2,397 research outputs found
A Model Ground State of Polyampholytes
The ground state of randomly charged polyampholytes is conjectured to have a
structure similar to a necklace, made of weakly charged parts of the chain,
compacting into globules, connected by highly charged stretched `strings'. We
suggest a specific structure, within the necklace model, where all the neutral
parts of the chain compact into globules: The longest neutral segment compacts
into a globule; in the remaining part of the chain, the longest neutral segment
(the 2nd longest neutral segment) compacts into a globule, then the 3rd, and so
on. We investigate the size distributions of the longest neutral segments in
random charge sequences, using analytical and Monte Carlo methods. We show that
the length of the n-th longest neutral segment in a sequence of N monomers is
proportional to N/(n^2), while the mean number of neutral segments increases as
sqrt(N). The polyampholyte in the ground state within our model is found to
have an average linear size proportional to sqrt(N), and an average surface
area proportional to N^(2/3).Comment: 8 two-column pages. 5 eps figures. RevTex. Submitted to Phys. Rev.
Theta-point universality of polyampholytes with screened interactions
By an efficient algorithm we evaluate exactly the disorder-averaged
statistics of globally neutral self-avoiding chains with quenched random charge
in monomer i and nearest neighbor interactions on
square (22 monomers) and cubic (16 monomers) lattices. At the theta transition
in 2D, radius of gyration, entropic and crossover exponents are well compatible
with the universality class of the corresponding transition of homopolymers.
Further strong indication of such class comes from direct comparison with the
corresponding annealed problem. In 3D classical exponents are recovered. The
percentage of charge sequences leading to folding in a unique ground state
approaches zero exponentially with the chain length.Comment: 15 REVTEX pages. 4 eps-figures . 1 tabl
A Census Of Highly Symmetric Combinatorial Designs
As a consequence of the classification of the finite simple groups, it has
been possible in recent years to characterize Steiner t-designs, that is
t-(v,k,1) designs, mainly for t = 2, admitting groups of automorphisms with
sufficiently strong symmetry properties. However, despite the finite simple
group classification, for Steiner t-designs with t > 2 most of these
characterizations have remained longstanding challenging problems. Especially,
the determination of all flag-transitive Steiner t-designs with 2 < t < 7 is of
particular interest and has been open for about 40 years (cf. [11, p. 147] and
[12, p. 273], but presumably dating back to 1965). The present paper continues
the author's work [20, 21, 22] of classifying all flag-transitive Steiner
3-designs and 4-designs. We give a complete classification of all
flag-transitive Steiner 5-designs and prove furthermore that there are no
non-trivial flag-transitive Steiner 6-designs. Both results rely on the
classification of the finite 3-homogeneous permutation groups. Moreover, we
survey some of the most general results on highly symmetric Steiner t-designs.Comment: 26 pages; to appear in: "Journal of Algebraic Combinatorics
Ground States of Two-Dimensional Polyampholytes
We perform an exact enumeration study of polymers formed from a (quenched)
random sequence of charged monomers , restricted to a 2-dimensional
square lattice. Monomers interact via a logarithmic (Coulomb) interaction. We
study the ground state properties of the polymers as a function of their excess
charge for all possible charge sequences up to a polymer length N=18. We
find that the ground state of the neutral ensemble is compact and its energy
extensive and self-averaging. The addition of small excess charge causes an
expansion of the ground state with the monomer density depending only on .
In an annealed ensemble the ground state is fully stretched for any excess
charge .Comment: 6 pages, 6 eps figures, RevTex, Submitted to Phys. Rev.
Effects of Self-Avoidance on the Tubular Phase of Anisotropic Membranes
We study the tubular phase of self-avoiding anisotropic membranes. We discuss
the renormalizability of the model Hamiltonian describing this phase and derive
from a renormalization group equation some general scaling relations for the
exponents of the model. We show how particular choices of renormalization
factors reproduce the Gaussian result, the Flory theory and the Gaussian
Variational treatment of the problem. We then study the perturbative
renormalization to one loop in the self-avoiding parameter using dimensional
regularization and an epsilon-expansion about the upper critical dimension, and
determine the critical exponents to first order in epsilon.Comment: 19 pages, TeX, uses Harvmac. Revised Title and updated references: to
appear in Phys. Rev.
Annealed lower tails for the energy of a polymer
We consider the energy of a randomly charged polymer. We assume that only
charges on the same site interact pairwise. We study the lower tails of the
energy, when averaged over both randomness, in dimension three or more. As a
corollary, we obtain the correct temperature-scale for the Gibbs measure.Comment: 27 page
Crumpling a Thin Sheet
Crumpled sheets have a surprisingly large resistance to further compression.
We have studied the crumpling of thin sheets of Mylar under different loading
conditions. When placed under a fixed compressive force, the size of a crumpled
material decreases logarithmically in time for periods up to three weeks. We
also find hysteretic behavior when measuring the compression as a function of
applied force. By using a pre-treating protocol, we control this hysteresis and
find reproducible scaling behavior for the size of the crumpled material as a
function of the applied force.Comment: revtex 4 pages, 6 eps figures submitted to Phys Rev. let
Division, adjoints, and dualities of bilinear maps
The distributive property can be studied through bilinear maps and various
morphisms between these maps. The adjoint-morphisms between bilinear maps
establish a complete abelian category with projectives and admits a duality.
Thus the adjoint category is not a module category but nevertheless it is
suitably familiar. The universal properties have geometric perspectives. For
example, products are orthogonal sums. The bilinear division maps are the
simple bimaps with respect to nondegenerate adjoint-morphisms. That formalizes
the understanding that the atoms of linear geometries are algebraic objects
with no zero-divisors. Adjoint-isomorphism coincides with principal isotopism;
hence, nonassociative division rings can be studied within this framework.
This also corrects an error in an earlier pre-print; see Remark 2.11
Collapse of Stiff Polyelectrolytes due to Counterion Fluctuations
The effective elasticity of highly charged stiff polyelectrolytes is studied
in the presence of counterions, with and without added salt. The rigid polymer
conformations may become unstable due to an effective attraction induced by
counterion density fluctuations. Instabilities at the longest, or intermediate
length scales may signal collapse to globule, or necklace states, respectively.
In the presence of added-salt, a generalized electrostatic persistence length
is obtained, which has a nontrivial dependence on the Debye screening length.Comment: 4 pages RevTex, 3 ps figures included using epsf, final version as
appeared in PR
First Passage Distributions in a Collective Model of Anomalous Diffusion with Tunable Exponent
We consider a model system in which anomalous diffusion is generated by
superposition of underlying linear modes with a broad range of relaxation
times. In the language of Gaussian polymers, our model corresponds to Rouse
(Fourier) modes whose friction coefficients scale as wavenumber to the power
. A single (tagged) monomer then executes subdiffusion over a broad range
of time scales, and its mean square displacement increases as with
. To demonstrate non-trivial aspects of the model, we numerically
study the absorption of the tagged particle in one dimension near an absorbing
boundary or in the interval between two such boundaries. We obtain absorption
probability densities as a function of time, as well as the position-dependent
distribution for unabsorbed particles, at several values of . Each of
these properties has features characterized by exponents that depend on
. Characteristic distributions found for different values of
have similar qualitative features, but are not simply related quantitatively.
Comparison of the motion of translocation coordinate of a polymer moving
through a pore in a membrane with the diffusing tagged monomer with identical
also reveals quantitative differences.Comment: LaTeX, 10 pages, 8 eps figure
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