24,491 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 strength of countable saturation
We determine the proof-theoretic strength of the principle of countable
saturation in the context of the systems for nonstandard arithmetic introduced
in our earlier work.Comment: Corrected typos in Lemma 3.4 and the final paragraph of the
conclusio
Constrained Orthogonal Polynomials
We define sets of orthogonal polynomials satisfying the additional constraint
of a vanishing average. These are of interest, for example, for the study of
the Hohenberg-Kohn functional for electronic or nucleonic densities and for the
study of density fluctuations in centrifuges. We give explicit properties of
such polynomial sets, generalizing Laguerre and Legendre polynomials. The
nature of the dimension 1 subspace completing such sets is described. A
numerical example illustrates the use of such polynomials.Comment: 11 pages, 10 figure
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
Monte Carlo simulation and global optimization without parameters
We propose a new ensemble for Monte Carlo simulations, in which each state is
assigned a statistical weight , where is the number of states with
smaller or equal energy. This ensemble has robust ergodicity properties and
gives significant weight to the ground state, making it effective for hard
optimization problems. It can be used to find free energies at all temperatures
and picks up aspects of critical behaviour (if present) without any parameter
tuning. We test it on the travelling salesperson problem, the Edwards-Anderson
spin glass and the triangular antiferromagnet.Comment: 10 pages with 3 Postscript figures, to appear in Phys. Rev. Lett
Grundstate Properties of the 3D Ising Spin Glass
We study zero--temperature properties of the 3d Edwards--Anderson Ising spin
glass on finite lattices up to size . Using multicanonical sampling we
generate large numbers of groundstate configurations in thermal equilibrium.
Finite size scaling with a zero--temperature scaling exponent describes the data well. Alternatively, a descriptions in terms of Parisi
mean field behaviour is still possible. The two scenarios give significantly
different predictions on lattices of size .Comment: LATEX 9pages,figures upon request ,SCRI-9
Glauber dynamics of phase transitions: SU(3) lattice gauge theory
Motivated by questions about the QCD deconfining phase transition, we studied
in two previous papers Model A (Glauber) dynamics of 2D and 3D Potts models,
focusing on structure factor evolution under heating (heating in the gauge
theory notation, i.e., cooling of the spin systems). In the present paper we
set for 3D Potts models (Ising and 3-state) the scale of the dynamical effects
by comparing to equilibrium results at first and second order phase transition
temperatures, obtained by re-weighting from a multicanonical ensemble. Our
finding is that the dynamics entirely overwhelms the critical and non-critical
equilibrium effects.
In the second half of the paper we extend our results by investigating the
Glauber dynamics of pure SU(3) lattice gauge on
lattices directly under heating quenches from the confined into the deconfined
regime. The exponential growth factors of the initial response are calculated,
which give Debye screening mass estimates. The quench leads to competing vacuum
domains of distinct triality, which delay equilibration of pure gauge
theory forever, while their role in full QCD remains a subtle question. As in
spin systems we find for pure SU(3) gauge theory a dynamical growth of
structure factors, reaching maxima which scale approximately with the volume of
the system, before settling down to equilibrium. Their influence on various
observables is studied and different lattice sizes are simulated to illustrate
an approach to a finite volume continuum limit. Strong correlations are found
during the dynamical process, but not in the deconfined phase at equilibrium.Comment: 12 pages, 18 figure
Instanton size distribution in O(3)
We present calculations of the size distribution of instantons in the 2d O(3)
non-linear sigma-model, and briefly discuss the effects cooling has upon the
configurations and the topological objects. (This preprint is also available
via anonymous ftp to suna.amtp.liv.ac.uk in /pub/pss/ as instdist.uue.)Comment: 17 pages, LaTeX, needs cite.sty (appended), with appended uuencoded
compressed tarfile of PostScript figures, Liverpool preprint LTH-33
A comparison of extremal optimization with flat-histogram dynamics for finding spin-glass ground states
We compare the performance of extremal optimization (EO), flat-histogram and
equal-hit algorithms for finding spin-glass ground states. The
first-passage-times to a ground state are computed. At optimal parameter of
tau=1.15, EO outperforms other methods for small system sizes, but equal-hit
algorithm is competitive to EO, particularly for large systems. Flat-histogram
and equal-hit algorithms offer additional advantage that they can be used for
equilibrium thermodynamic calculations. We also propose a method to turn EO
into a useful algorithm for equilibrium calculations.
Keywords: extremal optimization. flat-histogram algorithm, equal-hit
algorithm, spin-glass model, ground state.Comment: 10 LaTeX pages, 2 figure
A Decision Support Tool for Seed Mixture Calculations
Grassland species are normally seeded in mixtures rather than monocultures. In theory, seeding rates for mixtures are simply a sum of the amount of pure live seed (PLS) of each seed lot in the mix, an amount sufficient to ensure establishment and survival of each species. Mixtures can be complex because of the number of species used (especially in conservation and reclamation programs) and variations in seed purity and seed size. Soil limitations and seeding equipment settings need to be considered and in Canada, a metric conversion may be required. All these conditions make by-hand calculations of mixtures containing more than 3 species tedious and complicated. Thus, in practice, agronomists and growers use simple rules to set rates. The easiest rule is to estimate the mixture’s components as a percentage by weight of a standardized total weight of the seed required (e.g. 10% of 10 kg/ha). The resulting errors can be observed in the predominance of thin stands, the unexpected dominance of small seeded species and the added costs of interseeding to compete with weeds and fertilizer to increase yield. The objective of this project was to develop a decision support tool, a seed mixture calculator to simplify conversion and improve the estimates of seed required for individual seeding projects
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