232,774 research outputs found

    The Hamiltonian index of a graph and its branch-bonds

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    Let GG be an undirected and loopless finite graph that is not a path. The minimum mm such that the iterated line graph Lm(G)L^m(G) is hamiltonian is called the hamiltonian index of G,G, denoted by h(G).h(G). A reduction method to determine the hamiltonian index of a graph GG with h(G)2h(G)\geq 2 is given here. With it we will establish a sharp lower bound and a sharp upper bound for h(G)h(G), respectively, which improves some known results of P.A. Catlin et al. [J. Graph Theory 14 (1990)] and H.-J. Lai [Discrete Mathematics 69 (1988)]. Examples show that h(G)h(G) may reach all integers between the lower bound and the upper bound. \u

    The gravitational field of a global monopole

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    We present an exact solution to the non-linear equation which describes a global monopole in the flat space. We re-examine the metric and the geodesics outside the global monopole. We will see that a global monopole produces a repulsive gravitational field outside the core in addition to a solid angular deficit. The lensing property of the global monopole and the global monopole-antimonopole annihilation mechanism are studied.Comment: 8 pages, no figure

    The Carriers of the Interstellar Unidentified Infrared Emission Features: Constraints from the Interstellar C-H Stretching Features at 3.2-3.5 Micrometers

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    The unidentified infrared emission (UIE) features at 3.3, 6.2, 7.7, 8.6, and 11.3 micrometer, commonly attributed to polycyclic aromatic hydrocarbon (PAH) molecules, have been recently ascribed to mixed aromatic/aliphatic organic nanoparticles. More recently, an upper limit of <9% on the aliphatic fraction (i.e., the fraction of carbon atoms in aliphatic form) of the UIE carriers based on the observed intensities of the 3.4 and 3.3 micrometer emission features by attributing them to aliphatic and aromatic C-H stretching modes, respectively, and assuming A_34./A_3.3~0.68 derived from a small set of aliphatic and aromatic compounds, where A_3.4 and A_3.3 are respectively the band strengths of the 3.4 micrometer aliphatic and 3.3 micrometer aromatic C-H bonds. To improve the estimate of the aliphatic fraction of the UIE carriers, here we analyze 35 UIE sources which exhibit both the 3.3 and 3.4 micrometer C-H features and determine I_3.4/I_3.3, the ratio of the power emitted from the 3.4 micrometer feature to that from the 3.3 micrometer feature. We derive the median ratio to be ~ 0.12. We employ density functional theory and second-order perturbation theory to compute A_3.4/A_3.3 for a range of methyl-substituted PAHs. The resulting A_3.4/A_3.3 ratio well exceeds 1.4, with an average ratio of ~1.76. By attributing the 3.4 micrometer feature exclusively to aliphatic C-H stretch (i.e., neglecting anharmonicity and superhydrogenation), we derive the fraction of C atoms in aliphatic form to be ~2%. We therefore conclude that the UIE emitters are predominantly aromatic.Comment: 14 pages, 5 figures, 1 table; accepted for publication in The Astrophysical Journa

    Lattice Boltzmann modeling of multiphase flows at large density ratio with an improved pseudopotential model

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    Owing to its conceptual simplicity and computational efficiency, the pseudopotential multiphase lattice Boltzmann (LB) model has attracted significant attention since its emergence. In this work, we aim to extend the pseudopotential LB model to simulate multiphase flows at large density ratio and relatively high Reynolds number. First, based on our recent work [Li et al., Phys. Rev. E. 86, 016709 (2012)], an improved forcing scheme is proposed for the multiple-relaxation-time pseudopotential LB model in order to achieve thermodynamic consistency and large density ratio in the model. Next, through investigating the effects of the parameter a in the Carnahan-Starling equation of state, we find that the interface thickness is approximately proportional to 1/sqrt(a). Using a smaller a will lead to a wider interface thickness, which can reduce the spurious currents and enhance the numerical stability of the pseudopotential model at large density ratio. Furthermore, it is found that a lower liquid viscosity can be gained in the pseudopotential model by increasing the kinematic viscosity ratio between the vapor and liquid phases. The improved pseudopotential LB model is numerically validated via the simulations of stationary droplet and droplet oscillation. Using the improved model as well as the above treatments, numerical simulations of droplet splashing on a thin liquid film are conducted at a density ratio in excess of 500 with Reynolds numbers ranging from 40 to 1000. The dynamics of droplet splashing is correctly reproduced and the predicted spread radius is found to obey the power law reported in the literature.Comment: 9 figures, 2 tables, accepted by Physical Review E (in press

    Flexible protein folding by ant colony optimization

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    Protein structure prediction is one of the most challenging topics in bioinformatics. As the protein structure is found to be closely related to its functions, predicting the folding structure of a protein to judge its functions is meaningful to the humanity. This chapter proposes a flexible ant colony (FAC) algorithm for solving protein folding problems (PFPs) based on the hydrophobic-polar (HP) square lattice model. Different from the previous ant algorithms for PFPs, the pheromones in the proposed algorithm are placed on the arcs connecting adjacent squares in the lattice. Such pheromone placement model is similar to the one used in the traveling salesmen problems (TSPs), where pheromones are released on the arcs connecting the cities. Moreover, the collaboration of effective heuristic and pheromone strategies greatly enhances the performance of the algorithm so that the algorithm can achieve good results without local search methods. By testing some benchmark two-dimensional hydrophobic-polar (2D-HP) protein sequences, the performance shows that the proposed algorithm is quite competitive compared with some other well-known methods for solving the same protein folding problems