Contact Lie algebras of vector fields on the plane

The paper is devoted to the complete classification of all real Lie algebras of contact vector fields on the first jet space of one-dimensional submanifolds in the plane. This completes Sophus Lie's classification of all possible Lie algebras of contact symmetries for ordinary differential equations. As a main tool we use the abstract theory of filtered and graded Lie algebras. We also describe all differential and integral invariants of new Lie algebras found in the paper and discuss the infinite-dimensional case.Comment: 20 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTVol3/paper1.abs.htm

Bifurcation scenario to Nikolaevskii turbulence in small systems

We show that the chaos in Kuramoto-Sivashinsky equation occurs through period-doubling cascade (Feigenbaum scenario), in contrast, the chaos in Nikolaevskii equation occurs through torus-doubling bifurcation (Ruelle-Takens-Newhouse scenario).Comment: 8pages, 9figure

Effective Temperature in a Colloidal Glass

We study the Brownian motion of particles trapped by optical tweezers inside a colloidal glass (Laponite) during the sol-gel transition. We use two methods based on passive rheology to extract the effective temperature from the fluctuations of the Brownian particles. All of them give a temperature that, within experimental errors, is equal to the heat bath temperature. Several interesting features concerning the statistical properties and the long time correlations of the particles are observed during the transition.Comment: to be published in Philosophical Magazin

Electrophoresis of a rod macroion under polyelectrolyte salt: Is mobility reversed for DNA?

By molecular dynamics simulation, we study the charge inversion phenomenon of a rod macroion in the presence of polyelectrolyte counterions. We simulate electrophoresis of the macroion under an applied electric field. When both counterions and coions are polyelectrolytes, charge inversion occurs if the line charge density of the counterions is larger than that of the coions. For the macroion of surface charge density equal to that of the DNA, the reversed mobility is realized either with adsorption of the multivalent counterion polyelectrolyte or the combination of electrostatics and other mechanisms including the short-range attraction potential or the mechanical twining of polyelectrolyte around the rod axis.Comment: 8 pages, 5 figures, Applied Statistical Physics of Molecular Engineering (Mexico, 2003). Journal of Physics: Condensed Matters, in press (2004). Journal of Physics: Condensed Matters, in press (2004

Physical Origin of the Boson Peak Deduced from a Two-Order-Parameter Model of Liquid

We propose that the boson peak originates from the (quasi-) localized vibrational modes associated with long-lived locally favored structures, which are intrinsic to a liquid state and are randomly distributed in a sea of normal-liquid structures. This tells us that the number density of locally favored structures is an important physical factor determining the intensity of the boson peak. In our two-order-parameter model of the liquid-glass transition, the locally favored structures act as impurities disturbing crystallization and thus lead to vitrification. This naturally explains the dependence of the intensity of the boson peak on temperature, pressure, and fragility, and also the close correlation between the boson peak and the first sharp diffraction peak (or prepeak).Comment: 5 pages, 1 figure, An error in the reference (Ref. 7) was correcte

Symmetry analysis of magneto-optical effects: The case of x-ray diffraction and x-ray absorption at the transition metal L23 edge

A general symmetry analysis of the optical conductivity or scattering tensor is used to rewrite the conductivity tensor as a sum of fundamental spectra multiplied by simple functions depending on the local magnetization direction. Using this formalism, we present several numerical examples at the transition metal L23 edge. From these numerical calculations we can conclude that large deviations from the magneto-optical effects in spherical symmetry are found. These findings are in particular important for resonant x-ray diffraction experiments where the polarization dependence and azimuthal dependence of the scattered Bragg intensity is used to determine the local ordered magnetization direction