Elastic response and wrinkling onset of curved elastic membranes subjected to indentation test

Starting from a polymeric-fluid droplet, by vulcanization of the fluid free surface, curved elastic membranes, several nanometers thick and a few millimeters in diameter, which enclose a constant fluid volume, are produced. In an indentation-type test, carried out by pushing the membrane along its normal by means of a micro-needle, under some conditions, wrinkles are likely to appear around the contact region. Interestingly, we observe that the instability does not significantly alter the force-displacement relation: the relation between the force and the displacement remains linear and the associated stiffness is simply proportional to the tension of the membrane. In addition, we determine that the wrinkles develop when the stretching modulus of the membrane compares with its tension, which provides a useful method to estimate the elastic constant.     

Integrable scattering theories with unstable particles

We formulate a new bootstrap principle which allows for the construction of particle spectra involving unstable as well as stable particles. We comment on the general Lie algebraic structure which underlies theories with unstable particles and propose several new scattering matrices. We find a new Lie algebraic decoupling rule, which predicts the renormalization group flow in dependence of the relative ordering of the resonance parameters. The proposals are exemplified for some concrete theories which involve unstable particles, such as the homogeneous sine-Gordon models and their generalizations. The new decoupling rule can be validated by means of our new bootstrap principle and also via the renormalization group flow, which we obtain from a thermodynamic Bethe ansatz analysis.O.A. Castro-Alvaredo: Present addressLaboratoire de Physique, Ecole Normale Supérieure de Lyon, Allée dItalie, 69364 Lyon Cedex, FranceJ. Dreißig: Present address Universität Potsdam, Institut für Physik, Am Neuen Palais 10, 14469 Potsdam, GermanyA. Fring: Present address Centre for Mathematical Science, City University, Northampton Square, London EC1V 0HB, UK     

Do we understand the single-spin asymmetry for $\pi^0$ inclusive production in pp collisions?

The cross section data for inclusive production in pp collisions is considered in a rather broad kinematic region in energy , Feynman variable x _F and transverse momentum p _T. The analysis of these data is done in the perturbative QCD framework at the next-to-leading order. We find that they cannot be correctly described in the entire kinematic domain and this leads us to conclude that the single-spin asymmetry, A _N for this process, observed several years ago at FNAL by the experiment E704 and the recent result obtained at BNL-RHIC by STAR, are two different phenomena.Received: 10 March 2004, Revised: 19 May 2004, Published online: 14 July 2004preprint CPT-2003/P.4581(UMR 6207 is Unité Mixte de Recherche du CNRS and of Universités Aix-Marseille I and Aix-Marseille II and of Université du Sud Toulon-Var, Laboratoire affilié á la FRUMAM)     

Castaing’s instability in a trapped ultra-cold gas

We consider a trapped ultra-cold gas of (non-condensed) bosons with two internal states (described by a pseudo spin) and study the stability of a longitudinal pseudo spin polarization gradient. For this purpose, we numerically solve a kinetic equation corresponding to a situation close to the experiment at JILA [1]. It shows the presence of Castaings instability of transverse spin polarization fluctuations at long wavelengths. This phenomenon could be used to create spontaneous transverse spin waves.Received: 1st October 2002, Published online: 15 July 2003PACS: 03.75.Nt Other Bose-Einstein condensation phenomena - 51.10.+y Kinetic and transport theory of gases - 75.30.Ds Spin wavesO. Prévoté: Present address: Université de Cergy-Pontoise, Département de Physique, 5 mall Gay Lussac, Neuville-sur-Oise, 95031 Cergy-Pontoise, France.     

Moore and Seiberg's equations and 3D topological field theory

We prove that any solution to Moore and Seiberg's equations defines a Projective Rational Topological Field Theory (PRTFT) using surgery presentations for decorated three-manifolds and Kirby's calculus.After 1st October 1991: Laboratoire de Physique Théorique ENSLAPP de l'Ecole Normale Supérieure de Lyon, 46 Avenue d'Italie, F-69007 Lyon, France     

Parton distributions in the photon

We discuss in detail the photon structure function beyond the leading logarithm approximation. Of special concern is the factorization scheme and the hadronic input; we show how to naturally absorb large terms due to the factorization scheme in a modified hadronic component. The effect of the charm quark mass threshold is also discussed in relation to the phenomenology. A comparison with data shows that the modified hadronic component can be reasonably described by a VDM-type input.URA 14-36 du CNRS, associée à l'Ecole Normale Supérieure de Lyon, et au Laboratoire d'Annecy-le-Vieux de Physique des Particules     

Polynômes 3-Tangentiels Et Solutions t-Périodiques de KdV

Nous étudions, quel que soit le réseau , les courbes hyperelliptiques donnant lieu, via le dictionnaire de Krichever et la formule d’Its-Mateev, à des solutions méromorphes Λ-doublement périodiques en t de l’équation de Korteweg-de Vries. Ce sont des revêtements marqués finis particuliers de la courbe elliptique (X,q)=(C /Λ,0) que nous nommons paires osculatrices hyperelliptiques. Nous sommes amenés à définir la classe des polynômes 3-tangentiels symétriques et à considérer une surface algébrique réglée S→ X et la surface obtenue par un éclatement en huit points de S. Nous associons alors aux polynômes 3-tangentiels symétriques des diviseurs sur S et . En étudiant ces diviseurs, nous démontrons que les paires osculatrices non-ramifiées au point marqué se factorisent via et reconstruisons ensuite de telles paires sur sous certaines conditions numériques.     

Wrinkling of vesicles during transient dynamics in elongational flow

Recent experiments by Kantsler et al. [Phys. Rev. Lett. 99, 178102 (2007)10.1103/PhysRevLett.99.178102] have shown that the relaxational dynamics of a vesicle in external elongation flow is accompanied by the formation of wrinkles on a membrane. Motivated by these experiments we present a theory describing the dynamics of a wrinkled membrane. The formation of wrinkles is related to the dynamical instability induced by negative surface tension of the membrane. For quasispherical vesicles we perform analytical study of the wrinkle structure dynamics. We derive the expression for the instability threshold and identify three stages of the dynamics. The scaling laws for the temporal evolution of wrinkling wavelength and surface tension are established, confirmed numerically, and compared to experimental results.     

Nonlinear theory of solitary waves associated with longitudinal particle motion in lattices

The nonlinear aspects of longitudinal motion of interacting point masses in a lattice are revisited, with emphasis on the paradigm of charged dust grains in a dusty plasma (DP) crystal. Different types of localized excitations, predicted by nonlinear wave theories, are reviewed and conditions for their occurrence (and characteristics) in DP crystals are discussed. Making use of a general formulation, allowing for an arbitrary (e.g. the Debye electrostatic or else) analytic potential form and arbitrarily long site-to-site range of interactions, it is shown that dust-crystals support nonlinear kink-shaped localized excitations propagating at velocities above the characteristic DP lattice sound speed v₀. Both compressive and rarefactive kink-type excitations are predicted, depending on the physical parameter values, which represent pulse- (shock-)like coherent structures for the dust grain relative displacement. Furthermore, the existence of breather-type localized oscillations, envelope-modulated wavepackets and shocks is established. The relation to previous results on atomic chains as well as to experimental results on strongly-coupled dust layers in gas discharge plasmas is discussed.Received: 17 December 2003, Published online: 24 February 2004PACS: 52.27.Lw Dusty or complex plasmas; plasma crystals - 52.35.Fp Electrostatic waves and oscillations (e.g., ion-acoustic waves) - 52.25.Vy Impurities in plasmasI. Kourakis: On leave from: Université Libre de Bruxelles, Physique Statistique et Plasmas, C.P. 231, boulevard du triomphe, 1050 Brussels, Belgium; also: Faculté des Sciences Apliquées, C.P. 165/81, Physique Générale, avenue F.D. Roosevelt 49, 1050 Brussels, Belgium.     

L'asymptotique de Weyl pour les bouteilles magnétiques

Nous prouvons une formule pour le comportement asymptotique de la fonctionN() de dénombrement des valeurs propres de l'opérateur de Schrödinger avec un champ magnétique qui tend vers l'infini `a l'infini de ^d . La preuve utilise un résultat précis sur l'estimation des valeurs propres pour un champ magnétique constant dans un cube de ^d.     

Tilt modulus of a lipid monolayer

In addition to the familiar bending and stretching deformations, lipid monolayers and bilayers in their disordered state are often subjected to tilt deformations, occurring for instance in structural rearrangements accompanying membrane fusion, or upon insertion of oblique hydrophobic proteins into lipid bilayers. We study the elastic response of a flat lipid monolayer to a tilt deformation, using the spatial and conformational average of the chain end-to-end vector from the membrane normal to define a macroscopic membrane tilt. The physical origin and magnitude of the corresponding tilt modulus is analyzed using two complementary theoretical approaches. The first is a phenomenological model showing that the tilt and bending deformations are decoupled and the effects of inter-chain correlations on the tilt modulus is small. The second is based on a molecular-level mean-field theory of chain packing, enabling numerical evaluation of the tilt modulus for realistic, multi-conformation, chain models. Both approaches reveal that the tilt modulus involves two major contributions. The first is elastic in origin, arising from the stretching of the hydrocarbon chains upon a tilt deformation and reflecting the loss of chain conformational freedom associated with chain stretching. The second, purely entropic, contribution results from the constraints imposed by a tilt deformation on the fluctuations of chain director orientations. Using the chain-packing theory we compute the two contributions numerically as a function of the cross-sectional area per chain. The elastic and entropic terms are shown to dominate the value of for small and large areas per chain, respectively. For typical cross-sectional areas of lipid chains in biological membranes they areof comparable magnitude, yielding .Received: 12 May 2004, Published online: 3 August 2004PACS: 87.16.-b Subcellular structure and processes - 61.20.Gy Theory and models of liquid structure - 61.30.St Lyotropic phases     

Role of tensile stress in actin gels and a symmetry-breaking instability

It has been observed experimentally that the actin gel grown from spherical beads coated with polymerization enzymes spontaneously breaks the symmetry of its spherical shape, and yields a comet pushing the bead forward. We propose a mechano-chemical coupling mechanism for the initialization of this symmetry breaking. Key assumptions are that the dissociation of the gel takes place mostly in the region of the external surface, and that the rates of the dissociation depend on the tensile stress in the gel. We analyze a simplified two-dimensional model with a circular substrate. Our analysis shows that the symmetric steady state is always unstable against the inhomogeneous modulation of the thickness of the gel layer, for any radius of the circular substrate. We argue that this model represents the essential feature of three-dimensional systems for a certain range of characteristic lengths of the modulation. The characteristic time of the symmetry-breaking process in our model depends linearly on the radius of curvature of the substrate surface, which is consistent with experimental results, using spherical latex beads as substrate. Our analysis of the symmetry-breaking phenomenon demonstrates aspects of mechano-chemical couplings that should be working in vivo as well as in vitro.Received: 16 July 2003, Published online: 23 March 2004PACS: 87.17.Jj Cell locomotion; chemotaxis and related directed motion - 87.15.Rn Reactions and kinetics; polymerization - 62.40. + i Anelasticity, internal friction, stress relaxation, and mechanical resonancesK. Sekimoto: Present address: Université Louis Pasteur, 3 rue de lUniversité, 67084 Strasbourg, France.J. Prost: Also at ESPCI, 10 rue Vauquelin, 75231 Paris Cedex 05, France.F. Jülicher: Present address: Max Planck Institut für Physik komplexer Systeme, Nöthnitzer Str. 38, 01187 Dresden, Germany.A. Bernheim-Grosswasser: Present address: Chemical Engineering Department, Ben-Gurion University, P.O. Box 653, 84105 Beer-Sheva, Israel.     

Spin effects in the electron structure functions

The electron structure functions are studied in polarized e ⁺ e ^- scattering. The formulae for longitudinally and transversely polarized electrons are presented. The smallness of the electron mass leads to negligible cross-sections and asymmetries in some cases. Positivity constraints on the structure functions and parton densities are constructed and discussed. The cross-section asymmetries at very high energies, where the inclusion of all elecroweak bosons is necessary, are calculated. Numerical examples, using the asymptotic solutions for the parton densities inside the electron, are presented.Received: 23 June 2004, Revised: 26 October 2004, Published online: 17 December 2004PACS: 12.15.Ji, 12.38.QkJ. Szwed: Work supported by the European Commission contract ICA1-CT-2002-70013/INCO Strategic action on training and excellence, 5FP.Unité Mixte de Recherche du CNRS et des Universités de Provence, de la Méditerranée et du Sud Toulon-Var - Laboratoire affilié a la FRUNAM - FR 2291, CNRS-Luminy, Case 907, 13288 Marseille Cedex 9, France.     

TDPAC calculations for mixed SDW and Zeeman hyperfine interactions

The time differential perturbed angular correlation curves have been calculated for the hyperfine field distribution arising from the superposition of an isotropic system of spin density waves and of an external magnetic field. The results of these calculations have been applied to theCr–Ta system. The agreement between the experiments and the calculations is fair. This shows that the spin density waves of chromium are not significantly polarized by a 12 kOe magnetic field. However a large negative shift of the Zeeman interaction is observed in the liquid nitrogen experiment: H/H=–0.18±0.02. The negative sign of the shift shows that the hyperfine field is antiparallel to the local magnetization.

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Résumé Les courbes de corrélation angulaire différentielle ont été calculées pour une distribution de champs hyperfins résultant de la superposition des interactions d'un noyau avec un système d'ondes de densité de spin d'une part et avec un champ magnétique extérieur d'autre part. Les résultats de ces calculs ont été appliqués à l'alliageCr–Ta. L'accord entre l'expérience et les calculs est bon ce qui montre que les ondes de densité de spin ne sont pas polarisées par un champ magnétique de 12 kOe. Cependant un déplacement de l'interaction de Zeeman de –0.18±0.02 observé à 77 K permet d'affirmér que le champ hyperfin est opposé à l'aimantation locale.

     

The statistical parton distributions: status and prospects

New experimental results on polarized structure functions, cross sections for neutral and charge current reactions and ( ) charge current on isoscalar targets are compared with predictions using the statistical parton distributions, which were previously determined. New data on cross sections for Drell-Yan processes, single-jet data in collisions and inclusive production data in pp collisions are also compared with predictions from this theoretical approach. The good agreement which we find with all these tests against experiment strengthens our opinion on the relevance of the role of quantum statistics for parton distributions. We will also discuss the prospects of this physical framework.Received: 21 February 2005, Revised: 4 March 2005, Published online: 21 April 2005UMR 6207 - Unité Mixte de Recherche du CNRS et des Universités Aix-Marseille I, Aix-Marseille II et de lUniversité du Sud Toulon-Var - Laboratoire affilié á la FRUMAMPACS: 12.38.-t, 12.40.Ee, 13.10. + q, 13.60.Hb, 13.88. + ePreprint CPT-2004/P.090 UNIV. NAPLES DSF 032/04.     

Finite ion temperature effects on oblique modulational stability and envelope excitations of dust-ion acoustic waves

Theoretical and numerical investigations are carried out for the amplitude modulation of dust-ion acoustic waves (DIAW) propagating in an unmagnetized weakly coupled collisionless fully ionized plasma consisting of isothermal electrons, warm ions and charged dust grains. Modulation oblique (by an angle ) to the carrier wave propagation direction is considered. The stability analysis, based on a nonlinear Schrödinger-type equation (NLSE), exhibits a sensitivity of the instability region to the modulation angle , the dust concentration and the ion temperature. It is found that the ion temperature may strongly modify the waves stability profile, in qualitative agreement with previous results, obtained for an electron-ion plasma. The effect of the ion temperature on the formation of DIAW envelope excitations (envelope solitons) is also discussed.Received: 2 September 2003, Published online: 21 October 2003PACS: 52.27.Lw Dusty or complex plasmas; plasma crystals - 52.35.Fp Electrostatic waves and oscillations (e.g., ion-acoustic waves) - 52.35.Mw Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.) - 52.35.Sb Solitons; BGK modesI. Kourakis: On leave from: U.L.B., Université Libre de Bruxelles, Faculté des Sciences Apliquées, C.P. 165/81 Physique Générale, avenue F.D. Roosevelt 49, 1050 Brussels, Belgium.     

Localization for some continuous random Schrödinger operators

We study the spectrum of random Schrödinger operators acting onL ²(R ^d ) of the following type . The are i.i.d. random variables. Under weak assumptions onV, we prove exponential localization forH at the lower edge of its spectrum. In order to do this, we give a new proof of the Wegner estimate that works without sign assumptions onV.

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Résumé Dans ce travail, nous étudions le spectre d'opérateurs de Schrödinger aléatoires agissant surL ²(R ^d ) du type suivant . Les sont des variables aléatoires i.i.d. Sous de faibles hypothèses surV, nous démontrons que le bord inférieur du spectre deH n'est composé que de spectre purement ponctuel et, que les fonctions propres associées sont exponentiellement décroissantes. Pour ce faire nous donnons une nouvelle preuve de l'estimée de Wegner valable sans hypothèses de signe surV.

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U.R.A. 760 C.N.R.S.     

Confinement of molecular liquids: Consequences on thermodynamic,static and dynamical properties of benzene and toluene

We relate the dynamical behavior of molecular liquids confined in mesoscopic cylindrical pores to the thermodynamic properties, heat capacity and density and to the static structure by combining different experimental methods (H-NMR, calorimetry, elastic and inelastic neutron scattering, numerical simulations). The crystallization process is greatly reduced or avoided by confinement under standard cooling conditions, instead a glass transition temperature T _g at the 1000s time scale can be observed. The pore averaged local structure of the confined liquid is not noticeably affected when excluded-volume corrections are carefully applied, but follows the density changes reflected by the Bragg peak intensities of the porous matrices. The pore size dependence of T _g is dominated by two factors, surface interaction and finite-size effect. For the smallest pores ( , being the van der Waals radius of a molecule), one observes an increase of T _g and a broadening of the transition region, related to the interaction with the surface that induces a slowing-down of the molecules close to the wall. This is confirmed by neutron scattering experiments and molecular-dynamics simulations at shorter time scales and higher temperatures, which indicate a remaining fraction of frozen molecules. For larger pore sizes, taking the decrease of density under confinement conditions into account, a decrease of T _g is observed. This could be related to finite-size effects onto the putative cooperativity length that is often invoked to explain glass formation. However, no quantitative determination of this length (not to mention its T-dependence) can be extracted, since the interaction with the wall itself introduces an additional length that adds to the complexity of the problem.Received: 1 January 2003, Published online: 30 October 2003PACS: 64.70.Pf Glass transitions - 65.20. + w Thermal properties of liquids: heat capacity, thermal expansion, etc. - 61.12.-q Neutron diffraction and scatteringD. Morineau: Present address: Groupe Matiére Condensée et Matériaux, CNRS-UMR 6626, Bâtiment 11A, Université de Rennes 1, F-35042 Rennes, France.V. Teboul: Present address: Laboratoire des Propriétés Optiques des Matériaux et Applications, CNRS-UMR 6136, Université dAngers, F-49045 Angers, France.Y. Xia: Present address: School of Chemistry, The University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom.     

On universal Vassiliev invariants

Using properties of ordered exponentials and the definition of the Drinfeld associator as a monodromy operator for the Knizhnik-Zamolodchikov equations, we prove that the analytic and the combinatorial definitions of the universal Vassiliev invariants of links are equivalent.Supported by Fonds national suisse de la recherche scientifiqueURA 1436 du CNRS, associée à l'Ecole Normale Supérieure de Lyon et au laboratoire d'Annecyle-Vieux de Physique des Particules     

The role of strange sea quarks in chiral extrapolations on the lattice

Since the strange quark has a light mass of order , fluctuations of sea pairs may play a special role in the low-energy dynamics of QCD by inducing significantly different patterns of chiral symmetry breaking in the chiral limits N _f = 2 (m _u = m _d = 0, m _s physical) and N _f = 3 (m _u = m _d = m _s = 0). This effect of vacuum fluctuations of pairs is related to the violation of the Zweig rule in the scalar sector, described through the two O(p ⁴) low-energy constants L ₄ and L ₆ of the three-flavour strong chiral lagrangian. In the case of significant vacuum fluctuations, three-flavour chiral expansions might exhibit numerical competition between leading- and next-to-leading-order terms according to the chiral counting, and chiral extrapolations should be handled with special care. We investigate the impact of the fluctuations of pairs on chiral extrapolations in the case of lattice simulations with three dynamical flavours in the isospin limit. Information on the size of the vacuum fluctuations can be obtained from the dependence of the masses and decay constants of pions and kaons on the light quark masses. Even in the case of large fluctuations, corrections due to the finite size of spatial dimensions can be kept under control for large enough boxes ( fm).Received: 20 October 2004, Revised: 28 December 2004, Published online: 9 February 2005Laboratoire de Physique Théorique: LPT is an Unité Mixte de Recherche du CNRS et de lUniversité Paris-Sud 11 (UMR 8627).