Lagrangian flows: The dynamics of globally minimizing orbits

The objective of this note is to present some results, to be proved in a forthcoming paper, about certain special solutions of the Euler-Lagrange equations on closed manifolds. Our main results extend to time dependent periodic Lagrangians with minor modifications.We have chosen the autonomous case because this formally simpler framework allows to reach more easily the core of our concepts and results. Moreover the autonomous case exhibits certain special features involving the energy as a first integral that deserve special attention. They are closely related to the link found by Carneiro [C] between the energy and Mather's action function [Ma].Reprinted by permission of Addison Wesley Longman Ltd.     

Study of the gas-phase parameters affecting the silicon-oxide film deposition induced by an ArF laser

A study of the gas-phase parameters involved in ArF laser induced chemical vapour deposition of silicon-oxide thin films is presented. A complete set of experiments has been performed showing the influence of the concentration of the precursor gases, N₂O and SiH₄, and their influence on total and partial pressures on film growth and properties. In this paper we demonstrate the ability of this LCVD method to deposit silicon oxide films of different compositions and densities by appropriate control of gas composition and total pressure. Moreover, a material specific calibration plot comprising data obtained using different preparation techniques is presented, allowing determination of the stoichiometry of SiO _x films by using FTIR spectroscopy independently of the deposition method. For the range of processing conditions examined, the experimental results suggest that chemical processes governing deposition take place mainly in the gas phase.     

Diffusing particles with electrostatic repulsion

Summary. We study a diffusion model of an interacting particles system with general drift and diffusion coefficients, and electrostatic inter-particles repulsion. More precisely, the finite particle system is shown to be well defined thanks to recent results on multivalued stochastic differential equations (see [2]), and then we consider the behaviour of this system when the number of particles goes to infinity (through the empirical measure process). In the particular case of affine drift and constant diffusion coefficient, we prove that a limiting measure-valued process exists and is the unique solution of a deterministic PDE. Our treatment of the convergence problem (as ) is partly similar to that of T. Chan [3] and L.C.G. Rogers - Z. Shi [5], except we consider here a more general case allowing collisions between particles, which leads to a second-order limiting PDE. Received: 5 August 1996 / In revised form: 17 October 1996     

Laser systems specialized for laser spectroscopy at storage rings

Laser spectroscopy at storage rings often suffers from a limited resolution due to Doppler-broadened resonances. Broadening is caused by the velocity spread of the ions stored in the beam. In the following, the present status of our work on laser systems specialized on the specific needs of laser spectroscopy at storage rings is reported. Two pulsed laser systems were developed. One is a dye laser whose spectral bandwidth can be switched by inserting different Littrow-prisms into the resonator. An increase in bandwidth up to a factor of 45 was achieved. This laser was used for fast qualitative scans and high resolution measurements. The other laser system is a Nd : YAG laser pumped optical parametric oscillator. It is a tunable laser system covering the spectral range from 410 to 4000 nm. Furthermore, a continuous wave laser with a frequency shifted feedback cavity is described. It shows broadband emission with an adjustable bandwidth of up to 4.5 GHz. This laser can be advantageous for laser cooling of ion beams. This revised version was published online in August 2006 with corrections to the Cover Date.     

Twistor Geometry for Hyperkähler Metrics on Complex Adjoint Orbits

We study the hyperkähler geometry of complex adjoint orbits from the point of view of twistor theory. We introduce, for complex semisimple adjoint orbits, the associated spectral curve and construct the twistor space as a union of certain regular adjoint orbits; we also exhibit the family of twistor lines. Furthermore, we show how our methods may be applied for describing hyperkähler metrics associated to more general spectral curves. In particular, we give an algebraic characterisation of the twistor lines.     

Approximation in weighted Hardy spaces

This paper is concerned with several approximation problems in the weighted Hardy spacesH ^p(Ω) of analytic functions in the open unit disc D of the complex plane ℂ. We prove that ifX is a relatively closed subset of D, the class of uniform limits onX of functions inH ^p(Ω) coincides, moduloH ^p(Ω), with the space of uniformly continuous functions on a certain hull ofX which are holomorphic on its interior. We also solve the simultaneous approximation problems of describing Farrell and Mergelyan sets forH ^p(Ω), giving geometric characterizations for them. By replacing approximating polynomials by polynomial multipliers of outer functions, our results lead to characterizations of the same sets with respect to cyclic vectors in the classical Hardy spacesH ^p(D), 1 ⪯p < ∞. Dedicated to Professor Nácere Hayek on the occasion of his 75th birthday.     

Variations of constants and red-shift in 6D cosmology

On the basis of the general class of solutions of 6D vacuum Einstein equations and using well-known results of the 6D geometric model of electroweak and gravitational interactions, the variations of fundamental physical constants and their influence on the observed red-shift of galaxies are investigated. By considering the interpretation of extra components of the 6D metric as reproducing the properties of matter in the 4D curved space-time, the effective quantities of matter are obtained. In particular, the states of dust and radiation are shown. The corresponding 5D models were also investigated.     

Unreasonable effectiveness of symmetry in physics

We prove that in some reasonable sense, every possible physical law can be reformulated in terms of symmetries. This result explains the well-known success of the group-theoretic approach in physics.     

A system of parabolic equations in nonequilibrium thermodynamics including thermal and electrical effects

The time-dependent equations for a charged gas or fluid consisting of several components, exposed to an electric field, are considered. These equations form a system of strongly coupled, quasilinear parabolic equations which in some situations can be derived from the Boltzmann equation. The model uses the duality between the thermodynamic fluxes and the thermodynamic forces. Physically motivated mixed Dirichlet-Neumann boundary conditions and initial conditions are prescribed.The existence of weak solutions is proven. The key of the proof is (i) a transformation of the problem by using the entropic variables, or electro-chemical potentials, which symmetrizes the equations, and (ii) a priori estimates obtained by using the entropy function. Finally, the entropy inequality is employed to show the convergence of the solutions to the thermal equilibrium state as the time tends to infinity.