839 research outputs found
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
but different statistical segment lengths and 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
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 .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 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
where is average size of single random walk ring, the effective
topological interaction (free energy) scales .Comment: 16 pages, 3 figur
Mission to a comet - Preliminary scientific objectives and experiments for use in advanced mission studies
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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 -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
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