25,266 research outputs found
Multicanonical Recursions
The problem of calculating multicanonical parameters recursively is
discussed. I describe in detail a computational implementation which has worked
reasonably well in practice.Comment: 23 pages, latex, 4 postscript figures included (uuencoded
Z-compressed .tar file created by uufiles), figure file corrected
The smallest eigenvalue of Hankel matrices
Let H_N=(s_{n+m}),n,m\le N denote the Hankel matrix of moments of a positive
measure with moments of any order. We study the large N behaviour of the
smallest eigenvalue lambda_N of H_N. It is proved that lambda_N has exponential
decay to zero for any measure with compact support. For general determinate
moment problems the decay to 0 of lambda_N can be arbitrarily slow or
arbitrarily fast. In the indeterminate case, where lambda_N is known to be
bounded below by a positive constant, we prove that the limit of the n'th
smallest eigenvalue of H_N for N tending to infinity tends rapidly to infinity
with n. The special case of the Stieltjes-Wigert polynomials is discussed
Defect-induced spin-glass magnetism in incommensurate spin-gap magnets
We study magnetic order induced by non-magnetic impurities in quantum
paramagnets with incommensurate host spin correlations. In contrast to the
well-studied commensurate case where the defect-induced magnetism is spatially
disordered but non-frustrated, the present problem combines strong disorder
with frustration and, consequently, leads to spin-glass order. We discuss the
crossover from strong randomness in the dilute limit to more conventional glass
behavior at larger doping, and numerically characterize the robust short-range
order inherent to the spin-glass phase. We relate our findings to magnetic
order in both BiCu2PO6 and YBa2Cu3O6.6 induced by Zn substitution.Comment: 6 pages, 5 figs, (v2) real-space RG results added; discussion
extended, (v3) final version as publishe
Morse theory on spaces of braids and Lagrangian dynamics
In the first half of the paper we construct a Morse-type theory on certain
spaces of braid diagrams. We define a topological invariant of closed positive
braids which is correlated with the existence of invariant sets of parabolic
flows defined on discretized braid spaces. Parabolic flows, a type of
one-dimensional lattice dynamics, evolve singular braid diagrams in such a way
as to decrease their topological complexity; algebraic lengths decrease
monotonically. This topological invariant is derived from a Morse-Conley
homotopy index and provides a gloablization of `lap number' techniques used in
scalar parabolic PDEs.
In the second half of the paper we apply this technology to second order
Lagrangians via a discrete formulation of the variational problem. This
culminates in a very general forcing theorem for the existence of infinitely
many braid classes of closed orbits.Comment: Revised version: numerous changes in exposition. Slight modification
of two proofs and one definition; 55 pages, 20 figure
Testing Error Correcting Codes by Multicanonical Sampling of Rare Events
The idea of rare event sampling is applied to the estimation of the
performance of error-correcting codes. The essence of the idea is importance
sampling of the pattern of noises in the channel by Multicanonical Monte Carlo,
which enables efficient estimation of tails of the distribution of bit error
rate. The idea is successfully tested with a convolutional code
Monotonicity and logarithmic convexity relating to the volume of the unit ball
Let stand for the volume of the unit ball in for
. In the present paper, we prove that the sequence
is logarithmically convex and that the sequence
is strictly
decreasing for . In addition, some monotonic and concave properties of
several functions relating to are extended and generalized.Comment: 12 page
Kinematics of the swimming of Spiroplasma
\emph{Spiroplasma} swimming is studied with a simple model based on
resistive-force theory. Specifically, we consider a bacterium shaped in the
form of a helix that propagates traveling-wave distortions which flip the
handedness of the helical cell body. We treat cell length, pitch angle, kink
velocity, and distance between kinks as parameters and calculate the swimming
velocity that arises due to the distortions. We find that, for a fixed pitch
angle, scaling collapses the swimming velocity (and the swimming efficiency) to
a universal curve that depends only on the ratio of the distance between kinks
to the cell length. Simultaneously optimizing the swimming efficiency with
respect to inter-kink length and pitch angle, we find that the optimal pitch
angle is 35.5 and the optimal inter-kink length ratio is 0.338, values
in good agreement with experimental observations.Comment: 4 pages, 5 figure
Glueball masses in the large N limit
The lowest-lying glueball masses are computed in SU() gauge theory on a
spacetime lattice for constant value of the lattice spacing and for
ranging from 3 to 8. The lattice spacing is fixed using the deconfinement
temperature at temporal extension of the lattice . The calculation is
conducted employing in each channel a variational ansatz performed on a large
basis of operators that includes also torelon and (for the lightest states)
scattering trial functions. This basis is constructed using an automatic
algorithm that allows us to build operators of any size and shape in any
irreducible representation of the cubic group. A good signal is extracted for
the ground state and the first excitation in several symmetry channels. It is
shown that all the observed states are well described by their large
values, with modest corrections. In addition spurious states
are identified that couple to torelon and scattering operators. As a byproduct
of our calculation, the critical couplings for the deconfinement phase
transition for N=5 and N=7 and temporal extension of the lattice are
determined.Comment: 1+36 pages, 22 tables, 21 figures. Typos corrected, conclusions
unchanged, matches the published versio
An efficient, multiple range random walk algorithm to calculate the density of states
We present a new Monte Carlo algorithm that produces results of high accuracy
with reduced simulational effort. Independent random walks are performed
(concurrently or serially) in different, restricted ranges of energy, and the
resultant density of states is modified continuously to produce locally flat
histograms. This method permits us to directly access the free energy and
entropy, is independent of temperature, and is efficient for the study of both
1st order and 2nd order phase transitions. It should also be useful for the
study of complex systems with a rough energy landscape.Comment: 4 pages including 4 ps fig
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