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

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

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

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

Elasticity of entangled polymer loops: Olympic gels

In this note we present a scaling theory for the elasticity of olympic gels, i.e., gels where the elasticity is a consequence of topology only. It is shown that two deformation regimes exist. The first is the non affine deformation regime where the free energy scales linear with the deformation. In the large (affine) deformation regime the free energy is shown to scale as $F \propto \lambda^{5/2}$ where $\lambda$ is the deformation ratio. Thus a highly non Hookian stress - strain relation is predicted.Comment: latex, no figures, accepted in PRE Rapid Communicatio

Windings of the 2D free Rouse chain

We study long time dynamical properties of a chain of harmonically bound Brownian particles. This chain is allowed to wander everywhere in the plane. We show that the scaling variables for the occupation times T_j, areas A_j and winding angles \theta_j (j=1,...,n labels the particles) take the same general form as in the usual Brownian motion. We also compute the asymptotic joint laws P({T_j}), P({A_j}), P({\theta_j}) and discuss the correlations occuring in those distributions.Comment: Latex, 17 pages, submitted to J. Phys.

Critical exponents for random knots

The size of a zero thickness (no excluded volume) polymer ring is shown to scale with chain length $N$ in the same way as the size of the excluded volume (self-avoiding) linear polymer, as $N^{\nu}$, where $\nu \approx 0.588$. The consequences of that fact are examined, including sizes of trivial and non-trivial knots.Comment: 4 pages, 0 figure

Istodobno spektrofotometrijsko određivanje losartan kalija, amlodipin besilata i hidroklorotiazida u farmaceutskim pripravcima kemometrijskom metodom

In the present work, four different spectrophotometric methods for simultaneous estimation of losartan potassium, amlodipine besilate and hydrochlorothiazide in raw materials and in formulations are described. Overlapped data was quantitatively resolved by using chemometric methods, classical least squares (CLS), multiple linear regression (MLR), principal component regression (PCR) and partial least squares (PLS). Calibrations were constructed using the absorption data matrix corresponding to the concentration data matrix, with measurements in the range of 230.5350.4 nm (∆λ = 0.1 nm) in their zero order spectra. The linearity range was found to be 840, 15 and 315 μg ml1 for losartan potassium, amlodipine besilate and hydrochlorothiazide, respectively. The validity of the proposed methods was successfully assessed for analyses of drugs in the various prepared physical mixtures and in tablet formulations.U radu su opisane četiri spektrofotometrijske metode za istodobno određivanje losartan kalija, amlodipin besilata i hidroklorotiazida u sirovinama i farmaceutskim pripravcima. Podaci koji su se preklapali kvantitativno su razlučeni kemometrijskim metodama, klasičnom metodom najmanjih kvadrata (CLS), multiplom linearnom regresijom (MLR), regresijom glavnih komponenata (PCR) te metodom parcijalnih najmanjih kvadrata (PLS). Kalibracije su provedene koristeći podatke o ovisnosti apsorpcije o koncentracijama, mjereći spektre nultog reda u rasponu 230,5350,4 nm (∆λ = 0,1 nm). Linearnost za losartan kalij bila je 840, za amlodipin besilat 15, a za hidroklorotiazid 315 μg ml1. Valjanost predloženih metoda uspješno je potvrđena analizom navedenih lijekova u različitim pripremljenim smjesama i tabletama