Global Optimization by Energy Landscape Paving

We introduce a novel heuristic global optimization method, energy landscape paving (ELP), which combines core ideas from energy surface deformation and tabu search. In appropriate limits, ELP reduces to existing techniques. The approach is very general and flexible and is illustrated here on two protein folding problems. For these examples, the technique gives faster convergence to the global minimum than previous approaches.Comment: to appear in Phys. Rev. Lett. (2002

NP-hardness of the cluster minimization problem revisited

The computational complexity of the "cluster minimization problem" is revisited [L. T. Wille and J. Vennik, J. Phys. A 18, L419 (1985)]. It is argued that the original NP-hardness proof does not apply to pairwise potentials of physical interest, such as those that depend on the geometric distance between the particles. A geometric analog of the original problem is formulated, and a new proof for such potentials is provided by polynomial time transformation from the independent set problem for unit disk graphs. Limitations of this formulation are pointed out, and new subproblems that bear more direct consequences to the numerical study of clusters are suggested.Comment: 8 pages, 2 figures, accepted to J. Phys. A: Math. and Ge

Continuous extremal optimization for Lennard-Jones Clusters

In this paper, we explore a general-purpose heuristic algorithm for finding high-quality solutions to continuous optimization problems. The method, called continuous extremal optimization(CEO), can be considered as an extension of extremal optimization(EO) and is consisted of two components, one is with responsibility for global searching and the other is with responsibility for local searching. With only one adjustable parameter, the CEO's performance proves competitive with more elaborate stochastic optimization procedures. We demonstrate it on a well known continuous optimization problem: the Lennerd-Jones clusters optimization problem.Comment: 5 pages and 3 figure

Molecular geometry optimization with a genetic algorithm

We present a method for reliably determining the lowest energy structure of an atomic cluster in an arbitrary model potential. The method is based on a genetic algorithm, which operates on a population of candidate structures to produce new candidates with lower energies. Our method dramatically outperforms simulated annealing, which we demonstrate by applying the genetic algorithm to a tight-binding model potential for carbon. With this potential, the algorithm efficiently finds fullerene cluster structures up to ${\rm C}_{60}$ starting from random atomic coordinates.Comment: 4 pages REVTeX 3.0 plus 3 postscript figures; to appear in Physical Review Letters. Additional information available under "genetic algorithms" at http://www.public.iastate.edu/~deaven

Hydrogen molecule in a magnetic field: The lowest states of the Pi manifold and the global ground state of the parallel configuration

The electronic structure of the hydrogen molecule in a magnetic field is investigated for parallel internuclear and magnetic field axes. The lowest states of the $\Pi$ manifold are studied for spin singlet and triplet$(M_s = -1)$ as well as gerade and ungerade parity for a broad range of field strengths $0 \leq B \leq 100 a.u.$ For both states with gerade parity we observe a monotonous decrease in the dissociation energy with increasing field strength up to $B = 0.1 a.u.$ and metastable states with respect to the dissociation into two H atoms occur for a certain range of field strengths. For both states with ungerade parity we observe a strong increase in the dissociation energy with increasing field strength above some critical field strength $B_c$. As a major result we determine the transition field strengths for the crossings among the lowest $^1\Sigma_g$, $^3\Sigma_u$ and $^3\Pi_u$ states. The global ground state for $B \lesssim 0.18 a.u.$ is the strongly bound $^1\Sigma_g$ state. The crossings of the $^1\Sigma_g$ with the $^3\Sigma_u$ and $^3\Pi_u$ state occur at $B \approx 0.18$ and $B \approx0.39 a.u.$, respectively. The transition between the $^3\Sigma_u$ and $^3\Pi_u$ state occurs at $B \approx 12.3 a.u.$ Therefore, the global ground state of the hydrogen molecule for the parallel configuration is the unbound $^3\Sigma_u$ state for $0.18 \lesssim B \lesssim 12.3 a.u.$ The ground state for $B \gtrsim 12.3 a.u.$ is the strongly bound $^3\Pi_u$ state. This result is of great relevance to the chemistry in the atmospheres of magnetic white dwarfs and neutron stars.Comment: submitted to Physical Review

New Tetrahedral Global Minimum for the 98-atom Lennard-Jones Cluster

A new atomic cluster structure corresponding to the global minimum of the 98-atom Lennard-Jones cluster has been found using a variant of the basin-hopping global optimization algorithm. The new structure has an unusual tetrahedral symmetry with an energy of -543.665361, which is 0.022404 lower than the previous putative global minimum. The new LJ_98 structure is of particular interest because its tetrahedral symmetry establishes it as one of only three types of exceptions to the general pattern of icosahedral structural motifs for optimal LJ microclusters. Similar to the other exceptions the global minimum is difficult to find because it is at the bottom of a narrow funnel which only becomes thermodynamically most stable at low temperature.Comment: 3 pages, 2 figures, revte

Unbiased Global Optimization of Lennard-Jones Clusters for N <= 201 by Conformational Space Annealing Method

We apply the conformational space annealing (CSA) method to the Lennard-Jones clusters and find all known lowest energy configurations up to 201 atoms, without using extra information of the problem such as the structures of the known global energy minima. In addition, the robustness of the algorithm with respect to the randomness of initial conditions of the problem is demonstrated by ten successful independent runs up to 183 atoms. Our results indicate that the CSA method is a general and yet efficient global optimization algorithm applicable to many systems.Comment: revtex, 4 pages, 2 figures. Physical Review Letters, in pres

Lowering IceCube's energy threshold for point source searches in the Southern Sky

Observation of a point source of astrophysical neutrinos would be a "smoking gun" signature of a cosmic-ray accelerator. While IceCube has recently discovered a diffuse flux of astrophysical neutrinos, no localized point source has been observed. Previous IceCube searches for point sources in the southern sky were restricted by either an energy threshold above a few hundred TeV or poor neutrino angular resolution. Here we present a search for southern sky point sources with greatly improved sensitivities to neutrinos with energies below 100 TeV. By selecting charged-current ν μ interacting inside the detector, we reduce the atmospheric background while retaining efficiency for astrophysical neutrino-induced events reconstructed with sub-degree angular resolution. The new event sample covers three years of detector data and leads to a factor of 10 improvement in sensitivity to point sources emitting below 100 TeV in the southern sky. No statistically significant evidence of point sources was found, and upper limits are set on neutrino emission from individual sources. A posteriori analysis of the highest-energy (~100 TeV) starting event in the sample found that this event alone represents a 2.8σ deviation from the hypothesis that the data consists only of atmospheric background.Fil: Aartsen, M. G.. University of Adelaide; AustraliaFil: Abraham, K.. Technische Universität München; AlemaniaFil: Ackermann, M.. Deutsches Elektronen-Synchrotron; AlemaniaFil: Adams, J.. University Of Canterbury; Nueva ZelandaFil: Aguilar, J. A.. Université Libre de Bruxelles; BélgicaFil: Golup, Geraldina Tamara. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; ArgentinaFil: Wallace, A.. University of Adelaide; AustraliaFil: Wallraff, M.. Rwth Aachen University; AlemaniaFil: Wandkowsky, N.. University of Wisconsin; Estados UnidosFil: Weaver, Ch.. University of Alberta; CanadáFil: Wendt, C.. University of Wisconsin; Estados UnidosFil: Westerhoff, S.. University of Wisconsin; Estados UnidosFil: Whelan, B. J.. University of Adelaide; AustraliaFil: Whitehorn, N.. University of California at Berkeley; Estados UnidosFil: Wickmann, S.. Rwth Aachen University; AlemaniaFil: Wiebe, K.. Johannes Gutenberg Universitat Mainz; AlemaniaFil: Wiebusch, C. H.. Rwth Aachen University; AlemaniaFil: Wille, L.. University of Wisconsin; Estados UnidosFil: Williams, D. R.. University of Alabama at Birmingahm; Estados UnidosFil: Wills, L.. Drexel University; Estados UnidosFil: Wissing, H.. University of Maryland; Estados UnidosFil: Wolf, M.. Stockholms Universitet; SueciaFil: Wood, T. R.. University of Alberta; CanadáFil: Woschnagg, K.. University of California at Berkeley; Estados UnidosFil: Xu, D. L.. University of Wisconsin; Estados UnidosFil: Xu, X. W.. Southern University; Estados UnidosFil: Xu, Y.. Stony Brook University; Estados UnidosFil: Yanez, J. P.. Deutsches Elektronen-Synchrotron; AlemaniaFil: Yodh, G.. University of California at Irvine; Estados UnidosFil: Yoshida, S.. Chiba University; JapónFil: Zoll, M.. Stockholms Universitet; Sueci

The Bethe ansatz as a matrix product ansatz

The Bethe ansatz in its several formulations is the common tool for the exact solution of one dimensional quantum Hamiltonians. This ansatz asserts that the several eigenfunctions of the Hamiltonians are given in terms of a sum of permutations of plane waves. We present results that induce us to expect that, alternatively, the eigenfunctions of all the exact integrable quantum chains can also be expressed by a matrix product ansatz. In this ansatz the several components of the eigenfunctions are obtained through the algebraic properties of properly defined matrices. This ansatz allows an unified formulation of several exact integrable Hamiltonians. We show how to formulate this ansatz for a huge family of quantum chains like the anisotropic Heisenberg model, Fateev-Zamolodchikov model, Izergin-Korepin model, $t-J$ model, Hubbard model, etc.Comment: 4 pages and no figure