Colloidal interactions in two-dimensional nematics

The interaction between two disks immersed in a 2D nematic is investigated i) analytically using the tensor order parameter formalism for the nematic configuration around isolated disks and ii) numerically using finite-element methods with adaptive meshing to minimize the corresponding Landau-de Gennes free energy. For strong homeotropic anchoring, each disk generates a pair of defects with one-half topological charge responsible for the 2D quadrupolar interaction between the disks at large distances. At short distance, the position of the defects may change, leading to unexpected complex interactions with the quadrupolar repulsive interactions becoming attractive. This short-range attraction in all directions is still anisotropic. As the distance between the disks decreases, their preferred relative orientation with respect to the far-field nematic director changes from oblique to perpendicular. Received 1 October 2002 and Received in final form 12 November 2002 RID="a" ID="a"e-mail: miko@cii.fc.ul.pt     

Water droplets in a spherically confined nematic solvent: A numerical investigation

Recently, it was observed that water droplets suspended in a nematic liquid crystal form linear chains [Poulin et al., Science 275, 1770 (1997)]. The chaining occurs, e.g., in a large nematic drop with homeotropic boundary conditions at all the surfaces. Between each pair of water droplets a point defect in the liquid crystalline order was found in accordance with topological constraints. This point defect causes a repulsion between the water droplets. In our numerical investigation we limit ourselves to a chain of two droplets. For such a complex geometry we use the method of finite elements to minimize the Frank free energy. We confirm an experimental observation that the distance d of the point defect from the surface of a water droplet scales with the radius r of the droplet like .When the water droplets are moved apart, we find that the point defect does not stay in the middle between the droplets, but rather forms a dipole with one of them. This confirms a theoretical model for the chaining. Analogies to a second order phase transition are drawn. We also find the dipole when one water droplet is suspended in a bipolar nematic drop with two boojums, i.e., surface defects at the outer boundary. Finally, we present a configuration where two droplets repel each other without a defect between them. Received 11 December 1998     

Radiative lifetimes of 7d, 8d <Superscript>1</Superscript>D<Subscript>2</Subscript> excited states of Hg I

Radiative lifetimes of 7d, 8d ¹ D ₂ excited states of Hg I are measured using pulsed two-photon excitation from the ground [Xe]5d ¹⁰6s ^{2 1} S ₀ mercury state, detecting the decay of the laser-induced fluorescence. The results are compared with theoretical values, obtained by means of a Hartree-Fock single configuration method, taking into account electron configuration interaction. The radiative lifetime value dependence on the effective principal quantum number for the nd ¹ D ₂ series is analyzed and compared with the quantum defect dependence. Received 25 February 2000 and Received in final form 26 July 2000     

Line defect dynamics around a colloidal particle

We study experimentally the dynamics of a topological defect located around a colloidal particle suspended in a thermotropic nematic liquid crystal. The considered defect consists of a disclination loop encircling the particle at the equator. Under specific conditions, it is shown that this disclination continuously shrinks to a hedgehog defect located in the immediate vicinity of the particle. This phenomenon corresponds to a transition between an elastic quadrupolar configuration and an elastic dipolar configuration. We performed a basic numerical calculation to get an estimate of the dissipated energy during the transition; we compare the results with theoretical predictions that describe the elastic energy of particles surrounded by defects. Received 21 December 2001     

Disorder driven roughening transitions of elastic manifolds and periodic elastic media

The simultaneous effect of both disorder and crystal-lattice pinning on the equilibrium behavior of oriented elastic objects is studied using scaling arguments and a functional renormalization group technique. Our analysis applies to elastic manifolds, e.g., interfaces, as well as to periodic elastic media, e.g., charge-density waves or flux-line lattices. The competition between both pinning mechanisms leads to a continuous, disorder driven roughening transition between a flat state where the mean relative displacement saturates on large scales and a rough state with diverging relative displacement. The transition can be approached by changing the impurity concentration or, indirectly, by tuning the temperature since the pinning strengths of the random and crystal potential have in general a different temperature dependence. For D dimensional elastic manifolds interacting with either random-field or random-bond disorder a transition exists for 2<D<4, and the critical exponents are obtained to lowest order in . At the transition, the manifolds show a superuniversal logarithmic roughness. Dipolar interactions render lattice effects relevant also in the physical case of D=2. For periodic elastic media, a roughening transition exists only if the ratio p of the periodicities of the medium and the crystal lattice exceeds the critical value . For p<p _c the medium is always flat. Critical exponents are calculated in a double expansion in and and fulfill the scaling relations of random field models. Received 28 August 1998     

Steps and facets at the surface of soft crystals

We consider the shape of crystals which are soft in the sense that their elastic modulus μ is small compared to their surface tension γ, more precisely μa < γ where a is the lattice spacing. We show that their surface steps penetrate inside the crystal as edge dislocations. As a consequence, these steps are broad with a small energy which we calculate. We also calculate the elastic interaction between steps a distance d apart, which is a 1/d ² repulsion. We finally calculate the roughening temperatures of successive facets in order to compare with the remarkable shapes of lyotropic crystals recently observed by Pieranski et al. [#!Pieranski!#,#!EPJ!#]. Good agreement is found. Received 25 June 2001     

A spectroscopic investigation of Y 3 Al 5 O 12 :Pr 3 + in translucent ceramic form: Crystal field analysis assisted by configuration-interaction

This paper presents an investigation of Pr³⁺ doped in the D₂ site of Y₃Al₅O₁₂ (YAG), for the first time on a translucent ceramic sample free of spurious phases, impurity or pair sites. The optical study is carried out by optical absorption, excitation, and emission by selective excitation into ¹D₂ and ³P₀, at different temperatures between 20 K and 60 K, in the 4 300-23 000 cm^-1 range. A detailed account of the line assignments is given. 67 over 91 levels of the 4f² configuration are determined. Several crystal field calculations within the ground configuration 4f² and the larger matrix 4f^2+4f6p are carried out. The energy level fit is slightly improved by configuration interaction. The ³P₂ and ¹I₆ levels are strongly mixed together by the large 6th order crystal field parameters. In sintered samples with different Pr³⁺ concentrations, satellite lines with intensities increasing quadratically with the concentration are observed. A few weak lines forbidden in D₂ site symmetry are observed. Received 9 November 2001 and Received in final form 8 February 2002     

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     

Transport theory of multiterminal hybrid structures

We derive a microscopic transport theory of multiterminal hybrid structures in which a superconductor is connected to several spin-polarized electrodes. We discuss the non-perturbative physics of extended contacts, and show that such contacts can be well represented by averaging out the phase of the electronic wave function. The intercontact Andreev reflection and elastic cotunneling conductances are identical if the phase can be averaged out, namely in the presence of at least one extended contact. The maximal conductance of a two-channel contact is proportional to (e ²/h)(a ₀/D)²exp[-D/ξ(ω^*)], where D is the distance between the contacts, a₀ the lattice spacing, ξ(ω) is the superconducting coherence length, and ω^* is the cross-over frequency between a perturbative regime ( ω < ω^*) and a non perturbative regime ( ω^* < ω < Δ). Received 18 June 2001 and Received in final form 17 January 2002     

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     

Investigation of the hyperfine structure of Ta I lines (VI)

We have classified about 200 new lines and have discovered 13 energy levels with even parity and 1 level with odd parity by means of the systematic hyperfine structure investigation of a large number of spectral lines of the neutral tantalum atom. For the new levels we deduced their angular momenta, parity and magnetic hyperfine interaction constants A as well as the electric quadrupole interaction constants B. Received 8 August 2001     

Large scale correlations for energy injection mechanisms in swirling turbulent flows

We report an experimental study of large scale correlations in the power injected in turbulent swirling flows generated in the gap between two coaxial rotating disks. We measure the pressure fluctuations on the blades of one disk, as well as the pressure drop between the leading and the trailing edges of the rotating blades, i.e. the local drag force. Measurements at different positions on one blade and on two successive blades display a correlation length much larger than the ones usually expected in turbulent flows. The time lag for which the correlation between two points is maximum, strongly depends on the global flow configuration. These results help us to understand the statistical properties of the injected power fluctuations in turbulent swirling flows. Received 2 September 1999     

Quark model study of the η photo-production:

An extensive and systematic study of the recent η photo-production data up to 1.2 GeV is presented within a chiral constituent quark model. A model embodying all known nucleonic resonances shows clear need for a yet undiscovered third S₁₁ resonance in the second resonance region, for which we determine the mass (1.729 GeV) and the total width (183 MeV). Furthermore, we extract the configuration mixing angles, an important property of the quark-quark interaction in the quark model, for the resonances S ₁₁(1535) and S ₁₁(1650), as well as for the resonances D ₁₃(1520) and D ₁₃(1700). Our results agree well with the quark model predictions. In addition, the partial ηN decay widths and/or the photo-excitation helicity amplitudes for the nucleonic resonances S ₁₁(1535), S ₁₁(1650), P ₁₁(1710), P ₁₃(1720), D ₁₃(1520), D ₁₃(1700), D ₁₅(1675), and F ₁₅(1680) are also obtained in this approach. Received: 14 February 2001 / Accepted: 22 June 2001     

Hysteresis and elastic interactions of microasperities in dry friction

Velocity independent dry friction of a slider upon a base is due to an hysteretic response of relative displacement to a tangential driving force F. We show that the purely elastic model for multistability considered in a previous publication is in no way essential: multistability arises just as well from adhesion. We emphasize the physical consequences of multistability for dynamic/static, a.c./d.c. friction. When the slider is moved from rest by an amount the transition from the zero force static configuration to dynamic behaviour is progressive, spreading on a range equal to the width of the hysteresis cycle. When is small, an elastic restoring force ensues, in agreement with observations. The competition of that elastic pinning with bulk elasticity generates a screening length which we believe is the natural size of Burridge Knopoff blocks. We then study the effect of elastic interactions between asperities: it is weak for dilute asperities, but its long range makes it important. In lowest order the interaction mediated displacement of a given asperity has logarithmically divergent fluctuations: they become comparable to the asperity radius when the slider size reaches another characteristic “Larkin length”, which for dilute micronic asperities is exponentially large. We give arguments suggesting that individually monostable asperities display collective multistability on scales larger than . For individually multistable sites we show that elastic interactions give rise to cascade processes in which the spinodal jump of a given asperity triggers the jump of others. We estimate the size of these cascades that should show up in the noise spectrum. Received: 3 February 1998 / Accepted: 19 March 1998     

Self-similarity of far wake behind tandem of two disks

In this work we used digital particle image visualization (PIV) to experimentally establish the self-similarity of far wake behind a tandem of two disks of a diameter D (300 mm) with a common axis along the incident flow. The research was performed in a water flume (Re ≈ 2 · 10⁵) with variation of L, the longitudinal dimension of the tandem. The self-similarity of the velocity profile in the wake behind the tandem has been established; the level of turbulent fluctuations of the profile has been measured. Due to the influence of the second disk, the velocity deficit in the wake behind the tandem exceeded the corresponding value for a single disk, being independent of the distance between the disks (L = 4–8D). The velocity fluctuations behind the tandem did not differ much from the level of fluctuations in the case of a single disk up to a distance of forty calibers downstream, where the wake ceased to differ from the background of natural turbulent fluctuations of the incident flow. It has been found that the position of the second disk in the tandem affects the energy loss in the wake due to its expansion but does not influence the decay. The revealed patterns in the wake development behind tandems of bodies will enable optimization of construction of systems of repetitive elements and their movement in different flows.     

Functional renormalization description of the roughening transition

We reconsider the problem of the static thermal roughening of an elastic manifold at the critical dimension d=2 in a periodic potential, using a perturbative Functional Renormalization Group approach. Our aim is to describe the effective potential seen by the manifold below the roughening temperature on large length scales. We obtain analytically a flow equation for the potential and surface tension of the manifold, valid for low temperatures. On a length scale L, the renormalized potential is made up of a succession of quasi parabolic wells, matching onto one another in a singular region of width for large L. For strong periodic potential, the perturbation theory breaks down, and we argue, based on a variational calculation, that the transition becomes first order. We also obtain numerically the step energy as a function of temperature, and relate our results to the existing experimental data on ⁴He. Finally, we examine the case of a non local elasticity which is realized physically for the contact line. Received 16 April 1999 and Received in final form 11 October 1999     

Eu3+ luminescence and Gd3+-Eu3+ energy transfer in K5Li2GdF10:Eu3+

Polycrystalline samples of europium-doped K₅Li₂GdF₁₀ have been obtained by a slow cooling of melted compound and investigated using spectroscopy methods. Luminescence from the ⁵ D ₂ level of Eu³⁺ is found to be weak. Intense visible emission upon excitation into the ⁵ D ₂ or higher energy levels has been attributed to overlapping transitions from long-lived ⁵ D ₁ and ⁵ D ₀ levels. A strong increase of the ⁵ D ₀ emission at the expense of the ⁵ D ₁ emission occurs between 5 K and 25 K without significant change of the ⁵ D ₁ lifetime. To account for this, it is supposed that both the radiative and the nonradiative transition rates are temperature-dependent. Efficient energy transfer from the ⁶ G _J levels of Gd³⁺ to Eu³⁺ ions has been evidenced by excitation spectra in the VUV region and VUV-excited luminescence. It has been concluded that the cross relaxation contributes to the energy-transfer process. Received: 8 May 2001 / Accepted: 11 May 2001 / Published online: 25 July 2001     

Simulation study of lateral diffusion in lipid-sterol bilayer mixtures

We employ off-lattice Monte Carlo simulations to study lateral diffusion in lipid-sterol bilayers using a two-dimensional model system which has been designed to simulate the experimental phase diagrams of both lipid-cholesterol and lipid-lanosterol systems. We focus on the effects of varying sterol concentration and temperature on the tracer diffusion coefficient, D, which characterizes the lateral motion of single tagged lipids in a bilayer. Generally, we find that increasing the cholesterol concentration suppresses D due to an increased conformational ordering of lipid chains. We argue that this effect competes with an increase in the average free area per lipid, which favours an increase in D. At temperatures close to the main transition temperature, the competition between the two effects leads to intriguing behavior of D. Overall, the model results are in excellent qualitative agreement with available experimental results for lipid-cholesterol mixtures. Additional studies of a model lipid-lanosterol system, for which experimental diffusion results are not available, predict that the presence of lanosterol has a smaller effect than cholesterol on reducing D relative to the pure lipid system. We conclude that the molecular model employed contains the essential features required to describe many of the qualitative features of the lateral diffusion behavior in lipid-sterol systems. Received 24 November 2000 and Received in final form 30 April 2001     

Neighborhood preferences in random matching problems

We consider a class of random matching problems where the distance between two points has a probability law which, for a small distance l, goes like l^r. In the framework of the cavity method, in the limit of an infinite number of points, we derive equations for p_k, the probability for some given point to be matched to its kth nearest neighbor in the optimal configuration. These equations are solved in two limiting cases: r = 0 -- where we recover p _k = 1/2^k, as numerically conjectured by Houdayer et al. and recently rigorously proved by Aldous -- and r→ + ∞. For 0 < r < + ∞, we are not able to solve the equations analytically, but we compute the leading behavior of p_k for large k. Received 14 February 2001     

Interaction élastique de défauts ponctuels dans un cristal hexagonal semi-infini avec ou sans adsorbat

The energy of elastic interaction between a point defect and the (0001) surface of a hexagonal crystal is calculated, as well as the energy of the elastic interaction between two defects near such a surface. The defects are represented by the superposition of three mutually perpendicular double forces without moment. The calculation is done by means of a Green function method. As for an isotropic medium, the energy of a point defect presents a variation in x₃^?3 with the distance x₃ to the surface. On the other hand, the mutual interaction between two defects depends upon different geometric parameters, and not simply on an image factor. We also study the effect of a thin adlayer on these elastic interactions. This is done by showing that the presence of the adlayer is equivalent to effective boundary conditions at the surface of the substrate. We derive these conditions and then the elastic energies to the first order in the thickness h of the layer. Finally we present the mean square displacements of atoms in the presence of a clean or adsorbed surface.