Exotic baryons and monopole excitations in a chiral soliton model

We compute the spectra of exotic pentaquarks and monopole excitations of thelow-lying and baryons in a chiral soliton model. Once the low-lying baryon properties are fit, the other states are predicted without any more adjustable parameters. This approach naturally leads to a scenario in which the mass spectrum of the next to lowest-lying states is fairly well approximatedby the ideal mixing pattern of the representation of flavor SU(3). We compare our results to predictions obtained in other pictures for pentaquarks and speculate about the spin-parity assignment for and .Received: 21 April 2004, Revised: 19 May 2004, Published online: 23 July 2004PACS: 12.39.Dc Skyrmions - 14.20.-c Baryons (including antiparticles) - 14.80.-j Other particles (including hypothetical)     

Monte Carlo simulation of particle aggregation and gelation: II. Pair correlation function and structure factor

Diffusion-limited cluster aggregation and gelation are studied using lattice and off-lattice Monte Carlo simulations. The pair correlation function g(r) and the structure factor S(q) of the particle gels were investigated as a function of the volume fraction ( ) and time. At volume fractions below , the gel structure is fractal on small length scales with . g(r) shows a weak minimum at the correlation length ( ), before reaching the average concentration at large length scales. The cut-off function of g(r) varies during the aggregation process, but at a given , where is the gel time, it is a universal function of . At high volume fractions, the structure is dominated by excluded-volume interactions, while at low volume fractions, it is determined by the connectivity.Received: 27 April 2004, Published online: 26 October 2004PACS: 64.60.Ak Renormalization-group, fractal, and percolation studies of phase transitions - 02.70.Uu Applications of Monte Carlo methods     

Frequency dispersion of sound propagation in Rouse polymer melts via generalized dynamic random phase approximation

An extended generalization of the dynamic random phase approximation (DRPA) for L-component polymer systems is presented. Unlike the original version of the DRPA, which relates the matrices of the collective density-density time correlation functions and the corresponding susceptibilities of concentrated polymer systems to those of the tracer macromolecules and so-called broken-links system (BLS), our generalized DRPA solves this problem for the matrices of the coupled susceptibilities and time correlation functions of the component number, kinetic energy and flux densities. The presented technique is used to study propagation of sound and dynamic form-factor in disentangled (Rouse) monodisperse homopolymer melt. The calculated ultrasonic velocity and absorption coefficient reveal substantial frequency dispersion. The relaxation time is proportional to the degree of polymerization N, which is N times less than the Rouse time and evidences strong dynamic screening because of interchain interaction. We discuss also some peculiarities of the Brillouin scattering in polymer melts. Besides, a new convenient expression for the dynamic structure function of the single Rouse chain in representation is found.Received: 30 April 2003, Published online: 3 September 2003PACS: 43.35.Bf Ultrasonic velocity, dispersion, scattering, diffraction, and attenuation in liquids, liquid crystals, suspensions, and emulsions - 47.10. + g Fluid dynamics: General theory - 83.80.Sg Polymer melts     

Exact effective force between star-polymers in a $\Theta$-solvent

We re-examine here the computation of the effective force between two star-polymers of respective numbers of branches f₁ and f₂, immersed in a common -solvent. Such a force originates essentially from the repulsive three-body interactions. To achieve this, we take advantage of some established results using renormalization theory for three-dimensional star-polymers, or conformal invariance for two-dimensional ones. We first show that, in dimension d = 3, the force, , decreases with the center-to-center distance r as , with the exact universal amplitude . Second, in dimension d = 2, we find that the force decays more slowly as , with the exact universal amplitude . For high distances compared to the gyration radius, , of a single polymer chain at the -point, an exponential decay of the force is expected.Received: 3 February 2004, Published online: 24 May 2004PACS: 61.25.Hq Macromolecular and polymer solutions; polymer melts; swelling - 05.20.-y Classical statistical mechanics     

Deformation of adhering elastic tubes

Deformation of an elastic tube adhering onto a substrate due to van der Waals attractive force is investigated by means of numerical minimization and scaling theory. The onset of the deformation is determined by the critical value of , where is the bending constant, is the depth of the van der Waals potential, and N is the size of the tube. For a significantly deformed tube, we found a scaling behavior of the bending energy, which is explained within the shell theory.Received: 11 September 2003, Published online: 2 March 2004PACS: 68.35.-p Solid surfaces and solid-solid interfaces: Structure and energetics - 68.55.-a Thin film structure and morphology - 81.07.De Nanotubes     

Mechanical properties of mono-domain side chain nematic elastomers

We investigate the behavior of the shear rigidity modulus G = G + iG of three mono-domain side chain liquid-crystalline elastomers composed of side chain polysiloxanes cross-linked by either flexible or rigid cross-linkers. The measurements were taken in a frequency domain ranging form Hz to Hz applying the shear in a plane perpendicular to or containing the director. The measurements as a function of temperature show an anisotropy of G which appears around , when decreasing the temperature, and which is due to the expected lowering of coming from the coupling between the shear and the director. The measurements as a function of frequency show that G has two components for both geometries, in both the isotropic phase and in the nematic phase around the phase transition. One reflects the network behavior in its hydrodynamic regime (G is constant and , where f is the frequency), the other which appears at higher frequencies is characterized by a scaling law behavior ( ) of the Rouse type. We discuss the results in the framework of available theories and show that the three elastomers present a non-soft behavior, even for the elastomer for which the contrary was claimed, and that there is no separation of time scales between the director and the network. We also present data on a poly-domain sample and a non-mesomorphic one which complement these results.Received: 19 February 2004, Published online: 24 August 2004PACS: 83.80.Va Elastomeric polymers - 61.30.-v Liquid crystals - 83.60.Bc Linear viscoelasticityPresented at the First World Congress on Biomimetics and Artificial Muscles, 9-11 December 2002, Albuquerque, New Mexico, USA. Some aspects of this work have been published as an abridged version in the Proceedings of the Conference.     

Blobs,channels and “cigars”: Morphologies of liquids at a step

We have studied the equilibria of liquid droplets wetting a step edge with an opening angle by a combination of analytical and numerical methods. Depending on the wetting properties of the substrate walls and on the liquid volume, different locally or globally stable liquid morphologies are found. Complete spreading of the liquid along the bottom edge of the step is observed at equilibrium contact angles satisfying . If the contact angle exceeds a threshold value the liquid exists in a blob-like configuration. Surprisingly, we find an intermediate regime at a sufficiently high liquid volume and in a range of contact angles , in which cigar-shaped configurations arise in addition to the blob. We close the paper by a detailed discussion of the stability of this novel liquid morphology.PACS: 47.55.Dz Drops and bubbles - 61.30.Hn Surface phenomena: alignment, anchoring, anchoring transitions, surface-induced layering, surface-induced ordering, wetting, prewetting transitions, and wetting transitions - 68.08.Bc Wetting     

Nematic liquid crystal around a spherical particle: Investigation of the defect structure and its stability using adaptive mesh refinement

We investigate the orientation profile and the structure of topological defects of a nematic liquid crystal around a spherical particle using an adaptive mesh refinement scheme developed by us previously. The previous work [J. Fukuda et al., Phys. Rev. E 65, 041709 (2002)] was devoted to the investigation of the fine structure of a hyperbolic hedgehog defect that the particle accompanies and in this paper we present the equilibrium profile of the Saturn ring configuration. The radius of the Saturn ring r_d in units of the particle radius R₀ increases weakly with the increase of , the ratio of the nematic coherence length to R₀. Next we discuss the energetic stability of a hedgehog and a Saturn ring. The use of adaptive mesh refinement scheme together with a tensor orientational order parameter allows us to calculate the elastic energy of a nematic liquid crystal without any assumption of the structure and the energy of the defect core as in the previous similar studies. The reduced free energy of a nematic liquid crystal, , with L₁ being the elastic constant, is almost independent of in the hedgehog configuration, while it shows a logarithmic dependence in the Saturn ring configuration. This result clearly indicates that the energetic stability of a hedgehog to a Saturn ring for a large particle is definitely attributed to the large defect energy of the Saturn ring with a large radius.Received: 10 December 2003, Published online: 2 March 2004PACS: 61.30.Cz Molecular and microscopic models and theories of liquid crystal structure - 61.30.Jf Defects in liquid crystals - 82.20.Wt Computational modeling; simulation     

Dynamics of living polymers

We study theoretically the dynamics of living polymers which can add and subtract monomer units at their live chain ends. The classic example is ionic living polymerization. In equilibrium, a delicate balance is maintained in which each initiated chain has a very small negative average growth rate (velocity) just sufficient to negate the effect of growth rate fluctuations. This leads to an exponential molecular weight distribution (MWD) with mean . After a small perturbation of relative amplitude , e.g. a small temperature jump, this balance is destroyed: the velocity acquires a boost greatly exceeding its tiny equilibrium value. For the response has 3 stages: (1) Coherent chain growth or shrinkage, leaving a highly non-linear hole or peak in the MWD at small chain lengths. During this episode, lasting time , the MWDs first moment and monomer concentration m relax very close to equilibrium. (2) Hole-filling (or peak decay) after . The absence or surfeit of small chains is erased. (3) Global MWD shape relaxation after . By this time second and higher MWD moments have relaxed. During episodes (2) and (3) the fast variables ( ) are enslaved to the slowly varying number of free initiators (chains of zero length). Thus fast variables are quasi-statically fine-tuned to equilibrium. The outstanding feature of these dynamics is their ultrasensitivity: despite the perturbations linearity, the response is non-linear until the late episode (3). For very small perturbations, , response remains non-linear but with a less dramatic peak or hole during episode (1). Our predictions are in agreement with viscosity measurements on the most widely studied system, -methylstyrene.Received: 23 September 2003PACS: 82.35.-x Polymers: properties; reactions; polymerization - 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian Motion - 87.15.Rn Biomolecules: structure and physical properties; Reactions and kinetics; polymerization     

Variational theory for a single polyelectrolyte chain revisited

We reconsider the electrostatic contribution to the persistence length, , of a single, infinitely long-charged polymer in the presence of screening. A Gaussian variational method is employed, taking as the only variational parameter. For weakly charged and flexible chains, crumpling occurs at small length scales because conformational fluctuations overcome electrostatic repulsion. The electrostatic persistence length depends on the square of the screening length, , as first argued by Khokhlov and Khachaturian by applying the Odijk-Skolnick-Fixman (OSF) theory to a string of crumpled blobs. We compare our approach to previous theoretical works (including variational formulations) and show that the result found by several authors comes from the improper use of a cutoff at small length scales. For highly charged and stiff chains, crumpling does not occur; here we recover the OSF result and validate the perturbative calculation for slightly bent rods.PACS: 36.20.-r Macromolecules and polymer molecules - 82.70.-y Disperse systems; complex fluids - 87.15.-v Biomolecules: structure and physical properties     

Force between unlike star-polymers versus the solvent quality

We re-examine here the computation of the effective force between two star-polymers A and B of different chemical nature, which are immersed in a common solvent. This force originates from the excluded-volume interactions and chemical segregation. We assume that the solvent quality may be different for the two unlike star-polymers, that is the solvent can be 1) a good solvent for A and B, 2) a good solvent for A and a -solvent for B, or 3) a -solvent for the two polymers. The purpose is a quantitative study of the effect of the solvent quality on the effective force, which is a function of the center-to-center distance. Calculations are achieved using the renormalization theory applied to the Edwards continuous model. We first show that, when the mutual interactions are present, the effective force decays as the inverse of distance, but with a universal amplitude depending on the solvent quality. Second, we demonstrate the existence of three kinds of forces related to situations 1), 2) and 3) described above, and give the third-order -expansions ( , 4 is the critical dimension) of the corresponding amplitudes. These series can be resummed using the Borel-Leroy techniques to obtain the best three-dimensional values for the expected force amplitudes. Finally, this work must be regarded as a natural extension of a published one which dealt with the same problem, but where the solvent was assumed to be good for the two unlike star-polymers.Received: 3 February 2004, Published online: 24 May 2004PACS: 61.25.Hq Macromolecular and polymer solutions; polymer melts; swelling - 64.75. + g Solubility, segregation, and mixing; phase separation     

Surface and bulk interchange energy in binary mixtures of chain molecules

The interchange (interaction) parameter, controlling the phase behaviour of a binary mixture, is determined for the bulk and the surface of binary mixtures of different types of chain molecules, using surface tensiometry and a mean-field theory. For all mixtures and concentrations studied an identical behaviour is observed at the surface, depending only on the square of the reduced chain length mismatch , where and are the difference in and average of the number of carbons of the two components.Received: 21 December 2003, Published online: 25 March 2004PACS: 61.30.Hn Surface phenomena: alignment, anchoring, anchoring transitions, surface-induced layering, surface-induced ordering, wetting, prewetting transitions, and wetting transitions - 68.35.Md Surface thermodynamics, surface energies - 68.03.Cd Surface tension and related phenomena     

Power law polydispersity and fractal structure of hyperbranched polymers

Using the complementary approaches of Flory theory and the overlap function, we study the molecular weight distribution and conformation of hyperbranched polymers formed by the melt polycondensation of A-R_N0-B_{f - 1} monomers in their reaction bath close to the mean field gel point p_A = 1, where p_A is the fraction of reacted A groups. Here , N₀ is the degree of polymerisation of the linear spacer linking the A group and the f-1 B groups and condensation occurs exclusively between the A and B groups. For , we assume that the number density of hyperbranched polymers with degree of polymerisation N generally obeys the scaling form and we explicitly show that this scaling assumption is correct in the mean field regime (here N_l is the largest characteristic degree of polymerisation and the function cuts off the power law sharply for ). We find the upper critical dimension for this system is d_c = 4, so that for the mean field values for the polydispersity exponent and fractal dimension apply: , d_f = 4. For d = 3, mean field theory is still correct for where is the Ginzburg point; for , mean field theory applies on small mass scales N<N_c but breaks down on larger mass scales N>N_c where is a cross-over mass. Within the Ginzburg zone (i.e., d<d_c, ), we show that the hyperbranched chains on mass scales N>N_c are non-Gaussian with fractal dimension given by d_f = d (for d = 2,3,4). Our results are qualitatively different from those of the percolation model and indicate that the polycondensation of AB_f-1, unlike polymer gelation, is not described by percolation theory. Instead many of our results are similar to those for a monodisperse melt of randomly branched polymers, a consequence of the fact that so that polydispersity is irrelevant for excluded volume screening in hyperbranched polymer melts.Received: 15 December 2003, Published online: 2 March 2004PACS: 82.35.-x Polymers: properties; reactions; polymerization - 05.70.Jk Critical point phenomena     

Can the glass transition in bulk polymers be modeled by percolation picture?

Recent observations (Eur. Phys. J. E 9, 135 (2002)) showed that the vitrification process, which sets in during the linear bulk methyl methacrylate (MMA) polymerization carried out below glass transition temperatures, can be modelled by static percolation picture. To generalize this observation for different kind of bulk linear or crosslinked polymers not enough data are present in the literature. To cover partly this deficit we studied the glass transition of MMA and styrene (Sty) crosslinking copolymerization in varying ratios of MMA and Sty. Both the fluorescence intensity I and the lifetime of pyrene (Py) used as a nanosecond in situ fluoroprobe were monitored during the gelation time. Both I and increase dramatically as a result of the reduced mobility of the probes trapped in the glassy regions, appearing near the glass transition point. The average size of the glassy regions just below, and the strength of the infinite network formed upon the connection of the glassy regions above the glass transition point obey power law relations. The data around were interpreted on the basis of the percolation theory and we observed that the corresponding exponents and give static percolation values independent of the polymer composition.Received: 9 July 2004, Published online: 1 October 2004PACS: 64.60.Ak Renormalization-group, fractal, and percolation studies of phase transitions - 64.70.Pf Glass transitions - 82.35.Jk Copolymers, phase transitions, structure     

Influence of hydrodynamics on many-particle diffusion in 2D colloidal suspensions

We study many-particle diffusion in 2D colloidal suspensions with full hydrodynamic interactions through a novel mesoscopic simulation technique. We focus on the behaviour of the effective scaled tracer and collective-diffusion coefficients and , respectively, where D₀ is the single-particle diffusion coefficient, as a function of the density of the colloids . At low Schmidt numbers , we find that hydrodynamics has essentially no effect on the behaviour of . At larger Sc, seems to be enhanced at all densities, although the differences compared to the case without hydrodynamics are rather minor. The collective-diffusion coefficient, on the other hand, is much more strongly coupled to hydrodynamical conservation laws and is distinctly different from the purely dissipative case without hydrodynamic interactions.Received: 20 October 2003, Published online: 23 March 2004PACS: 68.35.Fx Diffusion; interface formation - 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion - 82.20.Wt Physical chemistry and chemical physics: Computational modeling; simulation     

Calculation of the persistence length of a flexible polymer chain with short-range self-repulsion

For a self-repelling polymer chain consisting of n segments we calculate the persistence length , defined as the projection of the end-to-end vector on the direction of the j-th segment. This quantity shows some pronounced variation along the chain. Using the renormalization group and -expansion we establish the scaling form and calculate the scaling function to order . Asymptotically, the simple result emerges for dimension d = 3. Also away from the excluded-volume limit is found to behave very similar to the swelling factor of a chain of length . We carry through simulations which are found to be in good accord with our analytical results. For d = 2 both our and previous simulations as well as theoretical arguments suggest the existence of logarithmic anomalies.Received: 17 November 2003, Published online: 30 March 2004PACS: 61.25.Hq Macromolecular and polymer solutions; polymer melts; swelling - 05.10.Cc Renormalization group methods     

Miscible displacement of non-Newtonian fluids in a vertical tube

The influence of rheology on the miscible displacement of a viscous fluid by a less viscous, Newtonian one in a vertical tube is studied experimentally as a function of the flow velocity. For Newtonian displaced fluids the transient residual film thickness is nearly of the tube radius at large viscosity ratios between the two fluids in agreement with experimental and numerical results from the literature. For shear-thinning fluids with a zero yield stress (mostly xanthan-water solutions), decreases down to of the radius for the most concentrated solutions. For fluids with a non-zero yield stess, further decreases down to 24-25% of the radius. The orders of magnitude of these values can be obtained through numerical simulations (commercial code) for the various types of fluids. Instabilities of the film at its boundary develop downstream and lead to a reduction of the final thickness of the film at longer times: this reduction is larger for lower viscosity ratios and larger velocities.Received: 15 February 2003, Published online: 8 July 2003PACS: 47.20.Gv Hydrodynamic stability: Viscous instability - 83.60.Wc Rheology: Flow instabilities     

Enhancement of the orientational order parameter of nematic liquid crystals in thin cells

We report measurements of birefringence of several nematic liquid crystals having transverse as well as longitudinal dipole moments in thin (1.4 to ) and thick (7 to cells. Rubbed polyimide-coated glass plates are used to get planar alignment of the nematic director in these cells. We find significant enhancement (6 to ) of ( , where S is the orientational order parameter) in thin cells in all compounds with aromatic cores even at temperatures far ( C) below the nematic-isotropic transition point. The enhancement is larger in compounds having several phenyl rings and lower if the number of phenyl rings is reduced. In a compound that does not have an aromatic core no significant enhancement is observed, implying that the strength of the surface potential depends on the aromaticity of the cores. Assuming a perfect orientational order at the surface, calculations based on the Landau-de Gennes theory show that the thickness averaged enhancement of S is sharply reduced as the temperature is lowered in the nematic phase. The measured order parameter S is further enhanced in thin cells because of the stiffening of the elastic constant which reduces the thermal fluctuations of the nematic director. The combined effect is however too small at low temperatures to account for the experimental data.Received: 22 February 2004, Published online: 24 May 2004PACS: 61.30.-v Liquid crystals - 61.30.Pq Microconfined liquid crystals: droplets, cylinders, randomly confined liquid crystals, polymer dispersed liquid crystals, and porous systems - 61.30.Hn Surface phenomena: alignment, anchoring, anchoring transitions, surface-induced layering, surface-induced ordering, wetting, prewetting transitions, and wetting transitionsSurajit Dhara: Present address: Department of Physics, Birla Institute of Technology and Science, Pilani 333 031, India.     

Phase chirality and stereo-selective swelling of cholesteric elastomers

Cholesteric elastomers possess a macroscopic phase chirality as the director rotates in a helical fashion along an optical axis z and can be described by a chiral order parameter . This parameter can be tuned by changing the helix pitch p and the elastic properties of the network at formation. The cholesterics also possess a local nematic order, changing with temperature or during solvent swelling. In this paper, by measuring the power of optical rotation , we discover how these two parameters vary as functions of temperature or solvent adsorbed by the network. The main result is a finding of pronounced stereo-selectivity of cholesteric elastomers, demonstrating itself in the retention of the correct chirality component of a racemic solvent. It has been possible to quantify the amount of such stereo-separation, and the basic dynamics of the effect.Received: 18 August 2003, Published online: 5 February 2004PACS: 33.55.Ad Optical activity, optical rotation; circular dichroism - 61.30.Vx Polymer liquid crystals - 87.80.Pa Morphometry and stereology     

Dynamics of propylene glycol and its oligomers confined in clay

The dynamics of propylene glycol (PG) and its oligomers 7-PG and PPG, with (about 70 monomers), confined in a Na-vermiculite clay have been investigated by quasi-elastic neutron scattering and dielectric spectroscopy. The liquids are confined to a single molecular layer between the clay platelets, thus giving a true 2D liquid. The results show that the average relaxation time , deduced from neutron scattering at a momentum transfer Q of about , is in perfect agreement with the dielectric -relaxation time, although neutron scattering does not only probe the main ( -) relaxation, but all motions of hydrogens on the experimental time scale. At room temperature is proportional to Q ², indicating that the relaxations are mainly due to ordinary translational diffusion. The most unexpected finding is that (or the dielectric -relaxation time) is almost unaffected by the 2D confinement, in contrast to the dielectrically active normal mode of PPG which is substantially slower in the confinement. Only the 7-mer has a significantly slower segmental translational diffusion in the clay. The results suggest that the interactions to the clay surfaces are weak and that the present 2D confinement has a very small influence on the time scale of all our observed relaxation processes, except the normal-mode relaxation.Received: 1 January 2003, Published online: 8 October 2003PACS: 61.25.Em Molecular liquids - 68.35.Ja Surface and interface dynamics and vibrations - 61.12.-q Neutron diffraction and scattering