23,801 research outputs found
Structure of the Energy Landscape of Short Peptides
We have simulated, as a showcase, the pentapeptide Met-enkephalin
(Tyr-Gly-Gly-Phe-Met) to visualize the energy landscape and investigate the
conformational coverage by the multicanonical method. We have obtained a
three-dimensional topographic picture of the whole energy landscape by plotting
the histogram with respect to energy(temperature) and the order parameter,
which gives the degree of resemblance of any created conformation with the
global energy minimum (GEM).Comment: 17 pages, 4 figure
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
Exchange Monte Carlo Method and Application to Spin Glass Simulations
We propose an efficient Monte Carlo algorithm for simulating a
``hardly-relaxing" system, in which many replicas with different temperatures
are simultaneously simulated and a virtual process exchanging configurations of
these replica is introduced. This exchange process is expected to let the
system at low temperatures escape from a local minimum. By using this algorithm
the three-dimensional Ising spin glass model is studied. The ergodicity
time in this method is found much smaller than that of the multi-canonical
method. In particular the time correlation function almost follows an
exponential decay whose relaxation time is comparable to the ergodicity time at
low temperatures. It suggests that the system relaxes very rapidly through the
exchange process even in the low temperature phase.Comment: 10 pages + uuencoded 5 Postscript figures, REVTe
Non-Perturbative U(1) Gauge Theory at Finite Temperature
For compact U(1) lattice gauge theory (LGT) we have performed a finite size
scaling analysis on lattices for fixed by
extrapolating spatial volumes of size to . Within the
numerical accuracy of the thus obtained fits we find for , 5 and~6
second order critical exponents, which exhibit no obvious
dependence. The exponents are consistent with 3d Gaussian values, but not with
either first order transitions or the universality class of the 3d XY model. As
the 3d Gaussian fixed point is known to be unstable, the scenario of a yet
unidentified non-trivial fixed point close to the 3d Gaussian emerges as one of
the possible explanations.Comment: Extended version after referee reports. 6 pages, 6 figure
Isospectrality and heat content
We present examples of isospectral operators that do not have the same heat
content. Several of these examples are planar polygons that are isospectral for
the Laplace operator with Dirichlet boundary conditions. These include examples
with infinitely many components. Other planar examples have mixed Dirichlet and
Neumann boundary conditions. We also consider Schr\"{o}dinger operators acting
in with Dirichlet boundary conditions, and show that an abundance of
isospectral deformations do not preserve the heat content.Comment: 18 page
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
Multicanonical Study of the 3D Ising Spin Glass
We simulated the Edwards-Anderson Ising spin glass model in three dimensions
via the recently proposed multicanonical ensemble. Physical quantities such as
energy density, specific heat and entropy are evaluated at all temperatures. We
studied their finite size scaling, as well as the zero temperature limit to
explore the ground state properties.Comment: FSU-SCRI-92-121; 7 pages; sorry, no figures include
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
Generalized-ensemble Monte carlo method for systems with rough energy landscape
We present a novel Monte Carlo algorithm which enhances equilibrization of
low-temperature simulations and allows sampling of configurations over a large
range of energies. The method is based on a non-Boltzmann probability weight
factor and is another version of the so-called generalized-ensemble techniques.
The effectiveness of the new approach is demonstrated for the system of a small
peptide, an example of the frustrated system with a rugged energy landscape.Comment: Latex; ps-files include
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
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