Bose-like condensation of Lagrangian particles and higher-order statistics in passive scalar turbulent advection

We establish an hitherto hidden connection between zero modes and instantons in the context of the Kraichanan model for passive scalar turbulent advection, that relies on the hypothesis that the production of strong gradients of the scalar is associated with Bose-like condensation of Lagrangian particles. It opens the way to the computation of scaling exponents of the N-th order structure functions of the scalar by techniques borrowed from many-body theory. To lowest order of approximation, scaling exponents are found to increase asymptotically as log N in two dimensions.Comment: 12 pages, 2 figure

About coherent structures in random shell models for passive scalar advection

A study of anomalous scaling in models of passive scalar advection in terms of singular coherent structures is proposed. The stochastic dynamical system considered is a shell model reformulation of Kraichnan model. We extend the method introduced in \cite{DDG99} to the calculation of self-similar instantons and we show how such objects, being the most singular events, are appropriate to capture asymptotic scaling properties of the scalar field. Preliminary results concerning the statistical weight of fluctuations around these optimal configurations are also presented.Comment: 4 pages, 2 postscript figures, submitted to PR

Homoclinic Tubes and Chaos in Perturbed Sine-Gordon Equation

In an early work, Bernoulli shift dynamics of submanifolds was established in a neighborhood of a homoclinic tube. In this article, we will present a concrete example: sine-Gordon equation under a quasi-periodic perturbation

Robot Manipulators: Modeling, Performance Analysis and Control

International audienceThis book presents the most recent research results about the modeling and control of robot manipulators. - Chapter 1 gives unified tools to derive direct and inverse geometric, kinematic and dynamic models of serial robots and addresses the issue of identification of the geometric and dynamic parameters of these models. - Chapter 2 describes the main features of parallel robots, the different architectures and the methods used to obtain direct and inverse geometric, kinematic and dynamic models paying special attention to singularity analysis. - Chapter 3 introduces global and local tools for performance analysis of serial robots. - Chapter 4 presents an original optimization technique for point-to-point trajectory generation accounting for the robot dynamics. - Chapter 5 presents standard control techniques in the joint space and task space for free motion (PID, computed torque, adaptive dynamic control, and variable structure control), and constrained motion (compliant force-position control). - In chapter 6, the concept of vision-based control is developed and Chapter 7 is devoted to specific issue of robots with flexible links. Efficient recursive Newton-Euler algorithms for both inverse and direct modeling are presented, as well as control methods ensuring position setting and vibration damping

A long-wave action of spin Hamiltonians and the inverse problem of the calculus of variations

We suggest a method of derivation of the long-wave action of the model spin Hamiltonians using the non-linear partial differential equations of motions of the individual spins. According to the Vainberg's theorem the set of these equations are (formal) potential if the symmetry analysis for the Frechet derivatives of the system is true. The case of Heisenberg (anti)ferromagnets is considered. It is shown the functional whose stationary points are described by the equations coincides with the long-wave action and includes the non-trivial topological term (Berry phase)

A Uniform Approach to Antiferromagnetic Heisenberg Spins on Low Dimensional Lattices

Using group theoretical methods we show for both the triangular and square lattices that in the continuum limit the antiferromagnetic order parameter lives on SO3 without respect of the initial lattice. For the antiferromagnetic chain we recover the Haldane decomposition. This order parameter interacts with a local gauge field rather than with a global one as implicitly suggested in the literature which in our approach appears in a rather natural manner. In fact this merely corresponds to a novel extension of the spin group by a local gauge field. This analysis based on the real division algebras applies to low dimensional lattices.Comment: 5 pages; REVTeX