Undulation instability in two-dimensional foams of magnetic fluid

Two-dimensional magnetic fluid foams are cellular structures whose framework is made of magnetic fluid. The features of these equilibrated patterns are driven by a control parameter: the amplitude of the applied magnetic field. When the latter is rapidly increased, an instability occurs: the walls between cells undulate. Such an instability has also been observed in other 2D cellular structures, which exist for instance in Langmuir monolayers or in magnetic garnets thin films. In this paper we give a theoretical analysis of this instability, the issues of which are shown to be well confirmed by experiments and numerical simulations. Received: 13 October 1997 / Received in final form: 28 January 1998 / Accepted: 9 March 1998     

Canonically invariant formulation of Langevin and Fokker-Planck equations

We present a canonically invariant form for the generalized Langevin and Fokker-Planck equations. We discuss the role of constants of motion and the construction of conservative stochastic processes. Received : 24 July 1997 / Revised : 30 October 1997 / Accepted : 26 January 1998     

Cooperative diffusion in weakly charged polyelectrolyte gels

A general expression for the cooperative diffusion constant of weakly charged gels is derived as a function of the thermodynamic parameters such as polyelectrolyte concentration, salt concentration, ionic strength, and the degree of crosslinking. In the low concentration range it decreases with the monomer concentration. Received: 30 January 1998 / Revised: 4 May 1998 / Accepted: 6 May 1998     

”Direct” causal cascade in the stock market

We use wavelets to decompose the volatility (standard deviation) of intraday (S&P500) return data across scales. We show that when investigating two-point correlation functions of the volatility logarithms across different time scales, one reveals the existence of a causal information cascade from large scales (i.e. small frequencies) to fine scales. We quantify and visualize the information flux across scales. We provide a possible interpretation of our findings in terms of market dynamics. Received: 9 January 1998 / Received in final form and accepted: 13 January 1998     

Quasi Bernoulli fluctuations in random and disordered systems

It is shown that quasi Bernoulli fluctuations, which appear at a morphological phase transition, can be considered as a statistical basis for multifractal processes with constant multifractal specific heat in a wide class of random and disordered systems. This class contains at least following processes: percolation, diffusion-limited aggregation and corrosion, Lorenz like attractors, and mesoscopic systems with Anderson transition. Received: 14 April 1998 / Revised and Accepted: 20 April 1998     

Hall Conductivity in the presence of repulsive magnetic impurities

The Hall conductivity of disordered magnetic systems consisting of hard-core point vortices randomly dropped on the plane with a Poissonian distribution, has a behavior analogous to the one observed experimentally by Haug, Gerhardts, Klitzling and Ploog, with repulsive scatterers [#!1!#]. We also argue that models of homogeneous magnetic field with disordered potential, have necessarily vanishing Hall conductivities when their Hilbert space is restricted to a given Landau level subspace. Received: 29 September 1998 / Accepted: 21 December 1998     

Stretched exponential distributions in nature and economy: “fat tails” with characteristic scales

To account quantitatively for many reported “natural” fat tail distributions in Nature and Economy, we propose the stretched exponential family as a complement to the often used power law distributions. It has many advantages, among which to be economical with only two adjustable parameters with clear physical interpretation. Furthermore, it derives from a simple and generic mechanism in terms of multiplicative processes. We show that stretched exponentials describe very well the distributions of radio and light emissions from galaxies, of US GOM OCS oilfield reserve sizes, of World, US and French agglomeration sizes, of country population sizes, of daily Forex US-Mark and Franc-Mark price variations, of Vostok (near the south pole) temperature variations over the last 400 000 years, of the Raup-Sepkoski's kill curve and of citations of the most cited physicists in the world. We also discuss its potential for the distribution of earthquake sizes and fault displacements. We suggest physical interpretations of the parameters and provide a short toolkit of the statistical properties of the stretched exponentials. We also provide a comparison with other distributions, such as the shifted linear fractal, the log-normal and the recently introduced parabolic fractal distributions. Received: 20 January 1998 / Received in final form: 27 January 1998 / Accepted: 6 February 1998     

Effect of the initial phase of the field in ionization by ultrashort laser pulses

We report on observable new features related to ionization of atoms by laser pulses of only few cycles and some intensity. We show that for particular photo-electron energies, the angular distribution becomes asymmetric and that this asymmetry is related to the initial phase of the field. Received: 4 November 1997/Revised: 21 January 1998/Accepted: 23 February 1998     

The lamellar-disorder interface: one-dimensional modulated profiles

We study interfacial behavior of a lamellar (stripe) phase coexisting with a disordered phase. Systematic analytical expansions are obtained for the interfacial profile in the vicinity of a tricritical point. They are characterized by a wide interfacial region involving a large number of lamellae. Our analytical results apply to systems with one dimensional symmetry in true thermodynamical equilibrium and are of relevance to metastable interfaces between lamellar and disordered phases in two and three dimensions. In addition, good agreement is found with numerical minimization schemes of the full free energy functional having the same one dimensional symmetry. The interfacial energy for the lamellar to disordered transition is obtained in accord with mean field scaling laws of tricritical points. Received: 28 March 1997 / Revised: 6 February 1998 / Accepted: 16 February 1998     

Clustering of volatility as a multiscale phenomenon

The dynamics of prices in financial markets has been studied intensively both experimentally (data analysis) and theoretically (models). Nevertheless, a complete stochastic characterization of volatility is still lacking. What is well known is that absolute returns have memory on a long time range, this phenomenon is known as clustering of volatility. In this paper we show that volatility correlations are power-laws with a non-unique scaling exponent. This kind of multiscale phenomenology has some analogies with fully developed turbulence and disordered systems and it is now pointed out for financial series. Starting from historical returns series, we have also derived the volatility distribution, and the results are in agreement with a log-normal shape. In our study, we consider the New York Stock Exchange (NYSE), daily composite index closes (January 1966 to June 1998) and the US Dollar/Deutsche Mark (USD-DM) noon buying rates certified by the Federal Reserve Bank of New York (October 1989 to September 1998). Received 1 February 2000     

“String” formulation of the dynamics of the forward interest rate curve

We propose a formulation of the term structure of interest rates in which the forward curve is seen as the deformation of a string. We derive the general condition that the partial differential equations governing the motion of such string must obey in order to account for the condition of absence of arbitrage opportunities. This condition takes a form similar to a fluctuation-dissipation theorem, albeit on the same quantity (the forward rate), linking the bias to the covariance of variation fluctuations. We provide the general structure of the models that obey this constraint in the framework of stochastic partial (possibly non-linear) differential equations. We derive the general solution for the pricing and hedging of interest rate derivatives within this framework, albeit for the linear case (we also provide in the appendix a simple and intuitive derivation of the standard European option problem). We also show how the “string” formulation simplifies into a standard N-factor model under a Galerkin approximation. Received: 30 January 1998 / Revised: 12 February 1998 / Accepted: 16 February 1998     

Application of B-splines finite basis sets to relativistic two-photon decay rates of level in hydrogenic ions

A theoretical study of the one- and two-photon spontaneous emission rates from the 2 s1/2 state of one-electron ions is presented. High-precision values of the relativistic emission rates for ions with nuclear charge Z up to 100 are obtained through the use of finite basis sets for the Dirac equation constructed from B-splines. Furthermore, we analyze the influence of the inclusion of quantum electrodynamics corrections in the initial and final state energies. Received: 6 January 1998 / Accepted: 31 March 1998     

A path integral approach to effective non-linear medium

In this article, we propose a new method to compute the effective properties of non-linear disordered media. We use the fact that the effective constants can be defined through the minimum of an energy functional. We express this minimum in terms of a path integral allowing us to use many-body techniques. We obtain the perturbation expansion of the effective constants to second order in disorder, for any kind of non-linearity. We apply our method to the case of strong non-linearities (i.e. , where is fluctuating from point to point), and to the case of weak non-linearity (i.e. where and fluctuate from point to point). Our results are in agreement with previous ones, and could be easily extended to other types of non-linear problems in disordered systems. Received: 13 May 1998 / Accepted: 27 July 1998     

On some natural and model 2D bimodal random cellular structures

The topological and metric properties of a few natural 2D random cellular structures, namely an armadillo shell structure and young soap froths, which are formed from two classes of cells, large and small, have been characterized. The topological properties of a model generated from a Kagome tiling, which mimics such random binary structures, have also been exactly calculated. The distribution of the number of cell sides is bimodal for the structures investigated. In contrast to the classical Aboav-Weaire law for homogeneous 2D random cellular structures, nm(n), the mean total number of edges of neighbouring cells of cells with n sides does not vary linearly with n. Only the nm(i, n) (i=1,2) determined separately for every class of cells are linear in n for all investigated structures. Topological properties and correlations between metric and topological properties are finally compared with the predictions of various literature models. Received: 24 December 1997 / Revised: 7 April 1998 / Accepted: 20 April 1998     

Electrostatics of DNA-cationic lipid complexes: isoelectric instability

We propose a Poisson-Boltzmann electrostatic theory for DNA/cationic lipid complexes modeled as a stack of aligned DNA chains intercalated with lipid bilayers, a structure suggested by the recent X-ray synchrotron studies of Radler et al. Poisson-Boltzmann theory is shown to predict that the isoelectric point - where the DNA and cationic lipid charges are in balance - is unstable against absorption of extra DNA or lipid material. The instability is caused by the entropy gain obtained following the release of small ions inside the complex and is manifested by singular behavior of the rod-rod spacing near the isoelectric point. We apply the theory to a discussion of the results of Radler et al. Received: 21 July 1997 / Received in final form: 19 January 1998 /Accepted: 5 March 1998     

Two interacting particles in a disordered chain IV: Scaling of level curvatures

The curvatures of two-particle energy levels with respect to the enclosed magnetic flux in mesoscopic disordered rings are investigated numerically. We find that the typical value of the curvatures is increased by interactions in the localised regime and decreased in the metallic regime. This confirms a prediction by Akkermans and Pichard (Eur. Phys. J. B 1, 223 (1998)). The interaction-induced changes of the typical curvatures at different energies and disorder strengths exhibit one-parameter scaling with a conductance-like single parameter. This suggests that interactions could influence the conductance of mesoscopic systems similarly. Received 24 August 1998     

Truncated Lévy laws and 2D turbulence

We study the probability distribution functions and scaling properties of truncated Lévy processes with sharp cut-offs. We find that they display features analog to those observed in some 2D numerical simulations of turbulence. Received: 29 October 1997 / Revised: 12 February 1998 / Accepted: 10 April 1998     

Non-classical behavior in multimode and disordered transverse structures in OPO

We employ the Q-representation to study the non-classical correlations that are present from below to above-threshold in the degenerate optical parametric oscillator. Our study shows that such correlations are present just above threshold, in the regime in which stripe patterns are formed, but that they also persist further above threshold in the presence of spatially disordered structures. Received: 13 September 2002 / Received in final form: 11 November 2002 Published online 28 January 2003     

Shear modulus and compliance in the range of the dynamic glass transition for metallic glasses

High-resolution synchrotron-radiation powder diffraction experiments were performed to observe structural changes induced by hydrogen loading in rapidly-quenched Ti-Zr-Ni alloy ribbons with dominant icosahedral character. Lattice expansion effects due to hydrogen storage in Ti-Zr-Ni quasicrystals as well as phonon and phason disorder coefficients are obtained from an analysis of diffraction linewidths. Received: 26 August 1997 / Revised: 8 January 1998 / Accepted: 10 February 1998     

Shapes of heaps and in silos

Experimental investigations on the shape of a heap formed in a Hele Shaw cell either on a flat base or in a two-dimensional silo are presented. We have focused our attention on the shape dependence on mass flux and initial energy of particles poured into the cell. Two kinds of granular media are considered: glass beads and sand and we shall point out their different behaviors. We described the variations of the angle of repose and of the size of the tail as a function of the experimental parameters. We also report the time evolution of the angle of repose during the formation of the heap. Received 28 September 1998 and Received in final form 20 January 1999