Topological Entanglement of Polymers and Chern-Simons Field Theory

In recent times some interesting field theoretical descriptions of the statistical mechanics of entangling polymers have been proposed by various authors. In these approaches, a single test polymer fluctuating in a background of static polymers or in a lattice of obstacles is considered. The extension to the case in which the configurations of two or more polymers become non-static is not straightforward unless their trajectories are severely constrained. In this paper we present another approach, based on Chern--Simons field theory, which is able to describe the topological entanglements of two fluctuating polymers in terms of gauge fields and second quantized replica fields.Comment: 16 pages, corrected some typos, added two new reference

Surface segregation of conformationally asymmetric polymer blends

We have generalized the Edwards' method of collective description of dense polymer systems in terms of effective potentials to polymer blends in the presence of a surface. With this method we have studied conformationally asymmetric athermic polymer blends in the presence of a hard wall to the first order in effective potentials. For polymers with the same gyration radius $R_g$ but different statistical segment lengths $l_{A}$ and $l_{B}$ the excess concentration of stiffer polymers at the surface is derived as % \delta \rho _{A}(z=0)\sim (l_{B}^{-2}-l_{A}^{-2}){\ln (}R_{g}^{2}/l_{c}^{2}{)%}, where $l_{c}$ is a local length below of which the incompressibility of the polymer blend is violated. For polymer blends differing only in degrees of polymerization the shorter polymer enriches the wall.Comment: 11 pages, 7 figures, revtex

Entangled Polymer Rings in 2D and Confinement

The statistical mechanics of polymer loops entangled in the two-dimensional array of randomly distributed obstacles of infinite length is discussed. The area of the loop projected to the plane perpendicular to the obstacles is used as a collective variable in order to re-express a (mean field) effective theory for the polymer conformation. It is explicitly shown that the loop undergoes a collapse transition to a randomly branched polymer with $R\propto lN^\frac{1}{4}$.Comment: 17 pages of Latex, 1 ps figure now available upon request, accepted for J.Phys.A:Math.Ge

Topological interactions in systems of mutually interlinked polymer rings

The topological interaction arising in interlinked polymeric rings such as DNA catenanes is considered. More specifically, the free energy for a pair of linked random walk rings is derived where the distance $R$ between two segments each of which is part of a different ring is kept constant. The topology conservation is imposed by the Gauss invariant. A previous approach (M.Otto, T.A. Vilgis, Phys.Rev.Lett. {\bf 80}, 881 (1998)) to the problem is refined in several ways. It is confirmed, that asymptotically, i.e. for large $R\gg R_G$ where $R_G$ is average size of single random walk ring, the effective topological interaction (free energy) scales $\propto R^4$.Comment: 16 pages, 3 figur

Mission to a comet - Preliminary scientific objectives and experiments for use in advanced mission studies

Scientific objectives and experiments for comet missio

On Abelian Multi-Chern-Simons Field Theories

In this paper a class of multi-Chern-Simons field theories which is relevant to the statistical mechanics of polymer systems is investigated. Motivated by the problems which one encounters in the treatment of these theories, a general procedure is presented to eliminate the Chern-Simons fields from their action. In this way it has been possible to derive an expression of the partition function of topologically linked polymers which depends explicitly on the topological numbers and does not have intractable nonlocal terms as it happened in previous approaches. The new formulation of multi-Chern-Simons field theories is then used to remove and clarify some inconsistencies and ambiguities which apparently affect field theoretical models of topologically linked polymers. Finally, the limit of disentangled polymers is discussed.Comment: 18 pages, plain LaTe

Deduction of skin friction by Clauser technique in unsteady turbulent boundary layers

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47083/1/348_2004_Article_BF00193426.pd

Area versus Length Distribution for Closed Random Walks

Using a connection between the $q$-oscillator algebra and the coefficients of the high temperature expansion of the frustrated Gaussian spin model, we derive an exact formula for the number of closed random walks of given length and area, on a hypercubic lattice, in the limit of infinite number of dimensions. The formula is investigated in detail, and asymptotic behaviours are evaluated. The area distribution in the limit of long loops is computed. As a byproduct, we obtain also an infinite set of new, nontrivial identities.Comment: 17 page

Three-Dimensional Adaptive Grid Computation with Conservative, Marker-Based Tracking for Interfacial Fluid Dynamics

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76614/1/AIAA-2006-1523-676.pd