Controlled nucleation of point defects on a disclination line near a free surface during smectic-A-to-nematic directional melting

A disclination line populated with point defects that break the translational symmetry forms near a free nematic (N) interface in a confined geometry. The disclination line is, however, absent in the smectic-A phase (SmA). We use this fact to control the formation of point defect distributions on a disclination line by directional melting of the SmA phase in a temperature gradient. A threshold velocity ( v _th) exists below which a defect-free disclination line is formed. The frequency of nucleation of point defects increases steadily for v > v _th and exhibits a remarkable regularity. We derive an empirical scaling for v _th in terms of the experimental tuning parameters. We propose a simple model that allows to understand the formation of the point defects. Received 1 October 2002 / Published online: 15 April 2003 RID="a" ID="a"Permanent address: Departament de Quımica Fısica, Universitat de Barcelona, Martı i Franquès 1, Barcelona 08028, Spain; e-mail: jignes@qf.ub.es     

Universal non-monotonic smectic fluctuations of liquid crystal films in a magnetic field

Free-standing liquid crystal films with positive diamagnetic susceptibility can have the smectic ordering enhanced by an external field applied perpendicular to the plane layers. Within a quadratic functional integral approach, we investigate the interplay between the smectic order induced by an external field H and that due to the surface tension γ between the film and the surrounding gas. We find that the average smectic fluctuation is a non-monotonic function of film thickness, with a characteristic thickness scale ξ _H delimiting the predominance of surface tension and magnetic field effects. This characteristic thickness obeys simple asymptotic power-law relations as a function of the ordering terms which allows us to represent the average smectic fluctuations in a universal scaling form. Received 7 January 2003 Published online 1st April 2003 RID="a" ID="a"e-mail: marcelo@ising.fis.ufal.br     

The roughening transition of vicinal surfaces

Facetting of a vicinal surface is due to an arrangement of parallel primary steps which is commensurate with the substrate in plane periodicity (for instance one step every pth atomic row). It was shown by [#!Grempel!#] that such a locking requires an interaction between steps together with a finite step stiffness. But this early approach only reveals part of the story, as it is limited to sharp solid-vacuum interfaces in which thermal excitation of energetically expensive kinks controls all fluctuations. In this paper the problem is taken afresh in a language which applies equally well to “soft” interfaces, with important changes in the conclusions. Received 26 June 2001     

Influence of surface ordering on the wetting of structured liquids

The substrate is shown to induce substantial ordering in diblock copolymer thin films above the bulk order-disorder transition (ODT) where, thermodynamically, a phase mixed state is favored. Initially, uniform films reorganize to form a hierarchy of transient surface patterns and stable film thicknesses that depend on the initial film thickness and on the substrate. Self-consistent field calculations of the free energy of the system for different situations, depending on the relative tendency for the different block components to be attracted to the substrate and/or free surface, provide an explanation of the formation of the stable film thicknesses. A continuum picture proposed earlier by Brochard et al.rovides an explanation of the wetting characteristics of this system. In some cases the ordering destabilizes the film so that dewetting occurs (wetting autophobicity), whereas in other cases the surface ordering results in a kinetic stabilization of a film that would otherwise dewet. Received 3 August 2001 and Received in final form 1 November 2001     

Bulk singularities at critical end points: a field-theory analysis

A class of continuum models with a critical end point is considered whose Hamiltonian [φ,ψ] involves two densities: a primary order-parameter field, φ, and a secondary (noncritical) one, ψ. Field-theoretic methods (renormalization group results in conjunction with functional methods) are used to give a systematic derivation of singularities occurring at critical end points. Specifically, the thermal singularity ∼ | t|^{2 - α} of the first-order line on which the disordered or ordered phase coexists with the noncritical spectator phase, and the coexistence singularity ∼ | t|^{1 - α} or ∼ | t|^β of the secondary density <ψ> are derived. It is clarified how the renormalization group (RG) scenario found in position-space RG calculations, in which the critical end point and the critical line are mapped onto two separate fixed points _CEP ^* and _λ ^*, translates into field theory. The critical RG eigenexponents of _CEP ^* and _λ ^* are shown to match. _CEP ^* is demonstrated to have a discontinuity eigenperturbation (with eigenvalue y = d), tangent to the unstable trajectory that emanates from _CEP ^* and leads to _λ ^*. The nature and origin of this eigenperturbation as well as the role redundant operators play are elucidated. The results validate that the critical behavior at the end point is the same as on the critical line. Received 18 January 2001     

Polymer mixtures in confined geometries: Model systems to explore phase transitions

While binary (A,B) symmetric polymer mixtures ind = 3 dimensions have an unmixing critical point that belongs to the 3d Ising universality class and crosses over to mean field behavior for very long chains, the critical behavior of mixtures confined into thin film geometry falls in the 2d Ising class irrespective of chain length. The critical temperature always scales linearly with chain length, except for strictly two-dimensional chains confined to a plane, for whichT _c ∝N ^5/8 (this unusual exponent describes the fractal contact line between segregated chains in dense melts in two spatial dimensions,d = 2). When the walls of the thin film are not neutral, but preferentially attract one species, complex phase diagrams occur due to the interplay between capillary condensation and wetting phenomena. For ‘competing walls’ (one wall prefers A, the other prefers B) particularly interesting interface localization-delocalization transitions occur, while analogous phenomena in wedges are related to the ‘filling transition’.     

Adhesion and fingering in the lifting Hele-Shaw cell: Role of the substrate

The lifting Hele-Shaw cell (LHSC) is used to study adhesion as well as viscous fingering. In the present paper we report a series of observations of development of the interface for different viscous fluids, both Newtonian and non-Newtonian, in a LHSC operated at a constant lifting force. Glass and perspex are used as the plates in two different sets of experiments. The objectives are 1) to measure the time required to separate the plates as a function of the lifting force and 2) to note the force above which viscous fingering appears. We find that for the Newtonian fluids, the plate separation time follows a universal power law with the lifting force, irrespective of fluid and substrate. The non-Newtonian fluids too, with proper scaling obey the same power law. The appearance of fingering, however, depends on the properties of the fluid as well as the substrate. We suggest a modified form of the capillary number which controls the onset of fingering; this new quantity, termed the “fingering parameter” involves the dielectric constants of the substrate and fluid in addition to the viscosity and surface tension.     

X-ray scattering study of the electric-field-induced layer deformations of an antiferroelectric Liquid Crystal

The effect of an external electric field on the local layer structure is investigated in the SmC^* _A, SmC^* _FI and SmC^* phases using X-ray diffraction. X-ray scattering and spontaneous polarization measurements are performed under several increasing (and decreasing) steps of AC applied voltage. The effects of the electric field differ significantly from one phase to the other. The chevron-to-bookshelf transition occurs abruptly at a high field value in the SmC^* _A phase whereas layer deformations are more progressive and occur at lower field values in the other phases. Comparison of the different behaviours suggests that the destruction of the chevron structure is mainly affected by the local molecular order. Received 16 July 2001 and Received in final form 7 December 2001     

Annihilation of nematic point defects: Pre-collision and post-collision evolution

The annihilation of the nematic hedgehog and anti-hedgehog within an infinite cylinder of radius R is studied. The semi-microscopic lattice-type model and Brownian molecular dynamics are used. We distinguish among the i) early pre-collision, ii) late pre-collision, iii) early post-collision, and iv) late post-collision stages. In the pre-collision stage our results agree qualitatively with the existing experimental observations and also continuum-type simulations. The core of each defect exhibits a ring-like structure, where the ring axis is set perpendicular to the cylinder symmetry axis. For ξ⁽⁰⁾_d/(2R) > 1 the interaction between defects is negligible, where ξ⁽⁰⁾_d describes the initial separation of defects. Consequently, the defects annihilate within the simulation time window for ξ⁽⁰⁾_d/(2R) < 1. For close enough defects their separation scales as ξ_d (t_c - t)^0.4±0.1, where t_c stands for the collision time. In elastically anisotropic medium the hedgehog is faster than the anti-hedgehog. In the early pre-collision stage the defects can be treated as point-like particles, possessing inherent core structure, that interact via the nematic director field. In the late pre-collision stage the cores reflect the interaction between defects. After the collision a charge-less ring structure is first formed. In the early post-collision stage the ring adopts an essentially untwisted circular structure of the radius ξ_r. In the late post-collision stage we observe two qualitatively different scenarios. For μ = ξ_r/R < μ_c ∼ 0.25 the ring collapses leading to the escaped radial equilibrium structure. For μ > μ_c the chargeless ring triggers the nucleation growth into the planar polar structure with line defects.     

3d Monte Carlo simulation of site-bond continuum percolation of spheres

We present off-lattice Monte Carlo simulations of site-bond percolation of semi-penetrable spheres or, equivalently, of hard spheres with a finite bond range. We will show that the crucial parameter is the effective volume fraction ( φ_e), i.e. the volume that is occupied or within the bond range of at least one particle. For the equivalent system of semi-penetrable spheres 1 - φ_e is the porosity. The bond percolation threshold (p _b) can be described in terms of φ_e by a simple analytical expression: log(φ_e)/log(φ_ec) + log(p _b)/log(p _bc) = 1, with p _bc = 0.12 independent of the bond range and φ_ec a constant that decreases with increasing bond range. Received: 10 March 2003 / Accepted: 23 April 2003 / Published online: 21 May 2003 RID="a" ID="a"e-mail: jean-christophe.gimel@univ-lemans.fr     

The Variational Principle for a Class of Asymptotically Abelian C*-Algebras

Let (A,α) be a C^*-dynamical system. We introduce the notion of pressure P _α(H) of the automorphism α at a self-adjoint operator H∈A. Then we consider the class of AF-systems satisfying the following condition: there exists a dense α-invariant *-subalgebra ? of A such that for all pairs a,b∈? the C^*-algebra they generate is finite dimensional, and there is p=p(a,b)∈ℕ such that [α ^j (a),b]= 0 for |j|≥p. For systems in this class we prove the variational principle, i.e. show that P _α(H) is the supremum of the quantities h _φ(α) −φ(H), where h _φ(α) is the Connes–Narnhofer–Thirring dynamical entropy of α with respect to the α-invariant state φ. If H∈A, and P _α(H) is finite, we show that any state on which the supremum is attained is a KMS-state with respect to a one-parameter automorphism group naturally associated with H. In particular, Voiculescu's topological entropy is equal to the supremum of h _φ(α), and any state of finite maximal entropy is a trace. Received: 19 April 2000 / Accepted: 14 June 2000     

Interface interaction and wetting of Sc<Subscript>2</Subscript>O<Subscript>3</Subscript> exposed to Cu–Al and Cu–Ti melts

Scandia is a thermodynamically stable oxide and could be used as a structural material for a crucible in order to avoid a melt contamination. In the present study wetting experiments of Cu–Al and Cu–Ti melts on Scandia substrate were preformed at 1423 K by a sessile drop method. It was established that Al and Ti additions lead to the improved wetting and that the final contact angle decreases with increasing the additives concentration. For Al containing melts, the contact angle changes gradually with time, and a relatively thick interaction layer, which consists of Al₂O₃, Sc₂O₃, and metallic channels, was formed at the Sc₂O₃/Cu–Al interface. For Ti containing melts, the final contact angle is achieved already during heating, and an extremely thin layer based on a Ti–Sc–O compound was detected by AES at the Sc₂O₃/Cu–Ti interface. The results of a thermodynamic analysis, which takes into account the formation free energy of the oxides, involved in the systems, and the thermodynamic properties of the liquid solutions are in a good agreement with the experimental observations.     

Influence of the reagent vibration on the stereo-dynamics of the reactions D- + H2 and H- + D2

Employing the quasi-classical trajectory method and the potential energy surface of Panda and Sathyamurhy [Panda A N and Sathyamurthy N 2004 J. Chem. Phys. 121 9343], the effect of the reagent vibration on vector correlation of the ion-molecule reactions D^- + H₂ and H^- + D₂ is studied at a collision energy of 35.7 kcal/mol. Four generalized polarization-dependent differential cross sections (2π/σ)(dσ₀₀/dω_t),(2π/σ)(dσ₂₀/dω_t),(2π/σ)(dσ₂₂/dω_t), and (2π/σ)(dσ₂₀/dω_t) are presented in the centre-of-mass reference frame, separately. At the same time, the effects on the product angular distributions P(θ_r), P(φ_r) and P(θ_r,φ_r) of the title reactions are also analysed. The calculated results show that the scattering tendencies of the product HD, the alignment and the orientation of j' sensitively depend on reagent molecule vibration.     

Distortion and unwinding of the helical structure in polymer-stabilized short-pitch ferroelectric liquid crystal

We report the effect of an anisotropic polymer network formed from an achiral photoreactive monomer in a short-pitch chiral SmC* phase on the distortion and the unwinding of the helical structure of the ferroelectric phase. The electro-optical behaviour and ferroelectric properties were experimentally determined for films containing various polymer concentrations. The critical field, E_u, for the transition from the distorted structure to the homogeneous state was measured as a function of polymer concentration. A linear increase of E_u versus polymer concentration was observed, showing that the helical structure of the short-pitch SmC* phase was stabilized by the polymer network. This behaviour was expected to be a consequence of the increase of the apparent elastic constants of the ferroelectric liquid crystal stabilized by the anisotropic polymer network films. The polymer network morphology was investigated using atomic-force microscopy, revealing a twisted structure of the polymer fibers. This twisted structure was transferred onto a polymer network during the polymerization process within a short-pitch SmC* phase. The increase of the apparent elasticity can then be interpreted by a strong interaction between polymer network and the liquid-crystal molecules. From our experimental data, the coupling coefficient, W_p, characterizing this interaction was evaluated for all studied polymer concentrations.     

Statics and dynamics of adhesion between two soap bubbles

An original set-up is used to study the adhesive properties of two hemispherical soap bubbles put into contact. The contact angle at the line connecting the three films is extracted by image analysis of the bubbles profiles. After the initial contact, the angle rapidly reaches a static value slightly larger than the standard 120^° angle expected from Plateau rule. This deviation is consistent with previous experimental and theoretical studies: it can be quantitatively predicted by taking into account the finite size of the Plateau border (the liquid volume trapped at the vertex) in the free energy minimization. The visco-elastic adhesion properties of the bubbles are further explored by measuring the deviation Δθ_d(t) of the contact angle from the static value as the distance between the two bubbles supports is sinusoidally modulated. It is found to linearly increase with Δr _c/r _c , where r_c is the radius of the central film and Δr _c the amplitude of modulation of this length induced by the displacement of the supports. The in-phase and out-of-phase components of Δθ_d(t) with the imposed modulation frequency are systematically probed, which reveals a transition from a viscous to an elastic response of the system with a crossover pulsation of the order 1rad · s^-1. Independent interfacial rheological measurements, obtained from an oscillating bubble experiment, allow us to develop a model of dynamic adhesion which is confronted to our experimental results. The relevance of such adhesive dynamic properties to the rheology of foams is briefly discussed using a perturbative approach to the Princen 2D model of foams.     

Improvement of the pinning properties of (Bi/Pb)-2223 textured ceramics by columnar defects introduced by 6 GeV Pb ions

Pinning properties of (Bi/Pb)-2223 textured ceramics have been improved by 6 GeV Pb ions irradiation. Two samples were irradiated at fluencesφ _t=5 × 10¹⁰ ions/cm² and 2 × 10¹¹ ions/cm², respectively. The magnetic irreversibility is clearly improved in the intermediate range of temperature: (30–35) K<T<60 K for magnetic fields lower than the “fluence equivalent field”B _φ =φ _t.φ ₀. Moreover the irreversibility line is shifted towards higher fields. The results reported here show that the introduction of columnar defects or other extended defects is a route to improve the screening properties of tubes or cans based on (Bi/Pb)-2223 material and operating in liquid nitrogen.     

Non-equilibrium behavior at a liquid-gas critical point

Second-order phase transitions in a non-equilibrium liquid-gas model with reversible mode couplings, i.e., model H for binary-fluid critical dynamics, are studied using dynamic field theory and the renormalization group. The system is driven out of equilibrium either by considering different values for the noise strengths in the Langevin equations describing the evolution of the dynamic variables (effectively placing these at different temperatures), or more generally by allowing for anisotropic noise strengths, i.e., by constraining the dynamics to be at different temperatures in d _|| - and d _⊥-dimensional subspaces, respectively. In the first, isotropic case, we find one infrared-stable and one unstable renormalization group fixed point. At the stable fixed point, detailed balance is dynamically restored, with the two noise strengths becoming asymptotically equal. The ensuing critical behavior is that of the standard equilibrium model H. At the novel unstable fixed point, the temperature ratio for the dynamic variables is renormalized to infinity, resulting in an effective decoupling between the two modes. We compute the critical exponents at this new fixed point to one-loop order. For model H with spatially anisotropic noise, we observe a critical softening only in the d _⊥-dimensional sector in wave vector space with lower noise temperature. The ensuing effective two-temperature model H does not have any stable fixed point in any physical dimension, at least to one-loop order. We obtain formal expressions for the novel critical exponents in a double expansion about the upper critical dimension d _c = 4 - d _|| and with respect to d _|| , i.e., about the equilibrium theory. Received 4 April 2002 Published online 13 August 2002     

Photoproduction of πmesons off protons from the Δ(1232) region to Eγ = 3 GeV

Photoproduction of π⁰-mesons was studied with the Crystal-Barrel detector at ELSA for incident energies from 300MeV to 3GeV. Differential cross-sections dσ/dΩ, dσ/dt, and the total cross-section are presented. For E _γ < 3GeV, the angular distributions agree well with the SAID parametrization. At photon energies above 1.5GeV, a strong forward peaking indicates t-channel exchange to be the dominant process. The rapid variations of the cross-section with energy and angle indicate production of resonances. An interpretation of the data within the Bonn-Gatchina partial-wave analysis is briefly discussed.     

A model of strain relaxation in hetero-epitaxial films on compliant substrates

0 these maximum relieved strains are φ₀/2, φ₀, 3φ₀/2 and 2φ₀ respectively, at the end of each of stages I–IV. Films relaxed in each stage are characterized by a specific set of macroscopic crystallographic features that can be observed experimentally, including lattice rotation, lattice tilt, and the presence of more than one variant in some cases. For example, complete untwisting is predicted for stage IV relaxation, resulting in the disappearance of the initial twist angle between the two lattices. To relax the elastic misfit strain, extensive plastic deformation of the substrate film is involved, thus making it compliant to the hetero-epitaxial film. This thin film substrate may be called the plastically compliant substrate (PCS). Received: 18 June 1997/Accepted: 27 June 1997     

The underdamped Josephson junction subjected to colored noises

The properties of the underdamped Josephson junction subjected to colored noises were investigated with large and small phase difference (φ). For the case of the large φ, we found numerically that: (i) the probability distribution function of φ exhibits monostability → bistability → monostability transitions as the autocorrelation rate (λ) of a colored noise increases; (ii) in the bistability region the multiplicative noise drives the phase difference to turn over periodically; (iii) the slope K of the linear response of the junction potential difference (〈V 〉) can be somewhat reduced by means of tuning an optimal λ; (iv) the amplitude of φ in response to external sinusoidal signals changes with λ. For the case of small φ, after deriving the analytical expressions of the potential difference amplitude (〈V 〉_max) and the K in the presence of a dichotomous noise, we found nonmonotonic behavior of 〈V 〉_max and the slope K as a function of λ.