance to diuron and copper, another contaminant of the river. These results suggest the importance of adaptation at the intraspecific level in the induction of periphytic community tolerance to toxicants and the probably low sensitivity of bioindication methods to assess river contaminations

Adiabatic times for Markov chains and applications

We state and prove a generalized adiabatic theorem for Markov chains and provide examples and applications related to Glauber dynamics of Ising model over Z^d/nZ^d. The theorems derived in this paper describe a type of adiabatic dynamics for l^1(R_+^n) norm preserving, time inhomogeneous Markov transformations, while quantum adiabatic theorems deal with l^2(C^n) norm preserving ones, i.e. gradually changing unitary dynamics in C^n

Formal symplectic groupoid of a deformation quantization

We give a self-contained algebraic description of a formal symplectic groupoid over a Poisson manifold M. To each natural star product on M we then associate a canonical formal symplectic groupoid over M. Finally, we construct a unique formal symplectic groupoid `with separation of variables' over an arbitrary Kaehler-Poisson manifold.Comment: 41 page, Lemma 13, several typos and notations correcte

Integration of Human Walking Gyroscopic Data Using Empirical Mode Decomposition

The present study was aimed at evaluating the Empirical Mode Decomposition (EMD) method to estimate the 3D orientation of the lower trunk during walking using the angular velocity signals generated by a wearable inertial measurement unit (IMU) and notably flawed by drift. The IMU was mounted on the lower trunk (L4-L5) with its active axes aligned with the relevant anatomical axes. The proposed method performs an offline analysis, but has the advantage of not requiring any parameter tuning. The method was validated in two groups of 15 subjects, one during overground walking, with 180° turns, and the other during treadmill walking, both for steady-state and transient speeds, using stereophotogrammetric data. Comparative analysis of the results showed that the IMU/EMD method is able to successfully detrend the integrated angular velocities and estimate lateral bending, flexion-extension as well as axial rotations of the lower trunk during walking with RMS errors of 1 deg for straight walking and lower than 2.5 deg for walking with turns

Lagrangian subcategories and braided tensor equivalences of twisted quantum doubles of finite groups

We classify Lagrangian subcategories of the representation category of a twisted quantum double of a finite group. In view of results of 0704.0195v2 this gives a complete description of all braided tensor equivalent pairs of twisted quantum doubles of finite groups. We also establish a canonical bijection between Lagrangian subcategories of the representation category of a twisted quantum double of a finite group G and module categories over the category of twisted G-graded vector spaces such that the dual tensor category is pointed. This can be viewed as a quantum version of V. Drinfeld's characterization of homogeneous spaces of a Poisson-Lie group in terms of Lagrangian subalgebras of the double of its Lie bialgebra. As a consequence, we obtain that two group-theoretical fusion categories are weakly Morita equivalent if and only if their centers are equivalent as braided tensor categories.Comment: 26 pages; several comments and references adde

Extended phase space for a spinning particle

Extended phase space of an elementary (relativistic) system is introduced in the spirit of the Souriau's definition of the `space of motions' for such system. Our formulation is generally applicable to any homogeneous space-time (e.g. de Sitter) and also to Poisson actions. Calculations concerning the Minkowski case for non-zero spin particles show an intriguing alternative: we should either accept two-dimensional trajectories or (Poisson) noncommuting space-time coordinates.Comment: 12 pages, late

Free motion on the Poisson SU(n) group

SL(N,C) is the phase space of the Poisson SU(N). We calculate explicitly the symplectic structure of SL(N,C), define an analogue of the Hamiltonian of the free motion on SU(N) and solve the corresponding equations of motion. Velocity is related to the momentum by a non-linear Legendre transformation.Comment: LaTeX, 10 page