The Hamiltonian index of a graph and its branch-bonds

Let $G$ be an undirected and loopless finite graph that is not a path. The minimum $m$ such that the iterated line graph $L^m(G)$ is hamiltonian is called the hamiltonian index of $G,$ denoted by $h(G).$ A reduction method to determine the hamiltonian index of a graph $G$ with $h(G)\geq 2$ is given here. With it we will establish a sharp lower bound and a sharp upper bound for $h(G)$, 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 $h(G)$ may reach all integers between the lower bound and the upper bound. \u

The gravitational field of a global monopole

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

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

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

Modeling and analysis of the variability of the water cycle in the upper Rio Grande basin at high resolution

Estimating the water budgets in a small-scale basin is a challenge, especially in the mountainous western United States, where the terrain is complex and observational data in the mountain areas are sparse. This manuscript reports on research that downscaled 5-yr (1999-2004) hydrometeorological fields over the upper Rio Grande basin from a 2.5° NCEP-NCAR reanalysis to a 4-km local scale using a regional climate model [fifth-generation Pennsylvania State University-National Center for Atmospheric Research Mesoscale Model (MM5), version 3]. The model can reproduce the terrain-related precipitation distribution - the trend of diurnal, seasonal, and interannual precipitation variability - although poor snow simulation caused it to overestimate precipitation and evapotranspiration in the cold season. The outcomes from the coupled model are also comparable to offline Variable Infiltration Capacity (VIC) and Land Data Assimilation System (LDAS)/Mosaic land surface simulations that are driven by observed and/or analyzed surface meteorological data. © 2007 American Meteorological Society

Modeling intraseasonal features of 2004 North American monsoon precipitation

This study examines the capabilities and limitations of the fifth-generation Pennsylvania State University-National Center for Atmospheric Research Mesoscale Model (MM5) in predicting the precipitation and circulation features that accompanied the 2004 North American monsoon (NAM). When the model is reinitialized every 5 days to restrain the growth of modeling errors, its results for precipitation checked at subseasonal time scales (not for individual rainfall events) become comparable with ground- and satellite-based observations as well as with the NAM's diagnostic characteristics. The modeled monthly precipitation illustrates the evolution patterns of monsoon rainfall, although it underestimates the rainfall amount and coverage area in comparison with observations. The modeled daily precipitation shows the transition from dry to wet episodes on the monsoon onset day over the Arizona-New Mexico region, and the multiday heavy rainfall (&gt;1 mm day-1) and dry periods after the onset. All these modeling predictions agree with observed variations. The model also accurately simulated the onset and ending dates of four major moisture surges over the Gulf of California during the 2004 monsoon season. The model reproduced the strong diurnal variability of the NAM precipitation, but did not predict the observed diurnal feature of the precipitation peak's shift from the mountains to the coast during local afternoon to late night. In general, the model is able to reproduce the major, critical patterns and dynamic variations of the NAM rainfall at intraseasonal time scales, but still includes errors in precipitation quantity, pattern, and timing. The numerical study suggests that these errors are due largely to deficiencies in the model's cumulus convective parameterization scheme, which is responsible for the model's precipitation generation. © 2007 American Meteorological Society

Flexible protein folding by ant colony optimization

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