898 research outputs found

### Principes en rhéologie des polymères fondus

URL: http://www-spht.cea.fr/articles/T93/082En théorie des polymères, pour des temps suffisamment longs, on peut s'attendre à observer un comportement universel qui intègre le concept de reptation valide pour des temps très longs et la relaxation de Rouse qui s'applique aux temps moins longs. Nous discutons ici l'agencement de ces principes

### Random Walk Model on a Hyper-Spherical Lattice

We use a one-dimensional random walk on $D$-dimensional hyper-spheres to
determine the critical behavior of statistical systems in hyper-spherical
geometries. First, we demonstrate the properties of such walk by studying the
phase diagram of a percolation problem. We find a line of second and first
order phase transitions separated by a tricritical point. Then, we analyze the
adsorption-desorption transition for a polymer growing near the attractive
boundary of a cylindrical cell membrane. We find that the fraction of adsorbed
monomers on the boundary vanishes exponentially when the adsorption energy
decreases towards its critical value. We observe a crossover phenomenon to an
area of linear growth at energies of the order of the inverse cell radius.Comment: to appear in NPB Proc. Suppl. of LATTICE'94, 3 pages, ps-file
uuencoded, 2 figures included, NO-NUM-

### Operator Product Expansion on a Fractal: The Short Chain Expansion for Polymer Networks

We prove to all orders of renormalized perturbative polymer field theory the
existence of a short chain expansion applying to polymer solutions of long and
short chains. For a general polymer network with long and short chains we show
factorization of its partition sum by a short chain factor and a long chain
factor in the short chain limit. This corresponds to an expansion for short
distance along the fractal perimeter of the polymer chains connecting the
vertices and is related to a large mass expansion of field theory.
The scaling of the second virial coefficient for bimodal solutions is
explained. Our method also applies to the correlations of the multifractal
measure of harmonic diffusion onto an absorbing polymer. We give a result for
expanding these correlations for short distance along the fractal carrier of
the measure.Comment: 28 pages, revtex, 4 Postscript figures, 3 latex emlines pictures.
Replacement eliminates conflict with a blob resul

### Self-Organization of Vortex Length Distribution in Quantum Turbulence: An Approach from the Barabasi-Albert Model

The energy spectrum of quantum turbulence obeys Kolmogorov's law. The vortex
length distribution (VLD), meaning the size distribution of the vortices, in
Kolmogorov quantum turbulence also obeys a power law. We propose here an
innovative idea to study the origin of the power law of the VLD. The nature of
quantized vortices allows one to describe the decay of quantum turbulence with
a simple model that is similar to the Barabasi-Albert model of large networks.
We show here that such a model can reproduce the power law of the VLD well.Comment: 4 pages including 5 figure

### Scattering functions of knotted ring polymers

We discuss the scattering function of a Gaussian random polygon with N nodes
under a given topological constraint through simulation. We obtain the Kratky
plot of a Gaussian polygon of N=200 having a fixed knot for some different
knots such as the trivial, trefoil and figure-eight knots. We find that some
characteristic properties of the different Kratky plots are consistent with the
distinct values of the mean square radius of gyration for Gaussian polygons
with the different knots.Comment: 4pages, 3figures, 3table

### Self-avoiding Tethered Membranes at the Tricritical Point

The scaling properties of self-avoiding tethered membranes at the tricritical
point (theta-point) are studied by perturbative renormalization group methods.
To treat the 3-body repulsive interaction (known to be relevant for polymers),
new analytical and numerical tools are developped and applied to 1-loop
calculations. These technics are a prerequisite to higher order calculations
for self-avoiding membranes. The cross-over between the 3-body interaction and
the modified 2-body interaction, attractive at long range, is studied through a
new double epsilon-expansion. It is shown that the latter interaction is
relevant for 2-dimensional membranes at the theta-point.Comment: 57 pages, gz-compressed ps-fil

### Large Orders for Self-Avoiding Membranes

We derive the large order behavior of the perturbative expansion for the
continuous model of tethered self-avoiding membranes. It is controlled by a
classical configuration for an effective potential in bulk space, which is the
analog of the Lipatov instanton, solution of a highly non-local equation. The
n-th order is shown to have factorial growth as (-cst)^n (n!)^(1-epsilon/D),
where D is the `internal' dimension of the membrane and epsilon the engineering
dimension of the coupling constant for self-avoidance. The instanton is
calculated within a variational approximation, which is shown to become exact
in the limit of large dimension d of bulk space. This is the starting point of
a systematic 1/d expansion. As a consequence, the epsilon-expansion of
self-avoiding membranes has a factorial growth, like the epsilon-expansion of
polymers and standard critical phenomena, suggesting Borel summability.
Consequences for the applicability of the 2-loop calculations are examined.Comment: 40 pages Latex, 32 eps-files included in the tex

### Individual Entanglements in a Simulated Polymer Melt

We examine entanglements using monomer contacts between pairs of chains in a
Brownian-dynamics simulation of a polymer melt. A map of contact positions with
respect to the contacting monomer numbers (i,j) shows clustering in small
regions of (i,j) which persists in time, as expected for entanglements. Using
the ``space''-time correlation function of the aforementioned contacts, we show
that a pair of entangled chains exhibits a qualitatively different behavior
than a pair of distant chains when brought together. Quantitatively, about 50%
of the contacts between entangled chains are persistent contacts not present in
independently moving chains. In addition, we account for several observed
scaling properties of the contact correlation function.Comment: latex, 12 pages, 7 figures, postscript file available at
http://arnold.uchicago.edu/~ebn

### Renormalization Theory for Interacting Crumpled Manifolds

We consider a continuous model of D-dimensional elastic (polymerized)
manifold fluctuating in d-dimensional Euclidean space, interacting with a
single impurity via an attractive or repulsive delta-potential (but without
self-avoidance interactions). Except for D=1 (the polymer case), this model
cannot be mapped onto a local field theory. We show that the use of intrinsic
distance geometry allows for a rigorous construction of the high-temperature
perturbative expansion and for analytic continuation in the manifold dimension
D. We study the renormalization properties of the model for 0<D<2, and show
that for d<d* where d*=2D/(2-D) is the upper critical dimension, the
perturbative expansion is UV finite, while UV divergences occur as poles at
d=d*. The standard proof of perturbative renormalizability for local field
theories (the BPH theorem) does not apply to this model. We prove perturbative
renormalizability to all orders by constructing a subtraction operator based on
a generalization of the Zimmermann forests formalism, and which makes the
theory finite at d=d*. This subtraction operation corresponds to a
renormalization of the coupling constant of the model (strength of the
interaction with the impurity). The existence of a Wilson function, of an
epsilon-expansion around the critical dimension, of scaling laws for d<d* in
the repulsive case, and of non-trivial critical exponents of the delocalization
transition for d>d* in the attractive case is thus established. To our
knowledge, this provides the first proof of renormalizability for a model of
extended objects, and should be applicable to the study of self-avoidance
interactions for random manifolds.Comment: 126 pages (+ 24 figures not included available upon request),
harvmac, SPhT/92/12

### Elastic Lattice Polymers

We study a model of "elastic" lattice polymer in which a fixed number of
monomers $m$ is hosted by a self-avoiding walk with fluctuating length $l$. We
show that the stored length density $\rho_m = 1 - /m$ scales asymptotically
for large $m$ as $\rho_m=\rho_\infty(1-\theta/m + ...)$, where $\theta$ is the
polymer entropic exponent, so that $\theta$ can be determined from the analysis
of $\rho_m$. We perform simulations for elastic lattice polymer loops with
various sizes and knots, in which we measure $\rho_m$. The resulting estimates
support the hypothesis that the exponent $\theta$ is determined only by the
number of prime knots and not by their type. However, if knots are present, we
observe strong corrections to scaling, which help to understand how an entropic
competition between knots is affected by the finite length of the chain.Comment: 10 page

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