3,161 research outputs found
MUBs inequivalence and affine planes
There are fairly large families of unitarily inequivalent complete sets of
N+1 mutually unbiased bases (MUBs) in C^N for various prime powers N. The
number of such sets is not bounded above by any polynomial as a function of N.
While it is standard that there is a superficial similarity between complete
sets of MUBs and finite affine planes, there is an intimate relationship
between these large families and affine planes. This note briefly summarizes
"old" results that do not appear to be well-known concerning known families of
complete sets of MUBs and their associated planes.Comment: This is the version of this paper appearing in J. Mathematical
Physics 53, 032204 (2012) except for format changes due to the journal's
style policie
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.
From Collapse to Freezing in Random Heteropolymers
We consider a two-letter self-avoiding (square) lattice heteropolymer model
of N_H (out ofN) attracting sites. At zero temperature, permanent links are
formed leading to collapse structures for any fraction rho_H=N_H/N. The average
chain size scales as R = N^{1/d}F(rho_H) (d is space dimension). As rho_H -->
0, F(rho_H) ~ rho_H^z with z={1/d-nu}=-1/4 for d=2. Moreover, for 0 < rho_H <
1, entropy approaches zero as N --> infty (being finite for a homopolymer). An
abrupt decrease in entropy occurs at the phase boundary between the swollen (R
~ N^nu) and collapsed region. Scaling arguments predict different regimes
depending on the ensemble of crosslinks. Some implications to the protein
folding problem are discussed.Comment: 4 pages, Revtex, figs upon request. New interpretation and emphasis.
Submitted to Europhys.Let
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.
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
Pseudo-boundaries in discontinuous 2-dimensional maps
It is known that Kolmogorov-Arnold-Moser boundaries appear in sufficiently
smooth 2-dimensional area-preserving maps. When such boundaries are destroyed,
they become pseudo-boundaries. We show that pseudo-boundaries can also be found
in discontinuous maps. The origin of these pseudo-boundaries are groups of
chains of islands which separate parts of the phase space and need to be
crossed in order to move between the different sub-spaces. Trajectories,
however, do not easily cross these chains, but tend to propagate along them.
This type of behavior is demonstrated using a ``generalized'' Fermi map.Comment: 4 pages, 4 figures, Revtex, epsf, submitted to Physical Review E (as
a brief report
Folding transitions of the triangular lattice with defects
A recently introduced model describing the folding of the triangular lattice
is generalized allowing for defects in the lattice and written as an Ising
model with nearest-neighbor and plaquette interactions on the honeycomb
lattice. Its phase diagram is determined in the hexagon approximation of the
cluster variation method and the crossover from the pure Ising to the pure
folding model is investigated, obtaining a quite rich structure with several
multicritical points. Our results are in very good agreement with the available
exact ones and extend a previous transfer matrix study.Comment: 16 pages, latex, 5 postscript figure
Connecting the time domain community with the Virtual Astronomical Observatory
The time domain has been identified as one of the most important areas of
astronomical research for the next decade. The Virtual Observatory is in the
vanguard with dedicated tools and services that enable and facilitate the
discovery, dissemination and analysis of time domain data. These range in scope
from rapid notifications of time-critical astronomical transients to annotating
long-term variables with the latest modeling results. In this paper, we will
review the prior art in these areas and focus on the capabilities that the VAO
is bringing to bear in support of time domain science. In particular, we will
focus on the issues involved with the heterogeneous collections of (ancillary)
data associated with astronomical transients, and the time series
characterization and classification tools required by the next generation of
sky surveys, such as LSST and SKA.Comment: Submitted to Proceedings of SPIE Observatory Operations: Strategies,
Processes and Systems IV, Amsterdam, 2012 July 2-
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.
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