Polymers with self-avoiding interaction in random medium: a localization-delocalization transition

In this paper we investigate the problem of a long self-avoiding polymer chain immersed in a random medium. We find that in the limit of a very long chain and when the self-avoiding interaction is weak, the conformation of the chain consists of many “blobs” with connecting segments. The blobs are sections of the molecule curled up in regions of low potential in the case of a Gaussian distributed random potential or in regions of relatively low density of obstacles in the case of randomly distributed hard obstacles. We find that as the strength of the self-avoiding interaction is increased the chain undergoes a delocalization transition in the sense that the appropriate free energy per monomer is no longer negative. The chain is then no longer bound to a particular location in the medium but can easily wander around under the influence of a small perturbation. For a localized chain we estimate quantitatively the expected number of monomers in the “blobs” and in the connecting segments. Received 13 November 2002 Published online 14 March 2003     

Aging and non-linear glassy dynamics in a mean field model

The mean field approach of glassy dynamics successfully describes systems which are out-of-equilibrium in their low temperature phase. In some cases an aging behaviour is found, with no stationary regime ever reached. In the presence of dissipative forces however, the dynamics is indeed stationary, but still out-of-equilibrium, as inferred by a significant violation of the fluctuation dissipation theorem. The mean field dynamics of a particle in a random but short-range correlated environment, offers the opportunity of observing both the aging and driven stationary regimes. Using a geometrical approach previously introduced by the author, we study here the relation between these two situations, in the pure relaxational limit, i.e. the zero temperature case. In the stationary regime, the velocity (v)-force (F) characteristics is a power law v∼F ⁴, while the characteristic times scale like powers of v, in agreement with an early proposal by Horner. The cross-over between the aging, linear-response regime and the non-linear stationary regime is smooth, and we propose a parametrization of the correlation functions valid in both cases, by means of an “effective time”. We conclude that aging and non-linear response are dual manifestations of a single out-of-equilibrium state, which might be a generic situation. Received 7 May 2000 and Received in final form 22 August 2000     

Glassy effects in the swelling/collapse dynamics of homogeneous polymers

We investigate, using numerical simulations and analytical arguments, a simple one-dimensional model for the swelling or the collapse of a closed polymer chain of size N, representing the dynamical evolution of a polymer in a Θ-solvent that is rapidly changed into a good solvent (swelling) or a bad solvent (collapse). In the case of swelling, the density profile for intermediate times is parabolic and expands in space as t ^1/3, as predicted by a Flory-like continuum theory. The dynamics slows down after a time ∝N ² when the chain becomes stretched, and the polymer gets stuck in metastable “zig-zag” configurations, from which it escapes through thermal activation. The size of the polymer in the final stages is found to grow as . In the case of collapse, the chain very quickly (after a time of order unity) breaks up into clusters of monomers (“pearls”). The evolution of the chain then proceeds through a slow growth of the size of these metastable clusters, again evolving as the logarithm of time. We enumerate the total number of metastable states as a function of the extension of the chain, and deduce from this computation that the radius of the chain should decrease as 1/ln(ln t). We compute the total number of metastable states with a given value of the energy, and find that the complexity is non-zero for arbitrary low energies. We also obtain the distribution of cluster sizes, that we compare to simple “cut-in-two” coalescence models. Finally, we determine the aging properties of the dynamical structure. The subaging behaviour that we find is attributed to the tail of the distribution at small cluster sizes, corresponding to anomalously “fast” clusters (as compared to the average). We argue that this mechanism for subaging might hold in other slowly coarsening systems. Received 23 October 2000     

Frequency dependence of the photonic noise spectrum in an absorbing or amplifying diffusive medium

A theory is presented for the frequency dependence of the power spectrum of photon current fluctuations originating from a disordered medium. Both the cases of an absorbing medium (“grey body”) and of an amplifying medium (“random laser”) are considered in a waveguide geometry. The semiclassical approach (based on a Boltzmann-Langevin equation) is shown to be in complete agreement with a fully quantum mechanical theory, provided that the effects of wave localization can be neglected. The width of the peak in the power spectrum around zero frequency is much smaller than the inverse coherence time, characteristic for black-body radiation. Simple expressions for the shape of this peak are obtained, in the absorbing case, for waveguide lengths large compared to the absorption length, and, in the amplifying case, close to the laser threshold. Received 8 August 2000     

Helix coil mixing in twist-storing polymers

Twist-storing polymers respond with elastic energy penalty to coherent or random twisting along the local chain axis away from its equilibrium, which can be straight (as in “ribbons”) or helical (as in DNA and other biopolymers). Here we study the equilibrium conformation of such polymers, focusing on the thermodynamic balance between twist and writhe, resulting from the competition between the random coil entropy and the potential energy stored in superhelical portions of the polymer chain. Two macroscopic variables characterise such a chain, the end-to-end distance R and the link number Lk, which is a topological invariant of a given polymer with clamped ends. We find that with increasing link number Lk, the chain accommodates its excess twist in growing plectonemes, unless forced out of this state by stretching its end-to-end distance R. We calculate the force-extension relation, which exhibits crossovers between different deformation regimes. Received 16 November 2000 and Received in final form 6 February 2001     

Orienting molecules using half-cycle pulses

Using a rigid-rotor model, we study the orientation dynamics of polar diatomic molecules excited by experimentally available half-cycle pulses. The results of the numerical solution of the time-dependent Schr?dinger equation are compared to those of an approximate “sudden-impact” impulsive model neglecting the molecular rotation during the pulse. We show that efficient orientation is achieved during time periods of several picoseconds for LiCl. For short pulses, where the kicked molecule model is valid, orientation turns out to be mainly sensitive to the time-integrated field amplitude and not the shape or rise time of the pulse. Received 16 August 2000 and Received in final form 4 December 2000     

Size and randomness effects on the temperature-dependent hopping conductivity of nanocrystalline chains

Developing a renormalization group approach, we study the hopping conductivity of nanocrystalline chains with different site energies. Exact calculations show that many parameters including nano-sizes, randomness of grain distributions, lattice distortions, site energies, transition rates, Fermi energy, and temperature influence the conductivity. Some new singular features, for example the frequency shift, the amplitude fluctuations, and the interchange between “peak” and “valley” behavior of the imaginary part of the conductivity can be caused by certain parameters mentioned above, while the interface distortions modulate mainly the overall amplitudes of the conductivity at the whole frequency region. Received 13 January 2000 and Received in final form 12 September 2000     

Ionization of a hydrogen atom from its ground state by a coherent bichromatic laser field

We study the “coherent phase control” between the three-photon ionization by a fundamental laser field and the one-photon ionization by its third harmonic for a hydrogen atom in its ground state. The relative phase δ of the harmonic field with respect to the fundamental laser radiation “modulates” the interference between the two ionization channels, which is important near the crossing points between the ionization rates of the two individual processes. Numerical results for the total ionization rate and for the angular distribution of the photoelectrons as a function of the phase δ are presented for frequencies located in the vicinity of the atomic resonances corresponding to the absorption of two laser photons. Received 31 August 2000 and Received in final form 6 February 2001     

Universal properties of shortest paths in isotropically correlated random potentials

We consider the optimal paths in a d-dimensional lattice, where the bonds have isotropically correlated random weights. These paths can be interpreted as the ground state configuration of a simplified polymer model in a random potential. We study how the universal scaling exponents, the roughness and the energy fluctuation exponent, depend on the strength of the disorder correlations. Our numerical results using Dijkstra's algorithm to determine the optimal path in directed as well as undirected lattices indicate that the correlations become relevant if they decay with distance slower than 1/r in d = 2 and 3. We show that the exponent relation 2ν - ω = 1 holds at least in d = 2 even in case of correlations. Both in two and three dimensions, overhangs turn out to be irrelevant even in the presence of strong disorder correlations. Received 20 December 2002 / Received in final form 10 April 2003 Published online 20 June 2003 RID="a" ID="a"e-mail: schorr@lusi.uni-sb.de     

Deformed foam structure and transitions in a tube

The “staircase” (2,1,1) foam structure in an ordered foam under expansion in a cylindrical tube and the structural transition to the “bamboo” (1,1,0) structure are studied experimentally, analytically, and numerically using the Surface Evolver minimization program. An analytical expression of the oblique interface in the (2,1,1) structure, a minimal surface, but curved by stretching of the foam, is given as a classic example of singular perturbation (boundary layer) theory. The structural transition from staircase structure to bamboo structure takes place at a considerable dilation. The transition is not due to an edge length tending to zero continuously with dilation, but results from the equilibrium (2,1,1) solution losing its stability due to a saddle node bifurcation. Received 3 August 2000     

Understanding the proton spin “puzzle” with a new “minimal” quark model

We investigate the spin structure of the nucleon in an extended Jaffe-Lipkin quark model. In addition to the conventional 3q structure, different (3q)(Q ) admixtures in the nucleon wave function are also taken into account. The contributions to the nucleon spin from various components of the nucleon wave function are discussed. The effect due to the Melosh-Wigner rotation is also studied. It is shown that the Jaffe-Lipkin term is only important when antiquarks are negatively polarized. We arrive at a new “minimal” quark model, which is close to the naive quark model, in order to understand the proton spin “puzzle”. Received: 4 November 2000 / Accepted: 23 October 2001     

Coherent control of the self-trapping transition

We discuss the dynamics of two weakly coupled Bose-Einstein condensates in a double-well potential, contrasting the mean-field picture to the exact N-particle evolution. On the mean-field level, a self-trapping transition occurs when the scaled interaction strength exceeds a critical value; this transition essentially persists in small condensates comprising about 1000 atoms. When the double-well is modulated periodically in time, Floquet-type solutions to the nonlinear Schr?dinger equation take over the role of the stationary mean-field states. These nonlinear Floquet states can be classified as “unbalanced” or “balanced”, depending on whether or not they entail long-time confinement of most particles to one well. Since the emergence of unbalanced Floquet states depends on the amplitude and frequency of the modulating force, we predict that the onset of self-trapping can efficiently be controlled by varying these parameters. This prediction is verified numerically by both mean-field and N-particle calculations. Received 5 November 2000 and Received in final form 16 February 2001     

Specific biomembrane adhesion --Indirect lateral interactions between bound receptor molecules

We studied biomembrane adhesion using the micropipet aspiration technique. Adhesion was caused by contact site A, a laterally mobile and highly specific cell adhesion molecule from Dictyostelium discoideum, reconstituted in lipid vesicles of DOPC (L-α-dioleoylphosphatidylcholine) with an addition of 5 mol % DOPE-PEG₂₀₀₀ (1,2-diacyl-sn-glycero-3-phosphatidylethanolamine-N-[poly(ethyleneglycol) 2000]). The “fuzzy” membrane mimics the cellular plasma membrane including the glycocalyx. We found adhesion and subsequent receptor migration into the contact zone. Using membrane tension jumps to probe the equation of state of the two-dimensional “gas” of bound receptor pairs within the contact zone, we found strong, attractive lateral interactions. Received 16 February 2001     

Temporal and spatial correlations in a viscoelastic model of heterogeneous faults

We study the temporal and spatial correlations in a one-dimensional model of a heterogeneous fault zone, in the presence of viscoelastic effects. As a function of dynamical weakening and of dissipation, the system exhibits three different “phases": one in which there are no time correlations between the events, a second, in which there are “Omori's law” type temporal correlations, and a third, runaway phase with quasiperiodic system size events. Received 30 May 2000 and Received in final form 7 September 2000     

Gravitational decoherence of atomic interferometers

We study the decoherence of atomic interferometers due to the scattering of stochastic gravitational waves. We evaluate the “direct” gravitational effect registered by the phase of the matter waves as well as the “indirect” effect registered by the light waves used as beam-splitters and mirrors for the matter waves. Considering as an example the space project HYPER, we show that both effects are negligible for the presently studied interferometers. Received 15 February 2002 / Received in final form 12 April 2002 Published online 19 July 2002     

Genetic Algorithms as a tool in the study of aperiodic order,with application to the case of X-Ray diffraction spectra of GaAs-AlAs multilayer heterostructures

We present the first application of Genetic Algorithms to the analysis of data from an aperiodically ordered system, high resolution X-Ray diffraction spectra from multilayer heterostructures arranged according to a deterministic or random scheme. This method paves the way to the solution of the “inverse problem”, that is the retrieval of the generating disorder from the investigation of the spectra of an unknown sample having non crystallographic, non quasi-crystallographic order. Received 18 March 2002 / Received in final form 3 July 2002 Published online 31 October 2002 RID="a" ID="a"e-mail: Evelyne.Lutton@inria.fr RID="b" ID="b"CNRS UMR 8502     

Vesicles in haptotaxis with hydrodynamical dissipation

We analyze the problem of vesicle migration in haptotaxis (a motion directed by an adhesion gradient), though most of the reasoning applies to chemotaxis as well as to a variety of driving forces. A brief account has been published on this topic [#!Cantat99a!#]. We present an extensive analysis of this problem and provide a basic discussion of most of the relevant processes of migration. The problem allows for an arbitrary shape evolution which is compatible with the full hydrodynamical flow in the Stokes limit. The problem is solved within the boundary integral formulation based on the Oseen tensor. For the sake of simplicity we confine ourselves to 2D flows in the numerical analysis. There are basically two regimes (i) the tense regime where the vesicle behaves as a “droplet” with an effective contact angle. In that case the migration velocity is given by the Stokes law. (ii) The flask regime where the vesicle has a significant (on the scale of the vesicle size) contact curvature. In that case we obtain a new migration law which substantially differs from the Stokes law. We develop general arguments in order to extract analytical laws of migration. These are in good agreement with the full numerical analysis. Finally we mention several important future issues and open questions. Received 24 June 2002 and Received in final form 4 February 2003 Published online: 16 April 2003 RID="a" ID="a"e-mail: isabelle.cantat@univ-rennes1.fr     

Probability distribution of inherent states in models of granular media and glasses

The present paper develops a Statistical Mechanics approach to the inherent states of glassy systems and granular materials by following the original ideas proposed by Edwards for granular media. We consider three lattice models (a diluted spin glass, a system of hard spheres under gravity and a hard-spheres binary mixture under gravity) introduced to describe glassy and granular systems. They are evolved using a “tap dynamics” analogous to that of experiments on granular media. We show that the asymptotic states reached in such a dynamics are not dependent on the particular sample history and are characterized by a few thermodynamical parameters. We assume that under stationarity these systems are distributed in their inherent states satisfying the principle of maximum entropy. This leads to a generalized Gibbs distribution characterized by new “thermodynamical” parameters, called “configurational temperatures” (related to Edwards compactivity for granular materials). Finally, we show by Monte Carlo calculations that the average of macroscopic quantities over the tap dynamics and over such distribution indeed coincide. In particular, in the diluted spin glass and in the system of hard spheres under gravity, the asymptotic states reached by the system are found to be described by a single “configurational temperature”. Whereas in the hard-spheres binary mixture under gravity the asymptotic states reached by the system are found to be described by two thermodynamic parameters, coinciding with the two configurational temperatures which characterize the distribution among the inherent states when the principle of maximum entropy is satisfied under the constraint that the energies of the two species are independently fixed. Received 19 March 2002 and Received in final form 14 June 2002     

Suppression of synchrotron radiation due to beam crystallization

With respect to a “hot”, non-crystallized beam the synchrotron radiation of a cold crystallized beam is considerably modified. We predict suppression of synchrotron radiation emitted by a crystallized beam in a storage ring. We also propose experiments to detect this effect. Received: 19 June 1998 / Revised version: 10 August 1998     

The effect of α, β crystalline structure on the mechanical properties of polypropylene

In order to study the effect of the α,β crystalline structure of polypropylene (PP) on its mechanical properties, it is necessary to prepare samples with variable α/β-phase content but with constant crystallinity and constant spherulite size. With this objective, heat treatment was first defined to be applied to an isotactic PP containing a β nucleating agent in order to achieve these conditions. Then study of the effect of the β-phase content on the tensile properties and fracture behaviour has been done at room temperature. The mechanical properties at fracture were assessed by three-point bending tests and were analysed on the basis of the “Essential Work of Fracture” (EWF). The results show that the elongation at fracture under tensile stress and the “near” Plane-Strain Essential Work of Fracture, w _Ie, increase substantially with the β-phase content. Besides, Young's modulus and the yield stress in tensile tests decrease slowly with the β-phase content. Finally, these results are analysed taking account the differences in structure of the α and β spherulites. Received 18 September 2000 and Received in final form 19 December 2000