Field-theoretical approach to a dense polymer with an ideal binary mixture of clustering centers

We propose a field-theoretical approach to a polymer system immersed in an ideal mixture of clustering centers. The system contains several species of these clustering centers with different functionality, each of which connects a fixed number segments of the chain to each other. The field-theory is solved using the saddle point approximation and evaluated for dense polymer melts using the Random Phase Approximation. We find a short-ranged effective inter-segment interaction with strength dependent on the average segment density and discuss the structure factor within this approximation. We also determine the fractions of linkers of the different functionalities.Comment: 27 pages, 9 figures, accepted on Phys. Rev.

Enhanced diffusion and ordering of self-propelled rods

Starting from a minimal physical model of self propelled hard rods on a substrate in two dimensions, we derive a modified Smoluchowski equation for the system. Self -propulsion enhances longitudinal diffusion and modifies the mean field excluded volume interaction. From the Smoluchowski equation we obtain hydrodynamic equations for rod concentration, polarization and nematic order parameter. New results at large scales are a lowering of the density of the isotropic-nematic transition and a strong enhancement of boundary effects in confined self-propelled systems.Comment: 4 pages, 2 figure

The Concentration-Density Relation of Galaxies in Las Campanas Redshift Survey

We report the results of the evaluation of the ``concentration-density'' relation of galaxies in the local universe, taking advantage of the very large and homogeneous data set available from the Las Campanas Redshift Survey (Shectman et al. 1996). This data set consists of galaxies inhabiting the entire range of galactic environments, from the sparsest field to the densest clusters, thus allowing us to study environmental variations without combining multiple data sets with inhomogeneous characteristics. Concentration is quantified by the automatically-measured concentration index $C$, which is a good measure of a galaxy's bulge-to-disk ratio. The environment of the sample galaxies is characterized both by the three-space local galaxy density and by membership in groups and clusters. We find that the distribution of C in galaxy populations varies both with local density and with cluster/group membership: the fraction of centrally-concentrated galaxies increases with local galaxy density, and is higher in clusters than in the field. A comparison of the concentration-local density relation in clusters and the field shows that the two connect rather smoothly at the intermediate density regime, implying that the apparent cluster/field difference is only a manifestation of the variation with the local density. We conclude that the structure of galaxies is predominantly influenced by the local density and not by the broader environments characterized by cluster/field memberships.Comment: 11 pages, 4 figures, ApJ in press, uses psfig.st

Entanglement reduction induced by geometrical confinement in polymer thin films

We report simulation results on melts of entangled linear polymers confined in a free-standing thin film. We study how the geometric constraints imposed by the confinement alter the entanglement state of the system compared to the equivalent bulk system using various observables. We find that the confinement compresses the chain conformation uniaxially, decreasing the volume pervaded by the chain, which in turn reduces the number of the accessible inter-chain contact that could lead to entanglements. This local and non-uniform effect depends on the position of the chain within the film. We also test a recently presented theory that predicts how the number of entanglements decreases with geometrical confinement.Comment: 28 pages, 10 figure

Classification of graph C*-algebras with no more than four primitive ideals

We describe the status quo of the classification problem of graph C*-algebras with four primitive ideals or less

A field theoretic approach to master equations and a variational method beyond the Poisson ansatz

We develop a variational scheme in a field theoretic approach to a stochastic process. While various stochastic processes can be expressed using master equations, in general it is difficult to solve the master equations exactly, and it is also hard to solve the master equations numerically because of the curse of dimensionality. The field theoretic approach has been used in order to study such complicated master equations, and the variational scheme achieves tremendous reduction in the dimensionality of master equations. For the variational method, only the Poisson ansatz has been used, in which one restricts the variational function to a Poisson distribution. Hence, one has dealt with only restricted fluctuation effects. We develop the variational method further, which enables us to treat an arbitrary variational function. It is shown that the variational scheme developed gives a quantitatively good approximation for master equations which describe a stochastic gene regulatory network.Comment: 13 pages, 2 figure

Polymer drift in a solvent by force acting on one polymer end

We investigate the effect of hydrodynamic interactions on the non-equilibrium drift dynamics of an ideal flexible polymer pulled by a constant force applied at one end of the polymer using the perturbation theory and the renormalization group method. For moderate force, if the polymer elongation is small, the hydrodynamic interactions are not screened and the velocity and the longitudinal elongation of the polymer are computed using the renormalization group method. Both the velocity and elongation are nonlinear functions of the driving force in this regime. For large elongation we found two regimes. For large force but finite chain length $L$ the hydrodynamic interactions are screened. For large chain lengths and a finite force the hydrodynamic interactions are only partially screened, which in three dimensions results in unusual logarithmic corrections to the velocity and the longitudinal elongation.Comment: 6 page

Topological versus rheological entanglement length in primitive path analysis protocols

Primitive path analysis algorithms are now routinely employed to analyze entanglements in computer simulations of polymeric systems, but different analysis protocols result in different estimates of the entanglement length, N_e. Here we argue that standard PPA measures the rheological entanglement length, typically employed by tube models and relevant to quantitative comparisons with experiment, while codes like Z or CReTA also determine the topological entanglement length. For loosely entangled systems, a simple analogy between between phantom networks and the mesh of entangled primitive paths suggests a factor of two between the two numbers. This result is in excellent agreement with reported values for poly-ethylene, poly-butadiene and bead-spring polymer melts.Comment: 3 pages, no figure

Nonlinear waves in a model for silicate layers

Some layered silicates are composed of positive ions, surrounded by layers of ions with opposite sign. Mica muscovite is a particularly interesting material, because there exist fossil and experimental evidence for nonlinear excitations transporting localized energy and charge along the cation rows within the potassium layers. This evidence suggest that there are different kinds of excitations with different energies and properties. Some of the authors proposed recently a one-dimensional model based in physical principles and the silicate structure. The main characteristic of the model is that it has a hard substrate potential and two different repulsion terms, between ions and nuclei. In a previous work with this model, it was found the propagation of crowdions, i.e., lattice kinks in a lattice with substrate potential that transport mass and charge. They have a single specific velocity and energy coherent with the experimental data. In the present work we perform a much more thorough search for nonlinear excitations in the same model using the pseudospectral method to obtain exact nanopteron solutions, which are single kinks with tails, crowdions and bi-crowdions. We analyze their velocities, energies and stability or instability and the possible reasons for the latter. We relate the different excitations with their possible origin from recoils from different beta decays and with the fossil tracks. We explore the consequences of some variation of the physical parameters because their values are not perfectly known. Through a different method, we also have found stationary and moving breathers, that is, localized nonlinear excitations with an internal vibration. Moving breathers have small amplitude and energy, which is also coherent with the fossil evidence.MINECO (Spain) FIS2015-65998-C2-2-PJunta de Andalucía 2017/FQM-280Universidad de Sevilla (España) grants VI PPIT-US-201

Global cross-over dynamics of single semiflexible polymers

We present a mean-field dynamical theory for single semiflexible polymers which can precisely capture, without fitting parameters, recent fluorescence correlation spectroscopy results on single monomer kinetics of DNA strands in solution. Our approach works globally, covering three decades of strand length and five decades of time: it includes the complex cross-overs occurring between stiffness-dominated and flexible bending modes, along with larger-scale rotational and center-of-mass motion. The accuracy of the theory stems in part from long-range hydrodynamic coupling between the monomers, which makes a mean-field description more realistic. Its validity extends even to short, stiff fragments, where we also test the theory through Brownian hydrodynamics simulations.Comment: 6 pages, 5 figures; updated with minor changes to reflect published versio