1,257 research outputs found
Optimisation of quantum Monte Carlo wave function: steepest descent method
We have employed the steepest descent method to optimise the variational
ground state quantum Monte Carlo wave function for He, Li, Be, B and C atoms.
We have used both the direct energy minimisation and the variance minimisation
approaches. Our calculations show that in spite of receiving insufficient
attention, the steepest descent method can successfully minimise the wave
function. All the derivatives of the trial wave function respect to spatial
coordinates and variational parameters have been computed analytically. Our
ground state energies are in a very good agreement with those obtained with
diffusion quantum Monte Carlo method (DMC) and the exact results.Comment: 13 pages, 3 eps figure
Effect of randomness and anisotropy on Turing patterns in reaction-diffusion systems
We study the effect of randomness and anisotropy on Turing patterns in
reaction-diffusion systems. For this purpose, the Gierer-Meinhardt model of
pattern formation is considered. The cases we study are: (i)randomness in the
underlying lattice structure, (ii)the case in which there is a probablity p
that at a lattice site both reaction and diffusion occur, otherwise there is
only diffusion and lastly, the effect of (iii) anisotropic and (iv) random
diffusion coefficients on the formation of Turing patterns. The general
conclusion is that the Turing mechanism of pattern formation is fairly robust
in the presence of randomness and anisotropy.Comment: 11 pages LaTeX, 14 postscript figures, accepted in Phys. Rev.
Balancing Minimum Spanning and Shortest Path Trees
This paper give a simple linear-time algorithm that, given a weighted
digraph, finds a spanning tree that simultaneously approximates a shortest-path
tree and a minimum spanning tree. The algorithm provides a continuous
trade-off: given the two trees and epsilon > 0, the algorithm returns a
spanning tree in which the distance between any vertex and the root of the
shortest-path tree is at most 1+epsilon times the shortest-path distance, and
yet the total weight of the tree is at most 1+2/epsilon times the weight of a
minimum spanning tree. This is the best tradeoff possible. The paper also
describes a fast parallel implementation.Comment: conference version: ACM-SIAM Symposium on Discrete Algorithms (1993
Electron correlation in C_(4N+2) carbon rings: aromatic vs. dimerized structures
The electronic structure of C_(4N+2) carbon rings exhibits competing
many-body effects of Huckel aromaticity, second-order Jahn-Teller and Peierls
instability at large sizes. This leads to possible ground state structures with
aromatic, bond angle or bond length alternated geometry. Highly accurate
quantum Monte Carlo results indicate the existence of a crossover between C_10
and C_14 from bond angle to bond length alternation. The aromatic isomer is
always a transition state. The driving mechanism is the second-order
Jahn-Teller effect which keeps the gap open at all sizes.Comment: Submitted for publication: 4 pages, 3 figures. Corrected figure
Vibrational signatures for low-energy intermediate-sized Si clusters
We report low-energy locally stable structures for the clusters Si20 and Si21. The structures were obtained by performing geometry optimizations within the local density approximation. Our calculated binding energies for these clusters are larger than any previously reported for this size regime. To aid in the experimental identification of the structures, we have computed the full vibrational spectra of the clusters, along with the Raman and IR activities of the various modes using a recently developed first-principles technique. These represent, to our knowledge, the first calculations of Raman and IR spectra for Si clusters of this size
Surface reconstruction induced geometries of Si clusters
We discuss a generalization of the surface reconstruction arguments for the
structure of intermediate size Si clusters, which leads to model geometries for
the sizes 33, 39 (two isomers), 45 (two isomers), 49 (two isomers), 57 and 61
(two isomers). The common feature in all these models is a structure that
closely resembles the most stable reconstruction of Si surfaces, surrounding a
core of bulk-like tetrahedrally bonded atoms. We investigate the energetics and
the electronic structure of these models through first-principles density
functional theory calculations. These models may be useful in understanding
experimental results on the reactivity of Si clusters and their shape as
inferred from mobility measurements.Comment: 9 figures (available from the author upon request) Submitted to Phys.
Rev.
A Physiologically-Inspired Model of Numerical Classification Based on Graded Stimulus Coding
In most natural decision contexts, the process of selecting among competing actions takes place in the presence of informative, but potentially ambiguous, stimuli. Decisions about magnitudes – quantities like time, length, and brightness that are linearly ordered – constitute an important subclass of such decisions. It has long been known that perceptual judgments about such quantities obey Weber's Law, wherein the just-noticeable difference in a magnitude is proportional to the magnitude itself. Current physiologically inspired models of numerical classification assume discriminations are made via a labeled line code of neurons selectively tuned for numerosity, a pattern observed in the firing rates of neurons in the ventral intraparietal area (VIP) of the macaque. By contrast, neurons in the contiguous lateral intraparietal area (LIP) signal numerosity in a graded fashion, suggesting the possibility that numerical classification could be achieved in the absence of neurons tuned for number. Here, we consider the performance of a decision model based on this analog coding scheme in a paradigmatic discrimination task – numerosity bisection. We demonstrate that a basic two-neuron classifier model, derived from experimentally measured monotonic responses of LIP neurons, is sufficient to reproduce the numerosity bisection behavior of monkeys, and that the threshold of the classifier can be set by reward maximization via a simple learning rule. In addition, our model predicts deviations from Weber Law scaling of choice behavior at high numerosity. Together, these results suggest both a generic neuronal framework for magnitude-based decisions and a role for reward contingency in the classification of such stimuli
High pressure diamond-like liquid carbon
We report density-functional based molecular dynamics simulations, that show
that, with increasing pressure, liquid carbon undergoes a gradual
transformation from a liquid with local three-fold coordination to a
'diamond-like' liquid. We demonstrate that this unusual structural change is
well reproduced by an empirical bond order potential with isotropic long range
interactions, supplemented by torsional terms. In contrast, state-of-the-art
short-range bond-order potentials do not reproduce this diamond structure. This
suggests that a correct description of long-range interactions is crucial for a
unified description of the solid and liquid phases of carbon.Comment: 4 pages, 5 figure
Quantum mechanical ab-initio simulation of the electron screening effect in metal deuteride crystals
In antecedent experiments the electron screening energies of the d+d
reactions in metallic environments have been determined to be enhanced by an
order of magnitude in comparison to the case of gaseous deuterium targets. The
analytical models describing averaged material properties have not been able to
explain the experimental results so far. Therefore, a first effort has been
undertaken to simulate the dynamics of reacting deuterons in a metallic lattice
by means of an ab-initio Hartree-Fock calculation of the total electrostatic
force between the lattice and the successively approaching deuterons via path
integration. The calculations have been performed for Li and Ta, clearly
showing a migration of electrons from host metallic to the deuterium atoms.
However, in order to avoid more of the necessary simplifications in the model
the utilization of a massive parallel supercomputer would be required.Comment: 11 pages, 12 figures, svjour class. To be published in Eur. Phys. J.
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