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     

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     

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     

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     

Saturation spectroscopy of the A-X transition of the ICl molecule

We describe the first saturation spectroscopy experiment concerning the A-X transition of ICl with considerably better resolution than previous works. Form our data, improved constants for the hyperfine structure of the excited state are determined. The A-X transition of ICl could be used to develop a set of secondary frequency standards and its metrologic qualities are discussed. Received: 27 July 1998 / Received in final form: 30 November 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     

Entropy and multi-particle correlations in two-dimensional lattice gases

We analyse the statistical entropy of two-dimensional lattice-gas models in terms of the contributions which arise from space correlations of increasing order. The “residual multiparticle entropy”, defined as the contribution to the excess entropy that is associated with correlations involving more than two particles, is calculated for the Ising and Coulomb lattice gases. The thermodynamic behaviour of the residual multiparticle entropy is then discussed in relation to the phase diagram of the model and the existence of underlying signatures of order-disorder phase transitions is also investigated. Received 31 December 1998 and Received in final form 8 March 1999     

Scaling of hysteresis in a multi-dimensional all-optical bistable system

We analyse the hysteresis enlargements of an optical bistable system involving three dynamical variables. We investigate, both experimentally and numerically, the local dynamics of the up- and down-switching process versus the sweeping frequency of the control parameter. In particular, we delineate the domain of validity of the scaling law predicted for one-dimensional systems. At high sweeping frequency, we show the appearance of another asymptotic scaling low in . Thereafter, we analyse the global evolution of the hysteresis loop induced by these processes. At low frequency, a scaling law is retrieved, whereas at high frequency, the dynamical behaviour is shown to strongly depend on the particular shape of the bistability curve. Received: 14 September 1998 / Received in final form: 15 February 1999     

Optimum ground states of generalized Hubbard models with next-nearest neighbour interaction

We investigate the stability domains of ground states of generalized Hubbard models with next-nearest neighbour interaction using the optimum groundstate approach. We focus on the -pairing state with momentum P=0 and the fully polarized ferromagnetic state at half-filling. For these states exact lower bounds for the regions of stability are obtained in the form of inequalities between the interaction parameters. For the model with only nearest neighbour interaction we show that the bounds for the stability regions can be improved by considering larger clusters. Additional next-nearest neighbour interactions can lead to larger or smaller stability regions depending on the parameter values. Received 30 March 1999 and Received in final form 3 May 1999     

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     

Tracer dispersion in power law fluids flow through porous media: Evidence of a cross-over from a logarithmic to a power law behaviour

An analytical model is presented to describe the dispersion of tracers in a power-law fluid flowing through a statistically homogeneous and isotropic porous medium. The model is an extension of Saffman's approach to the case of non-Newtonian fluids. It is shown that an effective viscosity depending on the pressure gradient and on the characteristics of the fluid, must be introduced to satisfy Darcy's law. An analytical expression of the longitudinal dispersivity is given as a function of the Peclet number Pe and of the power-law index n that characterizes the dependence of the viscosity on the shear rate . As the flow velocity increases the dispersivity obeys an asymptotic power law: . This asymptotic regime is achieved at moderate Peclet numbers with strongly non-Newtonian fluids and on the contrary at very large values when n goes to 1 ( for n=0.9). This reflects the cross-over from a scaling behaviour for towards a logarithmic behaviour predicted for Newtonian fluids (n=1). Received: 22 July 1997 / Revised and Accepted: 2 July 1998     

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     

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     

Properties of pulsed entangled two-photon fields

The dependence of one- and two-photon characteristics of pulsed entangled two-photon fields generated in spontaneous parametric down-conversion on the pump-pulse properties (shape of the pump-pulse spectrum and its internal structure) is examined. It is shown that entangled two-photon fields with defined properties can be generated. A general relation between the spectra of the down-converted fields is established. As a special case the interference of two partially overlapping pulsed two-photon fields is studied. The fourth-order interference pattern of entangled two-photon fields is investigated in the polarization analog of the Hong-Ou-Mandel interferometer. Received: 23 December 1998 / Received in final form: 14 April 1999     

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     

Statics and kinetics at the nematic-isotropic interface in porous media

We extend the random anisotropy nematic spin model to study nematic-isotropic transitions in porous media. A complete phase diagram is obtained. In the limit of relative low randomness the existence of a triple point is predicted. For relatively large randomness we have found a depression in temperature at the transition, together with a first order transition which ends at a tricritical point, beyond which the transition becomes continuous. We use this model to investigate the motion of the nematic-isotropic interface. We assume the system to be isothermal and initially quenched into the metastable régime of the isotropic phase. Using an appropriate form of the free energy density we obtain the domain wall solutions of the time-dependent Ginzburg-Landau equation. We find that including a random field leads to smaller velocity of the interface and to larger interface width. Received 12 November 1998 and Received in final form 15 March 1999     

A pseudopotential study of molecular spectroscopy in rare gas matrices: absorption of NO in argon

We present a pseudopotential method to study the absorption spectroscopy of NO in an argon matrix modeled by a large albeit finite cluster. The excited states of NO are described with the virtual orbitals of a NO⁺ Hartree-Fock calculation plus a core-polarization operator to account for the electron-NO⁺ correlation. The argon atoms of the matrix are replaced by pseudopotentials for the repulsive contributions and core-polarization operators to account for matrix polarization and correlation with the excited electron. The model is shown to account for the matrix-induced transition shifts and also for the cut-off of the Rydberg series for n >3 reported in absorption experiments from the ground state. Received: 6 March 1998 / Revised: 1st June 1998 / Accepted: 16 June 1998     

CuCl nanocrystals in alkali-halide matrices under hydrostatic pressure

CuCl nanocrystals in crystalline alkali-halide matrices have been investigated under hydrostatic pressures up to 18 GPa. The pressures of structural phase transitions in CuCl have been determined both for different nanocrystal sizes and for different matrices (NaCl, LiCl, KCl). For CuCl nanocrystals in NaCl an increase of the transition pressure with decreasing nanocrystal size is observed, which is explained by the increasing importance of surface pressure for small nanocrystals. We found higher transition pressures for the LiCl matrix than for the NaCl matrix. The reason for this is that the pressure which acts on the nanocrystal differs from the external pressure. A simple elastic model describes the effective pressure transmitted from the matrix to the nanocrystal. With CuCl nanocrystals embedded in KCl we have studied the behavior of nanocrystals during a phase transition of the matrix. Additionally we have determined the pressure coefficients of the exciton energies of the CuCl nanocrystals, which depend on the elastic properties of the matrix. Received 4 March 1999     

Quantum statistical mechanics of ideal gas obeying fractional exclusion statistics: a systematic study

The quantum statistical mechanics of an ideal gas with a general free-particle energy obeying fractional exclusion statistics are systematically investigated in arbitrary dimensions. The pressure relations, the relation between pressure and internal energy, the equation of state, as well as the thermodynamic properties are thoroughly discussed. Some novel results are obtained. Received: 23 January 1998 / Accepted: 17 March 1998