1,721,218 research outputs found
Statistical topology of closed curves: Some applications in polymer physics
No full textTopological entanglement in polymers and biopolymers is a topic that
involves different fields of science such as chemistry, biology,
physics, and mathematics. One of the main issues in this topic is to
understand how the entanglement complexity can depend on factors such as
the degree of polymerization, the quality of the solvent, and the
temperature or the degree of confinement of the macromolecule. In this
respect a statistical approach to the problem is natural and in the last
few years there has been a lot of work on the study of the entanglement
complexity of polymers within the statistical mechanics framework. A
review on this topic is given here stressing the main results obtained
and describing the tools most used with this approach
Hamiltonian dynamics reveals the existence of quasistationary states for long-range systems in contact with a reservoir
Full text linkWe introduce a Hamiltonian dynamics for the description of long-range
interacting systems in contact with a thermal bath (i.e., in the
canonical ensemble). The dynamics confirms statistical mechanics
equilibrium predictions for the Hamiltonian mean field model and the
equilibrium ensemble equivalence. We find that long-lasting
quasistationary states persist in the presence of the interaction with
the environment. Our results indicate that quasistationary states are
indeed reproducible in real physical experiments
Phase transitions of a two-dimensional periodic hydrophilic hydrophobic chain
No full textWe study a single self-avoiding hydrophilic hydrophobic polymer chain, through Monte Carlo lattice simulations. The affinity of monomer i for water is characterized by a (scalar) charge lambda(i), and the monomer-water interaction is short-ranged. Assuming incompressibility yields an effective short ranged interaction between monomer pairs (i, j), proportional to (lambda(i) + lambda(j)), In this article, we take lambda(i) = +1 (resp. (lambda(i) = -1)) for hydrophilic (resp, hydrophobic) monomers and consider a chain with (i) an equal number of hydrophilic and -phobic monomers (ii) a periodic distribution of the lambda(i) along the chain, with periodicity 2p. This model may be of interest in various situations (protein folding, polysoaps,...) The simulations are done on the square lattice (d = 2), for various chain lengths N. There is a critical value (p(c)(N) similar to 0.07N) of the periodicity, which distinguishes between different low temperature structures. For p > p(c), the ground state corresponds to a macroscopic phase separation between a dense hydrophobic core and hydrophilic loops. For p < p(c) (but not too small), one gets a microscopic (finite scale) phase separation, and the ground state corresponds to a chain or network of hydrophobic droplets, coated by hydrophilic monomers. These different cases will be explored through a Multiple Markov chain method. The results for the d = 3 case (where p(c)(N) similar to N-1/3) are similar
Incomplete equilibrium in long-range interacting systems
Full text linkWe use Hamiltonian dynamics to discuss the statistical mechanics of long-lasting quasistationary states particularly relevant for long-range interacting systems. Despite the presence of an anomalous single-particle velocity distribution, we find that the central limit theorem implies the Boltzmann expression in Gibbs' Gamma space. We identify the nonequilibrium submanifold of Gamma space characterizing the anomalous behavior and show that by restricting the Boltzmann-Gibbs approach to this submanifold we obtain the statistical mechanics of the quasistationary states
Monte Carlo results for projected self-avoiding polygons: a two-dimensional model for knotted polymers
No full textWe introduce a two-dimensional lattice model for the description of knotted polymer rings. A polymer configuration is modelled by a closed polygon drawn on the square diagonal lattice. with possible crossings describing pairs of strands of polymer passing on top of each other. Each polygon configuration can be viewed as the two-dimensional projection of a particular knot. We study numerically the statistics of large polygons with a fixed knot type, using a generalization of the BFACF algorithm for self-avoiding walks. This new algorithm incorporates both the displacement of crossings and the three types of Reidemeister transformations preserving the knot topology. Its ergodicity within a fixed knot type is not proven here rigorously but strong arguments in favour of this ergodicity are given together with a tentative sketch of proof. Assuming this ergodicity, we obtain numerically the following results for the statistics of knotted polygons: in the limit of a low crossing fugacity, we find a localization along the polygon of all the primary factors forming the knot. Increasing the crossing fugacity gives rise to a transition from a self-avoiding walk to a branched polymer behaviour
Phase separation dynamics on curved surfaces
No full textIn this work we present computer simulations of the dynamics of phase separation of a binary fluid on a variety of curved surfaces. The geometries considered range from sphere to ellipsoid, to models for budding cells, described as spheres with a bump. We study both the case in which there is no coupling between curvature and local composition, and the situation in which one of the two fluids, or lipids, prefers, or avoids, highly curved regions on the surface. Our results show that in these two cases there is a distinct difference in both the kinetic pathway to lipid sorting and the final localisation of the domains formed. Highlighting these differences should be useful, we expect, to discriminate between different theories for domain formation in a biophysical context
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