Absolute continuity in periodic thin tubes and strongly coupled leaky wires

Using a perturbative argument, we show that in any finite region containing the lowest transverse eigenmode, the spectrum of a periodically curved smooth Dirichlet tube in two or three dimensions is absolutely continuous provided the tube is sufficiently thin. In a similar way we demonstrate absolute continuity at the bottom of the spectrum for generalized Schr\"odinger operators with a sufficiently strongly attractive $\delta$ interaction supported by a periodic curve in $\mathbb{R}^d, d=2,3$.Comment: LaTeX 2e, 10 page

Adorno on Mimetic Rationality: Three Puzzles

In this paper, I examine Adorno’s controversial claim that human rationality is inherently mimetic. To do so, I break this claim down into three puzzles (the natural historical puzzle, the metaphysical puzzle, and the epistemic puzzle) and consider each in turn. The first puzzle originates in Adorno’s assertion that in the course of human history the mimetic moment of human thought “is melted together with the rational moment”. So whereas, on his narrative, mimesis has become an intrinsic component of human rationality, it appears that we are oblivious to this state of affair and unable to recognize the workings of mimesis in what we otherwise refer to as rationality. The second puzzle concerns the traditional metaphysical question regarding the possibility of knowledge. Adorno holds that the key to this question lies in the “mimetic moment of knowledge”, which he characterizes as the “moment of the elective affinity between the knower and the known.” The third puzzle concerns his views on how the mimetic moment of thought plays out in our epistemic practices. As he puts it, “consciousness knows of its other as much as it resembles that other,” which seems to entail that our very efforts to conceptualize objects somehow rely on imitative processes. I work out what I take to be the basics of Adorno’s understanding of mimesis and use them to make sense of each puzzle. I argue that Adorno’s insistence on the mimetic component of human rationality isn’t meant to promote more mimetic modes of comportment, but a reflexive awareness of the extent to which our rational activities already rely on imitative (or immersive) processes, even those we view as embodying the strongest claims to the contrary

Some properties of cellular automata with equicontinuity points

We investigate topological and ergodic properties of cellular automata having equicontinuity points. In this class surjectivity on a transitive SFT implies existence of a dense set of periodic points. Our main result is that under the action of such an automaton any shift ergodic measure converges in Cesaro Mean

On the polarization mechanism in the R Mon/NGC 2261 complex

The detection of circular polarization in R Mon and NGC 2261 is reported. This detection implies that the mechanism responsible for the linear and circular polarization is most likely multiple scattering in a flattened distribution. It replaces the previously suggested scenario where dichroic extinction by elongated dust grains aligned by a toroidal magnetic field was producing the polarization. The multiple scattering interpretation of linear polarization maps also means that these maps now provide direct evidence for a circumstellar disk around R Mon and possibly around many other young stellar objects

Euler-Lagrange models with complex currents of three-phase electrical machines and observability issues

A new Lagrangian formulation with complex currents is developed and yields a direct and simple method for modeling three-phase permanent-magnet and induction machines. The Lagrangian is the sum a mechanical one and of a magnetic one. This magnetic Lagrangian is expressed in terms of rotor angle, complex stator and rotor currents. A complexification procedure widely used in quantum electrodynamic is applied here in order to derive the Euler-Lagrange equations with complex stator and rotor currents. Such complexification process avoids the usual separation into real and imaginary parts and simplifies notably the calculations. Via simple modifications of such magnetic Lagrangians we derive new dynamical models describing permanent-magnet machines with both saturation and saliency, and induction machines with both magnetic saturation and space harmonics. For each model we also provide its Hamiltonian thus its magnetic energy. This energy is also expressed with complex currents and can be directly used in Lyapunov and/or passivity based control. Further, we briefly investigate the observability of this class of Euler-Lagrange models, in the so-called sensorless case when the measured output is the stator current and the load torque is constant but unknown. For all the dynamical models obtained via such variational principles, we prove that their linear tangent systems are unobservable around a one-dimensional family of steady-states attached to the same constant stator voltage and current. This negative result explains why sensorless control of three-phase electrical machines around zero stator frequency remains yet a difficult control problem.Comment: Revised version. Submitted for publicatio

Charge Distribution on Annealed Polyelectrolytes

We investigate the equilibrium charge distribution along a single annealed polyelectrolyte chain under different conditions. The coupling between the conformation of the chain and the local charge distribution is described for various solvent qualities and salt concentration. In salt free solution, we find a slight charge depletion in the central part of the chain: the charges accumulate at the ends. The effect is less important if salt is added to the solution since the charge inhomogeneity is localized close to the chain ends over a distance of order of the Debye length. In the case of poor solvent conditions we find a different charging of beads and strings in the framework of the necklace model. This inhomogeneity leads to a charge instability and a first order transition between spherical globules and elongated chains.Comment: 20 pages, 4 figure

Relating Weyl and diffeomorphism anomalies on super Riemann surfaces

Starting from the Wess-Zumino action associated to the super Weyl anomaly, we determine the local counterterm which allows to pass from this anomaly to the chirally split superdiffeomorphism anomaly (as defined on a compact super Riemann surface without boundary). The counterterm involves the graded extension of the Verlinde functional and the results can be applied to the study of holomorphic factorization of partition functions in superconformal field theory.Comment: (LATEX, 18 pages), MPI-Ph/92-38, LPTB 92-

Recent progress in inverse methods in France

Given the current level of jet engine performance, improvement of the various turbomachinery components requires the use of advanced methods in aerodynamics, heat transfer, and aeromechanics. In particular, successful blade design can only be achieved via numerical design methods which make it possible to reach optimized solutions in a much shorter time than ever before. Two design methods which are currently being used throughout the French turbomachinery industry to obtain optimized blade geometries are presented. Examples are presented for compressor and turbine applications. The status of these methods as far as improvement and extension to new fields of applications is also reported