Topologically Driven Swelling of a Polymer Loop

Numerical studies of the average size of trivially knotted polymer loops with no excluded volume are undertaken. Topology is identified by Alexander and Vassiliev degree 2 invariants. Probability of a trivial knot, average gyration radius, and probability density distributions as functions of gyration radius are generated for loops of up to N=3000 segments. Gyration radii of trivially knotted loops are found to follow a power law similar to that of self avoiding walks consistent with earlier theoretical predictions.Comment: 6 pages, 4 figures, submitted to PNAS (USA) in Feb 200

On practical applicability of the Jarzynski relation in statistical mechanics: a pedagogical example

We suggest and discuss a simple model of an ideal gas under the piston to gain an insight into the workings of the Jarzynski identity connecting the average exponential of the work over the non-equilibrium trajectories with the equilibrium free energy. We show that the Jarzynski identity is valid for our system due to the very rapid molecules belonging to the tail of the Maxwell distribution. For the most interesting extreme, when the system volume is large, while the piston is moving with large speed (compared to thermal velocity) for a very short time, the necessary number of independent experimental runs to obtain a reasonable approximation for the free energy from averaging the non-equilibrium work grows exponentially with the system size.Comment: 15 pages, 7 figures, submitted to JP

A coil-globule transition of a semiflexible polymer driven by the addition of spherical particles

The phase behaviour of a single large semiflexible polymer immersed in a suspension of spherical particles is studied. All interactions are simple excluded volume interactions and the diameter of the spherical particles is an order of magnitude larger than the diameter of the polymer. The spherical particles induce a quite long ranged depletion attraction between the segments of the polymer and this induces a continuous coil-globule transition in the polymer. This behaviour gives an indication of the condensing effect of macromolecular crowding on DNA.Comment: 12 pages, 4 figure

Error-proof programmable self-assembly of DNA-nanoparticle clusters

We study theoretically a new generic scheme of programmable self-assembly of nanoparticles into clusters of desired geometry. The problem is motivated by the feasibility of highly selective DNA-mediated interactions between colloidal particles. By analyzing both a simple generic model and a more realistic description of a DNA-colloidal system, we demonstrate that it is possible to suppress the glassy behavior of the system, and to make the self-assembly nearly error-proof. This regime requires a combination of stretchable interparticle linkers (e.g. sufficiently long DNA), and a soft repulsive potential. The jamming phase diagram and the error probability are computed for several types of clusters. The prospects for the experimental implementation of our scheme are also discussed. PACS numbers: 81.16.Dn, 87.14.Gg, 36.40.EiComment: 6 pages, 4 figures, v2: substantially revised version, added journal re

Shear Banding from lattice kinetic models with competing interactions

Soft Glassy Materials, Non Linear Rheology, Lattice Kinetic models, frustrated phase separation} We present numerical simulations based on a Boltzmann kinetic model with competing interactions, aimed at characterizating the rheological properties of soft-glassy materials. The lattice kinetic model is shown to reproduce typical signatures of driven soft-glassy flows in confined geometries, such as Herschel-Bulkley rheology, shear-banding and histeresys. This lends further credit to the present lattice kinetic model as a valuable tool for the theoretical/computational investigation of the rheology of driven soft-glassy materials under confinement.Comment: 8 Pages, 5 Figure

Localization in simple multiparticle catalytic absorption model

We consider the phase transition in the system of n simultaneously developing random walks on the halfline x>=0. All walks are independent on each others in all points except the origin x=0, where the point well is located. The well depth depends on the number of particles simultaneously staying at x=0. We consider the limit n>>1 and show that if the depth growth faster than 3/2 n ln(n) with n, then all random walks become localized simultaneously at the origin. In conclusion we discuss the connection of that problem with the phase transition in the copolymer chain with quenched random sequence of monomers considered in the frameworks of replica approach.Comment: 17 pages in LaTeX, 5 PostScript figures; submitted to J.Phys.(A): Math. Ge

Electrostatic image effects for counter-ions between charged planar walls

We study the effect of dielectric inhomogeneities on the interaction between two planparallel charged surfaces with oppositely charged mobile charges in between. The dielectric constant between the surfaces is assumed to be different from the dielectric constant of the two semiinfinite regions bounded by the surfaces, giving rise to electrostatic image interactions. We show that on the weak coupling level the image charge effects are generally small, making their mark only in the second order fluctuation term. However, in the strong coupling limit, the image effects are large and fundamental. They modify the interactions between the two surfaces in an essential way. Our calculations are particularly useful in the regime of parameters where computer simulations would be difficult and extremely time consuming due to the complicated nature of the long range image potentials.Comment: 21 pages, 8 figure

What thermodynamic features characterize good and bad folders? Results from a simplified off-lattice protein model

The thermodynamics of the small SH3 protein domain is studied by means of a simplified model where each bead-like amino acid interacts with the others through a contact potential controlled by a 20x20 random matrix. Good folding sequences, characterized by a low native energy, display three main thermodynamical phases, namely a coil-like phase, an unfolded globule and a folded phase (plus other two phases, namely frozen and random coil, populated only at extremes temperatures). Interestingly, the unfolded globule has some regions already structured. Poorly designed sequences, on the other hand, display a wide transition from the random coil to a frozen state. The comparison with the analytic theory of heteropolymers is discussed

Thermodynamics and Topology of Disordered Systems: Statistics of the Random Knot Diagrams on Finite Lattice

The statistical properties of random lattice knots, the topology of which is determined by the algebraic topological Jones-Kauffman invariants was studied by analytical and numerical methods. The Kauffman polynomial invariant of a random knot diagram was represented by a partition function of the Potts model with a random configuration of ferro- and antiferromagnetic bonds, which allowed the probability distribution of the random dense knots on a flat square lattice over topological classes to be studied. A topological class is characterized by the highest power of the Kauffman polynomial invariant and interpreted as the free energy of a q-component Potts spin system for q->infinity. It is shown that the highest power of the Kauffman invariant is correlated with the minimum energy of the corresponding Potts spin system. The probability of the lattice knot distribution over topological classes was studied by the method of transfer matrices, depending on the type of local junctions and the size of the flat knot diagram. The obtained results are compared to the probability distribution of the minimum energy of a Potts system with random ferro- and antiferromagnetic bonds.Comment: 37 pages, latex-revtex (new version: misprints removed, references added