Diffusive properties of motion on a bumpy plane

We report on experiments studying the statistical properties of the motion of balls on a bumpy surface. This motion is found to be diffusive. In the direction of the mean flow, the coefficient of diffusion is found to attain a constant value, independent of the size of the ball and the inclination angle. The diffusion transverse to the mean flow is characterized by a coefficient which decreases with the inclination of the plane, and scales with the size of moving ball. Received: 13 March 1997 / Revised: 10 December 1997 / Accepted: 17 February 1998     

Polymer depletion interaction between a particle and a wall

The attractive depletion interaction between a spherical particle and a planar wall in a dilute solution of long flexible nonadsorbing free polymer chains is found to depend crucially on the particle to polymer size ratio . While the polymer-induced force between particle and wall decreases monotonically with increasing distance for large , for small it has a maximum at a distance of the order of the polymer size. For ideal chains we study the crossover from large to small behavior in full quantitative detail. Besides the free energy of interaction and the force, we also discuss the spatial variations of the densities of chain-ends and chain-monomers near the wall and particle. Two independent procedures, (1) solving directly the diffusion equation for the density of ends in terms of planar and spherical waves and (2) minimizing the Ginzburg-Landau functional of the “magnetic analog” of the polymer problem, are used to obtain results numerically for a broad range of ratios of the three lengths particle size, polymer size and distance of particle from the wall. Besides previously known cases, we find two more interesting limiting regions of the length ratios for which analytical results can be obtained. [2mm] Received 11 December 1998     

Undulation instability of lamellar phases under shear: A mechanism for onion formation?

We consider a lamellar phase of bilayer membranes held between two parallel plates and subject to a steady shear. Accounting for the coupling with the shear flow of the short wavelength undulation modes that are responsible for the membrane excess area, we argue that the flow generates an effective force which acts to reduce the excess area. From the viewpoint of the macroscopic lamellar whose geometric dimensions are fixed, this force translates into an effective lateral pressure. At low shear rates this pressure is balanced by the elastic restoring forces of the lamellar. Above a critical shear rate , where d is the interlayer distance and D is the gap spacing, the lamellar buckles into a harmonic shape modulation, and we predict its wavelength and amplitude . We show that our model is isomorphic to a dilative strain, which is known to induce a similar buckling (undulation) instability. Indeed, at threshold the wavelength is and is identical in both cases. Using a non-linear analysis, we discuss how the wavelength and amplitude vary with shear rate away from the threshold. For we find and . We then focus on the coupling of the buckling modulation itself with the flow, and obtain a criterion for the limit of its stability. Motivated by experiments of D. Roux and coworkers, we assume that at this limit of stability the lamellar breakups into “onion"-like, multilamellar, vesicles. The critical shear rate for the formation of onions is predicted to scale as . The scaling with d is consistent with available experimental data. Received 15 April 1998 and Received in final form 4 March 1999     

Dynamical correlations in the one-dimensional electron gas with short-range interactions

We study the dynamical correlation effects in a one-dimensional Fermion gas with repulsive delta-function interaction within the quantum version of the self-consistent field approximation of Singwi, Tosi, Land, and Sj?lander [Phys. Rev. 176, 589 (1968)]. The dynamic correlation effects are described by a frequency dependent local-field correction . There is a corresponding local-field factor for the spin-density correlations. We investigate the structure factors, spin-dependent pair-correlation functions, the frequency dependences of and , and the plasmon dispersion relation within this formalism. We compare our results with other theoretical approaches, in particular the static version of the self-consistent field approximation to highlight the importance of dynamical correlations. Received 11 December 1998 and Received in final form 25 April 1999     

Brownian rotation of classical spins: dynamical equations for non-bilinear spin-environment couplings

Given two strings X and Y of N and M characters respectively, the Longest Common Subsequence (LCS) Problem asks for the longest sequence of (non-contiguous) matches between X and Y. Using extensive Monte-Carlo simulations for this problem, we find a finite size scaling law of the form for the average LCS length of two random strings of size N over S letters. We provide precise estimates of for .We consider also a related Bernoulli Matching model where the different entries of an array are occupied with a match independently with probability 1/S. On the basis of a cavity-like analysis we find that the length of a longest sequence of matches in that case behaves as where r=M/N and . This formula agrees very well with our numerical computations. It provides a very good approximation for the Random String model, the approximation getting more accurate as S increases. The question of the “universality class” of the LCS problem is also considered. Our results for the Bernoulli Matching model show very good agreement with the scaling predictions of [#!HwaLassig96_PRL!#] for Needleman-Wunsch sequence alignment. We find however that the variance of the LCS length has a scaling different from Var in the Random String model, suggesting that long-ranged correlations among the matches are relevant in this model. We finally study the “ground state” properties of this problem. We find that the number of solutions typically grows exponentially with N. In other words, this system does not satisfy “Nernst's principle”. This is also reflected at the level of the overlap between two LCSs chosen at random, which is found to be self averaging and to approach a definite value q _S <1 as . Received: 23 April 1998 / Revised: 30 July 1998 / Accepted: 14 August 1998     

Unified quantum mechanical picture for confined spinons in dimerized and frustrated spin chains

A quantum mechanical picture is presented to describe the behavior of confined spinons in a variety of S =1/2 chains. The confinement is due to dimerization and frustration and it manifests itself as a nonlinear potential , centered at chain ends () or produced by modulation kinks (b > 1). The calculation extends to weak or zero frustration some previous ideas valid for spinons in strongly frustrated spin chains. The local magnetization patterns of the confined spinons are calculated. A (minimum) enhancement of the local moments of about 11/3 over a single S =1/2 is found. Estimates for excitation energies and binding lengths are obtained. Received: 8 May 1998 / Revised and Accepted: 12 August 1998     

Spontaneous SU(2) symmetry breaking in one-dimensional quantum antiferromagnet

We present a Bethe Ansatz based investigation of a one-dimensional (1D) Heisenberg spin chain in a real 3D crystal lattice. We have shown that due to an influence of the lattice distortion on a crystalline field of ligands of magnetic ions, a Heisenberg antiferromagnetic spin chain is unstable under the appearance of a magnetic anisotropy of the “easy-plane” type. The effects of an external magnetic field and nonzero temperature onto such a phase transition are studied. Received: 19 January 1998 / Revised: 16 March 1998 / Accepted: 17 March 1998     

Two-colour operation of a Free-Electron Laser and applications in the mid-infrared

The two-colour operation of a Free-Electron Laser (FEL) has been demonstrated with the “CLIO” infrared facility. A two section undulator allows the production of picosecond laser pulses at two different wavelengths and simultaneously, in a wavelength range from to , and with a wavelength separation of two colours of up to . The time overlap, between both colours, has been measured on a picosecond time scale and on a microsecond time scale. An initial pump-probe application experiment has been performed with the two colours: stimulated emission has been measured in a 3-level Quantum-Well system. This is the best demonstration of the stability and reliability of the two-colour laser operation. Received: 4 November 1997 / Revised in final form: 31 March 1998 / Accepted: 10 April 1998     

Time distribution and loss of scaling in granular flow

Two cellular automata models with directed mass flow and internal time scales are studied by numerical simulations. Relaxation rules are a combination of probabilistic critical height (probability of toppling p) and deterministic critical slope processes with internal correlation time t_c equal to the avalanche lifetime, in model A, and ,in model B. In both cases nonuniversal scaling properties of avalanche distributions are found for , where is related to directed percolation threshold in d=3. Distributions of avalanche durations for are studied in detail, exhibiting multifractal scaling behavior in model A, and finite size scaling behavior in model B, and scaling exponents are determined as a function of p. At a phase transition to noncritical steady state occurs. Due to difference in the relaxation mechanisms, avalanche statistics at approaches the parity conserving universality class in model A, and the mean-field universality class in model B. We also estimate roughness exponent at the transition. Received: 29 May 1998 / Revised: 8 September 1998 / Accepted: 10 September 1998     

Pressure screening and fluctuations at the bottom of a granular column

We report sets of precise and reproducible measurements on the static pressure at the bottom of a granular column. We make a quantitative analysis of the pressure saturation when the column height is increased. We evidence a great sensitivity of the measurements with the global packing fraction and the eventual presence of shear bands at the boundaries. We also show the limit of the classical Janssen model and discuss these experimental results under the scope of recently proposed theoretical frameworks. Received 7 September 1998 and Received in final form 28 January 1999     

Transition from small to big charged unilamellar vesicles

The transition from small to big unilamellar vesicles predicted by a Poisson-Boltzmann Cell Model for the thermodynamics of a dilute phase of unilamellar charged vesicles is characterized. The radius as a function of experimental parameters is calculated and the coexistence region of small and big vesicles is identified. We further investigate the physical meaning in terms of simplified models, which allow for an identification of the role of parameters like the surface charge density or the Debye-length. Connections to experiments are discussed. Received: 20 October 1997 / Received in final form: 9 February 1998 / Accepted: 9 March 1998     

Theory of EPR on a rotating sample: An illustration of Berry's phase

We describe the theory of EPR in a crystal field multiplet under sample spinning. Berry phases arise because the crystal field is of lower symmetry than the full rotation group. The formal development is limited to pure J multiplets, crystal field doublets, and field and rotation axes parallel to a principal axis. Received: 4 August 1997 / Received in final form: 19 December 1997 / Accepted: 28 January 1998     

On granular surface flow equations

Conservation equations are written for surface flows (either fluid or granular). The particularity of granular surface flows is then pointed out, namely that the depth of the flowing layer is not a priori fixed, leading to open equations. It is shown how some hypothesis on the flowing layer allows to close the system of equations. A possible hypothesis, similar to that made for a fluid layer, but inspired from granular flow experiments, is presented. The force acting on the flowing layer is discussed. Averaging over the flowing depth, as in shallow water theory, then allows to transform these conservation laws into equations for the evolution of the profile of a granular pile. Apart from their interest for building models, these conservation laws can be used to measure experimentally the effective forces acting on a flowing layer. Received 25 July 1998 and Received in final form 14 January 1999     

The bulk dynamics of a compositionally asymmetric diblock copolymer studied using dynamic light scattering

We have studied the bulk dynamics of a compositionally asymmetric poly(ethylene propylene)-poly(dimethylsiloxane) (PEP-PDMS) diblock copolymer in a large temperature range both in the ordered and in the disordered state. The volume fraction of the PEP block is 0.22. Apart from the disordered state, the sample shows three ordered morphologies. Using dynamic light scattering, we have investigated the dynamics in all four phases and combined these results with those obtained using pulsed field gradient NMR. In the disordered state, we find--apart from the slow cluster mode--the heterogeneity mode related to the self-diffusion of single chains. The relaxation time of this mode, reduced by temperature and the zero-shear viscosity , , increases with temperature. In the cubic phase right below the ODT temperature, we observe two diffusive processes, and we attribute the faster one to the mutual diffusion of micelles and block copolymers not bound to micelles (“free chains”) through the PDMS matrix. The slower mode may either be due to the mutual diffusion of free chains and chains bound to PEP micelles or to the cooperative diffusion of micellar aggregates. In the non-cubic ordered state at intermediate temperatures, an additional weak diffusive mode is observed. The low-temperature ordered state is body-centered cubic, and here, only the mutual diffusion of micelles and free chains lies in our experimental time window. Received 19 March 1999 and Received in final form 25 August 1999     

Multiparticle correlations in resonance-matter formation

The effect of multiparticle correlations on resonance and pion populations, in relativistic nuclear reactions, is calculated in the context of an intranuclear cascade model which includes N-body (N > 2) collisional processes. The resonance-matter population present in the highly-compressed phase of nucleus-nucleus collisions is investigated, in reactions between different intermediate-mass nuclear systems. Received: 29 December 1998 / Revised version: 20 December 1999     

Finite-size scaling in the theory above the upper critical dimension

We derive exact results for several thermodynamic quantities of the O ( n ) symmetric field theory in the limit in a finite d-dimensional hypercubic geometry with periodic boundary conditions. Corresponding results are derived for an O ( n ) symmetric model on a finite d-dimensional lattice with a finite-range interaction. The leading finite-size effects near T_c of the field-theoretic model are compared with those of the lattice model. For 2 < d < 4, the finite-size scaling functions are verified to be universal. For d > 4, significant lattice effects are found. Finite-size scaling in its usual simple form does not hold for d > 4 but remains valid in a generalized form with two reference lengths. The finite-size scaling functions of the field theory turn out to be nonuniversal whereas those of the lattice model are independent of the nonuniversal model parameters. In particular, the field-theoretic model exhibits finite-size effects whose leading exponents differ from those of the lattice model. The widely accepted lowest-mode approach is shown to fail for both the field-theoretic and the lattice model above four dimensions. Received: 20 October 1997 / Accepted: 5 March 1998     

Spin glass behavior upon diluting frustrated magnets and spin liquids: a Bethe-Peierls treatment

A Bethe-Peierls treatment to dilution in frustrated magnets and spin liquids is given. A spin glass phase is present at low temperatures and close to the percolation point as soon as frustration takes a finite value in the dilute magnet model; the spin glass phase is reentrant inside the ferromagnetic phase. An extension of the model is given, in which the spin glass/ferromagnet phase boundary is shown not to reenter inside the ferromagnetic phase asymptotically close to the tricritical point whereas it has a turning point at lower temperatures. We conjecture similar phase diagrams to exist in finite dimensional models not constraint by a Nishimori's line. We increase frustration to study the effect of dilution in a spin liquid state. This provides a “minimal” ordering by disorder from an Ising paramagnet to an Ising spin glass. Received 9 April 1999 and Received in final form 27 September 1999     

Far-field fluorescence microscopy with repetitive excitation

We introduce the concept of repeatedly exciting an excited state of a photostable fluorescent entity to generate a nonlinear fluorescence signal which is solely based on the linear susceptibility of the molecule. The excitation cycle between the fluorescent state and another state prolongs the average lifetime of , with emphasis on those molecules that are in the center of the focus. The photons emitted by the long-lived molecules in the center are recorded by a temporal filter and constitute fluorescence that depends nonlinearly on the excitation intensity. Theoretical analysis reveals that this concept can provide three-dimensional imaging and improve the spatial resolution in far-field fluorescence microscopy. We show that despite the presence of diffraction the effective focal waist can in principle be narrowed down to the molecular scale at the expense of signal. Received: 3 December 1998     

Multifractal statistics of multiparticle production at high energies

It is shown that high energy multiparticle production near the morphological phase transition from monofractality to multifractality is characterized by a multifractal Bernoulli distribution. Experimental data on hadron-hadron, hadron-nucleus and on heavy ions collisions are used to show an universal character of this distribution (and, consequently, of the morphological phase transition) in multiparticle production at high energies. Received: 23 July 1998 / Revised version: 25 November 1998     

Thermoelectric transport properties in disordered systems near the Anderson transition

We study the thermoelectric transport properties in the three-dimensional Anderson model of localization near the metal-insulator transition (MIT). In particular, we investigate the dependence of the thermoelectric power S, the thermal conductivity K, and the Lorenz number L₀ on temperature T. We first calculate the T dependence of the chemical potential μ from the number density n of electrons at the MIT using an averaged density of states obtained by diagonalization. Without any additional approximation, we determine from the behavior of S, K and L₀ at low T as the MIT is approached. We find that and K decrease to zero at the MIT as and show that S does not diverge. Both S and L₀ become temperature independent at the MIT and depend only on the critical behavior of the conductivity. Received 5 February 1999